University of Southern California Dissertations and Theses

Experimental development and analysis of a continuous flow-through trace gas preconcentrator

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Experimental development and analysis of a continuous flow-through trace gas preconcentrator

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Content EXPERIMENT AL DEVELOPMENT AND ANAL YSIS OF A CONTINUOUS FLOW-THR OUGH TRACE GAS PRECONCENTRA TOR By Jihyun Kim A Dissertation Presented to the F A CUL TY OF THE GRADUA TE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial F ulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (AEROSP ACE ENGINEERING) December 2013 Copyright 2013 Jihyun Kim Contents 1 In tro duction 1 1.1 Preconcen tration Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Researc h motiv ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Benets of preconcen tration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.3 Gas preconditioning and preconcen tration . . . . . . . . . . . . . . . . . . . . 6 1.1.4 T yp es of preconcen tration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.5 General metho ds of preconcen tration . . . . . . . . . . . . . . . . . . . . . . 8 1.1.6 Cycled and con tin uous preconcen trators . . . . . . . . . . . . . . . . . . . . . 10 1.2 Mem branes for Gaseous Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.1 T yp es of mem branes and p orosit y . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Gas separation mec hanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.3 Separation Mec hanism near the Surface . . . . . . . . . . . . . . . . . . . . . 16 1.2.4 Nanoscale P orous Mem brane : Carb on-based mem branes . . . . . . . . . . . 17 1.3 Kinetic theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.1 Elemen tary transp ort theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.2 Flo w Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.3 Mean free path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 i 1.3.4 Mass o w rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.5 Hydro dynamic o w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3.6 T ransition o w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3.7 F ree molecular o w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.3.8 Kinetic eusion of molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.3.9 Molecular mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.4 Gaseous Diusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.4.1 Fic k’s la w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.4.2 F ree molecule diusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.4.3 Another expression of diusion . . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.5 Ph ysical Prop erties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.5.1 Gas adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.5.2 Quan tum eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2 Theory and Mo del of a New Approac h for the Preconcen trator 55 2.1 Preliminary Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.1.1 Gaseous mixture o w through a long tub e . . . . . . . . . . . . . . . . . . . . 56 2.1.2 Analysis of gas o w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.2 New Approac h to Preconcen trator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.2.1 Summary of the design and c haracterization . . . . . . . . . . . . . . . . . . . 61 2.2.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.2.3 Shap e of the main o w c hannel and concen tration . . . . . . . . . . . . . . . 67 2.3 Characterization of the Separation Mem brane . . . . . . . . . . . . . . . . . . . . . . 71 2.3.1 Microp orous mem branes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.3.1.1 Polyc arb onate membr anes . . . . . . . . . . . . . . . . . . . . . . . 73 ii 2.3.1.2 Metal membr anes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.3.1.3 Cer amic membr anes . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.3.1.4 Ze olite membr anes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.3.1.5 Mixe d-matrix membr anes . . . . . . . . . . . . . . . . . . . . . . . . 75 2.3.2 Carb on nanotub e mem branes . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.4 P erformances of Pumping Cham b er and Pump . . . . . . . . . . . . . . . . . . . . . 81 2.4.1 Pumping c ham b ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.4.2 Pump options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.5 Detecting Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.5.1 Detector p erformance and options : Electron Beam T ec hnology . . . . . . . . 85 2.5.2 Detector p erformance and options : Other t yp es . . . . . . . . . . . . . . . . 91 2.5.3 Detector p erformance and options : Sp ectrum . . . . . . . . . . . . . . . . . . 92 3 Characteristics of Preconcen trator 96 3.1 Predictions of the Preconcen trator P erformance . . . . . . . . . . . . . . . . . . . . . 96 3.2 Designs of Exp erimen t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.2.1 Main o w c hannel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.2.2 Separation mem branes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.2.3 Pumping c ham b ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.2.4 Exp erimen tal setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4 Analysis of the Preconcen trator’s P erformance 110 4.1 Exp erimen tal Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.1.1 Mass o w rate and gas o w sp eed of single gases . . . . . . . . . . . . . . . . 111 4.1.2 Prediction of ph ysical p erformance of single gases . . . . . . . . . . . . . . . 118 iii 4.1.3 Mass o w rate and gas o w sp eed of Mixed gases . . . . . . . . . . . . . . . 121 4.2 Impro v emen t of Theoretical Mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 5 Conclusion and F uture W ork 144 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5.2 Impro v emen t of a Preconcen trator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 iv List of Figures 1.2.1 Sc heme of mec hanisms for p ermeation of gases through mem branes (Bernardo et al. 2009). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.2 Relationship b et w een the kinetic diameter, d k , of a gas molecule and the p ermanence through Si 400 and Si 600 mem branes (P andey et al. 2001). This gur e is r eprinte d. 15 1.2.3 Illustration of molecular motion around surface of a single mem brane c hannel. (a) Separation mec hanism for gas comp onen ts, and (b) Mo v emen t of gas v olume in a z - axis. r c is a radius of a single mem brane c hannel, and c ′ is a thermal mean molecular sp eed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3.1 Circular tub e geometry sho wing k ey geometric and o w v ariable for a gas o w (Go- mosi, 1994). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.3.2 Circular tub e geometry sho wing molecular collision . . . . . . . . . . . . . . . . . . 29 1.3.3 All escaping molecules ha v e p ositiv e v z v elo cities through the orice (Gomosi 1994). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.3.4 Sc heme of oblique cylinder. A group of molecules with v elo cit y v ector in an innites- imal neigh b orho o d of v hit the orice area dS during the time in terv al dt (Gomosi 1994). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.4.1 Microp orous mem branes are c haracterized b y their tortuosit y . (Bak er et al. 2012) . . 39 1.4.2 Molar Flo w rate of gas through the ideal separation mem brane when F = 0.0042, r p = 15nm, h p = 6µm, P 1 −P 2 = 0.01atm, and T = 300K . . . . . . . . . . . . . . . 41 1.4.3 Illustration of the prop erties of Kn udsen to P oiseuille o w in a nely microp orous mem branes as a function of the p ore radius divided b y the mean p ore path of the gas (after Barrer) (Bak er 2012). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . 42 1.5.1 P oten tial energy PE(r) and transv erse motion energy lev els E i for a molecule in a c hannel with d c −d m ∼λ. Zero energy corresp onds to that of the molecule in a free space (Bak er 2012). The p oten tial w ell separation o ccurs b et w een a gas sp ecie and a w all material of the capillary tub es. This gur e is r eprinte d. . . . . . . . . . . . . . . 45 1.5.2 The b eha vior of the w ell depth ϵ and zero-p oin t energy E 0 as functions of c hannel diameter d c . Regions 1, 2 and 3 can b e attributed to classical geometrical, p oten tial and quan tum sieving, resp ectiv ely . The w ell depth is sk etc hed as a function of p ore diameter starting from its v alue ϵ fs at a at surface (Bak er 2012). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.1.1 Sc heme of the mixture gas o w through a p orous mem brane from the main o w c hannel to reserv oir : P 1 and P 2 are the high-side and lo w-side pressures acting on a mem brane (P 1 >P 2 ) and temp erature is constan t. . . . . . . . . . . . . . . . . . . . 59 v 2.2.1 Sc heme of a ideal con tin uous trace gas preconcen trator b y t w o (b ottom) and three (upp er) dimensions : one main o w c hannel connected with a detector transition, t w o separation mem branes, and t w o pumping c ham b ers connected with pumps. This is a dev eloping mo del from the preconcen trator prop osed b y Mun tz et al. (Mun tz et al. 2004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.2.2 Sc hemetic of a ideal preconcen trator including one main o w c hannel, t w o separation mem branes, and t w o pumping c ham b ers. . . . . . . . . . . . . . . . . . . . . . . . . 64 2.2.3 Concen tration ratio of trace gas with dieren t fractional op en area. . . . . . . . . . 70 2.2.4 Illustration of the main o w c hannel determined the shap e equation pro vided b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2008). . . . . . . . . . . . . . . . . . . . 71 2.4.1 Illustration of pumping c ham b ers and sk etc h inside pumping c ham b er prop osed b y Mun tz et al. (Mun tz et al. 2004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.4.2 Comparison of rep orted micropumps based on maxim um o w rate, maxim um pres- sure, and pac k age size. Self-pumping frequency is here dened as maxim um o w rate divided in to pac k age size (Laser et al. 2004). This gur e is r eprinte d. . . . . . . . . . 83 2.5.1 Jablonski diagram : the pro cess illustrated b y a simple electronic state diagram in- v olv es in creating an excited electronic singlet state b y optical absorption and subse- quen t emission of uorescence. Excitation, vibrational relaxation, Emission (Amer- sham 2002). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.5.2 Illustration of electron b eam gun and electron b eam tec hnique (Mun tz 1968). . . . 88 2.5.3 Electron b eam emission principle and Electron gun head (all dimensions in mm) b y Diop et al. (Diop et al. 2011). This gur e is r eprinte d. . . . . . . . . . . . . . . . . . 90 2.5.4 Xenon sp ectrum in the standard temp erature and pressure (STP) b y NIST . . . . . 92 3.1.1 Concen tration ratio of the trace gas increases in the main o w c hannel as a function of the length and as a function of transmission probabilit y , when α = α C = α T . The shap es and exit sizes of the main o w c hannel (left) and concen tration ratio of the trace gas ( log nT(x) nT(0) ) (righ t) when (a) α = 0.1, 0.01, 0.001, and 0.0001, and (b) 0.0025≤α≤ 0.01. The transmission probabilit y (α(model)) is calculated b y equation (2.2.8) (red solid line with circles). Then the conditions are 4.2×10 −3 in a p orosit y , and 0.5 in a ratio of gas n um b er densit y of the pumping c ham b er and main o w c hannel. 98 3.1.2 Concen tration ratio of the trace gas increases in the main o w c hannel as a function of the length of the main o w c hannel and as a function of transmission probabilit y and p orosit y , when αF =α C F C =α T F C . The shap es and exit sizes of the main o w c hannel (left) and the concen tration ratio of the trace gas ( log nT(x) nT(0) ) (righ t) when 10 −5 ≤αF ≤ 10 −4 . Then the mem brane is 10nm in p ore diameter, 6µm in thic kness, and 0.5 in a ratio of gas n um b er densit y of the pumping c ham b er and main o w c hannel. 100 3.2.1 Main o w c hannel part designed as the rst exp erimen tal protot yp e : the main o w c hannel is made out of the alumin um. The gas o w sp eed con trol area has m ulti- barries to deliv er a same gas o w sp eed to the en trance of main o w c hannel and to protect jet-o ws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 vi 3.2.2 Inlet gas o w sp eeds with t w o dieren t gases, helium (a) and air (b, c) : The inlet pressure of gas o w is 767Torr and the outlet pressure of gas o w is 760Torr at ro om temp erature. (a) When the inlet gas is helium, the maxim um gas o w sp eed at the exit of the main o w c hannel is ab out 20m/s. (b) When the inlet gas is air, the maxim um gas o w sp eed at the en trance of the gas o w con trol area is ab out 11.7m/s. (c) The gas o w sp eed of the en trance of the main o w c hannel sho w the reducing gas o w sp eed un til 1.757m/s. . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.2.3 P olycarb onate mem branes in scanning electron micrographs (SEM) image from the Cen ter for Electron Microscop e and Microanalysis at the Univ ersit y of Southern Cal- ifornia : (a) 10nm (30 ◦ ) and (b) 50nm in p ore diameters. . . . . . . . . . . . . . . . 105 3.2.4 Sc hemetic of pumping c ham b er and pressure con trol area and the total v olume. (a) This illustration sho ws an en tire view (left) and a side view (righ t) of one pumping c ham b er used, and (b) the total v olume (= v olume of main o w c hannel + v olume of pumping c ham b er) exp onen tially decreases along the length of the main o w c hannel. 107 3.2.5 P erformance of pump, 60Hz (Marathon electronics, 1VAF −18−M100X ) . . . . . 107 3.2.6 Sk etc h of the exp erimen tal setup and a protot yp e of preconcen trator . . . . . . . . . 108 4.1.1 Net ux (a) and normalized a v erage pressure dierence (b) for four single gases ( He, N 2 , Ar , and Xe) with mem branes (d c = 10nm and d c = 50nm) and without mem- branes in the preconcen trator. The inlet gas o w rate for eac h gas is measured as the same amoun t in air (60sccm). The net ux is obtained from Equation 1.4.12, and the n um b ers in paren theses are a v erage pressure dierences obtained b y exp erimen t. . . 113 4.1.2 Normalized a v erage mass o w rates (a) and gas o w sp eeds (b) for four single gases (He, N 2 , Ar , and Xe) with mem branes (d c = 10nm and d c = 50nm) and without mem branes in the preconcen trator. The inlet gas o w rate for eac h gas is measured as the same amoun t in air (60sccm). . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.1.3 Illustration of exit of the main o w c hannel. The shap e of the exit is c hanged from a rectangle to circle in order to connect to a mass o w meter and to main tain a constan t gas o w for the o v erall cross section. . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.1.4 Illustration of a mass o w rate of single gas through the main o w c hannel. A size of eac h segmen t is 5mm in x-axis. Eac h segmen t has dieren t n um b er of holes, d H = 3mm as men tioned in Chapter 3. Red arro ws are gas o ws in the main o w c hannel and blue arro ws are gas o ws escap ed through the holes of the hole-b o dy of the pumping c ham b er. The mem branes are attac hed to the upp er and lo w er surface of the main o w c hannel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.1.5 A v erage escap ed gas o w sp eed (a) and net mass o w rate (b) p er segmen t at a single hole for four single gases (He,N 2 ,Ar , andXe) when the mem branes are remo v ed from the system. The length of eac h segmen t is 5mm, and these equations and calculation data are describ ed in App endix T.2. Num b ers of holes p er eac h segmen t are mark ed ab o v e the nitrogen plot in (a) ( triangle). The length of the main o w c hannel is the length from exit to the en trance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.1.6 V ariation in the abundance of mixed gases for the 10nm mem brane (d c = 10nm) (a) with a pump o and (b) a pump on with initial mixing ratio of t w o gases ( Ar and Xe). Ar is the carrier gas, and Xe is the trace gas. Their c haracteristics of eac h gas are describ ed in App endix T.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 vii 4.1.7 V ariation in the abundance of mixed gases for the 50nm mem brane (d c = 50nm) (a) with a pump o and (b) a pump on with initial mixing ratio of t w o gases ( Ar and Xe). Ar is the carrier gas, and Xe is the trace gas. Their c haracteristics of eac h gas are describ ed in App endix T.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.1.8 V ariation in the abundance of mixed gases for the 10nm mem brane (d c = 10nm) (a) and 50nm mem brane (d c = 50nm) (b) with mixing ratio of t w o gases (Ar and Xe). Ar is the carrier gas, and Xe is the trace gas. Their c haracteristics of eac h gas are describ ed in App endix T.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.1.9 Molecular mass for the10nm mem brane (a) and 50nm mem brane (b) of mixture gases of t w o comp onen ts (Ar and Xe) and four comp onen ts (N 2 , O 2 , Ar , and Xe) with in- creasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. The c haracteristics are describ ed in App endix T.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.1.10 Molecular densit y for the10nm mem brane (a) and 50nm mem brane (b) of mixture gases of t w o comp onen ts (Ar and Xe) and four comp onen ts (N 2 , O 2 , Ar , and Xe) with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. The c haracteristics are describ ed in App endix T.1. . . . . . . . . . . . . . . . . . . . . . 130 4.1.11 Mass o w rate for the 10nm mem brane (a) and 50nm mem brane (b) of mixture gases suc h as Ar -Xe, and N 2 -O 2 -Ar -Xe with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. These are describ ed in App endix T.1. . . . . . . . . . . . 131 4.1.12 Gas o w sp eed for the 10nm mem brane (a) and 50nm mem brane (b) of mixture gases suc h as Ar -Xe, and N 2 -O 2 -Ar -Xe with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. These are describ ed in App endix T.1. . . . . . . . . . . . 132 4.1.13 Pressure diererences for the 10nm mem brane (a) and 50nm mem brane (b) of mixture gases (Ar -Xe) with increasing mixture ratio of initial gas with the pump on and pump o. Ar is the carrier gas and Xe is the trace gas. These are describ ed in App endix T.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.2.1 Shap e of main o w c hannel. The exp erimen t ( −··) obtains from the original equation that w as used in this study , other lines are related to new shap e equations (4.2.5) from the mass o w rate and (4.2.9) from the net ux. The co ecien ts used for shap e equation are a helium gas o w sp eed of 5cm/s, a pressure ratio of 0.5, and a p ore diameter of 30nm, a thic kness of 6µm and a p ore densit y of 6×10 8 /cm 2 of a mem brane. 137 4.2.2 Concen tration ratio of the trace gas. The exp erimen t (−··) obtains from the original equation that w as used in this study , other lines are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.10) from the net ux. The co ecien ts used for shap e equation are a helium gas o w sp eed of 5cm/s, a pressure ratio of 0.5, and a p ore diameter of 30nm, a thic kness of 6µm and a p ore densit y of 6× 10 8 /cm 2 of a mem brane. The co ecien ts for concen tration ratio are a xenon gas o w sp eed of 1.933cm/s, a pressure ratio of 0.996, and a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. . . . . . . . . . . . . . . . 138 viii 4.2.3 Concen tration ratio of the trace gas. The exp erimen t (−··) obtains from the original equation that w as used in this study , other lines are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.10) from the net ux. The co ecien ts for concen tration ratio are a xenon gas o w sp eed of 1.933cm/s, a pressure ratio of 0.996, and a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 4.2.4 Abundance of trace gas concen tration for the 10nm mem brane. The exp erimen t data ( and) obtained with the pump o (a) and pump on (b). The original equation is used in this study (•), and other data are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.13) from the net ux. Then y -axis is related to the abun- dance in p ercen t for the exp erimen tal results, and in times for the theoretical results. The co ecien ts for concen tration ratio are a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. . . . . . . . . . . . . . . . 140 4.2.5 Abundance of trace gas concen tration for the 50nm mem brane. The exp erimen t data ( and) obtained with the pump o (a) and pump on (b). The original equation is used in this study (•), and other data are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.13) from the net ux. Then y -axis is related to the abun- dance in p ercen t for the exp erimen tal results, and in times for the theoretical results. The co ecien ts for concen tration ratio are a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. . . . . . . . . . . . . . . . 141 ix List of T ables 1.1 T raditional lab oratory analytical tec hniques used to measure en vironmen tal p ollutan ts and impro v emen ts. (Horn y ak et al. 2009) . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Zero-p oin t energy , E 0 and lev el splitting, E 1 −E 0 as o ws from equation 2.3.2 for sev eral gases in dieren t c hannels with d c = 0.5, 10, and 50nm. Characteristic v alues of molecular diameter (HSS) and molecular w eigh ts are tak en from App endix T.1. . 47 2.1 Analytical applications of the dieren t kind of mem branes (Lop ez-Loren te et al. 2010). 77 2.2 Comparison of CNT Mem branes ; Hinds (Hinds 2004), Holts (Holts 2006), Kim et al. (Kim et al. 2007), Mi et al. (Mi et al. 2007), and Y u et al. (Y u et al. 2009). . . . . . 79 3.1 P erformance c haracteristics of p olycarb onate mem branes. (a) Inlet o w rates using preltered at 10psid (0.7kg/cm 2 ), and (b) The transmission probabilit y using equation (2.2.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.1 Normalized a v erage mass o w rates ab out four single gases ( He, N 2 , Ar , and Xe) with mem branes (d c = 10nm andd c = 50nm) and without mem branes. Eac h n um b er in the paren thesis is a gas o w rate of air. The mass o w rate w ere measured at the exit of the main o w c hannel. ’Without pumping eect’ are mass o w rates measured with the pump o, and ’With pumping eect’ is mass o w rates recorded with the pump on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 x 4.2 A v erage pressure dierences of four single gas o ws ( He,N 2 ,Ar , andXe) with t yp e of mem branes (d c = 10nm and d c = 50nm) and without mem branes. P a is the pressure dierence b et w een the main o w c hannel and pumping c ham b ers, P b is the pressure dierence b et w een the en trance and exit of the main o w c hannel, and P c is the pressure dierence b et w een atmospheric pressure and exit of the main o w c hannel. 117 4.3 A v erage pressure dierences and mass o w rates for mixed gases ( Ar and Xe) with t yp e of mem branes (d c = 10nm and d c = 50nm) and without mem branes. Eac h n um b er in the paren thesis is a p ercen t of gas o w rate with pumping eect. P a is the pressure dierence b et w een the main o w c hannel and pumping c ham b ers, P b is the pressure dierence b et w een the en trance and exit of the main o w c hannel, and P c is the pressure dierence b et w een atmospheric pressure and exit of the main o w c hannel. Here ’No pump’ means pressures measured when a mixed gas o ws without pumping eect, and ’With pump’ means pressures measured when a mixed gas o ws with pumping eect. The mass o w rates w ere recorded as mass o w rates of air. . 122 xi Nomenclature a a gas sp ecies a A cross sectional area (m 2 ) A jk probabilit y of radiativ e transition (s −1 ) b a gas sp ecies b c ligh t sp eed (m/s) c ′ thermal mean molecular sp eed (m/s) C concen tration of the gas (mol/m 3 ) d molecular diameter (m) d c diameter of a tub e or p ore diameter of mem brane c hannel (m) d H diameter of a hole of the hole-b o dy of pumping c ham b er (m) dV impact v olume of the impact cylinder (m 3 ) dt time in terv al (s) D diameter of exit of the main o w c hannel ( m) D s m utual diusion co ecien t or self diusion co ecien t ( m 2 /s) D s ab m utual diusion co ecien t or self diusion co ecien t in a binary mixture ( m 2 /s) D FP eectiv e diusion co ecien t D K Kn udsen diusion co ecien t D P co ecien t of baro diusion D T co ecien t for thermo diusion E 0 zero-p oin t energy (eV ) xii E i energy lev el (eV ) F esc Maxw ell-Boltzmann distribution function for escaping particles F i =F fractional op en area of p orous mem brane surface for molecule ( i =C : carrier gas, i =T : trace gas) G macroscopic quan tit y G P co ecien t h Planc k constan t (6.626×10 −34 m 2 kg/s) h c a v erage heigh t of a mem brane c hannel (thic kness of mem brane) (m) h f heigh t of main o w c hannel ( m) h g heigh t of gas v olume (m) h p (x) heigh t of pumping c ham b er (m) h EX photon of energy (eV ) j esc escap e ux ( m −2 s −1 ) J ux of concen tration ( mol/m 2 s) J Diff diusiv e mass ux of gas ( mol/m 2 s) J F Fic k’s ux ( mol/m 2 s) I jk emission in tensit y of a uorescence line in a transition from j to a lo w er state k k B Boltzmann constan t (1.38065×10 −23 J/K ) k P baro diusion ratio k T thermo diusion ratio Kn Kn udsen n um b er L length of a tub e (m) L c c haracteristic scale length (m) L f length of main o w c hannel ( m) m atomic (molecular) mass (kg ) m e electron mass (9.109×10 −31 kg ) m V mass in a v olume (kg ) _ m desorption o w rate (mL/min) _ m fex mass o w rate at the exit of the main o w c hannel ( g /s) _ m H mass o w rate of escaping gas through holes of hole-b o dy of the pumping c ham b er ( g /s) M molecular w eigh t (kg/mol) _ M mass o w rate ( kg/s) xiii _ M fr mass o w rate of free molecular o w ( kg/s) _ M hy mass o w rate of h ydro dynamic o w ( kg/s) _ M tr mass o w rate of transition o w ( kg/s) n n um b er densit y (m −3 ) n i0 =n i (0) n um b er densit y of molecules at an inlet to a o w c hannel ( i =D : carrier gas, i =T : trace gas) n T (x) n um b er densit y of trace gas at distance x in a o w c hannel ( m −3 ) N n um b er of molecule N molar o w rate of gas ( mole/m 2 s) N H n um b er of holes p er segmen t N i n um b er of molecule at x = 0 ( i =C : carrier gas, i =T : trace gas) _ N i (x) loss rate of molecules p er units distance x ( i =D : carrier gas, i =T : trace gas) N plate n um b er of theoretical plates of preconcen trator P pressure (N/m 2 ) P 1 partial pressure of the gas on the feed side (high-side pressure of mem brane) ) ( N/m 2 ) P 2 partial pressure of the p ermeate side (lo w-side pressure of mem brane) ( N/m 2 ) P a pressure dierence b et w een the main o w c hannel and pumping c ham b ers ( N/m 2 ) P av a v erage pressure (N/m 2 ) P b pressure dierence b et w een the en trance and exit of the main o w c hannel ( N/m 2 ) P c pressure dierence b et w een atmospheric pressure and the outlet pressure ( N/m 2 ) P in inlet pressure (at the en trance of the main o w c hannel) ( N/m 2 ) P out outlet pressure (at the exit of the main o w c hannel) ( N/m 2 ) P pc pressure in the pumping c ham b er (N/m 2 ) PE(r) p oten tial energy (eV ) PF preconcen trator factor △P pressure dierence across a mem brane c hannel ( N/m 2 ) _ Q v olumetric o w ( m 3 /s) R univ ersal gas constan t (J/mol·K) r radial co ordinate r 0 arbitrary p oin t in the spherical co ordinate r c radius of circular tub e (m) r m molecular radius (r mi =r m ) xiv S g gas saturation T absolute temp erature (K ) t R reten tion time (min) u bulk v elo cit y of uid in z-axis (longitudinal axis) ( m/s) u 0 inlet o w sp eed ( m/s) (u 0 =u D0 =u T0 ) u r =u(r) v elo cit y in radial axis (m/s) u slip slip v elo cit y (m/s) U unit atomic mass (1.66054×10 −27 kg ) v v elo cit y of a uid (a gas) ( m/s) v H escap ed gas o w sp eed through the hole ( m/s) v z v elo cit y of escaping molecules along the z -axis (m/s) V v olume (m 3 ) V desorbed desorb ed v olume (m 3 ) V sample sample v olume (m 3 ) w(0) en trance width of main o w c hannel ( m) w(x) width of main o w c hannel ( m) w ex exit width of main o w c hannel ( m) W p eak width at half heigh t (min) W h width of injection band (min) x axis in a cartesian co ordinate X i molar fraction of comp onen t i y axis in a cartesian co ordinate z axis in a co ordinate transmission probabilit y i transmission probabilit y of gas molecules through a separation mem brane ( i = C : carrier gas, i =T : trace gas) β co ecien t γ Bessel functions δ rarefaction parameter ϵ w ell depth (eV ) ϵ fs w ell depth in a at surface ( eV ) η accommo dation co ecien t xv λ mean free path (m) λ h mean free path in a hard sphere gas (m) λ f mean free path in thermo dynamic equilibrium (m) λ i mean free path for sp ecies i (m) (i =a, b) λ v mean free path with viscosit y (m) λ B mean radial De Broglie w a v elength (m) µ viscosit y of gas (Pa·s) µ mix viscosit y of mixture gas (Pa·s) jk frequency of the transition j−k (Hz ) ρ uid densit y ( kg/m 3 ) ρ t total mass densit y (kg/m 3 ) σ =πr 2 m utual collision cross section area (m 2 ) τ tortuosit y i ratio of n um b er densit y in a pumping c ham b er to inlet n um b er densit y in a main o w c hannel ( i =C : carrier gas, i =T : trace gas) total molecular o w ( s −1 ) xvi Abstract A new t yp e of con tin uous o w-through trace gas preconcen trator for rareed trace gas analysis, whic h has b een prop osed b y Mun tz et al. (Mun tz et al. 2008, Mun tz et al. 2004, Han et al. 2009) has b een built and consists of a main o w c hannel, pumping c ham b ers, and separation mem branes b et w een the main o w c hannel and the pumping c ham b ers. In this case, preconcen tration is not from stop, adsorption, and release; but is caused b y the con tin uously c hanging cross section of the main o w c hannel un til released through the detecting system suc h as gas c hromatograph y , mass sp ectrometry , or optical diagnostics. This has the p ossibilit y of ac hieving concen tration increase of v arious gases in a carrier gas b y using relativ ely simple micro/mesoscale mass diusion separation stages, without in terrupting the gas o ws, and is suitable for impro ving the time accuracy of analytical systems. The presen t study fo cused on the design and c haracterization of a new t yp e of preconcen trator that enables use with v arious gas detection units. The researc h describ ed here addressed for hea vier molecules, at atmospheric pressure and ro om temp erature optimized conditions and p ossibilities of the preconcen trator. The shap e equation w as in tro duced for the main o w c hannel and the concen tration ratio of the trace gas w as determined using a set of co ecien ts including; the fractional op en area, the transmission probabilit y , and the ratio of pressure b et w een the main o w c hannel and pumping c ham b ers. The fractional op en area (p orosit y) and transmission probabilit y w ere obtained from a p ore diameter, thic kness, and p ore densit y of a mem brane used. A ccording to these equations and co ecien ts, it w as p ossible to determine the shap e and size of the main o w c hannel, and t yp e of the sepa- ration mem brane appro ximately . In order to fabricate a preconcen trator protot yp e, the v ariables w ere limited with reasonable b oundary conditions, and could b e predicted with a v ailable n umerical data. Prop erties of the mem brane w ere used as main factors to decide the t yp e of the separation xvii mem branes. The pumping c ham b ers lo cated ab o v e and b elo w the main o w c hannel main tained to main tain a constan t gas o w sp eed in the main o w c hannel during the exp erimen t, and w ere designed to create relativ ely lo w er pressure than that in the main o w c hannel. A series of exp erimen ts w ere conducted in an attempt to v alidate the a v ailable n umerical data, suc h as the concen tration and gas o w sp eed of the newly con tin uous preconcen tration tec hnology . This study in v olv ed exp erimen tal in v estigations using argon mixed with xenon to obtain a base-line comparison of the existing n umerical predictions pro vided b y the protot yp e preconcen trator. The concen tration w as calculated b y pressure dierences b et w een the main o w c hannel and pumping c ham b ers, and b y mass o w rates obtained at exit of the main o w c hannel. The n umerical mo dels calculated an increase in concen tration under the follo wing conditions; 5cm/s for the helium gas o w sp eed, 4.2× 10 −5 for the p orosit y , 0.0066 for the transmission probabilit y , and 0.5 for the gas densit y ratio. Under these conditions, it is exp ected that the concen tration of xenon gas in a mixture of the argon and xenon gases increases ab out 32 times at the end of the main o w c hannel. Ho w ev er when the shap e equation w as reected in the concen tration equation, the concen tration ratio of the xenon gas increases ab out 32 times for the 10nm mem brane. Ho w ev er the xenon gas concen tration of the exp erimen tal results decreased appro ximately 10 p ercen t to the concen tration of xenon gas in an initial sampled gas for the all cases, and these concen trations increased ab out 1.07 times for some exp erimen ts used the 50nm mem brane. F rom these exp erimen tal results and n umerical mo dels, the protot yp e of preconcen trator can b e c hanged the concen tration ratio of v arious gases. Easily a v ailable gases in this study had a molecular mass ratio that is represen tativ e of t ypical, more complicated molecular structures that are encoun tered in actual situations. Subsequen tly , trace gas mixtures more t ypical of the complicated molecular structures found in hea vy molecules, will b e studied. With the exp erimen tal results it is p ossible to ev aluate the actual p erformance, and th us the p oten tial of the prop osed preconcen trator and detecting system. Miniaturization, based on the impro v emen ts made to theoretical mo dels, oers the further adv an tage of enabling the use of inexp ensiv e, disp osable substrates, and also enhances the analytical p erformance of the device. The miniaturization of analysis systems reduces the quan tities of sample required, allo ws assa ys to b e p erformed more quic kly , and enables p ortabilit y of the system. xviii References Han, Y. L. and M. Y oung, Con tin uous preconcen trator for trace-gas analysis , R e c ent Patents on Me chanic al Engine ering , 2 (2009) : 214 - 227. Mun tz, E. P ., M. Y oung, and Y.-L. Han, Con tin uous lo w p o w er pre-concen trations for distributed microscale trace gas analysis, IMECE 2004 (2004) : 60874. Mun tz, E. P ., Y.-L. Han, and M. Y oung, Pre-concen trator for trace gas analysis, T ec hnical Rep ort, U.S. Patent US2008/01786 , (2008 ). xix Chapter 1 Introduction In teresting sub jects in the gas detection eld suc h as, collectors, detectors sensors, and analyzers, curren tly enable the rapid sensing of a v ariet y of sp ecies at lo w concen trations and the miniaturization of analytical tec hniques ev en though the sensitivit y of a v ailable sensors is v ery lo w. In suc h a problem and tec hnological dev elopmen ts, a preconcen trator w as in tro duced to o v ercome the sensing problems, asso ciated with rapid resp onse times and extremely lo w trace gas concen trations. The commercially a v ailable gas sensors encoun ter man y detection diculties. Miniaturization also oers the further adv an tage of enabling the use of inexp ensiv e, disp osable substrates, and also enhances the analytical p erformance of the device. The miniaturization of analysis systems reduces the quan tities of sample required, allo ws assa ys to b e p erformed more quic kly , and enables p ortabilit y of the system. In addition, the expanding dev elopmen t of microfabrication tec hniques enables the pro duction of small devices suc h as; a reactor, a preconcen trator, a Lab on a c hip, and so on. The presen t study fo cuses on the design and c haracterization of a new t yp e of preconcen trator that enables use with v arious gas detectors or analyzers. The researc h describ ed here addresses optimized conditions and p ossibilities. The new approac h for the preconcen trator w as for hea vier molecules, at an atmospheric pressure and a ro om temp erature similar to our circumstances. Also this considers the a v ailable detecting systems that can b e op erated with the new preconcen trator. 1 1.1 Preconcentration Systems Preconcen trators, that can b e used to enhance the analytical p erformances, sensitivit y and selec- tivit y , of the gas analysis system, is a device that collects and concen trates analyte sample o v er a p erio d of time, and subsequen tly releases the concen trated analyte to a sensor. A gas detector is normally op erated b y pneumatically sampling am bien t air and analyte in to a c hemical detector (V oiculescu et al. 2006). The sample gas to b e analyzed o ws through the preconcen trator is ac- cum ulated during some time, then the sample gas is brough t to the detector (Camara et al. 2010). The adv an tages of the gas detector in incorp orating a preconcen trator device are enhanced sensi- tivit y and impro v ed selectivit y . The preconcen trator can b e in tegrated at the fron t-end of an y gas analysis systems, including gas c hromatographs, mass sp ectrometers, ion mobilit y sp ectrometers, and micro electromec hanical systems (MEMS) based c hemical sensors (V oiculescu et al. 2006, Do w et al. 2010). There are man y existing traditional preconcen trators whic h ha v e a ph ysically large size, ha v e a slo w resp onse time, require a large p o w er dra w during thermal desorption cycles, and are exp ensiv e (Gro v es et al. 1998, Serrano et al. 2009, Martin et al. 2007). These systems also require samples to b e collected in the eld and transp orted to the lab oratory for analysis b ecause they are not p ortable (Do w et al. 2010). 1.1.1 Researc h motiv ation Recen tly , miniaturized, and mobile, highly ecien t gas analysis microsystems ha v e b een dev elop ed extensiv ely and ha v e made it p ossible to apply strict regulatory monitoring in a v ariet y of elds. This includes indo or and outdo or en vironmen tal monitoring and b ev erage qualit y ev aluation. With the dev elopmen t of MEMS tec hnology , the limitations and disadv an tages of traditional preconcen trators can b e o v ercome b y signican tly reducing the device size, the time resp onse, and the required ap- plied p o w er (V oiculescu et al. 2006, Do w et al. 2010, Silv a et al. 2006). Moreo v er, a micromac hined preconcen trator can b e designed and fabricated to enhance the sensitivit y of the gas analysis system, esp ecially in the parts p er billion (ppb) gas concen tration range (Manginell et al. 2003, Tian et al. 2003). The miniaturization of the preconcen trators also allo ws their in tegration in p ortable, minia- turized analytical instrumen ts, suc h as micro gas c hromatographs and ion mobilit y sp ectrometers (V oiculescu et al. 2006). With this approac h, it is p ossible to optimize the individual comp onen ts 2 comp osing the system, and to enable their replacemen t in a mo dule fashion (Lewis et al. 2006, Lu et al. 2005). There are eorts underw a y to miniaturize analytical tec hniques b y MEMS tec hnology and nanotec h- nology suc h as; gas c hromatograph sp ectrometers (Mitra et al. 1993, Tian et al. 2003, Y eom et al. 2008), mass sp ectrometers (Con treras et al. 2008), ion mobilit y sp ectrometers (Spangler et al. 1992, Kan u et al. 2008), and electronic noses (Gardner et al. 1999, Alb ert et al. 2001, Y amanak a et al. 2003, Gardner et al. 2000, Cho et al. 2006). All of these can b e applied to the detection of hazardous materials b y monitoring to xic industrial c hemicals, or other emissions, for indo or and outdo or en vironmen ts. T able 1.1 sho ws some examples of traditional lab oratory analytical tec h- niques used to measure en vironmen tal p ollutan ts. Impro v emen ts, due to nanotec hnology , of v arious asp ects of the tec hniques and some nano-applications are pro vided - whether for the detector, the mec hanism that deliv ers the sample or other asso ciated features of the tec hnique (Horn y ak et al. 2009). These tec hniques still fo cus on analyzing particular samples, suc h as organic samples and hea vy metals, other than hea vy gas molecules. These miniaturized gas analysis systems are widely applicable for civil en vironmen ts to; securit y , health monitoring, atmospheric p ollution con trols, or explosiv e detections including the space prob es. Thousands of kinds of hazardous substances exist as particulates, organics, inorganics, and biological materials in air (indo or and outdo or), and as to xins in b o dies (Chiriac et al. 2007, Pijolat et al. 2007, Bec k er et al. 2000, Pinnadu w age et al. 2004, Chiriac et al. 2007). F or example, v olatile organic comp ounds (V OCs) form the largest class of hazardous p ollutan ts, along with to xic industrial c hemicals (TICs), whic h can cause serious health problems in the form of to xic, carcinogenic, and m utagenic eects with v ery lo w concen trations of ppb (Cho et al. 2006, Chiriac et al. 2007). F or applications asso ciated with explosiv es, the detection of 2, 4-dinitrotoluene (DNT) has b ecome a pressing issue, b ecause of the p ersisten t dev astation caused b y landmines. The detection sensitivit y of 300 parts-p er-trillion (ppt) should b e ac hiev ed within a few seconds of exp osure of the sensor to the v ap or stream (Pinnadu w age et al. 2004). The detection of c hemical w arfare agen ts (CW As) suc h as; T abun, Sarin, Soman, Cyclosarin, and Meth ylphosphonothiolic acid, whic h are found in defense applications are, also fatal within a few min utes for v ery lo w concen trations from sev eral ppb to sev eral h undreds ppb (Donald et al. 1994). These gases are dangerous at lo w concen trations and are dicult to analyze with con v en tional detectors/sensors. The Defense A dv anced Researc h 3 T ec hnique Samples Nano-enablemen t and nano-uses Gas c hromatograph y Organic p ollutan ts, Thinner capillary columns lled with nanomaterial supp orts; halogenated organic comp ounds enhanced detection systems GC/mass sp ectrometry Organic samples Microuidic samples con taining nanogram quan tities of material. (GC/MS) In situ analysis of carb on nanotub es b y mass sp ectrometry A tomic absorption Hea vy metals Nanospra y enhancemen ts /emission sp ectroscop y Inductiv ely coupled Hea vy metals ICP/MS with ppt to pp q (parts p er quin tillion) lev els of detection, plasma sp ectroscop y (ICP) nanoparticle in tro duction systems; ICP/MS to analyze gold nanoparticles Ion and ion-exclusion W aterb orne cations and anions, Ion exc hange c hromatograph y to separate c hromatograph y carb on nanotub es single-w alled carb on nanotub es based on electrical prop erties Fluorescence P athogens Nanophotonic ligh t sources for uorescence sp ectroscop y and cellular imaging T able 1.1: T raditional lab oratory analytical tec hniques used to measure en vironmen tal p ollutan ts and impro v emen ts. (Horn y ak et al. 2009) 4 Pro jects Agency (D ARP A) w an ted to create a dog’s nose to detect landmines with greater sensitivit y (Chiriac et al. 2007). As an example of other applications, the Jet Propulsion lab oratory (JPL) dev elop ed small mas sp ectrometers to monitor the air inside the space station, and an y future spacecrafts. A unit, a size of 30.5cm b y10.2cm, for preconcen trator/gas c hromatograph assem bly for the v ehicle cabin atmosphere monitor w as sc heduled for a one-y ear test run in the In ternational Space Station b eginning in 2010 (NASA 2007). Therefore, gas analysis microsystems, suc h as trace gas detectors/sensors, are required to fulll conditions of; p ortabilit y , extremely high sensitivit y , measuremen ts in eectiv ely real time, m ul- tiparameter capabilit y , simple design, lo w detection limits, high throughput, large w orking range, and rapid resp onse. Ho w ev er, the miniaturized gas analysis systems ha v e limited p erformance for accurately detecting analyte in the ppb range, so that the miniaturized gas sensors/detectors are particularly studied to solv e sensing problems for gas concen tration in the ppb range, whic h existing gas sensors/detectors face diculties to detect. Miniature trace gas sensors/detectors with rapid analysis times, lo w p o w er consumption, and suitable for mass man ufacturing need to b e dev elop ed. 1.1.2 Benets of preconcen tration Most p oten tial applications of gas c hromatographs including micro-gas c hromatograph has require detection limits of ppb or parts-p er-trillion (ppt) concen tration, but they ha v e inheren t detection limits in the high-ppb or lo w-parts-p er-million (ppm) range (V eeneman 2009). It is hence necessary to consider the preconcen tration step. If a gas c hromatograph used the pro cesses of adsorption and desorption, it pro vides a preconcen tra- tion factor, whic h can eectiv ely increase sensitivit y and reduce the limits of detection b y desorbing the captured target gases in to a m uc h smaller v olume than initially collected. The preconcen trator factor is then determined b y dividing the sample v olume V sample b y the desorb ed v olume V desorbed , PF = V sample V desorbed = V sample W h × _ m . (1.1.1) The desorb ed v olume is replaced b y m ultiplying the width of the injection band W h (min) b y the desorption o w rate _ m(mL/min) (Namiesnik 1998). Moreo v er, a n um b er of theoretical plates of 5 preconcen trator N plate is as a measure of column eciency and is calculated b y N plate = 5.545 ( t R W ) 2 , (1.1.2) where t R is the reten tion time (min) and W is the p eak width at half heigh t (min). A larger W , stemming from a larger injection band, yields a lo w er v alue for N plate (Hyv er 1989). If the micro- preconcen trator is designed and op erated as ecien tly as p ossible, a narro w injection band can b e ac hiev ed. The narro w injection band, c haracterized b y a smaller W , giv es a larger v alue for N plate , indicating a higher n um b er of a v ailable theoretical plate to ac hiev e separation (V eeneman 2009). Therefore the micro-preconcen trator enhances the p erformance of the resistance and the separation mo dule. A ccording to these t w o comp onen ts, it is p ossible to consider the smaller width of injection band with a constan t desorption o w rate to enhance the preconcen trator factor. In addition, the reten tion time ma y b e similar to the p eak width at half heigh t if it is considered only one or t w o theoretical plates, N = 1, as the presen t study . It means that the reten tion time of this researc h is as short as p ossible. 1.1.3 Gas preconditioning and preconcen tration In the analytical tec hniques dev elopmen ts, the gas preconditioning is usually imp ortan t. This ma y b e related to the alteration of a gas mixture and the eect of preconcen tration to impro v e the selectivit y , and to increase the sensitivit y of a detection device. In some applicativ e en vironmen ts, the gas concen tration is so lo w that the preconcen tration unit is needed at the en trance of the analytical device (Namiesnik 1998). Preconcen tration is the pro cess of target analyte enric hmen t, and can b e ac hiev ed b y collecting the target analytes o v er a p erio d of time, and then releasing them in the form of a highly concen trated sample for subsequen t analysis. When it is dealt with gas phase samples, preconcen tration metho ds can b e mostly used b y: ph ysisorption or c hemisoprtion. Ph ysisorption relies mainly on V an der W aals forces for sorption, while c hemisoprtion relies on the formation of c hemical b onds to ac hiev e sorption. Ph ysisorption in v olv es w eak in termolecular in teractions that are easily rev ersed. The simplicit y and rev ersibilit y of ph ysisorption mak es it the preferred metho d for preconcen tration. 6 Otherwise, c hemisoprtion is not easily rev ersed, since it requires breaking co v alen t b onds. Rev ersal of this pro cess requires a substan tial amoun t of energy and can b e a dicult pro cess. This is not a viable option for micro-analytical instrumen ts. Ph ysisorption can en tail adsorption and absorption or b oth. A dsorption o ccurs only on the surface of a solid, but absorption in v olv es diusion of the analyte in to a solid or liquid. Ph ysisorption can b e ac hiev ed b y absorption in to solution, cold trapping, and adsorption on solids or thic k sorb en t lms, usually p olymeric (V eeneman 2009), and solv en t or mem brane extraction. T rapping b y cry ogenic condensation (or cold trapping) is done b y passing the sample through a co oled tub e lled with glass b eads to pro vide large surface area. This approac h captures the analytes on a bare surface or on sorb en t that had b een co oled to b elo w ro om temp erature. The co oling is done with cry ogenic uids with whic h trapping temp eratures b et w een 150C to 170C are ac hiev ed. The cry o- genic preconcen tration is p ossible in com bination with sorb en t agen ts. The sorption trapping, whic h relies on sorption phenomena, is generally used as a term for indicating adsorption and absorption, whic h could tak e place sim ultaneously . The sorption phenomena also include c hemical adsorption, capillary condensation of gaseous analytes, dissolv ed substances on solid or liquid adsorb en t. When preconcen tration is used b y the sorption metho d, sorb en ts can b e thermally desorb ed directly in to the carrier gas. The sorb en ts are considered as activ e or passiv e sampling. The activ e sample is p erformed b y pumping air through a b ed of sorb en ts at a rate t ypically in the 10− 100mL/min range for a p erio d in the order of min utes. Sorb en t material in passiv e (or diusiv e) sampling is exp osed to air for a p erio d in the order of da ys (Alfeeli 2010). Ho w ev er adsorption on solid surfaces and absorption in to thic k-lms pro vide a more practical approac h to preconcen tration, b ecause b oth absorption in to solution and cry ogenic trapping are dicult to emplo y with microanalytical system (V eeneman 2009). Mem brane extraction is another metho d that the target analytes are separated from the sample passing through nanoscale tub es and a family of tec hniques that can b e applied to ma y extraction problems (Han et al. 2009, Jnsson 2003). The mem brane extraction is also able to pro vide high concen tration enric hmen t factors of h undreds or more. Systems based up on mem brane extraction can b e automated readily and connected on-line to c hromatograph y systems and other instrumen ts (Jnsson 2003). When the preconcen tration metho d based up on the absorption and desorption mec hanisms through p orous materials equated as an adsorb en t is considered, it is able to b e op erated 7 con tin uously , quite stable for long times and the sampled gas stream supplied to gas analyzed systems retains the time delit y . Therefore, the simplicit y of the pro cess, necessary equipmen t, and the exibilit y of the material c hoice are k ey adv an tages of a microanalytical system, and can b e minimized b y carefully c ho osing the sorb en t material and op erating parameters (Namiesnik 1998). 1.1.4 T yp es of preconcen tration Preconcen tration can b e considered t w o t yp es: equilibrium and exhaustiv e preconcen trations (V een- eman 2009). Preconcen trator devices with regard to exhaustiv e trapping capture all the analyte from a giv en range of sample v olumes, whic h directly impact the total analysis time (Namiesnik 1998, Egoro v et al. 2006). The analyte is then depleted from the sample. The exhaustiv e preconcen tration usually implies larger partition co ecien t and reten tion v olumes, meaning a larger sample v olume can b e used while still completely adsorbing all the analyte in the sample. When the pre-determined sample v olume is exceeded, a p ortion of the sampled concen tration ma y b e lost in this metho d. Equilibrium preconcen tration based on c hromatograph y relies on the concen tration on a surface or in a sorb en t lm b eing at equilibrium with the sampled air (Namiesnik 1998, Harp er 2000). In this metho d, the captured analyte mass is indep enden t of the sampled v olume, but directly dep enden t on the concen tration of the sampled air. While the equilibration of concen tration and collection of the analytical signal are somewhat slo w er than con v en tional thin-lm sensors, fast resp onse times are not required. This is b ecause subsurface sample concen trations do not c hange rapidly , and fast resp onse times are not required for long-term en vironmen tal monitoring applications with in situ sensors. The resp onse of the equilibration sensor dep ends on the sample concen tration, but unlik e a quan titativ e capture sensor, it is indep enden t of the amoun t of sample pump ed, so long as sucien t sample is precessed to ac hiev e equilibration (Egoro v et al. 2006). 1.1.5 General metho ds of preconcen tration Exhaustiv e or equilibrium preconcen tration, and reco v ery of the trapp ed analytes is a necessary step regardless of whic h metho ds of preconcen tration. Thermal dep osition is generally a viable metho d with microanalytical systems (V eeneman 2009). Thermal desorption ac hiev ed b y rapidly heating the 8 sorb en t ev ap orates the sample from the sorb en t to analyze the trapp ed analyte, and allo ws analysis of the en tire preconcen trated amoun t (Harp er 2000). The thermal desorption can lead to sample or sorb en t degradation, but the increase in sensitivit y , ac hiev ed with this metho d, out w eighs the p oten tial disadv an tage (V eeneman 2009, Harp er 2000). This includes o w rate through the device, heating rate, and desorption temp erature (Whiting et al. 2006). The go o d results are that the fast heating rates are ≥ 100 ◦ C/sec (Y eom et al. 2008), when p o w er consumptions are ignored, and the high o w rates are ≥ 5mL/min. The desorption temp erature is maximized to fully ev ap orate all the trapp ed sp ecies without exceeding the maxim um temp erature of the material or surpassing the thermal stabilit y temp erature of the analyte. A t higher temp eratures than thermal stabilit y of the material or analytes, op eration can b e yielded lo w regeneration of the material and decomp osition of the adsorbates (Sanc hez et al, 2005). Researc h of preconcen tration are related to dev elop the devices of thermal dep osition suc h as hot- plates or heaters (Camara et al. 2010, Do w et al. 2010, Lewis et al. 2006, Tian et al. 2005, Lu et al. 2002, Manginell et al. 2008, Y eom et al. 2008). F or examples, F ry e-Mason et al. dev elop ed micro- fabricated preconcen trators to detect sp ecic c hemical w arfare agen ts using a heated mem brane with a thin adsorb en t la y er (Lewis et al. 2006), and Tian et al. dev elop ed a thic k m ultiple-stage micro- fabricated preconcen trator with large carb on-particle-based-adsorb en ts, Carb opac k B, Carb opac k X and Carb o xen 1000 that ha v e sp ecic surface area, p ore morphology , and p ore size distribution (Tian et al. 2005). The p ore size distribution enables to handle comp ounds with a particular range of v ap or pressure (Lu et al. 2002). The three adsorb en ts ha v e dieren t surface area and are used to trap comp ounds with dieren t v olatilities. Manginell et al. consisted of a lo w heat capacit y of the microhotplate with an adsorb en t coating applied to its surface. The microhotplate is used to rapidly and ecien tly desorb and analyte sample collected in the adsorb en t (Manginell et al. 2008). Y eom et al. also designed and fabricated Si microheaters of the micropreconcen trator that has a small c ham b er v olume with a high surface area and lo w pressure drop structures, and consumes minimal p o w er and energy for heating to desired temp erature (Y eom et al. 2008). These t yp es of precon- cen trator are dev elop ed to w ard expanding the surface area for thermal desorption and decreasing consumption p o w er and increasing heating rate, but decreasing transp ort time is still an imp ortan t issue in this metho d b ecause the heating rate related to the transp ort time dep ends on the applied v oltage. 9 In order to o v ercome this problem, one of the attempted metho ds is used micro v alv es or thermore- sp onsiv e v alv es to con trol the collection, concen tration and injection times (Bae et al. 2007, Bae et al. 2006, Zhang et al. 2008). The micro v alv es pla y a k ey role b y injecting the sample in to the micro-preconcen trator, holding the analyte in a preconcen trator c ham b er while heating for desorp- tion, and injecting the concen trated analyte in to detectors. Bae et al. recen tly used a v e-v alv es micro-preconcen trator so that the resp onse time could b e reduced less than 50s (Bae et al. 2007, Bae et al. 2006, Zhang et al. 2008). In this researc h, t w o micro v alv es are used for loading, adsorbing, and v en ting the sample gas and three micro v alv es are used for pushing and injecting the concen trated gaseous sp ecies using a carrier gas in pulses as small as 50s in to the separation column in a micro gas c hromatograph or directly in to a detector. Another t yp e of the micro v alv e, thermoresp onsiv e v alv e, is able to con trol a uid o w (Zhang et al. 2008). In general preconcen tration also requires the pro duction of high-surface area adsorb en t materials b y p orous silicon (Bell et al. 1996, Galeazzo et al. 2003), alumin um lms (P erez et al. 2003, Y elton et al. 2002), nonp orous materials (Cansell et al. 2003, Lin et al. 2002, P olarz et al. 2002, Grate et al. 2005), or nanop o w er (Camara et al. 2010, Pijolat et al. 2007). P orous metal foams or lms facilitate thermal conductivit y and temp erature uniformit y throughout the b ed of the preconcen trator during heating (Grate et al. 2005). The p orous silicon materials or other nonp orous materials can b e used for b oth heating and measuring the a v erage temp erature of a preconcen trator unit, but do not w ork as a heating elemen t and serv e only as a heat spreader and housing of the p orous adsorb en t p o wder suc h as a carb on nano-p o wder (Pijolat et al. 2007, Ruiz et al. 2007, Fll et al. 2002, Gorban yuk et al. 2006, Salonen et al. 2006). A micro-preconcen trator suggested b y Camara et al. (Camara et al. 2010) is based on a micro-c hannel in p orous silicon lled with carb on nanop o wders b y a micro-uidic pro cess. It still remains the problem ab out reducing the resp onse time ev en though these metho ds are useful to main tain the constan t temp erature for the thermal desorption. 1.1.6 Cycled and con tin uous preconcen trators Preconcen tration systems can b e view ed as a system used to mo dify an incoming gas o w b y increas- ing the concen tration of analyte relativ e to a carrier gas, whic h pro vides conditions at the detector that minimizes the total amoun t of analyte that is required for detection. Widely t w o classes of preconcen trators ha v e b een dev elop ed: cycled preconcen trators (Lu et al. 2003, Grate et al. 2005, 10 Zheng et al. 2006), and con tin uous preconcen trators (Camara et al. 2009), but the b oundary of the classications is somewhat obscure. The distinction can b e related to collection times more than a total analysis time, including all sample preparation and detection, whic h is the imp ortan t sp eed metric for most applications. In the cycled preconcen tration systems suc h as the sample v olume adsorption t yp e, the collection time tends to dominate the detection time. The incoming gases of the analyte and carrier mixture ha v e to b e stopp ed, a desired amoun t adsorb ed, and then subsequen tly released as rapidly as p ossible to a detector (Spangler et al. 1992). The incoming mixture o ws o v er an adsorbing material, and some quan tit y of gas in the o wing mixture is adsorb ed for an appropriate length of time. The adsorbing material is generally heated at a con trolled o w rate to release the adsorb ed gas. It can b e rapidly heated to pro vide a sharp pulse of material that can b e exp osed to a gas c hromatograph for iden tication (Camara et al. 2010, Lewis et al. 2006). Otherwise, it can b e slo wly heated when eac h sp ecie desorbs at a dieren t temp erature and time, whic h separates the sp ecies in time and aids in detection (Lu et al. 2003). Con tin uous preconcen tration systems, whic h do not ha v e the pro cesses of stop, adsorption, and release, are exp ected to b e sup erior for detecting, in substan tial real time, ev en though concen trations of the adsorbing gas supplied for analysis is randomly v aried. It is w orth while, therefore, to view preconcen trator tec hnology as ha ving a con tin uous distribution of collection times, from collections times that dominate the detection time to collection times that are insignican t, compared to the detection time. Con tin uous preconcen trators ma y ha v e to op erate for some nite times b efore enough analyte reac hes the detector to b e detected. The con tin uous preconcen trators can b e used to increase the concen tration of target gas in a carrier gas suc h as air. This ma y primarily b e useful for the detection of hea vier gases, but it is op erated with a relativ ely short analysis time and sp ecically designed to b e p ortable. The con tin uous preconcen trators are more suitable for impro ving the time accuracy of analytical systems than the cycled ones. Therefore, the main goals of the researc h is to reduce the size, resp onse time, and consuming p o w er of the preconcen trator that can op erate con tin uously . A recen t paten t and researc h (Han et al. 2009) prop osed con tin uous o w through, trace gas pre- concen trators as time accurate, trace gas detection systems. The paten t (Mun tz et al. 2004) of a micro/mesoscale, con tin uous o w-through, trace gas preconcen trator has in tro duced a sp ecic appli- 11 cation, that has the p ossibilit y of ac hieving signican t trace gas concen tration, increase using one or t w o simple micro/mesoscale mass diusion separation stages, without in terrupting the gas o ws. The con tin uous preconcen trator requires signican tly less op erational time, and a p ossibly m uc h higher trace gas concen tration lev el with a smaller size device, compared with the adsorption-desorption cycled preconcen trators. Ho w ev er, the con tin uous o w-through trace gas preconcen trator, while paten ted and analyzed n umerically , had to b e in v estigated exp erimen tally . In this study , the new approac h ab out the con tin uous preconcen trator for the target or trace gas in the o w mixture is considered to o v ercome the v arious problems that still remain. 1.2 Membranes for Gaseous Separation Thomas Graham, who con tributed to the understanding of gas-diusion phenomena through mem- branes, rst attempted an exp erimen t on the transp ort of gases and v ap ors in p olymeric mem branes in 1829, and published concepts for gas p ermeation in 1866 (Philib ert 2005). In 1907, Benc hold w as to dene the relationship b et w een the p erformance of the mem branes and ph ysical prop erties suc h as p ore radius and surface tension (P andey et al. 2001). In the late 1970s industries w ere in terested in the gas separation of gas mixtures with mem branes and the dev elopmen t of mo dern mem brane science from 1960 (P andey et al. 2001). Mem brane gas separation emerged as a commercial pro cess on a large scale, and progress in mem brane science and tec hnology w as mad in virtually ev ery asp ect of mem branology , including impro v emen ts in mem brane formation pro cesses, c hemical and ph ysical structures, conguration and application during the 1980s (P andey et al. 2001, Kesting et al. 1965, F ritcsc he et al. 1989). All materials, metal, glass, ceramics and p olymers, that form sucien tly thin and stable lms can b e used as mem branes. 1.2.1 T yp es of mem branes and p orosit y The mem branes are sorted according to the p ore size or the size of the materials used to separate. General mem branes ha v e p ore sizes in larger than 5000nm, microltration mem branes ha v e in the range of 100∼ 5000nm, ultraltration mem branes, with p ore sizes of 2∼ 200nm, can remo v e large molecules, and nanoltration mem branes with p ore size of less than 1nm are passable to separate 12 small molecules, gas separation usually requires mem branes with a smaller p ore size (P andey et al. 2001, Cheriy an 1998, Kesting et al. 1993). Mem branes can b e classied broadly in to three classes: p orous, non-p orous and asymmetric mem- branes. A p orous mem brane is v ery similar in its structure and function to a con v en tional lter, and can exhibit v ery high lev els of ux but pro vide for lo w separation or selectivit y for gas separation. The separation of materials b y p orous mem brane is mainly a function of the p ermeate c haracter and mem brane prop erties, the molecular size of the mem brane p olymer, and p ore size and p ore size distribution. In general, microp orous mem branes are c haracterized b y the a v erage p ore diam- eter, the mem brane p orosit y , and the tortuosit y of the mem brane, and can eectiv ely separate gas molecules. The gas separation mec hanism b y non-p orous mem brane is dieren t from that of p orous mem branes. Non-p orous or dense mem branes pro vide high selectivit y or separation of gases from their mixtures but the rates of transp ort of the gases are usually lo w. The transp ort of gases through a dense p olymeric mem brane is usually describ ed b y a solution-diusion mec hanism. The imp ortan t abilit y of dense mem branes is to con trol the p ermeation of dieren t sp ecies. A separation is ac hiev ed b et w een the dieren t p ermanen ts b ecause of dierences in the amoun t of material diusing through the mem branes. The solution-diusion mec hanism is normally considered to consist of three steps: the absorption or adsorption at the upstream b oundary , activ ated diusion (solubilit y) through the mem brane, and desorption or ev ap oration on the other side. This assumes that the pressure within a mem brane is uniform, and that the c hemical p oten tial gradien t through the mem brane is expressed as a concen tration gradien t. Asysmmetric mem branes consist of t w o structurally distinct la y ers; one of whic h is a thin, dense selectiv e skin or barrier la y er, and the other a thic k, p orous matrix (substructure) la y er whose main function is to pro vide a ph ysical supp ort for the thin skin (P andey et al. 2001). 1.2.2 Gas separation mec hanisms Mem branes are used for separation of gases from gas mixtures b y the dieren tial p ermeation of the comp onen ts through them. The mem brane separation pro cesses ha v e man y adv an tages suc h as lo w er energy used and capital in v estmen ts. Eciency of the gas separation pro cess can b e determined b y p ermeabilit y and selectivit y of the mem brane material (P andey et al. 2001). The gas separation prop erties of mem branes dep end on the material (separation factors), mem brane 13 Figure 1.2.1: Sc heme of mec hanisms for p ermeation of gases through mem branes (Bernardo et al. 2009). This gur e is r eprinte d. structure and thic kness (p ermeabilit y), mem brane conguration (e.g., at, hollo w b er) and the mo dule and system design. The p ermeabilit y is the rate at whic h an y comp ound p ermeates through a mem brane. This dep ends on a thermo dynamic factor, partitioning of sp ecies b et w een feed phase and mem brane phase, and a kinetic factor, e.g, diusion in a dense mem brane or surface diusion in a microp orous mem brane. And selectivit y is the abilit y of a mem brane to accomplish a giv en separation (relativ e p ermeabilit y of the mem brane for the feed sp ecies). The selectivit y is a k ey parameter to ac hiev e high pro duct purit y at high reco v eries (Bernardo et al. 2009). Fiv e dieren t mec hanisms; surface diusion, capillary condensation, molecular sieving, laminar o w, and Kn udsen diusion, for gas transp ort across p orous mem branes dep end on the p ermeation of gases and mem branes suc h as Figure 1.2.1. The relativ e con tributions of the dieren t mec hanisms are dep enden t on the prop erties of the mem branes and the gases, as w ell as on op erating conditions lik e temp erature and pressure (P andey et al. 2001). Selectivit y of separation ac hiev ed b y the Kn udsen mec hanism is generally v ery lo w. Molecular siev e mec hanism exhibits high selectivit y and p ermeabilit y for the smaller comp onen ts of a gas mixture. Kn udsen diusion is lik ely to b e the dominan t mec hanism of gas transp ort at lo w pressures and raised temp eratures. Con tribution of viscous o w, resulting from a pressure dierence across the p ores, will b e quite small and ev en if it is presen t, and it do es not con tribute to the separation pro cess. Ho w ev er, this lea v es Kn udsen diusion as the only transp ort mec hanism con tributing to the separation of v arious comp onen ts in a gaseous mixture at elev ated temp eratures in a p orous mem brane. Gas p ermeation b y Kn udsen diusion v aries in v ersely with the square ro ot of the molecular w eigh t. The ideal separation for binary gas mixtures, therefore, equals the in v erse of the square ro ot of the ratio of the molecular masses. Kn udsen separation can also b e ac hiev ed with mem branes ha ving p ore 14 Figure 1.2.2: Relationship b et w een the kinetic diameter, d k , of a gas molecule and the p ermanence through Si 400 and Si 600 mem branes (P andey et al. 2001). This gur e is r eprinte d. sizes smaller than 50nm. Separation factors based on Kn udsen o w are attributed to bac k diusion, to non-separation diusion, concen tration p olarization on the p ermeate side and the o ccurrence of viscous o w in large p ores (P andey et al. 2001). Renate et al. in 1998 ha v e rep orted supp orted microp orous silica mem branes prepared b y coating a p orous γ -alumina mem brane in silica sols, follo w ed b y drying and calcication at t w o dieren t temp erature, 400 ◦ C [Si400] and 600 ◦ C [Si600], resp ectiv ely . Figure 1.2.2 sho ws that the p ermeabilit y of gases through these microp orous silica mem branes app ears to b e strongly related to their kinetic diameter, as exp ected from molecular sieving mec hanisms. The molecular sieving do es not happ en when the p ore sizes of mem branes are m uc h larger than the gas molecules, b ecause molecular siev e mem branes are p orous and con tain p ores of molecular dimensions (> 0.5nm) whic h can exhibit selectivit y according to the size of the molecule (P andey et al. 2001). Gas separation can b e aected b y partial condensation for some comp onen t of a gas mixture in the p ores, with the exclusion of others, and the subsequen t transp ort of the condensed molecules across the p ore. Gas separation mec hanism requires the p ore size of the mem brane to b e in the mesop orous size range (r c > 3nm) so that condensation of the comp onen t of a gas mixture can tak e place. A v ery high selectivit y of separation of the condemnable comp onen t can b e ac hiev ed b y the mec hanism, but condensation partial pressure of the comp onen t at the temp erature, p ore size and geometry of the mem brane limits the exten t of remo v al of the condensable comp onen t from the gas mixture (Uhlhorn et al. 1987). Selectiv e adsorption mec hanism can pro vide the most exible and attractiv e c hoice for 15 the practical separation of gas mixtures. The separation selectivit y is determined b y the preferen tial adsorption of certain comp onen ts of the gas mixture on the surface of the p orous mem brane, as w ell as b y the selectiv e diusion of the absorb ed molecules across the p ores. The surface diusion and capillary condensation can con tribute signican tly at lo w temp eratures withe p ore diameters in the range of 2nm, but b e unlik ely to exist at the elev ated temp eratures. Surface diusion and capillary condensation has b een studied as another metho d for enhancing separation factors (Bernardo et al. 2009, Lee et al. 1986, Uhlhorn et al. 1989, Rao et al. 1996). In meso- and microp orous mem branes, as the relativ e pressure is increased, the adsorb ed and capillary condensed materials p ermeate together, and the p orous media b ecome more and more lik e a semi- p ermeable mem brane through whic h the sorbable p ermeate o ws freely while the w eakly sorb ed comp onen t is blo c k ed (K oros et al. 1993). Mem branes functioned as a molecular siev e ha v e p ore diameters to b e similar to diameters of the gas molecules. Separation factors greater than 10 should b e ac hiev able as the p ores b ecome smaller than ab out 0.5nm. If the mem brane has p ore sizes b et w een the diameter of the smaller and the larger gas molecules, then only the smaller molecules can p ermeate and a v ery high separation w ould b e ac hiev ed. The gas p ermeabilit y is actually inuenced b y a com bination of transp ort mec hanisms. As the p ore size decreases, the distribution of p ore size in the mem brane is exp ected to decrease, resulting in a lo w er gas o w through the mem brane. Therefore, the p ore size and p orosit y m ust b e balanced to pro duce an ecien t mem brane (P andey et al. 2001). 1.2.3 Separation Mec hanism near the Surface It is p ossible to calculate the inciden t molecular ux of gas molecules through a single mem brane c hannel. Sev eral conditions can b e considered to compare the molecular ux of air, as a carrier gas, with the molecular ux of xenon, as a trace gas, in ppb at a ro om temp erature and atmospheric pressure. A sampled gas o w sp eed is 5cm/s, the radius of the mem brane c hannel is 5nm, and the pressure ab o v e the separation mem brane is larger than the pressure b elo w the separation mem brane, and then the v olume of the sampled gas in Figure 1.2.3 (b) has V = 4πr 3 c when the heigh t of the gas v olume, h g , is same with the diameter of mem brane c hannel. Then, the tra v el time that the sampled gas o w requires to pass a single p ore is ab out 0.4µs, and the inciden t molecular ux of the carrier gas is appro ximately 10,000 molecules p er a cross sectional area of the mem brane c hannel, when the 16 gas o w sp eed of the sampled gas v olume is only considered. The molecular ux of the trace gas in ppb is m uc h smaller than the molecular ux of the carrier gas in a small cylindrical v olume. 1.2.4 Nanoscale P orous Mem brane : Carb on-based mem branes Carb on-based mem branes can b e classied in to t w o classes: carb on molecular siev e mem branes and carb on nanotub es (CNT) mem branes (Bak er 2012). F or gas separation applications, carb on molecular siev e mem branes sho w go o d in trinsic p erformance. The gas separation mec hanism in carb on-based mem branes dep ends on the p ore size whic h determines the degree of in teraction b e- t w een molecules and p ores. Molecular sieving is generally dominan t when the p ore diameters are on the molecular scale (0.3∼ 0.5nm). The CNT mem branes for gas separation w as initially prop osed b y molecular dynamics sim ulations that predicted transp ort of gases inside single-w alled carb on nanotub es with a diameter of 1nm, or- ders of magnitude faster than in an y other kno wn materials with nanometer-scale p ores (Sk oulidas et al. 2002, Sokhan et al. 2002, Chen et al. (a) 2006, Chen et al. (b) 2006). CNT s are dieren t from other mem branes with atomic-scale p ores, o wing to the smo othness of the inner surface. A gas o w through the CNT mem brane is generally one or t w o orders of magnitude faster than through a commercial p olycarb onate nanop orous mem brane with 15nm p ore size (Sholl et al. 2006). T rans- p ort of gas through the nanotub es w as m uc h higher than predicted b y a classical diusion mo del. The transp ort rates observ ed b y Holt et al. (Holt et al. 2006) for dieren t gases are one to t w o orders of magnitude larger than w ould b e predicted b y assuming a Kn udsen description, whic h is in quan titativ e agreemen t with predictions from sim ulations (Ma jumder et al. 2005). Despite the exceptionally fast mass transp ort for gas, the enhancemen t of the selectivit y of CNT mem branes is still a big c hallenge. It will b e describ ed in more detail in Chapter 2 ab out the p orous mem branes. 1.3 Kinetic theory Kinetic theory is able to explain and predict the macroscopic prop erties of gases from the prop erties of their microscopic constituen ts, and is capable of deriving transp ort co ecien ts from the fundamen tal prop erties of the gas molecules (Gom b osi 1994). Gaskinetic theory is based on the concept that a gas is a collection of man y particles acted up on b y their surroundings and b y m utual encoun ters, 17 (a) (b) Figure 1.2.3: Illustration of molecular motion around surface of a single mem brane c hannel. (a) Separation mec hanism for gas comp onen ts, and (b) Mo v emen t of gas v olume in a z -axis. r c is a radius of a single mem brane c hannel, and c ′ is a thermal mean molecular sp eed. 18 and three fundamen tal appro ximations: molecular h yp othesis, assumption of classical conserv ation la ws, and the application of statistical metho ds. The molecular h yp othesis assumes that molecules are the smallest quan tit y of a substance that retains its c hemical prop erties, all molecules of a giv en substance are alik e, and the states of matter comp osed of small discrete units dier essen tially in the arrangemen t and state of motion of the molecules. In a gas, the molecules are widely separated from one another and mo v e ab out throughout the en tire space o ccupied b y the gas. Also, the molecules mo v e ab out freely and most of the time are separated b y larger distances, and are in straigh t lines un til t w o or more happ en to come so close together that they act strongly up on eac h other, and something lik e a collision o ccurs, after whic h they separate and mo v e o in new directions, generally with dieren t v elo cities. In the classical conserv ation la ws, relativistic corrections, quan tum mec hanical and non-p erfect gas eects are not considered, but sp ecic heats and collision cross sections are considered. The initial molecular structure matters only so far as it determines the exact nature of the in termolecular forces. The kinetic theory of gases is a statistical theory with dynamical metho d and in v olv es the description of a v ery large n um b er of individual molecules b y statistical metho ds. F or instance, there w ould b e altogether N v ector equations of motion with 6N in tegration constan ts ab out a gas with a system of N particles. These a v erage quan tities migh t b e the densit y , bulk v elo cit y , pressure, etc. 1.3.1 Elemen tary transp ort theory A ccording to Gom b osi (Gom b osi 1994), Macroscopic quan tities suc h as a gas bulk v elo cit y , temp er- ature, pressure, concen tration, etc. are slo wly v aried spatial prop erties. These conguration space gradien ts result in macroscopic transp ort phenomena, diusion or heat o w. In order to describ e macroscopic transp ort phenomena and to calculate appro ximate v alues for the transp ort co ecien ts, it is to use an elemen tary mean free path metho d. This is a p o w erful metho d to gain ph ysical in- sigh t in to the basic pro cesses of molecular transp ort. The mean free path metho d is based on the assumption that the gas is not in equilibrium, but the deviation from equilibrium is so small that the distribution of molecular v elo cities can lo cally b e appro ximated b y Maxw ellians. Ho w ev er, the macroscopic parameters of the lo cal Maxw ellians slo wly v ary with conguration space lo cation. This assumption can b e translated in to t w o basic conditions mathematically . The rst condition is that 19 the v ariation of all macroscopic quan tities is small within a mean free path. In other w ords the mean free path λ m ust b e m uc h smaller than a c haracteristic scale length L c of the fastest v arying macroscopic quan tit y , G: L c ≫λ (1.3.1) where L c is dened b y the follo wing equation: 1 L c = ∇G G . (1.3.2) The second one is related to the T a ylor series of the fastest v arying macroscopic quan tit y . The T a ylor series expansion of macroscopic quan tit y ab out an arbitrary p oin t in the gas r 0 m ust rapidly con v erge for distances comparable to the mean free path. This condition can b e written as |G(r 0 )|≫λ|∇G(r 0 )|≫λ 2 |∇ 2 G(r 0 )|≫λ 3 |∇ 3 G(r 0 )|≫··· . (1.3.3) The n umerical v alues are t ypically within a factor of t w o of the result of more rigorous calculations b ecause this theory leads to the correct dep endence of transp ort co ecien ts on the gas parameters. 1.3.2 Flo w Analysis A k ey non-dimensional parameter for understanding the o w b eha vior of gases is the Kn udsen n um b er Kn, dened as the ratio of the mean free path λ to a c haracteristic geometry of the o w, i.e., a diameter for a circular capillary . The mean free path is an a v erage distance that gas molecules tra v el b efore colliding with another molecule (Fissell et al. 2011). This determines the degree of rarefaction of a gas and is as follo ws: Kn = λ L c . (1.3.4) The Kn udsen n um b er is useful for determining whether statistical mec hanics or the con tin uum mec hanics form ulation of uid dynamics should b e used. Another quan tit y c haracterizing the gas rarefaction, rarefaction parameter δ , is used instead of the 20 Kn udsen n um b er. This parameter is in v ersely prop ortional to the Kn udsen n um b er (Sharip o v et al. 2002) δ = √ π 2 1 Kn = √ π 2 L c λ . (1.3.5) It means that larger v alues of δ corresp ond to the h ydro dynamic regime and small v alues of δ appropriate to the free molecular regime. In general, the Kn udsen n um b ers are broadly three regimes: the con tin uum or viscous regime, the transition or Kn udsen regime, and the free molecular regime. The gas is categorized to b e in the con tin uum o w regime for Kn≤ 0.01, in the transition o w regime for 0.1≤ Kn≤ 10, and in the free molecular o w regime for Kn≥ 10, resp ectiv ely (Bird 1994, Barisik et al. 2010). F or Kn udsen or transitional o w there are more collisions with the p ore w alls than b et w een gas molecules. A t atmospheric pressure, Kn udsen o w dominates when the p ore diameter is b et w een 2 and 50nm. And the free molecular o w is the dominan t mec hanism of gas o w through nanotub e arra ys. This division of the regimes of o w is v ery imp ortan t b ecause the metho ds used for calculation of the gas o ws dep end on the regime. 1.3.3 Mean free path In order to obtain the mean free path of the gas molecules to P oiseuille o w, viscous mean free path (Sharip o v et al. 2002, Sharip o v et al. 1998) is use its relations with the transp ort co ecien ts pro vided b y the kinetic theory of gases. It is to calculate λ v via the viscosit y co ecien t µ as λ v = µ P √ πk B T 2m , (1.3.6) where P and T are the pressure and the temp erature, resp ectiv ely , and m is a molecular mass. This denition has an adv an tage that it con tains the easily measurable quan tities ( P , T ) and the quan tities (µ, m) . This equation is used to calculate the mean free path in this researc h. A ccording to the ideal gas la w P =nk B T, (1.3.7) 21 and the uid densit y is ρ =mn, (1.3.8) where n is the n um b er densit y . Another denition with the ideal gas la w and the uid densit y is suggested b y Cercignani as the follo wing op erational denition for the mean free path: λ v = µ ρ √ πm 2k B T . (1.3.9) Here µ is the co ecien t of viscosit y and the expression of a hard sphere gas is b y Chapman-Ensk og theory , µ = 5 16σ √ mk B T π , (1.3.10) whereσ is the total cross section of molecular collisions. F or p erfect gases the h ydro dynamic viscosit y dep ends only on the gas temp erature while it is indep enden t of the uid densit y . In general, the mean free path in a homogeneous Maxw ell gas, whic h corresp onds to an actual gas at equilibrium, is λ = 1 √ 2nσ . (1.3.11) Another denition of the mean free path as functions of densit y (Morris et al. 1992) is that the mean free path λ h in the hard sphere gas from basic kinetic theory is written as, λ h = m √ 2πρd 2 , (1.3.12) where d is the molecular diameter. These t w o denitions of mean free path, equations (1.3.11) and (1.3.12), giv e similar results at lo w Kn udsen n um b er, but dramatically dier when the separation of p ore diameters is small. The mean free path in the hard sphere gas dep ends on the densit y and the diameter of a particle, while the viscous mean free path dep ends on the c haracteristic distance, p ore diameter, since an eectiv e viscosit y decreases with increasing Kn udsen n um b er. In other w ords, the viscous mean free path is the eectiv e distance tra v eled b y a particle b et w een collisions with 22 particles or w alls. F or a mixture gas comp osed of sp ecies a and b, the mean free path for diluen t sp ecies a is (Hudson 2008) λ ha = 1 n a σ aa √ 2+n b σ ab √ 1+m a /m b , (1.3.13) where, σ ab = 4 (d a +d b ) 2 is the a v erage cross sectional area of molecular radii of eac h sp ecies. When only one sp ecies in the gas is presen t, the familiar form ula, Equation (1.3.11) is reco v ered. When n a ≪n b , the rst term in the denominator, resulting from lik e-molecule collisions, is negligible. If the Kn udsen n um b er is the based in an exit pressure P exit for a simple gas of hard sphere molecules in thermo dynamic equilibrium b y Bird (Bird 1994), the mean free path of the gas is giv en b y λ f = k B T √ 2σP exit . (1.3.14) F ree molecular o w is generally observ ed in lo w pressures ( < 100Pa) en vironmen ts suc h as the upp er atmosphere and v acuum systems so the equation (1.3.14) is useful for these conditions. T able T.1 and T.4, and Figure F.1 in the app endix sho ws the mean free paths of sev eral molecules considered in this researc h, and the v alues in paren theses are for T = 273K and v arious pressure as w ell. In this study , the diameters of p orous mem branes are b et w een 10nm and 50nm, and a width of a main o w c hannel designed v aries from 10cm to 0.5cm along a length of one. The gases, He, Ar , N 2 , and Xe, in the p orous mem branes are considered as the transition o w except the helium gas for the p orous material in a 10nm diameter (free molecular o w). F or the main o w c hannel, the con tin uum o w regime can b e considered. 1.3.4 Mass o w rate A ccording to the conserv ation of mass, the amoun t of mass remains constan t within some problem domain, suc h as a tub e (or a c hannel), and can mo v e through the domain, while a densit y , v olume and shap e of the ob ject can c hange within the domain with time for a gas o w. Without accum ulation or destruction of mass through the tub e, the same amoun t of mass lea v es the tub e as en ters the tub e, and passes through an y plane p erp endicular to the cen ter line of the tub e. Then the amoun t of mass passing through a plane is a mass o w rate that is constan t through the tub e. The v alue of the mass o w rate can b e determined from the o w conditions (NASA 2008). If the gas passes 23 through an area A at v elo cit y v and an densit y ρof the mass m V con tained in the v olume, the mass o w rate can b e determined as _ M =ρAv. (1.3.15) This equation is useful to calculate the v elo cit y of gas through the c hannel that is considered in a macroscale. After Kn udsen in 1909 considered a tub e, that w as m uc h longer than its radius, with a small pressure dierence b et w een the inlet and the outlet and dev elop ed an expression for the mass o w rate b et w een free-molecular and con tin uum o w, a gas o w through a tub e from free molecular to con tin uum condition has b een the sub ject of man y exp erimen tal, theoretical, and computational in v estigations o v er the last cen tury (Gallis et al. 2012). This concept is more activ ely used for microscale devices with dev elopmen t of micro electromec hanical systems. The mass o w rate and the pressure prole is generally applied as a primary imp ortance, and a radial v ariation of the v elo cit y eld can b e applied as a secondary imp ortance (Gallis et al. 2011), but the radial v ariation of the v elo cit y through the tub e is not considered. The mass o w of gas decreases with a pressure drop that is reduced due to the c hange in gas densit y . Ho w ev er Kn udsen found that the mass o w reac hes a minim um v alue at lo w pressure and then increases with decreasing pressure, whic h is due to slip or non-zero uid v elo cit y at the w all for free molecule o w. In this study , the macro- and microscale mass o w rates are considered together, b ecause it is go v erned b y the macroscale in the main o w c hannel and op erated b y the microscale in the mem brane c hannels. 1.3.5 Hydro dynamic o w If the Kn udsen n um b er is v ery small (Kn≪ 1, or δ≫ 1 ), the mean free path is smaller than the c haracteristic geometry that the gas can b e considered as a con tin uous medium, and the h ydro dy- namic equation (P oiseuille o w) can b e applied to the gas o w. In this case, viscous o w o ccurs b ecause the mean free paths of the gas atoms or molecules are signican tly less than the diameter of the p ore c hannel. Hence the gas o w is collision dominated, meaning that the molecules undergo a v ery large n um b er of collision b efore tra v eling a distance comparable to the scale of the problem (Gom b osi 1994). The frequen t in termolecular collisions help to main tain a situation of small de- 24 Figure 1.3.1: Circular tub e geometry sho wing k ey geometric and o w v ariable for a gas o w (Gomosi, 1994). This gur e is r eprinte d. parture from lo cal thermo dynamic equilibrium, ev en in the presence of dissipativ e uxes originating from inhomogeneities suc h as w alls. Na vier-Stok es equations and its accompan ying no-slip b ound- ary conditions can b e deriv ed as the small Kn udsen n um b er limit of the Boltzmann equation of non-equilibrium statistical mec hanics (Fissell et al. 2011). Diusion t yp e pro cesses in this case are resp onsible for transp orting mass, momen tum and energy inside the gas (in the absence of macro- scopic bulk motion of the gas as a whole). This regime can b e v ery successfully describ ed with the metho ds of compressible uid dynamics (Gom b osi 1994). F or studying the gas o w through long straigh t tub e c hannels or capillaries of uniform circular cross sections, a signican tly simple alternativ e exists in the form of analytical theories that correct the Na vierStok es equations for rarefaction and slip eects. A t ro om temp erature and pressure the molecular mean free path is negligibly small compared to the radius of a long straigh t tub e c hannel r c . Assuming that the o w v elo cit y is not to o large and consequen tly the o w is not turbulen t, the steady-state motion of the gas is laminar and it is primarily con trolled b y the viscosit y . F or example, if it is considered gas molecules escap e from a con tainer through a small orice, imp ortan t applications are to calculate the rate at whic h gases can leak in to v acuum through v ery small holes suc h as the design of space v ehicles, and to calculate the thrust (net loss of momen tum through the hole in unit time) caused b y molecular eusion. Among other things this eect an result in spacecraft rotation, whic h can lead to loss of stabilization (Gom b osi 1994). In the Figure 1.3.1, t w o reserv oirs are connected b y a tub e of length L and diameter d c . Then P 1 ,T 1 andC 1 are the pressure, temp erature and concen tration, resp ectiv ely , of a gas o w in a left con tainer and P 2 , T 2 , and C 2 are the pressure, temp erature, and concen tration, resp ectiv ely , in a righ t one. The thic kness of the w all is assumed to b e negligible compared to the diameter of the tub e. When the tub e is long enough, it is p ossible to neglect end eects. F or the o w problem b y h ydro dynamic 25 metho ds, the linear dimensions of the reserv oirs are assumed to b e v ery large compared to the size of the tub e, and therefore the gas o w v elo cit y can b e tak en to b e near zero ev erywhere except in the immediate vicinit y of en trances of the tub e. The longitudinal axis of the tub e is axially symmetric so that the bulk v elo cit y of the uid u(r) that can b e sub divided in to coaxial cylindrical shells of thic kness dr is a function of the radial distance r in a cross sectional plane measured from the axis of the tub e, z -axis. The v elo cit y u(r) increases from zero, u(r c ) = 0, at the w all to a maxim um, u(r = 0) = u max , on the axis, b ecause the outermost la y er of gas adjacen t to the w all ma y ha v e a negligible o w v elo cit y due to the irregular surface of the w all. If the tub e is a short cylinder that has a length △z , t w o forces, pressure dieren t and viscous forces, are acting (Gom b osi 1994). The pressure dierence force is a base area times a pressure dierence b et w een the t w o bases of the cylinder, πr 2 △P = πr 2 [P(z +△z)−P(z)], and the viscous force is the surface area times the viscous stress, (2πr△z)× ( µ du dr ) . The pressure gradien t force accelerates all the gas inside the cylinder. Under steady state conditions, the pressure gradien t and viscous forces balance eac h other b y Gom b osi: (2πr△z)× ( µ du dr ) −πr 2 △p = 0. (1.3.16) The solution for u(r) with the b oundary condition, u(r c ) = 0, is the follo wing: u(r) =− r 2 c −r 2 4µ △p △z (1.3.17) Then a general expression of the total molecular o w ( s −1 ) across the cross section of the tub e is hy =n rc 0 2πru(r)dr =− 2πn 4µ △p △z rc 0 r(r 2 c −r 2 )dr =− πr 4 c n 8µ △p △z . (1.3.18) A in teresting denition, the mass o w rate in the con tin uum no-slip limit through a tub e can b e calculated (Fissell et al. 2011) _ M hy = πr 4 c ρ av 4µ △P △z , (1.3.19) whereρ av is the a v erage gas densit y of the gas densities at inlet and outlet of the tub e. 26 When a long tub e (L≫ r c ) is short enough for the t w o reserv oirs, the inlet and outlet of the gas o w are lo cated at z = 0 and z = L, resp ectiv ely . The tub e w all has a uniform temp erature T and the gas in the t w o reserv oirs also has the same temp erature T (T =T 1 =T 2 ), with inlet and outlet pressures P 1 and P 2 (P 1 ≥ P 2 ). The mass o w rate based on the con tin uum mec hanics equations in these conditions across a cross section (Sharip o v 2004) dev elop ed b y Sharip o v et al. (Sharip o v et al. 2005). The end eect is neglected the temp erature and pressure gradien ts. The mass o w rate is expressed as _ M L≫rc =πr 3 c P(z) √ m 2k B T ( − G P P(z) dP dz + G T T(z) dT dz ) , (1.3.20) where the co ecien t G P andG T dep end on the lo cal gas rarefaction δ , andP(z) is the v ariation along the tub e. This co ecien t can get from the n umerical data of Sharip o v (Sharip o v 1996, Sharip o v et al. 1998). When the temp erature is constan t, equation (1.2.20) can b e easily rewritten in _ M L≫rc =−πr 3 c G P √ m 2k B T dP dz . (1.3.21) The co ecien t G P along the tub e can b e assumed as (Sharip o v et al. 1994) G P = 1 P 2 −P 1 P2 P1 Q(δ)dP, (1.3.22) where for δ≥ 10 the Q(δ) appro ximates as follo ws Q(δ) = δ 4 +1.10162+ 0.5489 δ − 0.6081 δ 2 . (1.3.23) F rom equations (1.3.22) and (1.3.23), the co ecien t can b e expressed as G(P) = r c 4µ √ m 2k B T P 1 +P 2 2 +1.10162+ 0.5486µ (P 2 −P 1 )r c √ 2k B T m ln ( P 2 P 1 ) − 1.2162µ 2 k B T mr 2 c P 1 P 2 . (1.3.24) When the equations (1.3.19) and (1.3.21) are compared for the gas mass o w at inlet and outlet of the tub e, these equations sho w a similar result when it is considered only the rst term in equation (1.3.24). The equation (1.3.24) ma y b e considered for the problem ab out the mass o w rate at an y lo cation in the tub e. 27 1.3.6 T ransition o w The transitional regime (Kn∼ 1), when the Kn udsen n um b er is ab out unit y , is the most unexplored parameter regime. In this case, the mathematical description of the o w is complicated, b ecause the fundamen tal assumptions of uid dynamics are no longer v alid (Gom b osi 1994). There are no w ell dev elop ed standard tec hniques to handle problems in the transitional regime in general. The mean free path is smaller than the radius of the tub e but it is not negligibly small so that it is considered the slippage of the gas at the w alls of tub e, b ecause the mean free path is comparable to in termolecular collisions. A mo died P oiseuille form ula can b e obtained, corrected for the slippage of the gas at the w alls of tub e. By slippage the gas v elo cit y at the w all is dieren t than the w all v elo cit y . There are also more collisions with the p ore w alls than with other gas molecules (Kn udsen 1908). A t ev ery collision with the p ore w alls the gas molecules are momen tarily absorb ed and then reected in a random direction. As there are less n um b er of collisions among molecules than the p ore w alls, eac h molecule mo v es indep enden t of others. Hence, the separation of a gas mixture is ac hiev ed b ecause dieren t gas sp ecies mo v e at dieren t v elo cities. It is considered the slippage of the in teraction of gas molecules with a lo w densit y gas o w in a long circular tub e, the radius r c = dc 2 . The mean free path of molecular collisions is somewhat smaller than the radius, λ < r c . It is assumed that after colliding with a w all eac h molecule undergo es sev eral molecular collisions b efore it collides with the other w alls. T w o t yp es of collision b et w een the p ore w alls and the gas molecules are the elastic or sp ecular collision and diuse reection. The y comp onen ts of the a v erage v elo cit y of molecules righ t b efore and righ t after their collision with the w all are u z1 and u z2 , resp ectiv ely . When the tangen tial v elo cit y of the colliding molecule is conserv ed, therefore for elastic collisions, u z1 = u z2 . And when a molecule is temp orarily absorb ed and then re-emitted, the a v erage tangen tial v elo cit y of diusely reected particles is the same as the v elo cit y of the b oundary of the w all, therefore for these particles u z2 = u 0 . The relativ e dierence of the t w o reections is expressed with the accommo dation co ecien t η dened as the fraction of molecules undergoing diuse reection. The a v erage tangen tial v elo cit y righ t after collision can b e written as u z2 =ηu 0 +(1−η)u z1 . (1.3.25) 28 Figure 1.3.2: Circular tub e geometry sho wing molecular collision The a v erage gas tangen tial v elo cit y at the upp er w all u(r) =u r is the mean of the a v erage pre- and p ost-collision v elo cities, u r = uz1+uz2 2 . The expression for u r is as follo ws: u r = η 2 u 0 + 2−η 2 u z1 . (1.3.26) Here u z1 reects the a v erage tangen tial o w v elo cit y at a distance of 2 3 λ from the w all where the last collision o ccurred according to Gom b osi. One more equation needed to fully sp ecify these quan tities can b e obtained b y applying the mean free path metho d to the slip o w. u z1 =u r − 2 3 λ [ du dr ] r=rc . (1.3.27) In order to obtain u r , equations (1.3.26) and (1.3.27) can com bine as follo ws: u r =u 0 − 2−η η 2 3 λ [ du dr ] r=rc , (1.3.28) where the u 0 is also considered as a a v erage v elo cit y for Na vier-Stok es equations with a no-slip b oundary condition (P oiseuille o w). Gom b osi (Gom b osi 1994) dened as u 0 =− r 2 c −r 2 4µ dp dz . (1.3.29) The dierence b et w een the v elo cit y u 0 and the a v erage gas v elo cit y at the w all u r is called the slip v elo cit y u slip , and b e written as follo ws: u slip = 2−η η 2 3 λ [ du dz ] z=rc . (1.3.30) 29 When all molecules are reected diusely , i.e., if η = 1, the equation simplies to the follo wing: u slip = 2 3 λ [ du dz ] z=rc . (1.3.31) This expression describ es a nite slip v elo cit y . Ho w ev er, when all molecules are reected sp ecularly , i.e., η = 0 (p erfect slip), it is mathematically undened, u slip →∞. In most practical cases η > 0, therefore the slip v elo cit y remains nite. In the case of diuse reection, the slip v elo cit y b y P oiseuille o w with the exception of slippage at the w alls is u slip =− 1 3 λ r c µ dp dz , (1.3.32) b ecause the gas o ws in the direction of smaller pressure (△p < 0). The cross sectional v elo cit y prole of the o w can b e obtained b y solving the dieren tial equation with the slip o w b oundary condition. Then the solution is the follo wing: u r =u slip − r 2 c −r 2 4µ dp dz =− ( r 2 c + 4 3 λr c −r 2 ) 1 4µ dp dz . (1.3.33) One can use this slip o w cross sectional v elo cit y prole to calculate a mo died P oiseuille form ula for the total ux through the tub e: total =n rc 0 2πru(r)dr ==− πnr 4 c 8µ dP dz ( 1+ 8 3 λ r c ) . (1.3.34) When compared to the original P oiseuille form ula equation exhibits a correction factor of 8 3rc . This means that slippage decreases w all friction and therefore the gas resp onds more readily to the pressure gradien t. The net result is an increase in the gas ux. And also these v elo cities are related to the pressure gradien t dP dz and mass o w rate _ M b y the Na vier-Stok es equations through the tub e that the diameter is smaller than its length can b e dened as follo ws: dP dz = µ r ∂ ∂r ( r ∂u r ∂r ) =− 8u 0 µ r 2 c , (1.3.35) 30 and _ M tr = mπr 4 c P 8µk B T ( 1+ 8 3 λ r c ) dP dz . (1.3.36) 1.3.7 F ree molecular o w When the Kn udsen n um b er is v ery large (Kn≫ 1 or δ ≪ 1), the mean free path is so large that the collisions of molecules with the capillary w alls o ccur m uc h more frequen tly than the collisions b et w een molecules. Th us, the eects of in termolecular collisions on molecular tra jectories are statis- tically insignican t and these collision are either negligible or grossly simplied. The o w of gas is determined almost en tirely b y w all molecule collisions, and is practically unaected b y in termolec- ular collisions. In this case, the regime is called collisionless o w, and the motion of the upp er atmosphere at v ery high altitudes is often called collisionless (Gom b osi 1994). Also, the gas o w in teracted with collisionless gases with a nite size ob ject suc h as a long v acuum tub e is called free molecular o w. Under this condition, ev ery molecules mo v es indep enden tly of eac h other. Eac h collision o ccurs with complete thermalization so that the angle of reection is fully randomized with resp ect to the incidence angle. The n um b er of densit y is constan t in ev ery cross sectional area b e- cause molecular collisions are neglected. The c haracteristic scale length of L c is m uc h larger than the tub e radius r c . In other w ords the follo wing condition m ust hold: 1 L c = 1 n dn dz ≪ 1 r c . (1.3.37) In the case of a v ery long tub e with smaller radius r c , the condition Kn ≫ 1 is satised and the basic assumptions for viscous o w are not v alid an y more. F or the free molecular o w in a v ery long circular cylinder, the t w o ends are k ept at dieren t pressures, and the temp erature is uniform throughout the tub e. In the free molecular appro ximation the o w problem is reduced to determination of the eects of molecular collisions with the w all. In the case, the total net o w through the tub e p er unit time can b e simplied to the follo wing expression: =− 2r 3 c 3 √ 8πk B T m dn dz . (1.3.38) This result can b e compared to the h ydro dynamic ux densit y calculated with the mean free path 31 metho d. In this regime the tub e diameter b eha v es as an eectiv e mean free path λ = 2r c . This result is quite plausible, b ecause the molecules in teract only with the w all. In this case all particle has a same sp eed, c ′ and then the mass o w rate is, from Gom b osi (Gom b osi 1994), _ M fr =− 16σr 4 c P 3k B T √ πm k B T dP dz . (1.3.39) This result can b e compared with the P oiseuille form ula _ M hy =− 3π 16 σr 4 c P k B T √ mπ k B T dP dz . (1.3.40) The ratio of the uxes is close to 1 9 : _ M Poisseuille _ M = 9π 256 = 0.1105 (1.3.41) The n umerical factor in the expression for the P oisseuille o w is larger b y ab out a factor of 8.8 in the free molecular regime. After Kn udsen in 1909 studied exp erimen tally and theoretically the molecular o w in long tub es, he assumed a general relationship for the long tub e v arying cross sectional area and the mean thermal v elo cit y of molecules. The molecular o w conductance, v olumetric o w ( m 3 /s) of the thin tub e is directly related to the rate of collision of molecules o v er the cross sectional area A of the tub e (Laert y 1990) _ Q =A √ k B T 2πm . (1.3.42) The expression for the conductance of a long cylindrical tub e is _ Q =Aα √ k B T 2πm . (1.3.43) Here the transmission probabilit y for a long cylindrical tub e is α = 4d c 3L . (1.3.44) The transmission probabilit y for unit length increases as the length of the tub e increases. In Chap- 32 Figure 1.3.3: All escaping molecules ha v e p ositiv e v z v elo cities through the orice (Gomosi 1994). This gur e is r eprinte d. ter 2, the relationship b et w een the length and diameter of tub e of the transmission probabilit y is considered in more detail. Fissell (Fissell et al. 2011) dened another expression for the v olumetric o w when Kn > 10. The corresp onding relationship is: _ Q =α √ πk B T 2m r 2 c P exit △P, (1.3.45) where α is a geometry dep enden t shap e factor of the tub e expressed as α = r c L [ πlog ( 1 π + √ 1+ 1 π 2 ) +log ( 1+ √ 1+π 2 ) − 8 3 ( π 2 +1 ) 3=2 + 8 3π ( π 3 +1 ) ] . (1.3.46) 1.3.8 Kinetic eusion of molecules Problems of molecular eusion that escap e from a con tainer through a small orice use con tin uum gas dynamics and gaskinetic metho ds, but the t w o metho ds lead to dieren t results. Consider the assumption that the mean free path of the gas molecules is m uc h larger than the diameter of the orice, whic h is still m uc h larger than the molecular size. Eac h molecule can lea v e the con tainer with a v elo cit y that it had as it came up in the p erp endicular direction to the orice. If all particles through the orice satisfy the condition v z > 0 suc h as Figure 1.3.3, the v elo cit y distribution outside the orice can b e c haracterized b y a truncated Maxw ell-Boltzmann distribution function: 33 Figure 1.3.4: Sc heme of oblique cylinder. A group of molecules with v elo cit y v ector in an innitesimal neigh b orho o d of v hit the orice area dS during the time in terv al dt (Gomosi 1994). This gur e is r eprinte d. F esc ={ n ( m 2kBT ) 3=2 exp ( − m 2kBT (v 2 x +v 2 y +v 2 z ) ) if v z > 0 0 if v z ≤ 0 , (1.3.47) where n is the n um b er densit y in the reserv oir. The truncated distribution function of escaping molecules, F esc , is normalized to n/2. The molecules with v elo cit y v ector, v, m ust ha v e a p ositiv e v z comp onen t, but cannot lea v e the reserv oir so that these molecules are all con tained at the b eginning of the time in terv al, dt, in an oblique cylinder with base dS and altitude v z dt. Then the v olume of the impact cylinder is dV impact =v z dtdS. (1.3.48) The n um b er of particles with v elo cities b et w een v andv+d 3 v , whic h pass through the orice elemen t in time, is giv en b y the follo wing expression: d 6 N =F esc d 3 vdV impact =v z F esc d 3 vdtdS. (1.3.49) The ux escaping from the reserv oir through the orice is dened as the n um b er of particles lea ving the reserv oir p er unit orice area p er unit time. Then the escap e ux can b e expressed with the help of the distribution function of escaping particles: j esc = ∞ −∞ dv x ∞ −∞ dv y ∞ −∞ dv z v z F esc (v). (1.3.50) 34 P articles with v z < 0 cannot lea v e the reserv oir through the orice leads to the follo wing expression for the escap e ux: j esc =n ( m 2πk B T ) 3=2 ∞ −∞ dv x ∞ −∞ dv y ∞ 0 dv z v z exp ( − m 2k B T (v 2 x +v 2 y +v 2 z ) ) =n √ k B T 2πm . (1.3.51) The mean thermal sp eed of molecules in the reserv oir is c ′ = √ 8k B T πm . (1.3.52) The escap e ux from the reserv oir through the small orice can b e written as j esc = 1 4 n c ′ . (1.3.53) If molecules lea v e the original reserv oir through the orice in another reserv oir, the molecules, whic h just escap ed from the original reserv oir to another reserv oir, undergo man y collisions in second reserv oir b efore it reac hes the orice again. When the same argumen t applied to particles lea ving the second reserv oir, one can conclude that the escap e uxes from t w o reserv oirs do not inuence eac h other and therefore the net particle ux from the original reserv oir 1 to another reserv oir 2 can b e calculated as j net =j 1 −j 2 = 1 4 (n 1 c ′ 1 −n 2 c ′ 2 ). (1.3.54) 1.3.9 Molecular mo dels Molecular theories attempt to analyze the diusion pro cess in terms of sp ecic p ostulated motion of p enetran t molecules in p olymers. The hole or lattice v acancy theory assumes that a certain amoun t of w ork has to b e done on a matrix to create or expand a hole to accommo date the diusing p enetran t (Kumins et al. 1968). The p enetran t m ust b e giv en sucien t energy to o v ercome the p oten tial energy barrier of the mem brane (P andey et al. 2001). Molecular dynamics sim ulations are increasingly emplo y ed as a to ol for exploring the transp ort of small molecules in p olymeric systems. These sim ulations pro vide a link b et w een the p olymer c hain arc hitecture and the p enetran t transp ort that can b e emplo y ed in the rational design and 35 optimization of separation mem branes (Cuth b ert et al. 1999). Molecular dynamics sim ulations of gas diusion ha v e b een rep orted for a simple p olymer lik e p olycarb onate (Shah et al. 1986). There also allo w the transition from the solution-diusion (for dense, nonp orous mem branes) to the p ore-o w mec hanism (microp orous mem branes). As the micro ca vities b ecome larger, the transp ort mec hanism c hanges from the diusion pro cess to a p ore-o w mec hanism (Bak er 2012). 1.4 Gaseous Diusion When the p orous diameter of the mem brane is smaller than 100nm, there exist separation principles based on a certain ph ysical in teraction with the mem brane materials more than size exclusion. These include prev ailing collision of molecules with the w alls of mem brane c hannels (Kn udsen diusion), trapping of activ e molecules in an attractiv e p oten tial w ell of the w alls of mem brane c hannels, and space c harge eects induced b y the c harged w alls of mem brane c hannels (ionic nanoltration) (Ho et al. 2006). The p ore diameters d c of mem branes are classied as microp ores ( d c < 2nm), mesop ores (2nm<d c < 50nm), and macrop ores (d c > 50nm) b y the In ternational Union of Pure and Applied Chemistry (IUP A C) terminology . This classication pro vides appro ximate b oundaries for dieren t transp ort and separation mec hanisms that are relev an t for gases. In the macrop ore, the transp ort of gases can b e caused en tirely b y bulk diusion or viscous o w, driv en b y a mec hanical pressure dierence. The viscous transp ort in mem brane p ores can b e calculated from the Hagen-P oiseuille equation for stationary Newtonian o w in a cylindrical capillary (V erw eij et al. 2007). As the p ore diameter decreases, diusing gas molecules then ha v e more collisions with the p ore w alls than with other gas molecules. The molecules resp onse to the in teraction p oten tial of the w all, and their transp ort can b e describ ed in terms of constrained molecular diusion in the microp ore diameters. A t ypical microp ore mec hanism, dominated b y concen tration and mobilit y , ma y lead to m uc h more in teresting separation mec hanisms. The transp ort of gases in mesop ores generally o ccurs b y the Kn udsen diusion if the mean free path of the molecules is larger than the p ore diameter. The mean free path of the molecule is not mainly go v erned b y the c hannel diameter (Ro que-Malherb e et al. 2007). A t ev ery collision with the p ore w alls, the gas molecules are adsorb ed and then reected in a random direction. Molecule-molecule collisions are rare, so eac h gas molecule mo v es indep enden tly of all others. Hence with gas mixture in whic h the dieren t sp ecies mo v e at dieren t a v erage v elo cities, a separation is p ossible (Bak er 2012). 36 1.4.1 Fic k’s la w Since Graham exp erimen tally disco v ered imp ortan t relationships for gas diusion through a mem- brane in 1846, the gaseous diusion, whic h indicates ho w fast a p enetran t is transp orted through the p orous materials, is a imp ortan t topic in catalysis, gas c hromatograph y , and gas separation pro- cesses (Philib ert 2005, V erw eij et al. 2007). In 1863, Maxw ell calculated the diusion co ecien ts in gases from the Graham data. The results are amazing: His c o ecient of diusion of CO 2 in air is ac cur ate at ±5%. Isnt it extr aor dinary?. Maxw ells theory of diusion w as based on gas kinetics and mean free path estimates (Gorban et al. 2011). Fic ks t w o la ws (Ho et al. 2006) are the most p opular approac h to calculating gas diusion in no p orous media, b ecause it is extensiv ely applied to p orous media. Fic k used the conserv ation of matter and the analogy b et w een diusion and F ourier s la w for heat conduction in 1822, or Ohms la w for electricit y in 1827 (Gorban et al. 2011). The rst la w is related to the diusiv e ux of a gas comp onen t as a function of the concen tration gradien t under steady state condition and the second la w is the relationship of the unsteady diusiv e ux to the concen trations gradien t. The rst la w for a binary system states that the mole or mass ux is prop ortional to a diusion co ecien t times the gradien t of the mole or mass concen tration. The net diusion ux of particles in the z direction is the dierence b et w een the n um b er of up w ard and do wn w ard mo ving tracer molecules crossing unit in terface area p er unit time. T o a go o d appro ximation this ux of concen tration ( mol/m 2 s) is J F =−D s ∂C ∂z , (1.4.1) whereD s is the m utual diusion co ecien t or self diusion co ecien t ( m 2 /s) ,C is the concen tration of the gas in the mem brane (mol/m 3 ), and z is the distance. The negativ e sign indicates that the diusion is trying to eliminate the concen tration gradien t of the molecule. F or w eak in teractiv e gases, D s can b e assumed to b e indep enden t of concen tration. The diusion co ecien t for gases estimated from correlations as discussed b y Reid et al. is in v ersely prop ortional to the absolute pressure and directly prop ortional to the absolute temp erature to the 1.75 p o w er as giv en b y the F uller et al. in 1987 (Ho et al. 2006). The second la w deriv ed from the rst la w and the mass conserv ation without an y c hemical reactions relates the unsteady diusiv e ux to the concen tration 37 gradien t and it predicts ho w diusion causes the concen tration to c hange with time. ∂C ∂t =D s ∂ 2 C ∂x 2 . (1.4.2) The self diusion co ecien t or self diusivit y of the gas molecule describ es the net displacemen t of an individual, tagged particle. The diusion co ecien t is generally a pro duct of mean v elo cit y and mean free path. A ccording to P ollard in 1948, the self-diusion co ecien t in a long tub e can b e expressed as D s = 16r c 3π √ k B T 2m ., (1.4.3) when a transp ort due to in ter-diusion is asso ciated with a partial pressure gradien t of the tagged molecules, if a certain fraction of all the molecules is tagged b y some means without losing their iden tit y in other resp ects with the un tagged molecules. The self diusivit y is sometimes referred to as the tracer diusivit y (Ro que-Malherb e et al. 2007). This equation predicts that the diusion co ecien t is directly prop ortional to T 1=2 and in v ersely prop ortional to the particle densit y n. The predicted dep endence on the temp erature and densit y is w ell supp orted b y observ ations. In most cases the n umerical factor in the diusion co ecien t is not b etter than a factor of three or so. Ho w ev er, considering all the simplications in v olv ed in the mean free path metho d it is quite remark able that the dep endence on the macroscopic gas parameters is correct for p erfect gases (Morris et al. 1992). The molar o w rate of gas p er unit area and time through the mem brane in h ydro dynamic regime is J F = r 2 c F 8µh c (P 1 −P 2 )(P 1 +P 2 ) RT , (1.4.4) whereR is the univ ersal gas constan t (J/mol·K ), F is the fractional op en area of p orous mem brane surface, r c is the a v erage radius of mem brane c hannels, h c (=L) is the a v erage heigh t of mem brane c hannels or a thic kness of mem brane, and P 1 and P 2 are the absolute pressures of the gas sp ecies at the b eginning of the p ore and at the end (Bak er 2012). 38 Figure 1.4.1: Microp orous mem branes are c haracterized b y their tortuosit y . (Bak er et al. 2012) In a binary mixture of rigid elastic spherical molecules, the co ecien t of diusion is (Manginell 2003) D s ab = 3 8nr 2 ab √ k B T 2π ( 1 m a + 1 m b ) , (1.4.5) where m a and m b are the molecular masses, and σ ab is the a v erage of the molecular radii of eac h sp ecies, r ab = ra+r b 2 . In the p orous media, the diusion co ecien t in the Fic kian diusion regime can b e written as D FP =FS g τD s , (1.4.6) where D FP is the eectiv e diusion co ecien t for the gas in a p orous media, S g is the gas saturation, and τ is the tortuosit y . The tortuosit y correlation of Millington and Quirk (1961) is giv en b y τ =F 1=3 S 7=3 g . (1.4.7) The mem brane tortuosit y reects the length of the a v erage p ore compared to the mem brane thic kness sho wn in Figure 14.1. Simple cylindrical p ores at righ t angles to the mem brane surface ha v e a tortuosit y of 1, that is, the a v erage length of the p ore is the mem brane thic kness. Usually p ores tak e a more meandering path through the mem brane, so t ypical tortuosities are in the range 1.5∼ 2.5 (Bak er 2012). Therefore the tortuosit y factor for all gas condition reduces to the p orous medium v alue, or τ(S g = 1.0) =F 1=3 . (1.4.8) 39 Therefore the eectiv e diusion co ecien t can b e rewritten as D FP =F 4=3 D s . (1.4.9) The eectiv e diusion co ecien t subsumes all eects of gas molecule collisions with p ore w alls and other gas molecules, and the geometry of the p ore spaces through whic h gas tra v els. If the gas pressure is high, molecule-molecule collisions dominate and the system is said to b e in the normal or Fic kian regime (Hudson 2008). The Fic kian diusivit y , is also kno wn as the transp ort diusivit y , the c hemical diusivit y , or the collectiv e diusivit y , is of in terest in ph ysical applications in v olving net mass transfer (Chen et al. (a) 2006), and is dened as the prop ortionalit y constan t relating a macroscopic ux to a spatial concen tration gradien t of the second la w (Sk oulidas et al. 2005). The net mass is due to dierences in the concen tration, temp erature and pressure (Hudson 2008, Ho et al. 2006). 1.4.2 F ree molecule diusion When the gas molecular mean free path b ecomes of the same order as the tub e dimensions, free- molecule, or Kn udsen diusion b ecomes imp ortan t. Due to the inuence of w alls, Kn udsen diusion and congurational diusion implicitly include the eect of the p orous medium. A t lo w pressure, collisions are dominan tly b et w een molecules and the w alls, and the free path is restricted b y the geometry of the v oid space. In the free molecule diusion regime or Kn udsen regime, the presence of other gases no longer aects the transp ort, and the ux dep ends only on the densit y gradien t of the sp ecies of in terest. Mason and Malinausk as dene the molecular ux in 1983 (Hudson 2008, Sharip o v et al. 2005), J K =−D K ∂C ∂z , (1.4.10) where the Kn udsen diusion co ecien t D K is prop ortional to the mean v elo cit y . When a long, straigh t, circular capillary of radius is m uc h smaller than the mean free path of a molecule, the diusion co ecien t at lo w pressure can b e estimated as follo ws (Hudson 2008, Sharip o v et al. 2005), D K = 4r c 3 √ 2k B T πm . (1.4.11) 40 Figure 1.4.2: Molar Flo w rate of gas through the ideal separation mem brane when F = 0.0042, r p = 15nm, h p = 6µm, P 1 −P 2 = 0.01atm, and T = 300K . This equation ma y b e appropriate for the o w in w ell dened capillaries suc h as a CNT, but it is not directly useful for the p orous media suc h as mem brane applications. Ho w ev er, there is an alternativ e w a y to determine the Kn udsen diusion co ecien t that includes the complexit y of the p orous media. If an ideal p orous mem brane, whic h p ermits o w through it, is treated as a collection of straigh t circular capillaries, the rate of diusion through the mem brane is go v erned b y Kn udsen’s la w. The equiv alen t equation for p ermeation b y P oiseuille o w is J K = 8 3 √ 1 2πMRT Fr c h c (P 1 −P 2 ), (1.4.12) where M is the molecular w eigh t (kg/mol). Figure 1.4.2 sho ws the relationship b et w een the molar o w rate and the atomic mass through the p orous mem brane, with ne-p ored and man y p ores p er unit area, pro vided b y Hind (Hind 2004). The molar o w rate of gas decreases the increasing atomic w eigh t. It means the hea vier gas molecules are harder to escap e the p orous mem brane than the ligh ter gas molecules. Non-h ydro carb on gas- p ermeation exp erimen ts, H 2 , He, Ne, N 2 , O 2 , Ar , CO 2 , and Xe, of Holt (Holt 2006) also found as M −1=2 dep endence, that is, ligh ter gases diuse faster, in prop ortion to the molecule’s thermal v elo cit y . An imp ortan t feature of diusion in microp orous materials is that b oth J F and J K are functions of concen tration in the p ores. In molecular mo dels of gas diusion in rigid nanotub es, the dierence 41 Figure 1.4.3: Illustration of the prop erties of Kn udsen to P oiseuille o w in a nely microp orous mem branes as a function of the p ore radius divided b y the mean p ore path of the gas (after Barrer) (Bak er 2012). This gur e is r eprinte d. b et w een these t w o diusion co ecien ts, D s and D K , ma y b e more than t w o orders of magnitude. In gases, diusion co ecien ts are in the range of 10 −5 ∼ 10 −4 m 2 /s, and t ypical molecular diusion co ecien ts in glassy p olymers are 10 −14 ∼ 10 −13 m 2 /s, while diusion co ecien ts v arying from 10 −15 ∼ 10 −8 m 2 /s ha v e b een rep orted for zeolites (Chen et al. (a) 2006). Bak er (Bak er 2012) calculated the relationship b et w een the gas p ermeabilit y and the eect of the ratio rc on the relativ e prop ortions of Kn udsen to P oiseuille o w in a cylindrical capillary as sho wn in Figure 1.4.3. P oiseuille o w predominates when rc is greater than 1. F or Kn udsen o w to predominate and a separation to b e obtained, the mem brane p ore radius m ust b e less than 50nm b ecause the mean free path of gases at atmospheric pressure is in the range of 50∼ 200nm (Mun tz et al. 2004, Bak er 2012). 1.4.3 Another expression of diusion The diusiv e molecular ux of one gas a in another gas b at lo w v elo cities is giv en b y the general diusion equation: J Diffa =−ρ 0 ( D s ρ 0 ∂ρ a ∂z + D T T ∂T ∂z + D P P ∂P ∂z ) , (1.4.13) 42 where D T is the co ecien t for thermo diusion, and D P is the co ecien t of baro diusion. Ther- mo diusion and baro diusion are usually small compared with concen tration diusion (Landau, et al. 1987). The thermo diusion or temp erature diusion is that v ap or still diuses due to dif- ferences in the temp erature in a system without concen tration gradien ts, and the baro diusion or pressure diusion is related to the relativ e diusion of molecular sp ecies due to gradien ts in the total pressure (Manginell et al. 2003, (Manginell et al. 2003). Chapman and Co wling in tro duced the thermo diusion ratio for a mo del of rigid elastic spherical molecules (Hudson 2008): k T = D T D s = 5( 6 5 −1) ( s a n a n a +n b −s b n b n b +n b )( Q a n a n b +Q b n b n a +Q ab ) −1 , (1.4.14) where s a =−3m 2 b + 23m a m b 5 + √ 8m a (m a +m b ) 3 σ 2 aa 5σ 2 ab , s b =−3m 2 a + 23m a m b 5 + √ 8m b (m a +m b ) 3 σ 2 bb 5σ 2 ab , Q a = 2σ 2 aa 5σ 2 ab √ 1+ m b m a [ 6m 2 b + 13 5 m 2 a + 16 5 m a m b ] , Q b = 2σ 2 bb 5σ 2 ab √ 1+ m a m b [ 6m 2 a + 13 5 m 2 b + 16 5 m a m b ] , Q ab = 3(m 2 a −m 2 b )+ 344 25 m a m b + 16 25 (m a +m b ) 3 (σ aa σ bb ) 2 √ m a m b σ 4 ab . s 2 and Q 2 are in terc hanged indices. The thermo diusion co ecien t can b e p ositiv e or negativ e and v anishes for lo w concen trations. Landau and Lifshitz (1987) and Cunningham and Williams (1980) pro vided the baro diusion co ef- cien t in a mixture of t w o ideal gases (Hudson 2008): k P = D P D s = (m b −m a ) ρ a ρ t ( 1− ρ a ρ t )[ 1 m b ( 1− ρ a ρ t ) + 1 m a ρ a ρ t ] , (1.4.15) where ρ r is the total mass densit y and ρ a is the mass densit y of the sp ecies a. In a single uid, there is no baro diusion phenomenon, and the co ecien t v anishes. Ho w ev er, the co ecien t can b e also p ositiv e or negativ e for a mixture gas. In general, baro diusion is negligible when △P/P ≪ 1. 43 1.5 Physical Properties 1.5.1 Gas adsorption A p opular phenomenon is gas adsorption on the inner surface of a nanotub e whic h greatly reduces the self diusivit y of gases. In the case of gas-solid ph ysical adsorption, the gas adsorption could b e caused b y strong binding energy b et w een gas molecules and a surface (Egoro v et al. 2006). The gas adsorption pro cess is generally considered as a ph ysisorption pro cess in thermo dynamic equilibrium with the gas phase b ecause the molecular forces in v olv ed are normally of the v an der W aals. It is also exp ected that the molecular vibrations of the atoms in a nanotub e c hannel increase the energy accommo dation and therefore the adsorbabilit y of the nanotub e. The com bination of the binding energy , molecular vibration of the w all, and the nanotub e diameter mak es the gas transp ort in nano c hannels ev en more complex. F or small binding energies, the vibration of the w all has small inuence on the gas diusion. A lo cal maxim um in the self-diusion co ecien t is observ ed in the nanotub e of diameter equal to 2nm b ecause of the strong repulsiv e force b et w een the gas and w all. The w all could ha v e a great energy accommo dation due to the in ternal atomic vibrations. This will result in gas adsorption b ecause the w all absorbs energies from gas molecules. F or rigid w alls, the energy accommo dation is v ery lo w, and adsorption is only preferred at lo w temp eratures or v ery strong binding energy . 1.5.2 Quan tum eects Nanop orous materials with p ore diameters smaller than the ph ysical dimension of gas molecules can b e used to separate dieren t gas sp ecies (Mun tz et al. 2004). The required nanometer sized p ore dimensions hin t that quan tum eects ma y pla y a role in separating gases. The quan tum eects b ecome imp ortan t the gas o w in nanotub e at ro om temp erature when the mean radial De Broglie w a v elength, λ B = h mur (h is the Planc k constan t, and u r is the radial v elo cit y), of the molecules in the capillary b ecomes on the order of the uno ccupied radial dimension in the capillary . F or example, Helium has λ B ∼ 0.1nm at the ro om temp erature (Bak er 2012). It is apparen t that b oth p ore diameters of less than 1nm and lo w temp eratures are required to observ e quan tum eects in nanop orous mem brane. It app ears that it w ould b e dicult to mak e use of quan tum eects in separating large complicated trace molecules. Beenakk er et al. (Bak er 2012) considered 44 Figure 1.5.1: P oten tial energy PE(r) and transv erse motion energy lev els E i for a molecule in a c hannel with d c −d m ∼ λ. Zero energy corresp onds to that of the molecule in a free space (Bak er 2012). The p oten tial w ell separation o ccurs b et w een a gas sp ecie and a w all material of the capillary tub es. This gur e is r eprinte d. that molecular densities in the p ores are lo w enough to b e able to neglect the molecule-molecule in teraction so that the molecules in teract with the surface defects. It can b e separated in to t w o indep enden t comp onen ts; the axial and the radial ones. In the axial direction the motion is free b et w een t w o consecutiv e collisions with molecules or surface defects. In the radial direction, the molecules mo v e in a p oten tial w ell created b y the in teraction with the surface. Mo dels for predicting quan tum eects of the gas o w in a nanop orous c hannel ha v e t ypically assumed the in teraction p oten tial for the radial motion b y a circular square w ell with the depth ϵ with resp ect to zero p oten tial energy of the molecule in the free space sho wn as Figure 1.5.1, PE(r) =−ϵ for r <r c −r m PE(r) =−∞ for r≥ r c −r m . (1.5.1) ϵ dep ends on the c hannel diameter d c due to the o v erlap con tributions of dieren t parts of the w alls as sho wn Figure 1.5.2. The circular square w ell in a cylindrical tub e has the energy lev els E i = 2γ 2 i ~ 2 (d c −d m ) 2 m , i = 0, 1, 2, ··· , (1.5.2) where E i are coun ted with resp ect to the w ell b ottom, γ i are simply related to zeros of Bessel 45 Figure 1.5.2: The b eha vior of the w ell depth ϵ and zero-p oin t energy E 0 as functions of c hannel diameter d c . Regions 1, 2 and 3 can b e attributed to classical geometrical, p oten tial and quan tum sieving, resp ectiv ely . The w ell depth is sk etc hed as a function of p ore diameter starting from its v alue ϵ fs at a at surface (Bak er 2012). This gur e is r eprinte d. functions, e.g., γ 0 = 2.4, γ 1 = 3.8. The rst t w o energy lev els, E 0 /k B and E 1 /k B for sev eral gases, helium, nitrogen, argon, and xenon in d c = 0.5, 10, and 50nm c hannels are describ ed in T able 2.1. The size of nanotub e in 0.5nm diameter is close to De Broglie w a v elength (Bak er 2012), and other nanotub es in 10 and 50nm diameters will b ecome the a v erage size of mem branes, resp ectiv ely , that are used for exp erimen ts. As zero-p oin t energy E 0 decreases with increasing d c and m, quan tization of the transv erse motion cannot b e neglected for ligh t particles in narro w c hannels. If a v ailable p orous media con tain c hannels with d c as small as 0.3nm and v alues of d c −d m do wn to a few tens of an angstrom can b e ac hiev ed, the gas should b e exp erimen tally observ able at the ro om temp erature due to the strong increase of the lev el splitting with d c −d m decreasing. A ccording to the T able 1.2, the quan tum eects ab out all sampled gas molecules can b e neglected for the nanotub es in 10, and 50nm diameter. Num b er densit y of particles inside the c hannel p er unit length for equilibrium with the gas in the free space is n in = n out π(d c −d m ) 2 4 ∑ i exp ( ϵ−E i k B T ) , d c ≥d m . (1.5.3) Here n out is the gas densit y outside the c hannel and 4 (d c −d m ) 2 is the free v olume p er unit length of 46 Gas E 0 /k B (K ) (E 1 −E 0 )/k B (K ) d c (nm) 0.5 10 (×10 −3 ) 50 (×10 −5 ) 1.5 10 (×10 −3 ) 50 (×10 −5 ) He 19.58 14.64 56.38 29.51 22.05 84.95 N 2 35.24 2.64 9.88 53.11 3.98 14.88 Ar 20.62 1.55 5.78 31.07 2.33 8.71 Xe 7.77 0.48 1.74 11.71 0.72 2.63 T able 1.2: Zero-p oin t energy , E 0 and lev el splitting, E 1 −E 0 as o ws from equation 2.3.2 for sev eral gases in dieren t c hannels with d c = 0.5, 10, and 50nm. Characteristic v alues of molecular diameter (HSS) and molecular w eigh ts are tak en from App endix T.1. the c hannel a v ailable for the molecule treated as a p oin t particle (Gorban et al. 2010). This results from a v an der W aals in teraction of the eect of the molecular diameter. There are t w o parameters c haracterizing the quan tum eects predicted to o ccur for gas o ws in capillaries of a nanometer diameter: (1) E 0 /ϵ, the relativ e imp ortance of the zero-p oin t energy or ground state of vibrational energy with resp ect to the p oten tial energy originating from the molecule- w all in teraction, and (2) (E 1 −E 0 )/k B T , the excitation energy for the rst excited lev el compared to the thermal energy of the molecule (Mun tz et al. 2004, Bak er 2012). The rst eect o ccurs when the ground state of vibrational energy is greater than the p oten tial w ell depth in the nanop ore, E 0 /ϵ > 1. In this situation the zero-p oin t motion o v ercomp ensates the attractiv e molecule-surface in teraction, pro ducing an energy barrier so that the molecules en ter the c hannel from the free space encoun ter the energy barrier that can only b e o v ercome b y thermal excitation. The particle n um b er densit y in the tub e will b e reduced b y a Boltzmann factor giv en b y exp ( ϵ−E 0 k B T ) < 1. (1.5.4) In b oth cases, adsorption and molecular transp ort, the temp erature dep endence are dominated b y this factor and sho w a c haracter corresp onding to a thermally activ ated pro cess increased with increasing temp erature. The eect can b e called quan tum sieving when the adsorption in p orous media is dominated b y the v alue of the zero-p oin t energy dep ended on d c −d m . The quan tum sieving should alw a ys precede the classical one, molecular sieving with the decreasing tub e diameter. Smaller molecule suc h as helium should not b e adsorb ed b y a p orous medium large enough from a geometrical p oin t of view, d c ∼ 0.4nm (> d m ), while larger molecules suc h as nitrogen or argon are still adsorb ed. Ho w ev er 47 it is dicult to mak e realistic estimates of the rst eect due to diculties in assigning meaningful w ell p oten tials to m uc h more complicated atomic scale p ore geometries. The second quan tum eect o ccurs due to m uc h higher energy of the rst excited state for the ground state with decreasing d c and m as sho wn b y E 1 −E 0 k B T ≫ 1. (1.5.5) It o ccurs whenev er particles are trapp ed in the p oten tial w ells. The rst excited state is no longer p opulated for the larger lev el splitting in the p oten tial w ell, so the gas b eha v es eectiv ely still one-dimensional gas. The one-dimensional situation should b e exp erimen tally observ able at ro om temp eratures due to the increase of the lev el splitting with d c −d m decreasing. In the situation adsorption and transp ort in the c hannel are dominated b y the resp ectiv e v alues for E 0 in the Boltz- mann factor for the densit y in the c hannel. The quan tum sieving for the second quan tum eects should b e observ able in a wider range of c hannel diameters than the the rst one. Both quan tum eects generally o ccur for v ery ligh t gas sp ecies at lo w temp eratures and for p ore sizes v ery near the particle dimension. The eects will b e v ery imp ortan t when considering the p erformance of con tin uous separation mem branes at the p ore sizes where the eects b ecome imp ortan t (Mun tz et al. 2004). P ore densities or fractional op en area of mem branes are also an imp ortan t factor for the preconcen- trator application. The fractional op en area for trace gas molecules is v aried from zero, corresp onding to complete ph ysical ltration, to a fractional op en area for carrier gas molecules. An initial the- oretical analysis (Mun tz et al. 2004) has predicted that the mem branes ha v e fractional op en area of at least 0.01 for carrier and trace gas molecules. 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Grate, Single-w alled carb on nanotub e pap er as a sorb en t for organic v ap or preconcen tration, A nalytic al Chemistry , 78 (2006) : 2442 - 24. 54 Chapter 2 Theory and Model of a New Approach for the Preconcentrator A new t yp e of the con tin uous gas o w-through preconcen trator for a rareed trace gas analysis, whic h has b een prop osed b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008) includes; a main o w c hannel, pumping c ham b ers, and separation mem branes b et w een the main o w c hannel and the pumping c ham b ers. The con tin uous preconcen trator do es not ha v e the pro cesses of stop, adsorption, and release; but is caused b y the con tin uously c hanging cross-section of the main o w c hannel un til released through the detecting system suc h as gas c hromatograph y , mass sp ectrometry , or optical diagnostics b y electron b eam uorescence. The preconcen trator is used to increase the concen tration of v arious gases in a carrier gas, and is more suitable for impro ving the time accuracy of analytical systems b ecause it can op erate for short, although nite times b efore reac hing the detector. The preconcen trator has in tro duced a sp ecic application, whic h has the p ossibilit y of ac hieving signican t trace gas concen tration increase using relativ ely simple micro/mesoscale mass diusion separation stages, without in terrupting the gas o ws. In this c hapter, there are in tro duced the shap e equation of the main o w c hannel and concen tration ratio of the trace gas, and sho wn the theories for supp orting these equations. In addition, the co ecien ts, whic h are used to determine the shap e and exit size of the main o w c hannel, are obtained; a fractional op en area, transmission probabilit y , ratio of gas densit y b et w een the main 55 o w c hannel and pumping c ham b ers etc. The fractional op en area (p orosit y) and transmisison probabilit y are prop erties of the separation mem brane, and the ratio is the densit y of sampled gas molecules passed through the mem brane c hannels or rejected bac k in to the main o w c hannel. A ccording to these equations and co ecien ts, it is p ossible to determine the shap e and size of the main o w c hannel, and t yp e of the separation mem brane appro ximately . The pumping c ham b ers and pump are also an imp ortan t parts to determine the preconcen trator. The pumping c ham b ers lo cated upp er and lo w er the main o w c hannel op erate to main tain a constan t gas o w sp eed in the main o w c hannel during an exp erimen t. The pump connected with pumping c ham b ers m ust create constan t pressure dierences b et w een the main o w c hannel and pumping c ham b ers. This c hapter is in tro duced the a v ailable t yp e of the pumping c ham b ers and pump. A detector, that can measure the concen tration of the trace gas immediately at ro om temp erature and v arious pressures including an atmospheric pressure, generally connects with the exit of the main o w c hannel. The new t yp e of the preconcen trator suggested b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008) requires a minimized detecting system. Detectors in tro duced in this c hapter are p ossible to minimize reducing an fabrication cost of a complete system, but they do not determine in curren t researc h. 2.1 Preliminary Estimates 2.1.1 Gaseous mixture o w through a long tub e Gaseous mixtures are dealt with more complicated features. First, more parameters than a single gas o w can determine the gaseous mixture o w. Besides the gas rarefaction along with pressure and temp erature gradien ts, the mixture o ws dep end on the concen tration, sp ecies of the mixture comp onen ts, etc. Second, an additional driving force, i.e., the concen tration gradien t, arises in a mixture. Third, sev eral phenomena app ear in a nonequilibrium mixture, e.g., thermal diusion, baro diusion, etc (Sharip o v et al. 2002). In Figure 1.3.1 in Chapter 1, t w o reserv oirs con taining the same binary gaseous mixture are connected b y a tub e of length h c and diameter d c . Then P 1 , T 1 and C 1 are the pressure, temp erature and 56 concen tration, resp ectiv ely , of the mixture in the left con tainer and P 2 ,T 2 , andC 2 are the pressure, temp erature, and concen tration, resp ectiv ely , in the righ t one. Here, the concen tration of mixture C is dened as C = n a n a +n b , (2.1.1) where n i (i = a, b) is the n um b er densit y of gaseous sp ecies i. F or the mixture gas o w through a long capillary (h c ≫ d c ) the lo cal gradien ts of the pressure and temp erature are alw a ys small, ev en if the pressure and temp erature drops are large, and also the lo cal concen tration gradien t is alw a ys small in a long capillary . Th us it is p ossible to obtain the solution for an y drops of the pressure P 2 /P 1 , temp erature T 2 /T 1 , and concen tration C 2 /C 1 (Sharip o v et al. 2002). The gradien ts of pressure, temp erature concen tration across the z direction are expressed as K k = d c 2k ∂k ∂z , k =P, T, C, (2.1.2) and these gradien ts are v ery small: |K k |≪ 1, k =P, T, C. (2.1.3) A mean molecular mass of mixture is m =Cm a +(1−C)m b , (2.1.4) where m a and m b are the molecular masses of eac h gaseous sp ecies. Therefore the viscosit y of mixture gases can b e expressed suc h as µ mix = ∑ X i µ i √ M i ∑ X i √ M i , (i =a, b). (2.1.5) Here X i is the molar fraction of comp onen t i, and M i is the molar w eigh t of comp onen t i (Brok a w 1968). A ccording to equations (2.1.4) and (2.1.5), the mean free path for mixture gases for the h ydro dynamic o w can b e rewritten. The gaseous diusion of the separation pro cess dep ends on a separation eect, whic h arises from the 57 phenomenon of molecular eusion, the gas o w through small orices. One of the separation eects is related to the molecular mass. If a mixture of gases is conned in a con tainer and in thermal equilibrium with its surroundings, the ligh ter gas molecules generally hit the w alls more frequen tly relativ e to its concen tration than the hea vier gas molecules. This is the greater a v erage thermal v elo cit y of the ligh ter molecules. When the w alls of the con tainer are p orous, with sucien tly large holes to allo w the escap e of individual molecules, but small enough so that bulk o w of the gas as a whole is prev en ted b ecuase the ligh ter molecules escap e more readily . A separation factor, whic h is the ratio of the t w o molecular v elo cities, reects the relationship of ligh t v ersus hea vy molecules in escaping through the p ores in this sto c hastic separation pro cess. Since the kinetic energies of the t w o sp ecies are the same at the same temp erature, the ratio of the t w o v elo cities is also equal to the square ro ot of the in v erse ratio of the t w o molecular w eigh ts. Therefore it is p ossible to use the large ratio of the t w o molecular masses in order to enhance the separation factor. 2.1.2 Analysis of gas o w F ollo wing Bird (Bird 1994), the gas o w of a single sp ecies can b e describ ed b y listings of the p ositions, v elo cities, and in ternal states of ev ery molecule at a particular instan t. When a sampled gas is homogeneous in ph ysical space and con tains N iden tical molecules, eac h molecule has an a v erage random v elo cit y c’ (=v ) with comp onen ts u (=v x ), v (=v y ) and w (=v z ) in the directions of the Cartesian axes x, y , and z . Here u, v and w dene a v elo cit y space and x, y , and z dene a ph ysical space. As with the equation (1.3.50), The n um b er ux ( m −2 s −1 ) arriving at a surface, either imaginary or solid as same temp erature as the gas is pro vided b y j = dN dtdA = 1 4 nc ′ . (2.1.6) Here n is the n um b er densit y of the molecules b eing considered, and c ′ is the mean thermal v elo cit y from the Maxw ell-Boltzmann distribution la w for molecular v elo cities. The equation (2.1.6) is the kinetic theory expression for the n um b er of molecules p er unit surface area and unit time. During the tra v els of gas through the macroscale main o w c hannel, the molecular gas o w ( s −1 ) preferen tially 58 Figure 2.1.1: Sc heme of the mixture gas o w through a p orous mem brane from the main o w c hannel to reserv oir : P 1 and P 2 are the high-side and lo w-side pressures acting on a mem brane (P 1 > P 2 ) and temp erature is constan t. diuses through p orous mem branes called separation mem branes, = _ N = dN dt = 1 4 nc ′ dA ′ , (2.1.7) where dA ′ is the dieren tial cross sectional area of the o w c hannel, whic h can b e replaced b y the p orosit y of the mem brane, FdA, and added to the transmission probabilit y α’s, conductance of the long cylindrical tub e. As men tioned in Chapter 1, if molecules escap e from the main o w c hannel through the separation mem branes to other reserv oirs, the molecules undergo man y collisions in the reserv oirs b efore they reac h the p ores again. It is same as molecules lea ving the reserv oirs. The escap e uxes from b oth cases do not inuence eac h other. Then the net particle ux p er unit area from the main o w c hannel to b oth reserv oirs from equation (1.3.54) can b e calculated as = 1 2 ( n 1 c ′ 1 α 1 F 1 −n 2 c ′ 2 α 2 F 2 ) dA. (2.1.8) Assuming the temp erature of the surroundings is constan t, the ratio of the molecular densities b et w een the main o w c hannel and eac h reserv oir is the same as the pressure ratio across the separation mem branes. In the c ham b ers bac king the mem branes, the gas n um b er densit y is same the fraction of the gas n um b er densit y n 1 n 1 = P 1 P 2 , (2.1.9) 59 where (0<<1) is the ratio of gas n um b er densit y in the reserv oir that has a lo w er pressure compared to the inlet gas pressure in the main o w c hannel. F or the gas o w of one sp ecies and one p orous mem brane at a constan t temp erature, the terms are the same as c ′ 1 F 1 α 1 = c ′ 2 F 2 α 2 = c ′ Fα, therefore the net ux can b e written as = 1 2 n 1 (1−η) c ′ αFdA. (2.1.10) 2.2 New Approach to Preconcentrator The miniaturized con tin uous o w-through trace gas preconcen trator will lead to man y b enets; suc h as lo w op eration p o w er, rapid resp onse, p ortabilit y , and high sensitivit y to a small amoun t of an- alyte. The main goal of this researc h is to design, demonstrate, fabricate and test a con tin uous o w-through trace gas preconcen trator for trace gas detectors/sensors, and nd the optimized con- ditions for miniaturized preconcen trators. The preconcen trator in this study ha v e b een dev elop ed targeting the preconcen tration of hea vier molecules. This researc h fo cuses on: a substan tiation of the v alidit y of the a v ailable n umerical analysis; exp erimen tal data and the subsequen t determination of the preconcen trators p erformance; exten t of miniaturization that can b e tolerated; and determi- nation of the o v erall comp etitiv eness of the prop osed preconcen trator. There is an ob vious need to conduct a series of exp erimen ts, that v alidate the a v ailable n umerical data suc h as gas separation and concen tration mec hanisms, and the newly , prop osed con tin uous preconcen tration tec hnology . This exp erimen tal in v estigation is to obtain a base-line comparison with the existing n umerical predictions for shap es and sizes of a o w c hannel, and concen tration ratios pro vided b y the preconcen trator. F ollo wing the establishmen t of the soundness of the basic predictions, exp erimen ts in v olving sample gases mixed with hea vy complicated molecular structures, are undertak en to compare with n umer- ical predictions for these cases. The complicated molecules are those that ha v e b een iden tied in the a v ailable literature as acceptable, b enign surrogates. These easily a v ailable gases ha v e a molec- ular mass ratio that is represen tativ e of t ypical, more complicated molecular structures that are encoun tered in actual situations. Subsequen tly trace gas mixtures, more t ypical of the complicated molecular structures found in hea vy molecules, are studied. With the exp erimen tal results it is p ossible to ev aluate the actual p erformance, and th us the p oten tial of the prop osed preconcen trator. 60 Figure 2.2.1: Sc heme of a ideal con tin uous trace gas preconcen trator b y t w o (b ottom) and three (upp er) dimensions : one main o w c hannel connected with a detector transition, t w o separation mem branes, and t w o pumping c ham b ers connected with pumps. This is a dev eloping mo del from the preconcen trator prop osed b y Mun tz et al. (Mun tz et al. 2004). 2.2.1 Summary of the design and c haracterization The new t yp e of miniaturized con tin uous trace gas preconcen trator prop osed b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008) is that a con tin uous sampled gas from am bien t gas o ws is dra wn in to a o w c hannel from the lo cal atmosphere and the sampled gas ma y b e included as concen tration (1 to 10 −3 ppb) of dangerous trace gases as sho wn Figure 2.2.1. And the sample gas o ws also main tain a substan tially constan t o w sp eed, with t ypical v alues of 1cm/s to 10cm/s through the main o w c hannel. The con tin uously op erating preconcen trator for trace gas includes; a main o w c hannel, pumping c ham b ers upp er and lo w er separation mem branes resp ectiv ely , and separation mem branes b et w een the main o w c hannel and the pumping c ham b ers. The main o w c hannel has a constan t heigh t ( h f ≤ 500µm) and a width (1cm to a few µm) that decreases from the inlet to the outlet. The separation mem branes are congured to preferen tially remo v e carrier molecules in the sampled gas from the main o w c hannel, thereb y increasing con- cen tration of the trace gas in the main o w c hannel. The separation mem brane requires strength enough to supp ort the pressure dierence across the mem brane, and to main tain its shap e during 61 the o w of the sampled gas passes through the mem brane c hannels. The pumping c ham b ers ha v e constan t widths and t w o dimensional, v arying heigh ts. The cross sectional area p erp endicular to the x direction are c hanged along with the heigh t of the c ham b ers according to the requiremen ts of con tin uit y . In order to mak e pressure dierences b et w een the main o w c hannel and pumping c ham b ers, pumps are connected with the pumping c ham b ers directly . The pumps can con trol v ar- ied pressure dierences substan tially related to increasing the concen tration of trace gas. In order to minimize pumping energy consumption b oth the o w sp eed of the sampled gas and its n um b er densit y remain essen tially constan t throughout the o w c hannel. In general, the ligh ter and smaller carrier gas molecules of the sampled gas can preferen tially escap e, through the separation mem branes, from the main o w c hannel to the pumping c ham b ers. Then the width of the main o w c hannel decreases and the heigh ts of the pumping c ham b ers c hange along the length of the main o w c hannel, in order to main tain the constan t gas o w. It is resulted for b oth a constan t a v erage o w sp eed in the x direction and an appro ximately constan t n um b er densit y of carrier gas throughout the pumping c ham b ers. The concen tration of the trace gas, within the gas sample, can consequen tially b e raised to a lev el sucien t for the trace gas to b e detected in substan tial real time. By passing the gas sample, at a substan tially uniform o w sp eed through the main o w c hannel, the con tin uous preconcen trator uses non-adsorbing materials to analyze the trace gas, this also causes the sampled gas to o w con tin uously through the main o w c hannel. A t the same time, the concen tration of the trace gas in the sampled gas is raised b y causing the gas sample to lose a signican t fractional carrier gas through the separation mem branes. The pumping c ham b ers are com bined with pumps, and main tain a pressure that is signican tly lo w er than the pressure in the main o w c hannel. Generally , the ligh ter and smaller diluen t gases diuse from the lo w er and upp er surfaces of the separation mem branes to the pumping c ham b ers. The concen tration of the trace gas ma y b e increased in this w a y . The pressure ratio emplo y ed is relativ ely small but cannot b e large, b ecause it w ould aect the condition of the separation mem branes. The fraction of the n um b er densit y of carrier gas is related to the pressure dierence, and the ratio of the pressure dierences b et w een the pumping c ham b ers and the main o w c hannel is 0.25 to 0.75 according to Mun tz et al. (Mun tz et al. 2004). Ho w ev er the pressure dierence in the exp erimen tal test seems to b e smaller than the suggested pressure dierence b ecause of the slo w er gas o w sp eed and thinner separation mem brane. 62 The separation mem brane generally consists of an arra y of capillaries, whic h ha v e a diameter of ab out ten nanometers, and ha v e an areal p orosit y (or fractional op en area) greater than 0.01. The capillaries in the separation mem brane should ha v e relativ ely short lengths, as a ratio of the prop er length to diameter has a great inuence on the con tin uous preconcen trators p erformance. A ccording to Mun tz et al. (Mun tz et al. 2004), for larger mem brane c hannels (d c > 5nm), the in teraction p oten tial from the sides of the c hannel do not o v erlap, and the fractional op en area o ccupied b y the attractiv e surface p oten tial w ell is relativ ely small. F or smaller mem brane c hannels ( d c < 5nm), the fractional op en area o ccupied b y the w ell b ecomes increasingly signican t. The w ell attracts an increased concen tration of gas molecules in the vicinit y of the w all and separation o ccurs for dieren t molecules. Prop er c haracteristics of the separation mem brane are also nanoscale p ore diameters and faster transfer in capillaries suc h as carb on nanotub e (CNT) mem branes or other nanotub e mem branes. The detector that is one imp ortan t part but w as not men tioned b y Mun tz et al. is able to connect with the outlet of the main o w c hannel and is sucien tly sensitiv e to detect an extremely small n um b er of trace gas molecules. The detector is also p ossible to op erate con tin uously with short resp onse time when the sampled gas is collected and analyzed, and to b e miniaturized to op erate with the miniature preconcen trator. This will b e discussed in more detail in Chapter 6. 2.2.2 Assumptions New ideal preconcen trator prop osed b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008) in 2004 is to op erate with the con tin uous o w. The o w is able to b e driv en b y a small pressure dierence describ ed b y an initial gas o w sp eed u 0 . The con tin uous gas sample dra ws a mass o w ( kg/s) in to the cross sectional area A a =w(x)h f of the main o w c hannel at the constan t temp erature: _ M(x) =nmu 0 w(x)h f , (2.2.1) where h f and w(x) are the heigh t and width of the main o w c hannel, resp ectiv ely . The gas o w preferen tially diuses through the separation mem branes as the gas passes through the main o w c hannel. As sho wn in the Figure 2.2.1, eac h separation mem brane puts b et w een the main o w c hannel 63 Figure 2.2.2: Sc hemetic of a ideal preconcen trator including one main o w c hannel, t w o separation mem branes, and t w o pumping c ham b ers. and reserv oirs called as pumping c ham b ers. The cross sectional area of the pumping c ham b ers is p erp endicular to the x direction in the main o w c hannel. When the gas o w sp eed and the gas n um b er densit y are constan t ev erywhere in the main o w c hannel, the solution is written as the width of the main o w c hannel as a function of x, with the constrain t that a constan t gas o w sp eed is main tained throughout the one, with the loss of gas molecules through the separation mem branes tak en in to accoun t (Mun tz et al. 2004). F or increasing the concen tration of the gas molecules, the width of the main o w c hannel ma y b e reduced ( w(x 1 ) > w(x 2 )) while its heigh t is constan t along its length. It is imp ortan t to main tain the pressure in the main o w c hannel appro ximately constan t and as high as p ossible, b ecause pumping costs, in terms of energy , increase with pressure ratio. Then the pumping c ham b er can b e set relativ e to the constan t pressure of the main o w c hannel and not the lo w est pressure. In order to main tain the uniform pressure in the pumping c ham b ers, v olumes of the pumping c ham b ers are relativ ely larger than the v olume of the main o w c hannel p er unit length along the length of the main o w c hannel. In general, the pressure in the main o w c hannel is similar to the atmospheric pressure, or somewhat larger than 1atm for the inlet gas o w sp eed, and ma y b e larger than the pressure of the pumping c ham b ers, P 1 >P 2 sho wn in Figure 2.2.2. It is p ossible to mo dify the pumping pressure ratio in the in terc hange b et w een separation and pumping energy requiremen ts. The gas sample is a binary mixture of a diluen t or carrier gas suc h as an am bien t gas and a trace 64 gas with lo w er concen tration, and tra v els together do wn the main o w c hannel. Then the molecular w eigh t or diameter of the trace gas is m uc h larger than the ones of the carrier gas, and the conduc- tance of the separation mem branes is larger for the carrier gases. Therefore it ma y exist an increased concen tration of the trace gas molecules near eac h mem brane. The lo w er concen tration of the trace gas molecules ma y not aect to the o w dynamics in the main o w c hannel. It means that once the carrier gas o w is determined, the trace gas molecules are in tro duced b y linear sup erp osition. The trace molecules are distributed uniformly b y diusion o v er the heigh t of the main o w c hannel at eac h x p osition, while the distribution of trace molecules ma y b e assumed to b e unaected b y diusion along the x axis. The carrier and trace molecules ha v e their o wn conductance 1 4 c ′ j F j α j (j =C or T ) p er unit area of the mem brane. If the concen tration of the trace gas is extremely lo w as ppb or ppt ranges, the trace gas molecule analysis can b e indep enden tly app ended to the solution for the carrier gas o w. When the mean free path of the gas molecules is m uc h larger than a radius of the mem brane c hannel, whic h is still m uc h larger than the molecular size, eac h molecule can lea v e the main o w c hannel. Then, the total loss rate of mixture gas molecules p er unit length dx of the main o w c hannel in the x direction, through the t w o separation mem branes at a p osition x (x 1 ≤x≤x 2 ), is from equation (2.1.10) (x) =− 1 2 C(1−) c ′ αFw(x)dx, (2.2.2) where C is the concen tration of mixture at the main o w c hannel. F or the extremely lo w concen- tration of the trace gas, the equation (2.2.2) can b e written as follo ws (Mun tz et al. 2004): (x) = dN dt = 1 2 (1− i )n i c ′ i α i F i w(x)dx (i =C, T) (2.2.3) b ecause eac h factor is indep enden t eac h other. Here the sym b ols C and T mean carrier gas and trace gas resp ectiv ely , n i is the n um b er densit y and c ′ i is the mean thermal sp eed of eac h molecule, F i is the fractional op en area of the separation mem brane surfaces, i is the ratio of n um b er densit y in a pumping c ham b er to inlet n um b er densit y in the main o w c hannel, and α i is the transmission probabilit y . The p orosit y and transmission probabilit y are indep enden t of the sp ecies of molecules. Those molecules that en ter a capillary pass through a mem brane c hannel and end up in one of the 65 pumping c ham b ers. The gas o w sp eed u 0 can b e dened as u 0 = dx dt , and the n um b er of molecules N =nV can b e written as N =Ch f w(x)dx =nh f w(x)dx . Through the in tegration of the equation (2.2.2), dN N = (1−)c ′ αF 2u 0 h f dx, (2.2.4) and it can b e solv ed directly to giv e N(x) =N(0)exp [ (1−)c ′ αF 2u 0 h f x ] . (2.2.5) Here the conditions at the do wnstream end of the main o w c hannel are giv en b y setting x = L f , where L f is the length of the main o w c hannel (Mun tz et al. 2008). The transmission probabilit y , or a geometry dep enden t shap e factor, ha v e b een deriv ed for a n um b er of dieren t shap es either theoretically or Mon te-Carlo metho ds. A ccording to Laert y (Laert y 1990), the transmission prob- abilit y is ob vious that for a unit length it increases as the length of the tub e increases. F or example, the transmission probabilit y at 10 unit lengths is almost t wice the exp ected v alue (Fissell et al. 2011). This reects the eect of the random molecular distribution near the en trance compared with the molecular distribution whic h ev olv es further do wn the tub e. Therefore it can dep end on the shap e and ratio of heigh t to width of the cross sectional area of the tub e. T ransmission probabilit y α, rst in tro duced the concept b y Clausing, also consider in the mem brane c hannel. IfN 1 molecules arriv e at the en trance plane of a tub e of the surface of separation mem brane, then the n um b er of these whic h reac h the exit plane is N 1 α, and N 1 (1−α) molecules return to the en trance. Similarly , if N 2 molecules strik e the exit plane from a do wnstream c ham b er, N 2 α reac h the en trance. The net ux of molecules from en trance to exit is then ( N 1 −N 2 )α. Although prop ortional to the pressure dierence across the tub e, the net ux is not driv en b y a pressure dierence. Some of the molecules whic h en ter the tub e will return to the en try plane after one or more w all collisions. The o w dynamics are th us v ery dieren t to the con tin uum o w case in whic h all molecules crossing the en trance plane will lea v e the exit apart from the p ossibilit y of bac k diusion whic h can o ccur in some circumstances (Laert y 1990). Kn udsen in 1909 assumed the transmission probabilit y of a 66 long cylindrical tub e a diameter d c as follo ws: α K = 4 3 ε. (2.2.6) where ε is the ratio of the diameter to length of the cylindrical tub e, dc hc (h c =L) and Berman deriv ed the solution as an asymptotic expansion as α B = 4ε 3 − ε 2 2 ln ( 2 ε ) − 91ε 2 72 + 4ε 3 3 ln ( 2 ε ) ··· . (2.2.7) F or ε ≪ 1 this reduces to equation (2.2.6) that needs correct for h c < 50d c . San teler deriv ed a simpler and more con v enien t form ulation and calculates the transmission probabilit y for the short tub e as α S = 7d 2 c +2d c h c 7d 2 c +9d c h c +1.5h 2 c . (2.2.8) F or designing the main o w c hannel, α S is used instead of α B , b ecause one a v erage capillary of the separation mem branes ma y b e ab out 200 larger in length for diameter of the tub e. Under this condition, α S and α B are similar to eac h other. A ctually the gas o w through the main o w c hannel is in the con tin uum o w regime for atmospheric pressure, but the o w through the separation mem branes is in the free molecular o w regime. One has to consider the metho d that can connect t w o dieren t regimes to explain the ph ysical mec hanism in the system. 2.2.3 Shap e of the main o w c hannel and concen tration A ccording to Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008), a shap e of the main o w c hannel is based on the requiremen t for a constan t o w sp eed and and results in substituting equation (2.2.5) for the n um b er of carrier gas molecules N C (x) to pro vide w(x) =w(0)exp   ( 1− P2 P1 ) c ′ C α C F C 2u 0 h f x   , (2.2.9) 67 where w(0) is the en trance width of the main o w c hannel. The width decreases along the length suc h that the gas o w sp eed is constan t. The suggested main o w c hannels b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008) are t ypically 1 to 2cm long for a few ten ths of a second of transit times, and 100µm heigh t. The gas o w is in to the h ydro dynamic o w for the atmospheric pressure, but the the o w through the separation mem branes is in the free molecular regime. In order to design the main o w c hannel for the primary test with the equation (2.2.9), the en trance width, length and heigh t of the main o w c hannel are ab out 10 times lager than the ideal case. It is to analyze the concen trations of trace gas and the t yp e of separation mem branes, and to understand the separation pro cess in the general conditions. Based on the t ypical extremely lo w concen trations of trace gas molecules, ev en after preconcen tration, the target molecules cannot aect the uid dynamics in the main o w c hannel of the preconcen trator (Mun tz et al. 2004). The trace gas molecules can b e collected near the inner w alls of the separation mem branes. Because t ypical heigh ts of mem brane c hannels are from 5 to 100µm, the trace gas concen tration can b e assumed to remain eectiv ely uniform o v er the heigh t of the mem brane c hannel h c . There is also no signican t diusion of trace gas molecules in the o w direction. It is then easy to write the n um b er densit y of trace gas, from N T (x) =n T (x)V(x) =n T (0)V(0), as n T (x) n T (0) = w(0) w(x) . (2.2.10) Ho w ev er there are generally considered to some transmissions of trace gas molecules through the mem brane c hannels. In this case, equation (2.2.5) can b e adapted to the description of the trace gas o w N T (x) =N T (0)exp [ (1− T )c ′ T α T F T 2u 0 h f x ] , (2.2.11) where N T (x) = n T (x)w(x)h f dx and the gas o w sp eed u D0 = u T0 = u 0 due to the constrain ts on the carrier gas o w. An expression for the trace gas concen tration increase in the o w c hannel as a 68 function of x can b e giv en as n T (x) n T (0) = w(0) w(x) exp [ (1− T )c ′ T α T F T x 2u 0 h f ] = exp   ( (1− C )c ′ C α C F C −(1− T )c ′ T α T F T ) x 2u 0 h f   , (2.2.12) where T = γ C , with γ < 1. The nal equation of the concen tration ratio of trace gas are not related to the en trance size of the main o w c hannel an y more. Without doing a detailed n umerical mo deling ab out the en tire o w system, the determination of γ is somewhat uncertain. F or γ = 0, there w ould b e no bac ko w of trace gas molecules from the pumping c ham b ers. Since the trace gas concen trations near the separation mem branes in the pumping c ham b ers is dicult to estimate, a considerable v alue of γ = 0.1, has b een c hosen according to Mun tz et al. (Mun tz et al. 2004). Mun tz et al. also considered the fractional op en area for the trace gas molecules, F T , is v aried from 0, corresp onding to eectiv ely complete ph ysical or quan tum ltration of the trace molecules, to F C , the same fractional op en area as for the carrier molecules. F or F T = F C the concen tration is pro vided only b y the dierence in mean thermal sp eeds of the carrier and trace molecules. Figure 2.2.3 illustrates the concen tration ratio of the trace molecules with the dieren t fractional op en area at a distance, x, from the en trance to the exit of the main o w c hannel. Then the air is the same as the carrier gas and the xenon is considered as the trace gas. The pressure ratio is 0.5 for C and T , the gas o w sp eed u 0 is 5cm/s, the main o w c hannel has 0.5cm of heigh t and 10cm of length, the fractional op en areal of trace gas F T is 0.0042, and the ratio b et w een the length and the diameter of the mem brane c hannel L dc is 200. F rom Figure 2.2.3 and at a distance 10cm it is p ossible to concen trate the trace molecules b y a factor of 3.685 with no fraction op en area of trace gas (with complete size ltration), but the concen tration increase is a factor of 1.998 when the fractional op en area of trace gas is the same as the fractional op en area of carrier gas (with no size ltration). This sho ws somewhat dieren t result with the calculation b y Mun tz et al. (Mun tz et al. 2004), ev en though the trace gas concen tration increases along the length of the main o w c hannel. The reasons are that the fraction op en area of carrier gas is smaller and the transmission probabilit y is larger. Ho w ev er the concen tration ratio of trace gas increase a factor of 670 with complete size ltration and a factor of 32 with no size ltration if the heigh t of the main o w c hannel is 0.1cm. In general, the fractional op en area is one of the t ypical 69 Figure 2.2.3: Concen tration ratio of trace gas with dieren t fractional op en area. prop erties of the mem brane. If the p ore diameters are constan t and larger enough than the diameters of the trace and carrier molecules, the p ores are uniformly distributed o v er the separation mem brane, and the fractional op en area, p orosit y , is same for b oth molecules. Ho w ev er the fractional op en area of the trace molecules can b e smaller than one of the carrier molecules, if the p ore diameters are similar to the diameters of molecules. In order to calculate the shap e of the main o w c hannel, the conditions are the same as previous suggestions. Then equation (2.2.9) can calculate the exit size and the shap e of main o w c hannel sho wn as Figure 2.2.4. As men tioned b efore, the shap e and the exit size of main o w c hannel are more related to the t yp e of carrier gas. In general, the preconcen trator suggested b y Mun tz et al. is to increase the concen tration of hea vier molecules in the air. In other w ords, the carrier gas considered in this calculation is air. Therefore the exit size of the main o w c hannel for air and 10cm of the en trance width of the main o w c hannel decreases gen tly and is w(L f ) = 0.3cm. The equations (2.2.9) and (2.2.11) suggested b y Mun tz et al. include v arious factors that are p ossible to con trol ph ysically . Other b enets of this t yp e of the preconcen trator are that it do es not need an y heaters and c hemical reactions. Th us it is p ossible to reduce the reaction time b ecause it do es not need the time to raise temp erature of the heater. No c hemical reaction need to consider c hemical comp ounds that help increase the concen tration. The new t yp e of the preconcen trator considers 70 Figure 2.2.4: Illustration of the main o w c hannel determined the shap e equation pro vided b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2008). mass ratio b et w een trace and carrier gases and separation pro cess of the nanop orous mem brane. Therefore it has man y p ossible applications with v arious v ariables. 2.3 Characterization of the Separation Membrane The researc h of the separation mem brane is an imp ortan t issue in this w ork. The trace gas con- cen tration in the main o w c hannel of the suggested preconcen trator is related to conditions, p ore diameter, p orosit y , thic kness, and so on, of the separation mem branes that are lo cated b et w een the main o w c hannel and the pumping c ham b ers as men tioned b efore. The mem brane c hannels are mo deled as an arra y of nanometer diameter capillaries or ap ertures and ha v e relativ ely short length with transmissions. The imp ortance of mem brane c hannel sizes that ma y aect the gas transp ort is emphasized since the p oten tial energy is related to the structure of the mem brane c hannel. There is the com bination of the binding energy , molecular vibration of the w all, and c hannel size that can mak e ev en more complex the gas transp ort in nano c hannels. Similarly , there ma y b e considered inuence of sepa- ration mec hanisms around holes of the separation mem brane. The p ore densit y and p ore size of the separation mem brane are imp ortan t factors, not ab out an escap e of the gas molecules through 71 the mem brane, but ab out gas-molecule in teraction or surface-molecule around holes. The gas o w through the mem brane c hannel ma y b e hindered b y the attraction or repulsion b et w een the surface and molecule. If the attraction existed b et w een them, the p ore size of capillary is smaller and smaller b ecause molecules can mak e a barrier around a hole. This eect is similar to the gas adsorption inside the nanotub e and is related to a life time of the separation mem brane. Otherwise, the repul- sion can prev en t molecules escaping through c hannels but cannot eect the life time. It ma y not b e a main factor for increasing the concen tration of trace gas in the main o w c hannel, but can b e considered the relation b et w een the molecule-surface in teraction and the concen tration increase. Most researc hes ab out ph ysical prop erties of gas molecular motion are ac hiev ed in nanoscale capil- laries. Whether sampled gas molecules are p ermitted to pass through the mem brane c hannels, the result is related to a consequence of diusiv e selection, mass selection, size selection, p oten tial w ell separation, and rejection or quan tum sieving of molecules from the nanotub es. These are based on the gas-molecule in teraction or surface-molecule in teraction in a nanotub e. While the fundamen- tal theory of mass diusion separation for the t yp e of preconcen trator has b een studied extensiv ely , other separation mec hanisms need further in v estigation due to molecule-c hannel surface in teractions. The most p ossible separation mec hanisms refer to remo v al of the trace gas within the sampled gas through the separation mem branes. Mem brane-based separation, as opp osed to con v en tional tec h- niques suc h as pressure swing adsorption, should reduce facilit y and equipmen t costs and energy consumption and allo w for con tin uous op eration. 2.3.1 Microp orous mem branes A microp orous mem brane, that generally has the diameter from 10nm to 10µm, is v ery similar in structure and function to a con v en tional lter, and has a rigid, highly v oided structure with randomly distributed, in terconnected p ores (Bak er 2012). Ho w ev er these p ores dier from those in the con v en tional lter b y b eing extremely small, on the other of 0.01 ∼ 10µm in diameter. It is p ossible to consider rejection or quan tum sieving of molecules from the nanotub es. These are based on the gas-molecule in teraction or surface-molecule in teraction and ma y aect around an individual c hannel that the diameter is sligh tly larger. All particles larger than the largest p ores are completely rejected b y the mem brane, and particles smaller than largest p ores but larger than the smallest p ores are partially rejected, according to the p ore size distribution of the mem brane. P articles m uc h smaller than the smallest p ores will pass through the mem brane. Th us, the gas separation b y microp orous 72 mem branes is mainly a function of molecular size and p ore size distribution. Only molecules that dier considerably in size generally can b e separated eectiv ely b y microp orous mem branes, for example, in ultraltration and microltration. The mem brane p orosit y is the fraction of the total mem brane v olume that is p orous. T ypical micro- p orous mem branes ma y ha v e a v erage p orosities in the range 0.3∼ 0.7. The most imp ortan t prop ert y c haracterizing a microp orous mem brane is the p ore diameter. Although microp orous mem branes are usually c haracterized b y a single p ore diameter v alue, most mem branes actually con tain a range of p ore sizes. The p ore diameter in microltration is dened in terms of the largest particles able to p enetrate the mem branes. This p ore diameter can b e 5∼ 10 times smaller than the apparen t p ore diameter based on direct microscopic examination of the mem branes (Bak er 2012). A ccording to Li et al. (Li et al. 2007) the gas transp ort in nano c hannels has attracted a lot of in terests b ecause of its p oten tial applications suc h as gas separation, nano device design, and gas storage in nanotec hnology and energy systems. The gas transp ort in nano-connemen ts is also exp ected to b e notably dieren t from that at micro- or macroscales due to the w all eect. Strong binding energy b et w een gas molecules and the surface could induce the gas adsorption, a p opular phenomenon, on the inner surface of the microp orous mem brane c hannel that greatly reduces the self-diusion co ecien t of gases, and the molecular vibrations of the atoms in the c hannel increase the energy accommo dation and the adsorbabilit y of the c hannel. Hence the imp ortance of c hannel sizes that ma y aect the gas transp ort is again emphasized b ecause the p oten tial energy inside the c hannel is related to the structure of the c hannel. Ho w ev er the com bination of the binding energy , molecular vibration of the w all, and c hannel size mak e ev en more complex the gas transp ort in the nano c hannels. 2.3.1.1 Polyc arb onate membr anes Commercial straigh t p ored p olycarb onate mem brane, one of the T rac k-Etc h mem branes dev elop ed b y the General Electric Corp oration Sc henectady Lab oratory (Bak er 2012), is used; the mem brane thic kness is smaller than 10µm, and the a v erage p ore diameters of the mem brane are v arious from10nm to 25mm (Ito et al. 1990). In general it is exp osed to c harged particles in a n uclear reactor and the exp osure time of the mem brane to radiation determines the n um b er of mem brane 73 p ores. The next pro cess is that the mem brane is passed through a solution that etc hes the p olymer and the etc h time determines the p ore diameter (Bak er 2012, Ito et al. 1990, Harv ath et al. 1980). The p ores b y the trac k-etc h preparation tec hnique are uniform cylinders tra v ersing the mem brane at righ t angles. The mem brane tortuosit y τ is therefore close to one, and all p ores ma y ha v e the same diameter. These mem branes are widely used to measure the n um b er and t yp e of susp ended particles in air or w ater b ecause of an almost p erfect screen lter. A kno wn v olume of uid is ltered through the mem brane, and all particles larger than the p ore diameter can b e captured on the surface of the mem brane and smaller particles for the p ore diameter can b e passed through the mem brane c hannels. Under these condition, the p olycarb onate mem brane can b e a go o d candidate as the separation mem branes due to relativ ely lo w costs and larger sizes of mem brane. 2.3.1.2 Metal membr anes In metal mem brane the gas transp ort is a k ey to the high selectivit y and p ermeance (Bak er 2012). F or instance, eac h individual h ydrogen atom from the sampled gas is sorb ed on the mem brane surface where they disso ciated in to h ydrogen atoms, loses its electron to the metal lattice, and diuses through the lattice as an ion. Only h ydrogen is transp orted through the mem brane b y the mec hanism; emerging at the p ermeate side of the mem brane reasso ciate to form h ydrogen molecules, then desorb, completing the p ermeation pro cess, while all other gases are excluded. The h ydrogen atoms on the mem brane surface are in equilibrium with the gas phase, if the sorption and disso ciation of h ydrogen molecules is a rapid pro cess. The surface sorption and disso ciation pro cesses of the h ydrogen atom are fast with high temp erature as a function of diusion of atomic h ydrogen through the metal lattice. Ho w ev er, these pro cesses on the mem brane surface are deviated from the square ro ot of h ydrogen gas pressure at lo w er temp erature. Despite adv an tages of metal mem branes suc h as extraordinary p ermeation and selectivit y prop erties, they ha v e found v ery limited industrial application and are around 100 times the total cost of t ypical p olymeric mem branes used for gas separation. 2.3.1.3 Cer amic membr anes Ceramic mem branes as microltration are made from alumin um, titanium, or silicon o xides (Bak er 2012). The main adv an tage of this mem branes is stable at high temp eratures. P ore diameters in ceramic mem branes range from 10nm to 10µm. The most commercial ceramic mem branes made b y 74 a slip coating-sin tering pro cedure are generally in the form of tub es or p erformated blo c ks. Other tec hniques, particularly sol-gel metho ds, can b e used to pro duce mem branes with p ores from 1 to 10nm. Sol-gel mem branes are the sub ject of considerable researc h in terest, particularly for gas separation applications, but so far ha v e found no commercial use. Man y researc h ab out the other t yp es of preconcen trators are used and considered these ceramic mem branes (Szczypiski et al. 2011, Camara et al. 2010, Zhang et al. 2008). 2.3.1.4 Ze olite membr anes In recen t y ears, there ha v e b een a n um b er of attempts to dev elop zeolite mem branes. Zeolites are microp orous materials comprised of silicalite or aluminosilicate materials and natural p olymorphic minerals, but man y syn thetic v ersions ha v e b een dev elop ed for exp erimen tal and industrial use. Applications of zeolites b elong to separation via molecular sieving, ion-exc hange, size-exclusion etc (Horn y ak et al. 2009). Zeolites can tolerate high temp eratures and pressures, and form in to pinhole- free mem branes. In a zeolite structure, individual cages are link ed together in v arious geometric forms that create p ore op enings with dened regular shap es and sizes. the p ore ranges are generally from 0.3 to 0.8nm (Bak er 2012). Channel diameter in six and eigh t mem b er ring zeolites range from 0.3 to 0.4nm; 10-mem b er ring zeolites ha v e c haracteristic p ore diameter ranging from 0.5 to 0.6nm; and large p ore zeolites ha ving 12-mem b er rings ha v e p ores 0.7 ∼ 0.8nm (Horn y ak et al. 2009). The mem branes are dicult to mak e and are usually more than 10µm thic k so p ermeances are lo w ev en though the diameters of the zeolite mem branes is in the range of in teresting p ore sizes. The mem branes are prohibitiv ely exp ensiv e for most separations. Lo w-cost facilitated syn thesis, highly ordered structures, and exibilit y in design ha v e made zeolites a leading nanotaterial for mem brane separation tec hnology (Bak er 2012). 2.3.1.5 Mixe d-matrix membr anes Mem branes can b e supp orted on alumina or silica substrates, called comp osite mem branes, or fabri- cated as free-standing con tiguous lms-limited in size to a few square cen timeters. The mem branes called as mixed-matrix mem branes are considered as com bining the selectivit y of zeolite mem branes with the lo w cost and ease of man ufacture of p olymer mem brane (Horn y ak et al. 2009). The mixed- matrix mem brane ma y b e b est describ ed as a con tin uous zeolite phase con taining disp ersed particles 75 of p olymer (Bak er 2012). In general, gas p ermeation o ccurs b y a com bination of diusions through the p olymer phase and the p ermeable zeolite particles for relativ ely lo w loading of zeolite particles. Otherwise, some small islands of in terconnected particles form and these islands gro w and connect to form extended path w a ys at higher loading. The gas diusion through this mem brane is not easy to consider a mathematical expression actually due to the complicated structure. 2.3.2 Carb on nanotub e mem branes The microp orous carb on nanotub e (CNT) mem branes w ere rst pro duced b y Barrer in the 1950s and 1960s b y compressing high surface area carb on p o wders at v ery high pressures (Bak er 2012). P ore diameters had 0.5∼ 3nm diameter and w ere used to study diusion of gases and v ap ors. The mem branes failed commercially b ecause they w ere v ery brittle and dicult to mak e defect-free on large scale. Ho w ev er, the mem branes had exceptional separation prop erties for some mixtures and so the preparation of carb on mem branes remains an activ e area of researc h for gas separation and some ev ap oration applications. Lik e ceramic and zeolite mem branes, carb on mem branes separate b y a com bination of size sieving and surface diusion. They are also susceptible to p oisoning b y strongly adsorb ed minor comp onen ts in the sampled gas. CNT mem branes ha v e a high selectivit y and p ermanence that are dictated b y an anit y of the molecules to b e adsorb ed and the relativ e sp eed with whic h they can diuse through the mem branes ma y b e ideal platforms for analytical separations (Mun tz et al. 2004). The separation pro cess of mem branes requires careful con trol of p ore sizes and uniformit y in the mem brane. It is dicult to decide on a suitable separation mem brane for the exp erimen tal v alidation of the con tin uous o w through trace gas preconcen trators, but there are more higher p ossibilities of successful creation of candidate mem brane with rapid gro wth of CNT tec hnology . A main adv an tage of CNT s pro vides a uniform p ore size mem brane. The dev elopmen t of adv anced mem brane tec hnologies with con trolled and no v el p ore fabrications is imp ortan t to ac hiev e more ecien t results. The mem branes based on CNT s exhibit remark able electrical and thermal conductivit y . Single w alled CNT s (SWNT s) generally ha v e outer diameters in the range of 1∼ 3nm with inner diameters of 0.4 ∼ 2.4nm, and m ulti-w alled CNT s (MWNT s) can ha v e outer diameters ranging from 2nm (double w alled carb on nanotub es) up to 100nm with tens of w alls. Lop ez-Loren te et al. (Lop ez-Loren te et al. 2010) and Sears et al. (Sears et al. 2010) rep orted 76 T yp e of mem brane Filtration mec hanism Selectivit y Stabilit y Mem branes with v ertically aligned CNT s Aligned CNT s Size exclusion Mo dest separation factors; Go o d em b edded on a matrix or sieving through op en CNT s increased b y CNT tip functionalization, mem branes with smaller diameters, size exclusion Aligned CNT s Size exclusion or sieving through op en Go o d; ac hiev ed b y compression Mo derate CNT s or their in terstitial space (p ore-tunable prop ert y) or CNT w all functionalization Mem branes with bundles of CNT s Bundles of CNT s on inert mem branes Based on sorption capabilities Lo w; separation is based on − electrostate in teractions Go o d Buc kypap er Based on sorption capabilities Lo w; separation is based on − electrostate in teractions P o or T able 2.1: Analytical applications of the dieren t kind of mem branes (Lop ez-Loren te et al. 2010). 77 t w o t yp es of CNT macroscopic structures for mem brane applications. In T able 2.1, Buc ky-pap er mem branes and isop orous CNT mem branes ha v e dieren t structure and arrangemen t of the CNT s. Buc ky-pap er mem branes or carb on molecular siev e mem branes are one of the rst macroscopic structures fabricated from CNT s and their mec hanical, electrical and thermal prop erties ha v e b een extensiv ely studied. These mem branes tend to form a highly p orous net w ork of randomly en tangled CNT s suc h as pap ers or non w o v en so that they ha v e large p orosit y and sp ecic surface area, and can b e highly exible and mec hanically robust. The Buc ky-pap er mem branes are fabricated from MWNT s gro wn b y Chemical V ap or Dep osition (CVD), and ha v e an a v erage p ore size of ab out 25nm and the p orosities of ab out 91%. Nanometer-sized CNT s ha v e a tendency to self-aggregate via strong v an der W aals forces. This in trinsic prop ert y of CNT s can b e used to obtain the Buc ky- pap er mem branes from disp ersed nanotub es. They are self-supp orting en tangled assem blies of CNT s arranged as a planar lm held together b y v an der W aals in teractions at tub e-tub e junctions. They consist solely of pac k ed bundles of CNT s. Ideally , The Buc ky-pap er mem branes should ha v e all CNT s connected with one another to form a net w ork structure and the nanotub es should b e long and straigh t. V ertically aligned carb on nanotub e (V A-CNT) in isop orous CNT mem branes use as the cylindrical p ore across. These t yp es of mem branes ha v e w ell con trolled nanop orosit y with the hollo w CNT in terior b ecause of small CNT diameter.(d c < 0.7nm). It is p ossible to predict rapid ux through capillary c hannels due to the CNT’s smo oth, frictionless in terior and diameters less than 2nm. Sev eral researc hes for V A-CNT mem branes with high uxes ha v e demonstrated and T able 2.2 sho ws comparison of these prop erties that w ere rep orted b y v e researc h groups (Hinds 2004, Holt 2006, Kim et al. 2007, Mi et al. 2007, Y u et al. 2009). Hinds (Hinds 2004) rep orted aligned MWNT s mem branes with inner diameter of 6 ∼ 7nm b y using p olyst yrene, a con tin uous p olymer lm, to ll spaces b et w een the CNT s. Dual-w alled CNT s (D WNT s) mem branes b y Holt (Holt 2006) w ere formed small p ores of a v erage 1.6nm diameter using a predep osited nano catalyst (10nm Al 2 O 3 , 0.3nm Mo, 0.5nm Fe) on a silicon w afer. The spaces b et w een the CNT s w ere lled with silicon nitride Si 3 N 4 . With these treatmen ts b efore the tips of nanotub es are etc hed op en and the length of the nanotub es within the p olymer can consequen tly b e reduced b y selectiv e electro c hemical o xidation, the MWNT s rep orted b y Hinds (Hinds 2004) and Holt (Holt 2006) can sp ecially ha v e the mem brane thic kness robust. They exp erimen tally observ ed the fast mass transp ort through CNT mem branes for gas molecules. The o w rates of sev eral solv en ts through CNT mem branes measured b y Hinds (Hinds 2004) ha v e o w sp eeds of four to v e orders of magnitude faster than con v en tional uid o w predicted through p ores of 7nm diameter at 1Torr . 78 Study Hinds et al. Holt et al. Kim et al. Mi et al. Y u et al. Mem brane Structure F ree-standing Silicon w afer PTFE lter P orous alumina supp ort P orous iron supp ort Morphology CNT/p olymer CNT/Si 3 N 4 CNT/p olymer CNT/p olymer CNT and (P olyst yrene) comp osite comp osite (P olysulfone) comp osite (P olyst yrene) comp osite in terstitial p ores Structure Multi-w alled Double-w alled Single-w alled Multi-w alled - La y er thic kness(m) 510 2 0:6 10 750 CNT real densit y (#=cm 2 ) 610 10 2:510 11 7:01:7510 10 1:8710 9 1:410 11 (2:910 12 ) CNT outer diameter (nm) NA 2 - 20 - P ore diameter (dm ) (nm) 7:5 1:6 1:2 6:3 3:0 (A v erage inner diameter) A v erage distance 41 20 38 - 28(6) b et w een CNT s (nm) Areal p orosit y 2:7 0:5 0:079 0:062 1(21) (CNT v olume o ccupancy %) Kn udsen n um b er 1 1070 - 1:22:2 - T able 2.2: Comparison of CNT Mem branes ; Hinds (Hinds 2004), Holts (Holts 2006), Kim et al. (Kim et al. 2007), Mi et al. (Mi et al. 2007), and Y u et al. (Y u et al. 2009). 79 Holt (Holt 2006) measured the mass o w rates of air through CNT mem branes of 1.3nm to 2nm diameters and the v alues are one to t w o orders of magnitude larger than what w ere predicted b y the Kn udsen diusion mo del. The transp ort diusivities are also kno wn ab out three orders of magnitude greater in CNT mem branes than in silicalite mem branes with the same thic kness. The fast mass transp ort in a mem brane is exp ected to substan tially increase the preconcen trator eciency . Kim et al. (Kim et al. 2007) ltrated v ertically aligned, SWNT s with a tetrauoro eth ylene lter. SWNT s mem branes ha v e m uc h small p ore diameter of a v erage 1.2nm and p olysulfone p olymer sealed the space b et w een the CNT s b y spin coating. Mi et al. (Mi et al. 2007) also grew aligned, MWNT s mem branes on macrop orous α-alumina supp orts b y CVD, lling the in ter-CNT gaps with p olyst yrene. These mem branes ha v e a p ore diameter of ab out 6.3nm smaller than Hinds’ CNT s and a lo w er p orosit y . A ccording to a recen t pap er rep orted b y Y u et al. (Y u et al. 2009), the normally closed ends of the CNT s w ere etc hed op ened. The length of the nanotub es within the p olymer can b e reduced b y selectiv e electro c hemical o xidation. The free-standing V A-CNT mem branes with high CNT densities (ab out CNT p orosit y) w ere fabricated b y shrinking free-standing V A-CNT arra ys that w ere gro wn b y CVD. As men tioned in Chapter 1, the carb on-based mem branes, carb on molecular siev e mem branes and CNT mem branes, w ell p erform in gas separation mec hanism dep ended on the p ore sizes of capillar- ies. A ccording to the exp erimen t b y Sholl and Johnson (Sholl et al. 2006), the gas o w through the mem brane is one or t w o orders of magnitude faster than through the commercial p olycarb onate mem brane with 15nm p ore size b ecause of smo othness of the inner surface of c hannel. The faster gas transp ort of CNT mem branes are useful to enhance the concen tration large enough for the con- tin uous op erated the preconcen trator during more short times. Ho w ev er these expansiv e mem branes are still hard to pro duce larger area mem branes than 1cm 2 . The pressure dierence emplo y ed is relativ ely small, but can b e large enough to aect the condition of the separation mem branes. There- fore, condition of the separation mem branes limits larger pressure dierences b et w een the pumping c ham b ers and main o w c hannel. Nev ertheless, these mem branes are one of go o d candidates for the separation mem branes of the microscaled preconcen trator suggested b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008). 80 2.4 Performances of Pumping Chamber and Pump In this w ork, the imp ortan t issues are to design pumping c ham b ers and to decide pumps for the miniaturized preconcen trator as one device. The pumping c ham b ers are lo cated upp er and lo w er the main o w c hannel op erate that the gas o w sp eed inside the main o w c hannel should k eep b eing constan t during the gas passes through the one. And also the pumps connected with pumping c ham b ers w ork to create pressure dierences b et w een the pumping c ham b ers and main o w c hannel, and constan tly ha v e to op erate. In this researc h, it is hard to use the oil-lled pumps b ecause of the mem branes. The p ore diameters of the sep eration mem branes are to o small to b e easily p olluted b y oil particles. Hence it ma y need to use oil-free pumps that can w ork consisten tly . 2.4.1 Pumping c ham b ers The pumping c ham b ers ha v e constan t widths and v arying heigh ts and bac k eac h of the separation mem branes as men tioned to previous researc hes b y Mun tz et al. (Han et al. 2009, Mun tz et al. 2004, Mun tz et al. 2008). They generally can main tain an appro ximately constan t n um b er densit y of carrier gas and a pressure that is lo w er than a pressure in the main o w c hannel. In other w ords, since pumping costs increase with pressure ratio, it is imp ortan t to k eep the pressure nearly constan t and high enough in the main o w c hannel and pressures in the pumping c ham b ers can b e set relativ e to the constan t pressure in the one. Generally , the ligh ter and smaller carrier gases diuse from the lo w er and upp er surfaces of the separation mem brane to the pumping c ham b ers, and the concen tration of the trace gas will b e increased in this w a y . The fraction of the n um b er densit y of carrier gas is related to the pressure dierence and the ratio of the pressure dierences b et w een the pumping c ham b ers and main o w c hannel ma y b e v arious. In other w ords, if the diameter of separation mem brane is larger than the diameter of trace gas molecule, a bac ko w from the pumping c ham b er to the o w c hannel of trace gas molecules is substan tially related to the pressure dierence. Ho w ev er, the bac ko w is only pro vided for the carrier gas molecules if the diameter of separation mem branes has a v alue b et w een a larger diameter than carrier gas molecule and a smaller diameter than trace gas molecule. Figure 2.4.1 sho ws that the pumping c ham b ers are lo cated upp er and lo w er of the main o w c hannel in the top and one part of pumping c ham b ers is sho w ed in the b ottom. The constan t width w(0) and constan t across the length L are same with an en tire system, but the heigh t, h p , ma y b e v aried 81 Figure 2.4.1: Illustration of pumping c ham b ers and sk etc h inside pumping c ham b er prop osed b y Mun tz et al. (Mun tz et al. 2004). across the length. The heigh t is larger than the heigh t of the main o w c hannel, but cannot b e larger than the length and width of the one. The heigh t ma y b e appro ximately larger than 500µm but it ma y dep end on the thic kness of separation mem branes. The shap e and size of the pumping c ham b ers ma y b e an imp ortan t k ey for main taining the same pressure dierence when the heigh t is close to the heigh t main o w c hannel or larger separation mem branes. Ho w ev er the v olume of pumping c ham b er, e.g. heigh t, ma y b e larger enough in order to main tain the constan t pressure in the pumping c ham b ers. 2.4.2 Pump options In order to generate the pressure dierence b et w een the lo w er surface and the upp er surface of the separation mem branes to increase the concen tration of the trace gas in the main o w c hannel, the pumps can con trol v aried pressure dierences. This section will in tro duce sev eral candidate tec hnologies for the pumps required to main tain the pressure ratio for ecien t separation and pump tec hnologies are w orth considering for application in con tin uous gas separation tec hnologies for the miniaturized preconcen trator. F or the miniaturized preconcen trator, the microscale pumps are useful. A ccording to Laser et al. (Laser et al. 2004) who surv ey ed ab out the dev elopmen t of microscale devices for pumping uids, pumps in general fall in to one of t w o ma jor categories: displacemen t pumps and dynamic pumps. The displacemen t pumps exert pressure forces on the w orking uid through one or more mo ving b oundaries. They op erate in a p erio dic manner, incorp orating some means of reactifying p erio dic uid motion to pro duce a net gas o w. The pressure and o w rate generated b y recipro cating 82 Figure 2.4.2: Comparison of rep orted micropumps based on maxim um o w rate, maxim um pressure, and pac k age size. Self-pumping frequency is here dened as maxim um o w rate divided in to pac k age size (Laser et al. 2004). This gur e is r eprinte d. displacemen t pumps dep end on the dierence b et w een the maxim um and minim um v olumes of the pumping c ham b er o v er the course of the pump cycle. Another t yp e, the dynamic pumps suc h as cen trifugal pumps con tin uously add energy to the w orking uid in a manner that increases either its momen tum or its pressure directly , and ha v e only b een miniaturized to a limited exten t. V arious factors other than the pressure and o w rate p erformance are related to the selection of a dynamic pumps. Miniaturization of dynamic pumps has also b een precluded b y t ypically scaling of eciency with decreasing Reynolds n um b er and the limitations of microfabrication tec hnologies. Figure 2.4.2 b y giv en Laser et al. (Laser et al. 2004) sho ws v arious micropumps in terms of all three of these metrics. The size of the data p oin t mark ers indicates the asso ciated △P max range for eac h pump. The electro osmotic micropump rep orted b y Y ao et al. (Y ao et al. 2003) and the piezo electric- driv en recipro cating displacemen t micropump rep orted b y Li p erform in terms of absolute o w rate and pressure generation. These pumps are v ery dieren t man ufacturing pro cess and op erational nature. More compact piezo-driv en recipro cating displacemen t micropumps, prop osed b y Rob erts et al. (Rob erts et al. 2003) larger than Li’s micropump deliv er normalized o w rate p erformance, but generally at some cost in pressure generation. Thermopneumatically driv en micropumps tend to pro duce lo w o w rates ev en relativ e to their size, as w ell as lo w maxim um pressure, but this 83 p erformance m ust b e w eighed against exp ected lo w man ufacturing costs for these micropumps. V argo et al. (V argo et al. 1999) in v estigated applications of Kn udsen compressor, another t yp e of pump, as b oth microscale and macroscale v acuum pumps op erates b y utilizing the thermal transpi- ration eect. The Kn udsen Compressor ha v e b een exp erimen tally demonstrated at the cen timeter scale and can mak e initial energy estimates. It w as found that the Kn udsen compressor is an at- tractiv e p ossibilit y for microscale pumps do wn to a pressure of ab out 1mTorr and for macroscale pumps to ab out 0.1mTorr . The ma jor issue of these pumps is the o w in the connector section that m ust ha v e dimensions signican tly greater than the mean free path of the pro cess gas. The Kn udsen compressor requires a trade-o b et w een cascade size and minim um of useful pumping pressures. The original analysis of Kn udsen compressor’s p erformance is based on the assumption of an ideal situation of free molecule o w in the capillary section and con tin uum o w in the connector section of a compressor stage. Cabuz et al. (Cabuz et al. 2001) dev elop ed one t yp e of the ap erio dic displacemen t pumps. The dual diaphragm pump (DDP), whic h consists of a c ham b er and t w o thin diaphragms, is a unique mesoscale diaphragm pump that can pro vide a limited pressure head of 14.7Torr , but m ultiple stage can b e cascaded to pro vide m uc h larger pressure rations in theory . It is assumed that eac h stage pro duces a mass o w and pressure dierence that v aries linearly with an a v erage pressure. F or concen trations with no size ltration, the DDP w ould require 460mW to pro duce a o w rate of 7.3ml/min, while the requiremen t of p o w er with size ltration can b e reduced to ab out 50mW . The DDP is fully symmetrical, ha ving true bi-directional op eration, has virtually zero dead space, sho ws p erfect rectication, and is fully scalable. 2.5 Detecting Systems It is imp ortan t to determine a detector that can coun t atoms and measure the concen tration of trace gas immediately at ro om temp erature and v arious pressures including an atmospheric pressure. In general, it is a similar cross sectional area b et w een the inlet of detector transition that directly connects with the main o w c hannel and the outlet of the detector transition that will connect with a detector. Miniaturization of the o w-through trace gas preconcen trator requires minimized detecting system that will b e needed a minim um total amoun t of analyte to b e able to conclusiv ely detect a target 84 sp ecies. Miniaturizing the dieren t, highly sophisticated and ecien t detection metho ds b enets from scaling with size and allo ws in tegration. The miniature detecting system w ould ha v e an im- p ortan t role in reducing the the fabrication cost of the complete system. In order to detect atoms or molecules emitted from the detector transition, it needs to excite them b y some energy sources. Detectors, b e in tro duced in this section, are related to the t yp es of electron b eam that is useful to excite the particles. Ho w ev er the detectors do not researc h in this w ork and will b e considered for the en tire system in future w ork. 2.5.1 Detector p erformance and options : Electron Beam T ec hnology One of the most p ossible detecting systems that can b e used in this researc h is an electron b eam tec hnology . The electron b eam tec hnology has existed for o v er a cen tury . During this time, it has dev elop ed from lab oratory exp erimen ts to a p o w erful industrial to ol in v arious applications (Electron b eam, http://twi.c o. kr ). The p o w erful, con trollable, precise and v ersatile electron b eams are generated in a high v acuum en vironmen t, t ypically via a thermal catho de heated to more than 2000 ◦ C , and an accelerating p oten tial of at least 10keV . The electron b eam uorescence tec hnique has con tributed to b oth hardw are orien ted researc h prob- lems and basic studies in gas dynamics. The emission or uorescence excited b y an electron b eam has a sp ectrum p eculiar to the comp osition and temp erature of the gas through whic h the b eam passes. The most imp ortan t prop ert y of the observ ed emission is that it m ust b e the result of direct excitation-emission sequence. The uorescence is a consequence of an electronic transition from a state whic h can b e reac hed b y direct excitation from the original electronic conguration of the gas atoms or molecules. In addition, the emission m ust b e an allo w ed electric dip ole transition with a transition probabilit y for emission greater than ab out 10 7 /sec. These restrictions are necessary , since otherwise the excitation-emission pro cess migh t require suc h an extended p erio d of time that the uorescence w ould tend to b e blo wn do wnstream in a gas o w; a feature that is of course undesirable, since the measuremen t w ould b e a function of the o w v elo cit y (Mun tz 1968). As sho wn in Figure 2.5.1, uorescence results from a pro cess that o ccurs when certain molecules called uorophores, uoro c hromes, or uorescen t dy es absorb ligh t. The absorption of ligh t b y a p opulation of these molecules raises their energy lev el to a brief excited state . It means that it creates the excited, unstable electronic singlet state (S 1 ), when a photon of energy h EX supplied b y 85 Figure 2.5.1: Jablonski diagram : the pro cess illustrated b y a simple electronic state diagram in v olv es in creating an excited electronic singlet state b y optical absorption and subsequen t emission of uorescence. Excitation, vibrational relaxation, Emission (Amersham 2002). This gur e is r eprinte d. an external source is absorb ed b y a uorophore. The excited state is c haracterized b y a v ery short time, usually on the orders of a few nanoseconds . During this p erio d, the excited molecules relax to w ard the lo w est vibrational energy lev el within the electronic excited state. The energy lost in this relaxation is dissipated as heat. As they deca y from this excited state , they emit a uorescen t ligh t (Amersham 2002), and it is p ossible to obtain vibrational and rotational temp eratures from this emission. Mun tz (Mun tz 1968) in 1968 discussed the electron b eam uorescence tec hnique’s dev elopmen t, one of the candidates as the detecting tec hnique for the preconcen trator, and its applications to studies of gas o w in 1978. This is accomplished b y measuring relativ e in tensities in the vibrational and rotational ne structure of the molecule emission excited b y the electron b eam in Figure 2.5.2. A one or t w o millimeter (1∼ 2mm) diameter, w ell collimated b eam of electrons is passed through the gas o w concen trated. If the gas densit y is reasonably lo w, sa y b elo w that equiv alen t to a pressure of sev eral Torr at ro om temp erature, an electron b eam with an energy of around 50keV will not b e signican tly atten uated o v er a distance of 10 or 20cm. The b eam is visible as a thin line of uorescence. By optical means an y place along the b eam length can b e selected for observ ation and a p oin t measuremen t of the b eam stim ulated emission can b e accomplished. The p oin t size corresp onds appro ximately to the diameter of the uorescen t cylinder that is caused b y the b eam and the length of the emission that is observ ed. The uorescence from the selected p oin t has prop erties that can b e used to measure directly the lo cal state of the gas at that p oin t (Mun tz 1968). The electron source of b eam comes from a lamen t, made of v arious t yp es of materials suc h as tungsten that functions as the catho de. and The ano de, whic h is p ositiv e with resp ect to the 86 lamen t, forms p o w erful attractiv e forces for electrons. This causes electrons to accelerate to w ard the ano de. The b eam of electrons is attracted through the ano de condensed b y a condenser lens and fo cused as a v ery ne p oin t on the sample b y the ob jectiv e lens. The scan coils create a magnetic eld whic h deects the b eam bac k and forth in a con trolled pattern. The electron b eam hits the sampled gas, pro ducing secondary electrons from the sample. These electrons are collected b y a secondary detector or a bac k scatter detector, con v erted to a v oltage, and amplied. The application of electron excitation to lo w densit y gas dynamics researc h w as suggested b y Sc h u- mac her and Grun in 1955. The uorescence could b e used to measure gas densit y at p oin ts in a lo w densit y gas o w, since it w as exp ected that the emission in tensit y w ould b e directly dep enden t on gas densit y . When the b eam of fast, energetic electrons (energy m uc h greater than the ionization p oten tial of the gas) is passed through a gas, there are a n um b er of in teractions that tak e place b et w een the b eam electrons and the gas atoms, and it undergo es t w o broad categories to describ e electron scattering, namely , elastic and inelastic collisions with the gas particles. The electronic excitation that pro duces the uorescence is the most imp ortan t elemen t in the use of uorescence as a prob e. This is only the case if it is clearly understo o d ho w a particular emission is excited. In general the electron b eam uorescence tec hnique is w ell suited to pro viding lo cal measuremen ts in lo w densit y and high sp eed o ws ( < 10 22 molecules/m 3 ), and the use of an energetic electron b eam (t ypically 25keV ) in the lo w densit y induces a complicated set of excitations in the gas all along the b eam (Mohamed et al. 2009). A t high electron energies with resp ect to sa y the ionization p oten tial of a particular gas, it w ould b e exp ected that a strong emission should b e observ ed only from those transitions whose upp er states corresp ond to optically allo w ed transitions from the ground state. The elastic scattering of primary electrons results in little (< 1eV ) or no c hange in energy of the scattered electron and o ccurs b et w een the negativ e electron and the p ositiv e n ucleus.The elastic scattering do es not add to the in tensit y of the uorescence and the elastic dieren tial scattering curv e app ears rather broader than the inelastic curv e. Secondary electrons are sp ecimen electrons that obtain energy b y inelastic collisions with b eam electrons. The secondary electrons are predominan tly pro duced b y the in teractions b et w een energetic b eam electrons and w eakly b onded conduction-band electrons. These secondary excitations can o ccur o v er a relativ ely long distance do wnstream from the electron b eam dep ending of the o w v elo cit y and the relaxation time of the secondary electrons 87 Figure 2.5.2: Illustration of electron b eam gun and electron b eam tec hnique (Mun tz 1968). 88 (Mun tz 1968, Mohamed et al. 2009). The emission in tensit y of a uorescence line in a transition from j to a lo w er state k is I jk =hcν jk A jk n j =hcν jk ∑ n ep ν ep σ ij (E ep )n i ∑ A jk /A jk ∞n 0 , (2.5.1) where n i and n j are the p opulations on lev els i and j and are prop ortional to the total densit y n 0 of the gas, n ep is the densit y of primary electrons, ep is the v elo cit y of primary electrons, E ep = 1 2 m e 2 p is the energy of primary electrons when m e is the electron mass, ij (E ep ) is the cross section of the excitation b y electron impact, A jk is the probabilit y of radiativ e transition in s −1 , h is the Planc k constan t, jk is the frequency of the transition j−k , and c is the ligh t sp eed. The in tensit y of a uorescence line is therefore prop ortional to the total densit y of the gas n 0 as n i is prop ortional to n 0 (Mohamed et al. 2009), so it is p ossible to calculate the in tensit y of the concen trated gas throughout the outlet of main o w c hannel. The radiativ e lifetime of the excited molecules is v ery short (∼ 60ns) for v elo cities less than 10km/s to freeze the mo v emen t of the column at eac h p oin t of excitation. Therefore the ligh t collected is quite lo w so that image accum ulation m ust b e used to enhance detection, but this is p ossible only if the o w v elo cit y is constan t (Mohamed et al. 2009). These electron gun to generate the electron b eam fabricated b y Mun tz (Mun tz 1968) in 1983 w as to o large to b e hard to connect with the miniaturized preconcen trator. the Nev ertheless the sizes of commercial electron guns are curren tly m uc h smaller than this electron gun, generally 20∼ 30cm in the total length and 3∼ 5cm diameter of cylindrical t yp e, but they are not easy to b e considered as the detecting systems b ecause of the larger size of p o w er generator and fo cuser. In order to o v ercome these problems, Diop et al. (Diop et al. 2011) in 2011 made an electron gun that can b e op erated with an energy of ab out 20keV and a diameter of a few mm propagating a few tens of cm in a lo w pressure (< 100Pa) gas presen t at 60 to 80km altitude zone. The total size of their compact system including the electron gun, pump, CCD camera, sp ectrometer, and p o w er supplies is 300mm× 295mm× 200m. They generally used the commercial pro ducts, one turb omolecular pump b y Pfeier to main tain the pressure 2 ∼ 8Pa in the pumping c ham b er, t w o p o w er supplies for plasma and electron b eam b y Ultra v olt, and one sp ectrometer b y Ocean optics. Therefore this application suggests a p ossibilit y for the nal complete system for this researc h ev en though the man ufacturing costs is exp ensiv e. 89 Figure 2.5.3: Electron b eam emission principle and Electron gun head (all dimensions in mm) b y Diop et al. (Diop et al. 2011). This gur e is r eprinte d. 90 2.5.2 Detector p erformance and options : Other t yp es A ccording to the in v estigation b y Skrob ol et al. (Skrob ol et al. 2009), v arious gas laser systems had b een rep orted from 1980 to 2006, but only a limited n um b er of principle sc hemes of op eration ha v e found practical use for example excimer lasers, ion lasers, and the nitrogen, helium-neon, and carb on dio xide laser. They ha v e dev elop ed a w a y to scale do wn the devices for electron b eam excitation of dense gases. Thin mem brane of 30nm thic k ceramic foils allo ws the use of electron energies on the order of 10keV , with p ermissible energy and consequen tly p o w er losses in the en trance foil. They demonstrated the p ossibilit y to use the lo w energy and smallest electron b eams for gas laser pumping, whic h the o v erall size of the electron b eam pump ed laser is 14cm in length and 4cm in diameter without con taining the v acuum pumps and lab oratory gas supply systems. The pumping p o w er to eac h laser is 0.037W . It is exp ected that this system ma y b e w ell matc hed with the miniaturized preconcen trator in this w ork due to the small size of the system and lo w p o w er. Heine et al. and W elzbac h et al. (Heine et al. 2010, Wilzbac h et al. 2009) in tro duced an optical b er- based atom detector whic h is mec hanically v ery robust and capable of state selectiv e single detection at a eciency design b y coun ting uorescence photons, and is fully in tegrated on an atom c hip, alignmen t free b y fabrication. The detection of single neutral atoms, one of the essen tial ingredien ts for dev eloping quan tum atom optics, atomic ph ysics based quan tum tec hnologies, and prerequisite for man y quan tum information exp erimen ts, is also p erformed optically using uorescence or adsorption detection. Fluorescence detection of single atoms can b e v ery ecien t if the atom remains lo calized, since long in tegration times allo w collecting man y uorescence photons, while uorescence detection of mo ving atoms whic h ha v e a short, nite in teraction time with the detector is signican tly more dicult. It requires b oth: a supreme bac kground repression and a high collection eciency to reac h single atom sensitivit y . There is no fundamen tal limit to the eciency of a uorescence detector as long as the atom is not lost from the observ ation region, but free neutral atoms are harder to detect b ecause the few scattered photons are dicult to distinguish from bac kground ligh t. Detections of the presence of neutral atoms in atomic ph ysics and quan tum information can b e distinguished t w o big branc hes: the direct detection of sp on taneously emitted photons using high qualit y optics, or the observ ation of c hanges in ligh t transmission through ca vit y mirrors due to strong atom photon coupling. T erraciano et al. (T erraciano et al. 2009) and Norris et al. (Norris et al. 2009) approac hed com binations of these t w o metho ds b y detecting an atom in a driv en ca vit y mo de, 91 Figure 2.5.4: Xenon sp ectrum in the standard temp erature and pressure (STP) b y NIST through the collection of sp on taneous emission and forw ard scattering in to an undriv en, orthogonally p olarized ca vit y mo de. The researc hers at the Join t Quan tum Institute (JQI) in College P ark (a researc h partnership b et w een the Univ ersit y of Maryland and the National Institute of Standards and T ec hnology) and the Univ ersidad de Concep cin in Chile in v en ted a new single atom detection system that uses t w o p olarizations of ligh t sim ultaneously through ca vit y mirrors. The single atom detector, a t w o mo de ca vit y quan tum electro dynamic system, is more than 99.7% accurate and can discern the arriv al of a neutral atom in less than one million th of a second. This tec hnique is a classical determination of atom presence rather than a pro jection on to a pure quan tum state. One signican t adv an tage is that it is sensitiv e enough to w ork without strong coupling of the ca vit y and atoms. This metho d of atomic detection, using a conditional measuremen t, is w ell suited for some quan tum con trol proto cols. 2.5.3 Detector p erformance and options : Sp ectrum The in teresting, dangerous target molecules usually ha v e hea vier molecular w eigh ts. It is actually hard to use the hazard hea vier molecules suc h as sarin or soman in a lab oratory condition. And also this researc h will b e more expanded to v arious applications, detecting univ ersal particles. Th us the hea vier atom used as the trace gas is xenon. The xenon is a colorless, o dorless noble gas and o ccurs in the Earth’s atmosphere in trace amoun ts. If the electron b eam uorescence as the detecting system is considered, the sp ectral lines of xenon should b e kno wn. The sp ectrum of xenon in is illustrated Figure 2.5.4 can b e obtained from the 92 w ebsite of the National Institute of Standards and T ec hnology (NIST). The strongest sp ectral line is 467.123nm in a visible range. 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Szczypiski1, Rafa, Jacek Grzelk a, Anna Baraniec k a, Marianna Grsk a, Jan Lesiski, Jan ysk o, Remigiusz Gro dec ki, Dorota G. Pijano wsk a, and Piotr Grabiec, Microuidic preconcen trator and microuidic c hip for bacterial cells detection, Optic a Applic ata , V ol. XLI, No. 2 (2011). T erraciano , M. L., R. O. Knell, D. G. Norris, J. Jing, A. F ernandez, and L. A. Orozco, Photon burst detection of single atoms in an optical ca vit y, Natur e physics , 5 (2009) : 480 - 484. V argo , S. E., E. P . Mun tz, G. R. Shiett, and W. C. T ang, Kn udsen compressor as a micro- and macroscale v acuum pump without mo ving parts or uids, Journal of V acuum Scienc e and T e chnolo gy A , 174 (1999) : 2308 - 2312. 94 Wilzbac h , M., D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Sc hmiedma y er, Simple in tegrated single-atom detector, Optics letters , V ol. 34, No. 3 (2009). Y ao, Sh uh uai and Juan G. San tiago, P orous glass electro osmotic pumps: theory , Journal of Colloid and In terface, Scienc e , 268 (2003) : 133 - 142. Y u, M., H. H. F unk e, J. L. F alconer, and R. D. Noble, High densit y , v ertically-aligned carb on nanotub e mem branes, Nano L etters , V ol. 9, No. 1 (2009). Zhang, Y aop eng, Shinji Kato, and T ak anori Anaza w a, A micro c hannel concen trator con trolled b y in tegral thermoresp onsiv e v alv es, Sensors and A ctuators B , 129 (2008) : 481 - 486. 95 Chapter 3 Characteristics of Preconcentrator As describ ed in Chapter 2, the newly prop osed preconcen trator (Mun tz et al. 2008) requires the optimization of man y v ariables to seek an ideal guage. T o reasonably fabricate a preconcen trator protot yp e, the v ariables can b e limited with b oundary conditions predicted with a v ailable n umerical data. F or example, determining the p erformance of appropriate separation mem branes lo cated the upp er and lo w er main o w c hannel is closely related to the shap e and exit size of the main o w c hannel. In other w ords, prop erties of the mem brane suc h as transmission probabilit y and p orosit y are used as main factors to decide a t yp e of the separation mem branes. Other co ecien ts, the ratio of gas densit y b et w een the main o w c hannel and pumping c ham b ers, gas o w sp eed, mean thermal sp eed, and initial sizes of the main o w c hannel (length, heigh t, and width of the en trance), are considered as p ossible n um b ers to obtain the trace gas concen tration large enough at an exit of the main o w c hannel. In this c hap eter, the reasonable v alues of the v ariables are determined to fabricate a protot yp e of the preconcen trator. 3.1 Predictions of the Preconcentrator Performance The primary fo cus of the curren t researc h is to determine a shap e and exit size of the main o w c hannel using equation (2.2.9), as sho wn in Figure 2.2.4. The shap e of the main o w c hannel is critical increasing the concen tration ratio of the trace gas in a sample as sho wn b y equation (2.2.12). Determining the shap e and exit width of the main o w c hannel dep end on m ultiple v ariables 96 including; the gas o w sp eed u 0 , en trance width w(0), heigh t of main o w c hannel h f , pressure ratio , t yp e of gas, and prop erties of the separation mem brane. F or this exp erimen t the en trance width, heigh t, and length of the main o w c hannel w ere 10cm, 0.5cm, and 10cm, resp ectiv ely , and the gas o w sp eed u 0 is 5cm/s. A ccording to equation (2.2.12), the concen tration ratio of trace gas increases along the length of the main o w c hannel when the ratio of molecular w eigh ts of carrier gas to trace gas is m uc h smaller than 1 ( √ m T ≪ √ m C ), assuming other co ecien ts related to b oth gas molecules are constan t. Therefore, the smallest and ligh test noble helium is attractiv e as the carrier gas molecule, b ecause the trace gas molecules usually ha v e molecular w eigh ts hea vier than 100U . The transmission probabilit y α, related to the ratio of the length and diameter to the mem brane c hannel hc dc , can b e obtained from equation (2.2.8) when the ratio is smaller than 500. As men tioned in Chapter 2, the transmission probabilit y of the carrier gas, α C , is the same as the transmission probabilit y of the race gas, α T in the same separation mem brane, b ecause the transmission prob- abilit y can b e considered as one of the prop erties of the p orous mem brane and is indep enden t of molecular sp ecies. Ho w ev er, this assumption is con trary dieren t to the n umerical mo dels of the preconcen trator suggested b y Mun tz et al. (Mun tz et al. 2008). The transmission probabilities of carrier gas and trace gas in the paten t w ere dieren t b ecause it dep ended on the molecule sp ecies. Mun tz et al. more comprehensiv ely used the denition of the transmission probabilit y including the prop erties of the p orous memrbane and molecular sp ecies. Ho w ev er, it w as not clear ho w the molec- ular sp ecies is related to the transmission probabilit y . Therefore, this co ecien t is only considered as the prop ert y of the p orous mem brane in this researc h. Figure 3.1.1 sho ws calculations of the concen tration ratio of the trace gas from equation (2.2.12) and shap es of the main o w c hannel calculated using equation (2.2.8) with v arious transmission probabilities. Then the conditions are 10cm of the width and length and 0.5cm of the heigh t of the main o w c hannel, 5cm/s of the gas o w sp eed, 4.2×10 −3 of the p orosit y , and 0.5 of the pressure ratio. The exit size of the main o w c hannel is larger than 10nm, when the transmission probabilit y is smaller than 0.01, as sho wn in Figure 3.1.1.(a). The concen tration ratio of the trace gas for α = 0.01 is ab out 10 7 times larger than one of the trace gas for α = 0.001 at the end of the main o w c hannel, while the width of the main o w c hannel rapidly decreases along the length of the main o w c hannel for α = 0.01. The exit width is increased as the transmission probabilit y approac hes zero, and the length of the 97 Figure 3.1.1: Concen tration ratio of the trace gas increases in the main o w c hannel as a function of the length and as a function of transmission probabilit y , when α = α C = α T . The shap es and exit sizes of the main o w c hannel (left) and concen tration ratio of the trace gas ( log n T (x) nT(0) ) (righ t) when (a) α = 0.1, 0.01, 0.001, and 0.0001, and (b) 0.0025≤α≤ 0.01. The transmission probabilit y (α(model)) is calculated b y equation (2.2.8) (red solid line with circles). Then the conditions are 4.2×10 −3 in a p orosit y , and 0.5 in a ratio of gas n um b er densit y of the pumping c ham b er and main o w c hannel. 98 main o w cahnnel ma y b e relativ ely short compared to the width with larger the transmission probabilit y . In this case, the concen tration ratio of the trace gas ma y increase a few times. With these conditions, it is p ossible to determine the t yp e of separation mem branes whic h can b e used in this researc h. F or example, the relativ ely thinner CNT mem branes suggested b y Holt (Holt 2006) and Kim et al. (Kim et al. 2007) from T able 2.2 ha v e the transmission probabilit y of 0.003 and 0.0027, resp ectiv ely , b y equation (2.2.8). With these transmission probabilities, the exit size of the main o w c hannel and the concen tration ratio of the trace gas are reasonable as sho wn in Figure 3.1.1. Another imp ortan t factor in the mem brane is the p orosit y , F , (or fractional op en area) of the mem- brane in relation to the p ore densit y and diameter. The eect of the p orosit y on the concen tration ratio of the trace gas and the shap e and size of the main o w c hannel is similar to that of the transmission probabilit y . The p orosit y also limits increases in concen tration with a reasonable main o w c hannel shap e and exit width. Under the same conditions as Figure 3.1.1 and α = 0.0066, the concen tration ratio of the trace gas increases with increasing p orosit y . The p orosit y is limited 0.003 < F < 0.01 for a reasonable shap e of the main o w c hannel and concen tration ratio of the trace gas. The p orosities of CNT mem branes b y Kim et al. (Kim et al. 2007) and Mi et al. (Mi et al. 2007) from T able 2.2 are 7.9×10 −4 and 6.2×10 −4 , resp ectiv ely , so it ma y b e p ossible to use as the separation mem brane for the new t yp e of the preconcen trator suggested b y Mun tz et al. (Mun tz et al. 2008). Figure 3.1.2 sho ws the relationships b et w een the concen tration ratio of the trace gas, the shap e of the main o w c hannel, and b oth co ecien ts, transmission probabilit y and p orosit y . When αF is larger than 2.5× 10 −5 and smaller than 7.5× 10 −5 , the exit sizes and shap es of the main o w c hannel are p ossible to fabricate for a main o w c hannel for this researc h. In T able 2.2, the co ecien ts, αF , for CNT mem branes range from 4.89×10 −7 to 2.65×10 −5 , and the co ecien ts of commercial p olycarb onates can b e from 10 −4 to 10 −6 . The CNT mem brane b y Hind (Hind 2004) ( αF = 2.65×10 −5 ) and some commercial p olycab onates (αF = 2.79×10 −5 ) w ere also considered for the sep eration mem brane in this researc h. Ho w ev er, other CNT mem branes do not satisfy all of the required conditions, so other co ecien ts, suc h as pressure dierence, gas o w sp eed etc, should b e c hanged to use others. F or example, the pressure ratio of gas n um b er densit y of the pumping c ham b er and main o w c hannel, , ma y b e larger than 0.5, or the thermal mean sp eed ma y b e larger. Otherwise, the heigh t of the main o w c hannel is smaller than 0.5cm, or the gas o w sp eed 99 Figure 3.1.2: Concen tration ratio of the trace gas increases in the main o w c hannel as a function of the length of the main o w c hannel and as a function of transmission probabilit y and p orosit y , when αF =α C F C =α T F C . The shap es and exit sizes of the main o w c hannel (left) and the concen tration ratio of the trace gas ( log nT(x) nT(0) ) (righ t) when 10 −5 ≤ αF ≤ 10 −4 . Then the mem brane is 10nm in p ore diameter, 6µm in thic kness, and 0.5 in a ratio of gas n um b er densit y of the pumping c ham b er and main o w c hannel. is slo w er than 5cm/s. Ho w ev er ac hieving a faster thermal mean sp eed is not p ossible, b ecause the helium is considered as the carrier gas, and the thermal mean sp eed of helium is the highest at ro om temp erature. Hence the other co ecien ts m ust b e c hanged to create fa v orable conditions. Finally the ratio of gas n um b er densit y of the pumping c ham b er and main o w c hannel ma y b e simply related to the pressure dierence b et w een t w o reserv oirs according to equation (2.1.9). In this case, the ratio for the carrier gas and trace gas are the same, = C = T , and the results, = 0.5, are already sho wn in Figures 3.1.1 and 3.1.2. Otherwise the ratio for trace gas ma y b e smaller than that of the carrier gas, C > T , when the ratio is considered as a distribution function of gas n um b er densit y . Then the concen tration ratio of the trace gas is usually smaller than the rst case at the end of the main o w c hannel. In other w ords, when the ratio, T C , approac hes 1, the concen tration ratio of the trace gas is highest, while concen tration ratio of the trace gas is signican tly decreased when T C go es to 0. The p ore diameter of nanotub e is larger than the diameter of the carrier gas, and smaller than the diameter of trace gas. The smallest p ore diameter of the mem brane is around d m = 0.5nm for increasing the trace gas concen tration. Ho w ev er, most diameters of nanotub e mem branes rep orted and commercialized is larger than d m = 1nm. Therefore the bac ko w rate from the pumping 100 c ham b ers to the main o w c hannel m ust b e considered and ma y b e con trolled b y pressure dierences b et w een the pumping c ham b ers (lo w pressure) and the main o w c hannel (atmospheric pressure). These results oer to fabricate a protot yp e, but the p ossibilities for a suitable t yp e of miniaturized preconcen trator are still op ened and innite. 3.2 Designs of Experiment 3.2.1 Main o w c hannel F or the main o w c hannel, the en trance width, length, and heigh t of the main o w c hannel is 10cm, 10cm, and 0.5cm, resp ectiv ely . In order to increase the concen tration ratio of trace gas, a thinner main o w c hannel is desired. The gas o w sp eed is 5cm/s, and the carrier gas is helium. The separation mem brane used to design the main o w c hannel is a p olycarb onate mem brane that has 30nm in a v erage p ore diameter, 6×10 8 in p ore densit y , and 6µm in thic kness. Th us the p orosit y is ab out 4.2×10 −3 and the transmission probabilit y is ab out 0.0066. The theoretical pressure dierence b et w een the pumping c ham b er and main o w c hannel is 0.5. These are based on prop erties of an ideal mem brane and optimizing for the largest concen tration ratio of trace gas and the exit size of the main o w c hannel is 0.3mm. Figure 3.2.1 sho ws the ideal main o w c hannel made b y alumin um. The main o w c hannel has a large en trance, w(0) = 10cm, and it is dicult to supply a constan t inlet gas o w sp eed across the en tire area during the exp erimen ts. The gas o w sp eed con trol area uses m ultiple barriers to create constan t inlet gas o w. Figure 3.2.2 sho ws the sim ulations of gas o w sp eed inside the main o w c hannel b y COMSOL m ultiph ysics. T w o dieren t gas o ws, helium and air, w ere considered to compare the distribution of gas o w sp eed in the main o w c hannel. When the gas o w is laminar, the inlet pressure of gas o w is 767Torr and outlet pressure of gas o w is 760Torr , based on exp erimen tal data. When the inlet gas is helium, the maxim um gas o w v elo cit y is around 20m/s at the end of the main o w c hannel. Ho w ev er the maxim um gas o w sp eed is around 11.7m/s at the en trance of the gas o w sp eed con trol area, when the inlet gas is air. And the maxim um gas o w sp eed of helium is larger than that of air. The gas o w sp eed in the main o w c hannel is slo w er than 8m/s for helium and 2m/s for air, and the gas o w sp eed is gen tly increased along the length of the main o w c hannel. A ccording to the these sim ulations, the o w sp eeds are 101 Figure 3.2.1: Main o w c hannel part designed as the rst exp erimen tal protot yp e : the main o w c hannel is made out of the alumin um. The gas o w sp eed con trol area has m ulti-barries to deliv er a same gas o w sp eed to the en trance of main o w c hannel and to protect jet-o ws. still m uc h larger than the desired gas o w sp eed of 5cm/s, b ecause these sim ulations do not consider the diusion eects through separation mem branes. Ho w ev er, these sim ulations sho w that the gas o w sp eed is relativ ely uniform in the main o w c hannel with the gas o w sp eed con trol area. The gas o w sp eed con trol area and m ultiple barriers supply the relativ ely uniform inlet gas o w to the main o w c hannel. 3.2.2 Separation mem branes As men tioned section 3.1 and Chapter 2, the separation mem branes ha v e to satisfy the follo wing requiremen ts : 1) con tain arra ys of nanometer diameter capillaries or ap ertures, 2) ha v e an αF of larger than 2.5×10 −5 and smaller than 7.5×10 −5 , 3) b e strong enough to sustain mo derate pressure dierences, and 4) ha v e relativ ely uniform p ore distributions. The CNT mem branes considered as separation mem branes do not satisfy condition three except the CNT mem brane b y Hind (Hind 2004), and these mem branes curren tly cannot b e man ufactured large enough. Moreo v er, the cost of CNT mem branes still is prohibitiv e. A thin, microp orous p olycarb onate lm material made b y trac k-etc hing tec hnique from GE W ater & Pro cess T ec hnologies (GE W ater & Pro cess T ec hnologies) can b e used as the separation mem brane. 102 Figure 3.2.2: Inlet gas o w sp eeds with t w o dieren t gases, helium (a) and air (b, c) : The inlet pressure of gas o w is 767Torr and the outlet pressure of gas o w is 760Torr at ro om temp erature. (a) When the inlet gas is helium, the maxim um gas o w sp eed at the exit of the main o w c hannel is ab out 20m/s. (b) When the inlet gas is air, the maxim um gas o w sp eed at the en trance of the gas o w con trol area is ab out 11.7m/s. (c) The gas o w sp eed of the en trance of the main o w c hannel sho w the reducing gas o w sp eed un til 1.757m/s. 103 P ore size P ore densit y Nominal thic kness T ypical o w rates of Air F (nm) (pores=cm 2 ) (m) (L=min·cm 2 ) (a) (b) 10 6×10 8 6 0:0075 1:0423×10 −6 30 6×10 8 6 0:075 2:7928×10 −5 50 6×10 8 6 0:37 1:2826×10 −4 80 6×10 8 6 0:75 0:0519 T able 3.1: P erformance c haracteristics of p olycarb onate mem branes. (a) Inlet o w rates using preltered at 10psid (0.7kg/cm 2 ), and (b) The transmission probabilit y using equation (2.2.8). The absolute p ore size and densit y pro vide o w con trol for uids mo ving through the mem brane and can capture 100 p ercen t of particles larger than the p ore size. A tensile strength of 207 bar (> 3000 psi) main tains p ore size and densit y and the material do es not stretc h. Hydrophilic or h ydrophobic a v ailabilit y allo ws for a wide range of pro duct applications. The GE p olycarb onate mem brane is pro duced through a t w o step, proprietary man ufacturing pro cess that emplo ys high qualit y standards. The trac k-etc hing pro cess allo ws for increased con trol o v er p ore size and densit y to ensure the ph ysical prop erties of eac h mem brane are precise and uniform. In the rst step, a thin p olycarb onate lm is exp osed to collimated, c harged particles from a n uclear pile. As these particles pass through the p olycarb onate material, they lea v e sensitized trac ks. In the second step, the p olymer trac ks are dissolv ed with an etc hing solution to form cylindrical p ores. V arying the temp erature and strength of the etc hing solution, and the exp osure time, pro duces precisely con trolled p ore sizes. The resulting mem brane is a thin, translucen t and microp orous p olycarb onate lm with a smo oth, at surface. The p olycarb onate mem brane is a v ailable in rolls measuring 1.3 to 50.8cm wide, or sheets, cut discs, capsules and cartridges, with a p ore sizes ranging from 0.01µm to 20µm. And the p ore densit y is from 4×10 4 pores/cm 2 to 6×10 8 pores/cm 2 , and the thic kness is generally from 5µm to 12µm. T able 3.1 sho ws the p erformance c haracteristics of the nanop orous p olycarb onate mem branes and the v alues of αF . The results are similar to the CNT mem branes. Ho w ev er the mem brane that has a p ore diameter of 80nm cannot b e used as the separation mem brane b ecause the αF is so large that it is hard to c hange other factors suc h as pressure dierence, gas o w sp eed etc to obtain an acceptable design. Other nanop orous mem branes are p ossible to use as the separation mem branes of the preconcen trator. Figure 3.2.3 sho ws the scanning electron micrographs ( JSM-6610L V ) images of these mem branes. JSM-6610L V lo w v acuum SEM b y Cen ter for Electron Microscop e and Microanalysis at the Univ er- 104 (a) (b) Figure 3.2.3: P olycarb onate mem branes in scanning electron micrographs (SEM) image from the Cen ter for Electron Microscop e and Microanalysis at the Univ ersit y of Southern California : (a) 10nm (30 ◦ ) and (b) 50nm in p ore diameters. sit y of Southern California w as a p oin t-to-p oin t resolution of 3nm at 30kV in high v acuum mo de. The a v erage p ore diameter of the 50nm p olycarb onate mem brane is ab out 59nm, while the a v er- age p ore diameter of the 10nm p olycarb onate mem brane is ab out 27nm. The GE p olycarb onate mem branes can ha v e larger p ore diameters than the describ ed p ore diameter, and the distribution of p ores do es not app ear uniform according to these images. Nev ertheless, the GE p olycarb onate mem branes are considered as the separation mem branes of the preconcen trator b ecause of the arra ys of capillaries, wide area, and lo w cost. 3.2.3 Pumping c ham b ers A ccording to Mun tz et al. (Mun tz et al. 2004) and Figure 2.4.1, the suggested pumping c ham b ers ha v e constan t widths, w(0), and v arying heigh ts, h p (x), along the length, L, of the main o w c hannel, b ecause it w as p ossible to main tain an appro ximately constan t n um b er densit y of carrier gas p er unit v olume and a constan t gas o w sp eed in the main o w c hannel. In addition, the unit v olume along the length of the main o w c hannel migh t b e constan t, when the unit v olume w as a sum of v olumes of pumping c ham b ers and main o w c hannel. The heigh t of the pumping c ham b er w as appro ximately larger than the heigh t of the main o w c hannel dep ending on the thic kness of separation mem branes. In other w ords, the heigh t of the pumping c ham b er could b e describ ed as a function of a thic kness of mem brane and a heigh t of the main o w c hannel. The pumps w ere lo cated at the exit of the main o w c hannel, x = L, and connected with the largest heigh t of the pumping c ham b er to driv e a force to w ard a direction of gas o w. Ho w ev er, it remains dicult to determine the relationship 105 b et w een the v arying heigh t and thic kness of mem brane and the relationship is not considered in this researc h since the preconcen trator protot yp e is a macroscale device, and the thic kness of mem brane is smaller than the heigh t of the pumping c ham b er, h c ≪h p . In this study , the pumping c ham b ers ha v e a dieren t mo del than the pumping c ham b ers suggested b y Mun tz et al. (Mun tz et al. 2004). Figure 3.2.4 (a) sho ws the pumping c ham b er and a pressure con trol area to main tain uniform pressure along the o v erall surface of the pumping c ham b er. The pumping c ham b er consists of t w o parts, the solid-b o dy (1) and the hole-b o dy (2). The solid-b o dy has a same shap e and a larger heigh t, h p = 1cm, of the main o w c hannel. The hole-b o dy has a constan t hole diameter (d h = 0.3cm), a dieren t n um b er of holes at ev ery unit line, and an in terv al b et w een holes and hold-b o dy thic kness of 5mm. The total v olume is exp onen tially decreased along thex-axis as it is also go v erned b y the equation of shap e of the main o w c hannel. The main purp ose of the pumping c ham b er in the exp erimen t researc h is to deliv er a constan t pressure to the main o w c hannel and a constan t force to the separation mem branes. In order to maximize the eect of this preconcen trator, it is imp ortan t to create a larger pressure dierence b et w een the main o w c hannel and pumping c ham b ers and to main tain the pressure ratio for ecien t separation. Moreo v er a pump can b e applied in con tin uous gas separation tec hnologies for the miniaturized preconcen trator. As describ ed in Chapter 2, man y pumps suc h as displacemen t pumps and dynamic pumps are p ossible to use as microscale pumps. F or the primary test, a minimized pump is not a main issue, but it is imp ortan t to consider a oil-less v acuum pump. The oil-less v acuum pump (Marathon electronics, 1VAF−18−M100X ) is op erated in an alternating curren t. A ccording to the Figure 3.2.5, the maxim um pumping sp eed is ab out 1.8cfm (cubic feet p er min ute), and the a v erage v olume o w rate of the pump v aries dep ending on eac h of the gases remaining in the c ham b er b ecause momen tum transfer and en trapmen t pumps are more eectiv e on some gases than others. It is p ossible to main tain ab out a pressure of 60Torr , and the pumping rate of xenon gas is lo w er than pumping rate of argon gas. 3.2.4 Exp erimen tal setup Figure 3.2.6 sho ws a sc hemetic of the exp erimen tal setup and the protot yp e of the new preconcen- trator. In this exp erimen t, four dieren t gases are considered: helium as the ligh test noble gas, nitrogen as the most similar gas with air, and argon as another noble gas are used as the carrier 106 Figure 3.2.4: Sc hemetic of pumping c ham b er and pressure con trol area and the total v olume. (a) This illustration sho ws an en tire view (left) and a side view (righ t) of one pumping c ham b er used, and (b) the total v olume (= v olume of main o w c hannel + v olume of pumping c ham b er) exp onen tially decreases along the length of the main o w c hannel. Figure 3.2.5: P erformance of pump, 60Hz (Marathon electronics, 1VAF −18−M100X ) 107 Figure 3.2.6: Sk etc h of the exp erimen tal setup and a protot yp e of preconcen trator gases, and xenon is used as the trace gas. In this researc h, the ratio b et w een trace and carrier molecular w eigh ts is an imp ortan t k ey to increase the concen tration of trace gas. The most to xic and dangerous gases are hea vier molecular w eigh ts than 140U , and the molecular w eigh t of air is 28.94U , where U is the unit of atomic w eigh t. Therefore the molecular w eigh t of trace gas is gener- ally from 5 times to 7 times larger than carrier gas. A ccording to this consideration, mixture gases can b e helium-nitrogen ( mN 2 mHe = 7), nitrogen-xenon ( mXe mN 2 = 4.7), and argon-xenon ( mXe mAr = 3.3). The carrier gas concen tration is 10 times or 20 times larger than the trace gas concen tration in the mix- ture gas. In general the trace gas concen trations in the sample gas are larger than the concen tration considered b y Mun tz et al. (Mun tz et al. 2004). The inlet gas o w sp eed of sampled gases can b e con trolled smaller than 2.5cm/s. F or the primary exp erimen ts, the en trance width, exit width, length, and heigh t of the main o w c hannel are 0.3cm, 10cm, 10cm, and 0.5cm, resp ectiv ely . The en trance and exit also connect with mass o w meters that read the mass o w rates and pressures of inlet and outlet gas o w. Finally the abundance of eac h gas sp ecies in the sampled gas is read from a gas c hromatograph/mass sp ectrograph (Agilen t 5975C ) with a reference gas of helium, and the concen tration of inlet and outlet gas of h te preconcen trator are compared. References GE w ater & Pro cess T ec hnologies, GE P olycarb onate T rac k Etc h (PCTE) Mem branes, http://www.gewater. c om/p df/F act%20She ets_Cust/A meric as/English/FS1066EN.p df. 108 Hinds , B. J., Aligned m ultiw alled carb on nanotub e mem branes, Scienc e , 303, (2004) : 62 - 65. Holt, K., F ast mass transp ort through sub-2-nanometer carb on nanotub es. Scienc e , 312, (2006) : 1034 - 1037. Kim, S., J. R. Jinsc hek, H. Chen, D. S. Sholl, and E. Marand, Scalable fabrication of carb on nanotub e/p olymer nano comp osite mem branes for high ux gas transp ort, Nano L etters , 7 (2007) : 2806 - 2811. Mi, W., Y.S. Lin, and Y. Li , V ertically aligned carb on nanotub e mem branes on macrop orous alumina supp orts, Journal of Membr ane Scienc e , 304 (2007) : 1 - 7. Mun tz, E. P ., M. Y oung, and Y.-L. Han, Con tin uous lo w p o w er pre-concen trations for distributed microscale trace gas analysis, IMECE 2004 (2004) : 60874. Mun tz, E. P ., Y.-L. Han, and M. Y oung, Pre-concen trator for trace gas analysis, T ec hnical Rep ort, U.S. Patent US2008/0178658 (2008). 109 Chapter 4 Analysis of the Preconcentrator’s Performance Exp erimen ts are required to v alidate the a v ailable n umerical data, suc h as the concen tration and gas separation of the newly prop osed con tin uous preconcen tration tec hnology , and the assumptions in Chapter 3. Exp erimen ts in this w ork obtained a base-line comparison of the existing n umerical predictions for shap es and sizes pro vided b y the protot yp e preconcen trator. F ollo wing the establish- men t of the soundness of the basic predictions, exp erimen ts in v olving argon gas, instead of helium gas, mixed with smaller concen tration of xenon gas, w ere undertak en to compare with a v ailable n u- merical predictions. The mixtures had a v ariet y of argon and xenon gases in dieren t prop ortions, and t w o used p olycarb onate mem branes ha v e a v erage diameters of 10nm and 50nm, resp ectiv ely , and ha v e the same thic kness and p ore densit y . Subsequen tly , the concen tration w as calculated b y pressure ratios b et w een the main o w c hannel and pumping c ham b ers, and b y mass o w rates at exit of the main o w c hannel. 110 T yp e of Mem brane Mass o w rate ( sccm) He N 2 Ar Xe Without pumping eect 56 (60) 62.3 (60) 49.1 (60) 48 (60) 10nm With pumping eect 15.04 (16.10) 20.73 (19.88) 13.39 (16.35) 14.41 (17.94) Pumping rate 37.28 (39.99) 39.93 (38.52) 29.57 (37.90) 29.24 (35.63) 50nm With pumping eect 19.19 (20.44) 26.02 (24.95) 16.38 (19.92) 16.39 (20.60) Pumping rate 34.63 (37.04) 33.55 (32.34) 27.21 (34.81) 25.83 (30.85) No mem brane With pumping eect 21.56 (23.09) 25.31 (24.29) 17.00 (20.67) 13.94 (17.51) (d H = 3mm) Pumping rate 32.36 (34.66) 32.58 (31.42) 25.08 (32.22) 26.02 (31.07) T able 4.1: Normalized a v erage mass o w rates ab out four single gases ( He, N 2 , Ar , and Xe) with mem branes (d c = 10nm and d c = 50nm) and without mem branes. Eac h n um b er in the paren thesis is a gas o w rate of air. The mass o w rate w ere measured at the exit of the main o w c hannel. ’Without pumping eect’ are mass o w rates measured with the pump o, and ’With pumping eect’ is mass o w rates recorded with the pump on. 4.1 Experimental Results 4.1.1 Mass o w rate and gas o w sp eed of single gases In order to compare the exp erimen tal data with the n umerical data of the trace gas concen tration, the pressure ratio b et w een the main o w c hannel and pumping c ham b ers and gas o w sp eed inside the main o w c hannel m ust b e recorded as a function of the size and shap e of the main o w c hannel. Moreo v er, it is imp ortan t to determine an appropriate mem brane that can maximize p erformance of the preconcen trator con tin uously op erated. Characterizing a concen tration ratio of gas m ust b e tested individually with single gases. Exp erimen ts with four single gases, helium, nitrogen, argon, and xenon, w ere considered previous to test with mixed gases, b ecause eac h gas could pro vide basic information under the same exp erimen tal conditions for mixed gases. Separation mem branes used in these exp erimen ts w ere GE h ydrophobic p olycarb onate mem branes of 10nm and 50nm in the a v erage p ore diameters in tro duced in Chapter 3. In addition, a con trol case remo v ed mem branes from the system in order to kno w the p erformance of the separation mem branes. As men tioned in Chapter 3, the pumping rate can b e dieren t for eac h of the test gases, and the a v erage v olume o w rate of the pump v aries dep ending on the c hemical comp osition of the gases remaining in the c ham b er. F or all those cases, the pumping rate of xenon gas is the smallest , and the pumping rate of helium gas is relativ ely large as sho wn in T able 4.1 and Figure 4.1.1. The pumping rate is related to the net ux through an ideal mem brane pro vided b y Hinds (Hinds 2004) as sho wn in Chapter 1. The next ux generally decreases as an increase of molecular w eigh ts. A ccording to the calculation with exp erimen tal data suc h as pressure dierences and parameters of mem branes, 111 the lighest molecule, helium, excap es through mem branes more than the hea vier molecule, xenon. No mem brane is considered as a case where a gas passes through a hole-b o dy of a pumping c ham b er, describ ed in Figure 3.2.4. An inlet mass o w rate of air is set at the same v alue ( 60sccm) for eac h gas, but eac h gas actually presen ts a dieren t inlet mass o w rate for a same inlet gas o w rate of air. Digital mass o w meters (OMEGA M3704) can read gas o w rates of individual gases in sccm (standard cubic cen timeter). Therefore the gas o w rates of air should b e recorded together to compare eac h of mass o w rates. In general, the oil-less v acuum pump (Marathon electronics, 1VAF−18−M100X ) used in this researc h constan tly op erates to the helium, nitrogen, and argon gases, but it do es not regularly w ork for the xenon gas. The pumping rate of xenon gas v aries roughly and is hard to predict accurately . Outlet gas o w rates measured at the exit of the main o w c hannel, as sho wn in T able 4.1 and Figure 4.1.2, are dieren t according to the mem branes and gases used. ’ Without pumping ee ct ’ w ere mass o w rates measured at the exit of the main o w c hannel with the pump o, and the ’ With pumping ee ct ’ w ere mass o w rates recorded at the same p osition with the pump on. A ccording to T able 4.1 and Figure 4.1.2.(a), The gas o w of nitrogen gas with the pump on is relativ ely large compared of other gases. The a v erage pumping rates of gases are generally the lo w est when mem branes w ere not attac hed, and the highest for the 10nm mem brane ev en though one of xenon gas sho ws a somewhat dieren t result. The mass o w rates of eac h gas with pumping eect generally increase with larger p ore diameter of the mem brane except the xenon gas o w. F or the single gas o w, the mass o w rates at the exit of the main o w c hannel increases with an increasing p ore diameter with the pump on when the gas o w rates of all gases w ere constan t with the pump o. In other w ords, the pumping rates of eac h gas decrease with larger p ore diameter. Therefore it can b e assumed that a pressure ratio b et w een the main o w c hannel and pumping c ham b er is larger when the 10nm mem branes are attac hed eac h side of the main o w c hannel. Figure 4.1.2.(b) sho ws gas o w sp eeds at the exit of the main o w c hannel. The gas o w sp eed obtained b y Equation (1.3.15) is expressed as u 0 = _ M ρA , (4.1.1) where ρ is the mass densit y , A is the cross sectional area of the exit, and _ M is the mass o w rate. The exit of the main o w c hannel is a rectangle with a exit width of 3mm and a heigh t of 5mm as sho wn in Figure 4.1.3. The rectangular exit gradually c hanges to a circular cross section connect 112 (a) (b) Figure 4.1.1: Net ux (a) and normalized a v erage pressure dierence (b) for four single gases ( He, N 2 , Ar , and Xe) with mem branes (d c = 10nm and d c = 50nm) and without mem branes in the preconcen trator. The inlet gas o w rate for eac h gas is measured as the same amoun t in air (60sccm). The net ux is obtained from Equation 1.4.12, and the n um b ers in paren theses are a v erage pressure dierences obtained b y exp erimen t. 113 (a) (b) Figure 4.1.2: Normalized a v erage mass o w rates (a) and gas o w sp eeds (b) for four single gases (He, N 2 , Ar , and Xe) with mem branes (d c = 10nm and d c = 50nm) and without mem branes in the preconcen trator. The inlet gas o w rate for eac h gas is measured as the same amoun t in air (60sccm). 114 Figure 4.1.3: Illustration of exit of the main o w c hannel. The shap e of the exit is c hanged from a rectangle to circle in order to connect to a mass o w meter and to main tain a constan t gas o w for the o v erall cross section. to a detecting system or mass o w meter. These are also a similar cross sectional area b et w een the rectangular exit and circular exit, and the diameter of circular exit is ab out D = 4.37mm. An individual gas o w sp eed at the circular exit w as obtained with dieren t gases and mem branes, and related to the mass o w rate. The gas o w sp eeds for all gases w ere smaller than the designed gas o w sp eed of 5cm/s used to create the protot yp e of preconcen trator, and the range of gas o w sp eed is b et w een 1.418cm/s and 2.311cm/s. The agron gas o w sp eeds are ab out 1.5cm/s for the 10nm mem brane and 1.82cm/s for the 50nm mem brane, and w as assumed as 1.59cm/s for the main o w c hannel with the 30nm mem brane. Using this correlation, the gas o w sp eed can b e predicted b y the mass o w rate under the same conditions, and then times required are ab out 4s to 7s to obtain the sampled gas at the exit of the main o w c hannel. Pressure ratio b et w een the main o w c hannel and pumping c ham b ers can b e c hanged to increase the trace gas concen tration of the preconcen trator as suggested b y Mun tz et al. (Mun tz et al. 2008). In the theoretical mo dels for the shap e equation of the main o w c hannel and concen tration ratio of the trace gas, the gas n um b er densit y of the main o w c hannel is generally assumed to b e a few times larger than that inside the pumping c ham b ers. Ho w ev er it w as hard to con trol the ratio of a gas n um b er densit y in the pumping c ham b er to initial gas n um b er densit y exp erimen tally , and to 115 measure the gas n um b er densit y in the pumping c ham b er w as dicult in the presen t exp erimen t. Therefore the ratio of gas n um b er densities is c hanged b y pressure ratios that can b e measured easily , as in tro duced in Chapter 2. The pressure dierences b et w een the main o w c hannel and pumping c hamp ers in the test are sho wn in T able 4.2. The pressure of the preconcen trator w ere measured at four dieren t p ositions; t w o pumping c ham b ers P pc , the en trance of the main o w c hannel P in (pressure of initial gas o w), and the exit of the main o w c hannel P out (pressure of outlet gas o w). T ec hnically , it is hard to measure an accurate pressure at the en trance of the main o w c hannel so pressure of the initial gas o w w as measured at the en trance of the gas o w sp eed con trol area as sho wn Figure 4.1.3. The pressure dierences b et w een this p osition and sev eral p ositions in the main o w c hannel w ere also recorded sim ultaneously comparing these results, the pressure dierence w as almost zero. Therefore the pressure of initial gas o w can b e considered as the v alue measured at the en trance of the gas o w sp eed con trol area. As sho wn in T able 4.2, the a v erage pressure dieren tials, P a , b et w een the main o w c hannel and pumping c ham b ers are lo w er than the v alue suggested b y the theoretical mo dels for all cases. P a increases with an increase of the molecular w eigh t for the 10nm and 50nm mem branes, but the tendency is not sho wn when the mem branes are remo v ed, and the v acuum pump is turned on. The pumping eect app eares with the mem branes ev en though the pressure dierence is not large enough to obtain a large gas concen tration, and the pumping eect for a giv en pressure dierence, P a , is not clearly related to the t yp e of mem brane. The pressure dierence, P b , b et w een the en trance and exit of the main o w c hannel is related to the inlet and outlet mass o w rate. The inlet gas o w rate of the individual gases w ere similar, th us the P b without pumping eect is also similar as ab out 6Torr . The pressure dierence P b is around 2Torr when the pump op erates, and is close to P a with the 10nm and 50nm mem branes. The P b w as considered main taining the constan t initial gas o ws during the exp erimen ts. Therefore the relativ ely similar pressures for all tho ese cases mean the similar gas o w rates for all the cases. The last pressure dierence, P c , b et w een atmospheric pressure and the outlet pressure is a reference pressure to conrm the outlet gas o w, and serv es as a data for the o v erall gas o w rate. 116 T yp e of Mem brane Pressure Pa = P mfc Ppc P b =jP in Poutj Pc =jPatmPoutj (Torr ) He N 2 Ar Xe He N 2 Ar Xe He N 2 Ar Xe 10nm Without pumping eect 0.10 0.01 0.13 0.81 6.29 6.07 6.14 6.09 3.10 3.79 3.62 3.97 With pumping eect 1.05 1.57 1.96 2.43 1.96 2.23 1.62 2.10 0.43 0.95 0.96 0.78 50nm Without pumping eect 0.17 0.02 0.14 1.28 6.36 6.01 6.23 6.12 3.02 4.05 3.62 4.05 With pumping eect 0.75 1.57 1.69 3.72 2.14 2.74 2.00 2.45 0.95 1.38 0.86 0.86 No mem brane Without pumping eect 0.02 0.05 0.05 0.10 5.91 6.15 5.74 5.64 3.62 3.88 4.14 4.14 (d H = 3mm) With pumping eect 0.08 0.22 0.06 0.06 2.20 2.39 1.64 1.92 1.29 1.55 1.55 0.78 T able 4.2: A v erage pressure dierences of four single gas o ws ( He, N 2 , Ar , and Xe) with t yp e of mem branes (d c = 10nm and d c = 50nm) and without mem branes. P a is the pressure dierence b et w een the main o w c hannel and pumping c ham b ers, P b is the pressure dierence b et w een the en trance and exit of the main o w c hannel, and P c is the pressure dierence b et w een atmospheric pressure and exit of the main o w c hannel. 117 Figure 4.1.4: Illustration of a mass o w rate of single gas through the main o w c hannel. A size of eac h segmen t is 5mm in x-axis. Eac h segmen t has dieren t n um b er of holes, d H = 3mm as men tioned in Chapter 3. Red arro ws are gas o ws in the main o w c hannel and blue arro ws are gas o ws escap ed through the holes of the hole-b o dy of the pumping c ham b er. The mem branes are attac hed to the upp er and lo w er surface of the main o w c hannel. 4.1.2 Prediction of ph ysical p erformance of single gases The mass o w rate at the exit of the main o w c hannel ( g/s) b y equation (1.3.15) can b e written as _ M = _ m fex =ρu 0 w exi h f , (4.1.2) when the mem branes are not attac hed at the main o w c hannel. Here u 0 is an gas o w sp eed, h f is the heigh t and w ex is the exit width of the main o w c hannel. u 0 and h f are constan t, while w(x) v aries along the length of the main o w c hannel from w(0) to w ex . Otherwise, the mass o w rate of gas lost through holes of the hole-b o dy is similarly expressed as the equation (4.2.2); _ m Hi =v H ρπ ( d H 2 ) 2 N Hi (i = 1, ··· , 20) (4.1.3) where d H is the diameter of a hole, N Hi is the n um b er of holes p er segmen t, v H is the escap ed gas o w sp eed through eac h hole, and i is the index of eac h segmen t. The escap ed gas o w sp eed is assumed to b e constan t for all holes in this mo del. F rom the previous section, the mass o w rate _ m and gas o w sp eed u 0 at the exit of the main o w c hannel are kno wn. If these are no gas leak es in the system, the mass o w rate _ m fex is the same as the dierence b et w een the mass o w rate _ m f1 and 2 _ m H1 whic h is mass o w rates escap ed through 118 the upp er and lo w er directions at the rst segmen t resp ectiv ely . It is again expressed as 2 _ m Hi = _ m fi − _ m fi−1 (i = 1, ··· , 20), (4.1.4) when the n um b er of holes N H1 is sho wn in Figure 4.1.4. A ccording to the equations (4.1.2), (4.1.3), and (4.1.4), the escap ed gas o w sp eed v H (m/s) through eac h hole can b e expressed as v Hi = 2 _ m fex N Hi ρπd 2 H w i −w i−1 w ex (i = 1, ··· , 20). (4.1.5) Figure 4.1.5 sho ws the data calculated b y these equations (4.1.4) and (4.1.5). The escap ed gas o w sp eed from a hole at eac h segmen t is not constan t for all four gases, b ecause the equation is related to the function of the width that is exp onen tially decreased along the length of the main o w c hannel. Then a v erage escap ed gas o w sp eeds p er eac h gas are 0.626cm/s for helium, 0.733cm/s for nitrogen, 0.493cm/s for argon, and 0.404cm/s for xenon. The mass o w rate p er segmen t for all gases, calculated with the a v erage sp eeds v H , is increased from the exit to en trance of the main o w c hannel. Then initial gas o w rate can b e obtained b y this calculation, but the amoun ts for all gases w ere appro ximately 10 times larger than the exp erimen tal initial gas o w rates. Ho w ev er the gas o w rates did not follo w the net ux prop osed b y Hinds in 2004 (Hinds 2004) without the mem brane, so the exp erimen tal data ma y not compare with the n umerical results. One assumptions can b e made from these result. It is p ossible to impro v e the hold-b o dy of the pumping c ham b er in order to obtain a constan t escap ed gas o w sp eed. Therefore the hole diameter p er segmen t is no longer constan t. When the separation mem branes are attac hed the upp er and lo w er surfaces of the main o w c hannel, the escap ed gas o w sp eeds are also c hanged. In this case, area A should include a factor of p orosit y . The p orosities of p olycarb onate mem brane are ab out 4.7×10 −4 for a 10nm mem brane and 0.01178 for the 50nm mem brane, resp ectiv ely . Then, a v erage sp eeds for eac h gas are 13.319m/s for helium, 15.599m/s for nitrogen, 10.493m/s for argon, and 8.598m/s for xenon in the case of the 10nm mem brane, and 0.533m/s for helium, 0.624m/s for nitrogen, 0.420m/s for argon, and 0.344m/s for xenon in the case of the 50nm mem brane. The escap ed gas o w sp eeds with the separation mem branes are m uc h larger than the case where the mem branes w ere remo v ed. Under the same conditions, it can b e predicted that the separation eect is enhanced b ecause of the increase of 119 (a) (b) Figure 4.1.5: A v erage escap ed gas o w sp eed (a) and net mass o w rate (b) p er segmen t at a single hole for four single gases (He, N 2 , Ar , and Xe) when the mem branes are remo v ed from the system. The length of eac h segmen t is 5mm, and these equations and calculation data are describ ed in App endix T.2. Num b ers of holes p er eac h segmen t are mark ed ab o v e the nitrogen plot in (a) ( triangle). The length of the main o w c hannel is the length from exit to the en trance. 120 the escap ed gas o w sp eed, when the mem brane has a smaller p ore diam ter or p orosit y and the molecular mass ratio of a mixed gas is larger. Ho w ev er these n umerical predictions do not include the transmission probabilit y of mem brane. The a v erage sp eeds and mass o w rates are o v er the assuming v alues, so it ma y need to impro v e and dev elop the new theoretical mo dels related to these. 4.1.3 Mass o w rate and gas o w sp eed of Mixed gases The carrier gas considered when creating the protot yp e preconcen trator w as helium b ecause it is the lighest and smallest noble gas. Ho w ev er the gas c hromatograph/mass sp ectrograph (Agilen t 5975C ), whic h w as used to measure the abundance of eac h gas sp ecies in a mixed gas, uses helium as a reference gas, so other noble gases w ere considered exp erimen tally as the carrier gas. In general, nitrogen gas w as exp ected to b e the carrier gas b ecause nitrogen is the primary comp onen t ( 78%) of air. Ho w ev er it w as dicult to measure an exp erimen tal abundance v ariation of nitrogen, b ecause this system in teracted with the surroundings. Therefore the ratio of nitrogen and o xygen in sampled gases (N 2 : O 2 = 3.73 : 1) w as a measure to insp ect the exp erimen tal condition instead of using nitrogen as the carrier gas. In other w ords, exp erimen tal data w as ignored in n umerical analysis if the comp onen t ratio of nitrogen and o xygen in the sampled gas w ere extremely dieren t. Finally another noble gas, argon w as used as the carrier gas, and xenon w as considered as a trace gas. The atomic w eigh t of xenon is appro ximately 3.29 times larger than that of argon. Also, the concen tration of argon gas in the gas mixture c ham b er, as sho wn in Figure 3.2.6, w as roughly 10 times or 20 times larger than that of xenon gas. As with the exp erimen ts for single gases, the exp erimen t w as run for mixed gases with 10nm and 50nm p olycorb onate mem branes and no mem brane. The digital mass o w meter (OMEGA M3704) can only read the gas o w rates of single gases, and a mixture ratio of trace and carrier gases in the sampled gas cannot predict exactly . Th us the mass o w rates of the mixed gas w ere recorded as the mass o w rate of air or argon and xenon gas. Therefore the follo wing results n umerically ha v e relativ e meanings. The exp erimen tal results sho wn in T able 4.2 and T able 4.3 sho w a simlilar tendency of the pressure dierences and mass o w rates. Con tin uous initial gas o ws supplied to the preconcen trator in all cases w ere similar, but the mass o w rates at the exit of the main o w c hannel v aried as m uc h as 16sccm, when the pump w as not op erated. F or the cases with mem branes, gas molecules escap e more from the 50nm mem brane b ecause of the larger p orosit y . It w as exp ected that the mass o w rate in the case with mem branes remo v ed w as the smallest, but this w as not seen in exp erimen ts. Lik e 121 T yp e of Mem brane Mass o w rate Pressure Pa P b Pc [In air] (sccm) (Torr ) P mfc Ppc jP in Poutj jPatmPoutj 10nm 62.21 Without pumping eect 0.25 6.87 2.31 17.54 With pumping eect 2.89 2.02 0.68 50nm 46.36 Without pumping eect 0.12 5.02 2.4 9.79 With pumping eect 0.82 1.42 0.2 No mem brane 50.88 Without pumping eect 0.41 4.91 2.76 (d H = 3mm) 12.35 With pumping eect 0.35 1.21 0.03 T able 4.3: A v erage pressure dierences and mass o w rates for mixed gases ( Ar andXe) with t yp e of mem branes (d c = 10nm and d c = 50nm) and without mem branes. Eac h n um b er in the paren thesis is a p ercen t of gas o w rate with pumping eect. P a is the pressure dierence b et w een the main o w c hannel and pumping c ham b ers, P b is the pressure dierence b et w een the en trance and exit of the main o w c hannel, and P c is the pressure dierence b et w een atmospheric pressure and exit of the main o w c hannel. Here ’No pump’ means pressures measured when a mixed gas o ws without pumping eect, and ’With pump’ means pressures measured when a mixed gas o ws with pumping eect. The mass o w rates w ere recorded as mass o w rates of air. the exp erimen ts of single gas o ws, the pumping rate of mixed gases is decreased with an increase of p oro cit y . The a v erage pumping rates with mixed gases w ere 40.02sccm for the 10nm mem brane, 31.52sccm for the 50nm mem brane, and 30.34sccm for no mem brane. As sho wn in T able 4.3, the pressure dierence P a b et w een the main o w c hannel and pumping c ham b er and pressure dierence P b b et w een the en trance and exit of the main o w c hannel with pumping eect are somewhat larger than that without pumping eect. Also P a and P b of the 10nm mem brane are larger. Ho w ev er the pressure dierence P a is still not large enough to apply to the n umerical mo del suggested b y Mun tz et al. (Mun tz et al. 2008). Figure 4.1.6 and Figure 4.1.7 sho w v ariation in the abundance of argon and xenon gases with the initial mixing ratio of t w o gases in the gas mixture c ham b er for the 10nm and 50nm mem branes with the pump on and pump o. With regard to the exp erimen ts of single and mixed gases, the pressure dierences are to o small, so it can b e asssumed a question ab out that the pumping eect is needed to increase the gas concen tration. In order to conrm the pumping eect, all tests w ere considered for b oth cases, with the pump on and o. F or the 10nm mem brane, the concen tratins w ere decreased in the most cases, but the abundance distribution o v erall mo v es up with the pumping eect. F or the 50nm mem brane, it is more clear. The abundance distribution mo v es up and increases of xenon gas concen tration are sho wn more with the pump on. Then the gas concen trations increase roughly 1 to 20 p ercen t, but is a few cases. The xenon gas concen tration (trace gas) decrease around 10 p ercen t from the initial sampled gases and less than the argon gas concen tration when 122 Figure 4.1.6: V ariation in the abundance of mixed gases for the 10nm mem brane (d c = 10nm) (a) with a pump o and (b) a pump on with initial mixing ratio of t w o gases ( Ar and Xe). Ar is the carrier gas, and Xe is the trace gas. Their c haracteristics of eac h gas are describ ed in App endix T.1. 123 the pump op erates. This tendency is more clear for the 10nm mem brane, but do es not follo w for the 50nm mem brane. Nev erthless, these exp erimen tal results sho w the p ossibilit y to increase the gas concen tation more with the pump on for the new approac h to the preconcen trator ev en though the pressure dierences w ere not large enough as suggested b y the theoretical mo del, and the case decresed the gas concen tration is more than increases of gas concen tration. Figure 4.1.8 sho ws v ariation in the abundance with a few cases. The abundance, that is dieren tly used in Figure 4.1.6 and Figure 4.1.7, is describ ed as Abundance(%)| Exit = C Ar CXe Initial − C Ar CXe Exit C Ar CXe Initial ×100(%), (Exit =on, off). (4.1.6) Here CAr CXe Initial ( Ar Xe Initial ) is the initial mixing ratio of argon and xenon gases in the gas mixture tank, and CAr C Xe Exit ( Ar Xe Exit ) is the mixing ratio of argon and xenon gases at the exit of the main o w c hannel. And also Abundance| On is the v ariation of a mixing ratio of argon and xenon gases with the pump on (with pumping eect), and Abundance| Off is the v ariation of a mixing ratio of argon and xenon gases with the pump o (without pumping eect). x-axis is related to a dierence b et w een Abundance| On and Abundance| Off , and y -axis is for an increase or decrease of CAr CXe Exit . The data in Figure 4.1.8 is ordered as the magnitude of v ariation in the abundances. Most exp erimen tal data in (I) and (II) sho w that CAr CXe Exit are smaller than CAr CXe Initial , and only a few data p oin ts in (III) and (IV) sho w that C Ar CXe Exit are larger than C Ar CXe Initial for the b oth mem branes. Exp erimen tal data in (I) and (III) are that Abundance| On is smaller than Abundance| Off , and the data in (II) and (IV) are that Abundance| On is larger than Abundance| Off . A ccording to the theoretical mo del prop osed b y Mun tz et al. (Mun tz et al. 2008), the concen tration ratio of trace gas at the exit of the main o w c hannel should increase, but exp erimen tal data sho w dieren t result. In general, the concen trations of trace and carrier gases decrease for b oth mem branes when the sampled gas passes through the main o w c hannel. The concen tration of t w o gases with pumping eect decreases less than no pumping eect except p oin ts mark ed in section (II) for b oth mem branes. In order to compare the theoretical mo del and exp erimen tal data for the concen tration ratio of the trace gas, Equations (2.1.1), (2.1.4), and (2.1.5) in Chapter 2 w ere used to calculate the gas o w sp eed u 0 in the main o w c hannel for the mixed gases. T w o dieren t comp ositions of the mixed gas are considered; one case only con tains argon and xenon, and another do es nitrogen, o xygen, argon, 124 Figure 4.1.7: V ariation in the abundance of mixed gases for the 50nm mem brane (d c = 50nm) (a) with a pump o and (b) a pump on with initial mixing ratio of t w o gases ( Ar and Xe). Ar is the carrier gas, and Xe is the trace gas. Their c haracteristics of eac h gas are describ ed in App endix T.1. 125 (a) (b) Figure 4.1.8: V ariation in the abundance of mixed gases for the 10nm mem brane (d c = 10nm) (a) and 50nm mem brane (d c = 50nm) (b) with mixing ratio of t w o gases (Ar andXe). Ar is the carrier gas, and Xe is the trace gas. Their c haracteristics of eac h gas are describ ed in App endix T.1. 126 and xenon. The mixture consisted of argon and xenon gases can b e considered as an ideal case, and another mixture can b e considered as a real mixed gas. In the rst case, the molecular mass of the mixture is m Ar−Xe and is related to the concen tration of mixture C Ar−Xe = nXe nXe+nAr . It can b e written as m Ar−Xe =C Ar−Xe m Xe +(1−C Ar−Xe )m Ar . (4.1.7) And the viscosit y of mixture can b e written as µ Ar−Xe = X Ar µ Ar √ M Ar +X Xe µ Xe √ M Xe X Ar √ M Ar +X Xe √ M Xe . (4.1.8) In the second case, comp onen ts of nitrogen and o xygen are simply added in these equations (4.1.7) and (4.1.8). Molecular mass and viscosit y of o xygen are 32U and 19.19µPa·s resp ectiv ely , and ph ysical prop erties of argon, nitrogen, and xenon are sho wn in App endix T.1. The a v erage viscosities of t w o comp onen ts, ⟨µ Ar−Xe ⟩ are similar. These are 22.17µPa· s for the 10nm mem brane and 22.18µPa·s for the 50nm mem brane at 273K for the initial gas o w and exit gas o ws, with pump on and pump o. And the a v erage viscosities of four comp onen ts, ⟨µ Ar−Xe−N2−O2 ⟩ at 273K are dieren t for all those cases. There are 21.52µPa·s for initial gas o ws, 20.12µPa·s for outlet gas o ws without pumping eect, and 20.50µPa·s for outlet gas o ws with pumping eect for the 10nm mem brane, and 22.54µPa·s for initial gas o ws, 19.81µPa·s for outlet gas o ws without pumping eect, and 20.16µPa·s for outlet gas o ws with pumping eect for the 50nm mem brane. These viscosities v alues at ro om temp erature are larger than the calculated data. Molecular masses and densit y of the Ar−Xe mixture and the Ar−Xe−N 2 −O 2 mixture are sho wn dieren t results as sho wn in Figures 4.1.9 and 4.1.10. The molecular mass and densit y of initial gas o w (triangle) for the 10nm and 50nm mem branes are related to the mixing ratio of initial gas, and the molecular mass and densit y of outlet gas o ws (rectangle and circle) for the b oth mem branes gradually decreases along the x-axis for the Ar−Xe mixture. When the N 2 −O 2 −Ar−Xe mixture are considered, these molecular masses and densities at the same mixing ratio are smaller than the v alues for the mixture of argon and xenon. In addition the molecular mass and densit y for outlet gas o ws with the pump on and pump o are smaller than these v alues of the initial gas o w. As sho wn the second case, the molecular w eigh ts of initial gas is generally larger than that of other 127 (a) (b) Figure 4.1.9: Molecular mass for the10nm mem brane (a) and 50nm mem brane (b) of mixture gases of t w o comp onen ts (Ar andXe) and four comp onen ts (N 2 ,O 2 ,Ar , andXe) with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. The c haracteristics are describ ed in App endix T.1. 128 cases, b ecause the initial gases less include the air, nitrogen and o xygen. The molecular masses with puming eect are larger than tho es with the pump o. It can b e considered that the agron gas concen tration ma y decrease more than the xenon gas concen tration, or xenon gas concen tration ma y increase more than agron gas concen tration. F or these results, it is p ossible to calculate the gas o w sp eed u 0 for b oth mem branes and dieren t mixtures of gases. The gas o w sp eed and mass o w rate ha v e similar patterns and v alues whether the mixed gas including nitrogen and o xygen or not as sho wn in Figure 4.1.11 and Figure 4.1.12, ev en though the mass o w rates are smaller for the case included nitrogen and o xygen. In addition, the gas o w sp eeds and mass o w rates for the 10nm mem brane are larger than those for the 50nm mem brane. Finally , the gas pressure dierence b et w een the main o w c hannel and pumping c ham b er is one of the imp ortan t parameter to compare the exp erimen tal data with the n umerical prediction. The a v erage pressure dierences with pumping op eration is ab out 1.39Torr or 8.43Torr for the 10nm memrbane and 0.82Torr for the 50nm mem brane as sho wn in Figure 4.1.13. F or the 10nm mem brane, the pressure dierences w ere larger ab out one case where the dieren t 10nm mem brane w as c hanged. Ho w ev er it w as not clear wh y it has larger pressure dierences. 4.2 Improvement of Theoretical Models Extended eorts of this study are fo cusing on the newly impro v ed theoretical mo dels of con tin uous preconcen tration tec hnology . Mun tz et al. (Mun tz et al. 2011) attempted to describ e the theoretical mo dels of the preconcen trator b y a mass o w rate. Ho w ev er a new p ossibilit y w as suggested to obtain other t yp es of theoretical mo dels for the preconcen trator ev en though the theoretical mo dels w ere not satised with these exp erimen tal results. A ccording to equations (1.3.15), (1.3.20), (1.3.36), and (1.3.39) in Chapter 1, the mass o w rate is expressed dieren tly in eac h regime. When the mass o w rate through the main o w c hannel can b e written as _ m(x) =nmu 0 h f w(x), (4.2.1) where n is the initial n um b er densit y of carrier gas, m is the molecular mass of carrier gas, u 0 is the gas o w sp eed, and h f is the heigh t of the main o w c hannel. n, m, u 0 , and h f are constan t. Then 129 (a) (b) Figure 4.1.10: Molecular densit y for the10nm mem brane (a) and 50nm mem brane (b) of mixture gases of t w o comp onen ts (Ar and Xe) and four comp onen ts (N 2 , O 2 , Ar , and Xe) with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. The c haracteristics are describ ed in App endix T.1. 130 (a) (b) Figure 4.1.11: Mass o w rate for the 10nm mem brane (a) and 50nm mem brane (b) of mixture gases suc h as Ar -Xe, and N 2 -O 2 -Ar -Xe with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. These are describ ed in App endix T.1. 131 (a) (b) Figure 4.1.12: Gas o w sp eed for the 10nm mem brane (a) and 50nm mem brane (b) of mixture gases suc h as Ar -Xe, and N 2 -O 2 -Ar -Xe with increasing mixture ratio of initial gas with and without pumping eect. Ar is the carrier gas, Xe is the trace gas, and N 2 and O 2 are comp onen ts of air. These are describ ed in App endix T.1. 132 (a) (b) Figure 4.1.13: Pressure diererences for the 10nm mem brane (a) and 50nm mem brane (b) of mixture gases (Ar -Xe) with increasing mixture ratio of initial gas with the pump on and pump o. Ar is the carrier gas and Xe is the trace gas. These are describ ed in App endix T.1. 133 the mass o w rate at the en trance of the main o w c hannel is _ m(0) =nmu 0 h f w(0). Therefore, the mass o w rate for eac h regime can b e written as follo ws; _ m(x) H = _ m(0)exp ( − 2r c G P F(P 1 −P 2 ) nmu 0 h f h c √ m 2k B T x ) = _ m(0)e −Hx (Kn≪ 1), (4.2.2) for the h ydro dynamic o w, _ m(x) Tr = _ m(0)exp ( − 2πr 2 c FP av (P 1 −P 2 ) 8µk B Tnu 0 h f h c ( 1+ 8 3 λ r c ) x ) = _ m(0)e −Trx (Kn∼ 1), (4.2.3) for the transition o w and _ m(x) F = _ m(0)exp ( − 32σr 2 c FP av (P 1 −P 2 ) 3k B Tnmu 0 h f h c √ m πk B T x ) = _ m(0)e − F x (Kn≫ 1), (4.2.4) for the free molecular o w. Here G P is sho wn in equation (1.3.24), λ is sho wn in equation (1.3.12), r c is the radius of the mem brane c hannel, h c is the thic kness of the mem brane c hannel, σ is the m utual collision cross section area, and P av = P1+P2 2 is the a v erage pressure. The co ecien t G P is included in equation (4.2.2) when the rarefaction parameter δ is larger than 10, but otherwise the co ecien t is approac hed to ab out 1.1062. Therefore the shap e equations of the main o w c hannel can b e simply expressed as resp ectiv ely , w i (x) =w(0)e −ix , (i =H, Tr, F). (4.2.5) When the n um b er densit y of trace gas is not constan t along the length of the main o w c hannel, the mass o w rate is written as _ m T (x) = n T (x)m T u 0 h f w(x) at some p osition in x-axis, and _ m T (0) = n T (0)m T u 0 h f w(0) at the en trance of the main o w c hannel. Therefore the concen tration ratio of the trace gas is simply written as n T (x) n T (0) i =exp((β−β T ) i )x, (i =H, Tr, F). (4.2.6) Here Hr is the h ydro dynamic o w, Tr is the transition o w, and F is the free molecular o w. When the concept of mass o w rate is used to induce the new theoretical mo dels, it is comprehensiv e n umerical mo dels to describ e o v erall regimes. It can pro vide a guideline to reinforce an unkno wn 134 parameter of the prior theoretical mo del for all regimes. The molecular densit y ratio of bac ko w from the pumping c ham b ers to main o w c hannel w as c hanged to pressure ratio in this researc h. Ho w ev er this parameter do es not describ e the prop erties of molecules clearly . F rom equations of the mass o w rate, it is p ossible to describ e the parameters for all regimes. Therefore the parameter for eac h regime can b e written as follo ws; 1−η = 1− = 4 √ πmG P P 1 3ρk B T ( 1− P 2 P 1 ) (4.2.7) for the h ydro dynamic o w, 1−η = 1− = r c P 1 12µ √ π 3 m 8k B T ( 1+ 8 3 λ r c ) ( 1− ( P 2 P 1 ) 2 ) (4.2.8) for the transition o w and 1−η = 1− = 32σr c P 1 9 √ 2k B T ( 1− ( P 2 P 1 ) 2 ) (4.2.9) for the free molecular o w. F or h ydro dynamic and transition o ws, these are p ossible to predict the co ecien ts, but the co ecien t is smaller for the free molecular o w. Nev erthless, they include the parameters related to the prop erties of molecules suc h as molecular mass, viscosit y , and collisional cross section. Ho w ev er it should b e generalized the co ecien t ab out the molecular densit y ratio to obtain a general form of those equations o v erall regimes. The theoretical mo dels suggested b y Mun tz et al. (Mun tz et al. 2008, Mun tz et al. 2004, Mun tz et al. 2009) w ere generally considered in the free molecular o w. Ho w ev er the h ydro dynamic o w should b e applied for a gas o w through the main o w c hannel in this researc h, and the transition o w is applied for a gas o w through mem branes of the larger p ore diameter. New theoretical mo dels b y the net ux ha v e b een applied for eac h regime. A ccording to equations (1.4.4) for the h ydro dynamic o w and (1.4.12) for the transition o w and free molecular o w in Chapter 1, those 135 equations can b e again expressed as 1 N dN HN =− r 2 c F 4µu 0 h c h f (1−)(P 1 +P 2 )dx (4.2.10) for the h ydro dynamic o w, and 1 N √ N dN TFN =− 8 3u 0 h f √ 2k B T πm Fr c h c (1−)dx (4.2.11) for the transition o w and free molecular o w, resp ectiv ely , when the n um b er of carrier molecule is N(x) = nw(x)h f dx at some p osition at x-axis and N(0) = nw(0)h f dx at the en trance of the main o w c hannel. Therefore the shap e equation of the main o w c hannel for the h ydro dynamic o w b y equation (4.2.7) can b e written as w HN (x) =w(0)exp ( − r 2 c F 4µu 0 h c h f (1−)(P 1 +P 2 )x ) =w(0)e −HNx . (4.2.12) With the same metho d, the concen tration ratio of the trace gas b y equations (4.2.7) and (4.2.9) is expressed as n T (x) n T (0) HN = exp ( − r 2 c F 4u 0 h c h f (1−)(P 1 +P 2 ) ( 1 µ − 1 µ T ) x ) , (4.2.13) when the n um b er of trace molecule is N T (x) = n T (x)w(x)h f dx at some p osition at x-axis and N T (0) = n T (0)w(0)h f dx at the en trance of the main o w c hannel. Ho w ev er, the shap e equation of the main o w c hannel and the concen tration ratio of the trace gas for the transition o w and free molecular o w are dicult to obtain with the same metho d, b ecause the equation of n um b er of molecule is expressed as 1 √ N(x) − 1 √ N(0) TFN =− 2x 3u 0 h f √ 8k B T πm Fr c h c (1−). (4.2.14) Figure 4.2.1 is ab out shap e equations of the main o w c hannel for eac h case. The shap e equation used in this researc h had an exit width of 0.3cm and the width of the main o w c hannel w as exp onen tially decreased along the length of the main o w c hannel. Other equations are also decreased exp onen tially under the same conditions as the exp erimen tal equation, but the exit widths are dieren t. The shap e equations obtained from free molecular o w induced b y mass o w rate and h ydro dynamic 136 Figure 4.2.1: Shap e of main o w c hannel. The exp erimen t ( −··) obtains from the original equation that w as used in this study , other lines are related to new shap e equations (4.2.5) from the mass o w rate and (4.2.9) from the net ux. The co ecien ts used for shap e equation are a helium gas o w sp eed of 5cm/s, a pressure ratio of 0.5, and a p ore diameter of 30nm, a thic kness of 6µm and a p ore densit y of 6×10 8 /cm 2 of a mem brane. o w induced b y net ux ha v e larger exit widths at x = 10cm, but these ha v e relativ ely similar exit widths for h ydro dynamic o w and transition o w induced b y mass o w rate. If a factor 4rc 3hc in all these equations w ere replaced b y transmission probabilit y , the exit widths are somewhat extended as follo ws: w Hr = 0.97cm, w Tr = 0.51cm, w F = 6.25cm, and w HN = 9.41cm, resp ectiv ely . These exp erimen ts are related to the h ydro dynamic o w and transition o w, so those shap e equations sho w a similar result to the exp erimen tal equation. These results are also similar for the concen tration ratio equations as sho wn Figure 4.2.2. The concen tration ratio of trace gas are deriv ed from equations (4.2.5) and (4.2.9) and can b e considered in t w o dieren t w a ys. One w a y is that a term related to the shap e of the main o w c hannel is considered as a part of the concen tration ratio equation, and another option included the carrier gas factors in the concen tration ratio equation. As sho wn in Figure 4.2.2, the shap e equation is reected in the concen tration equation (2.2.12) as follo ws; n T (x) n T (0) = exp [ x 2h f ( (1− I )c ′ I α I F I u 0I − (1− T )c ′ T α T F T u 0 )] , (4.2.15) 137 Figure 4.2.2: Concen tration ratio of the trace gas. The exp erimen t (−··) obtains from the original equation that w as used in this study , other lines are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.10) from the net ux. The co ecien ts used for shap e equation are a helium gas o w sp eed of 5cm/s, a pressure ratio of 0.5, and a p ore diameter of 30nm, a thic kness of 6µm and a p ore densit y of 6×10 8 /cm 2 of a mem brane. The co ecien ts for concen tration ratio are a xenon gas o w sp eed of 1.933cm/s, a pressure ratio of 0.996, and a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. where I represen ts the initial conditions used to create the main o w c hannel. In this case, it is ob vious that an increase of the exit width of the main o w c hannel decreases the concen tration ratio of the trace gas, when the concen tration ratio equation is not related to the t yp e of the carrier gas. The co ecien ts used for the shap e equation are a helium gas o w sp eed of 5cm/s, a pressure ratio of 0.5, and a p ore diameter, thic kness, and p ore densit y of 30nm, 6µm, and 6×10 8 /cm 2 of a mem brane resp ectiv ely . The exp erimen tal data to obtain the concen tration ratio w ere a xenon gas o w sp eed of 1.933cm/s, a pressure ratio of 0.996, and a p ore diameter, thic kness, and p ore densit y of 10nm, 6µm, and 6× 10 8 /cm 2 of a mem brane resp ectiv ely . The trace gas concen tration for the equation used for the this exp erimen t increases ab out 32 times to an initial gas o w, and other cases sho w smaller increases of the trace gas concen tration. Ho w ev er the results are dieren t with exp erimen tal results. Figure 4.2.3 sho ws another case where the concen tration ratio of the trace gas do es not dep end on the shap e of the main o w c hannel and is related to the mixture of carrier gas and trace gas. The exp erimen tal conditions w ere a xenon gas o w sp eed of 1.933cm/s, a pressure ratio of 0.996, and a p ore diameter, thic kness, and p ore densit y of 10nm, 6µm, and 6×10 8 /cm 2 of a mem brane 138 Figure 4.2.3: Concen tration ratio of the trace gas. The exp erimen t (−··) obtains from the original equation that w as used in this study , other lines are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.10) from the net ux. The co ecien ts for concen tration ratio are a xenon gas o w sp eed of 1.933cm/s, a pressure ratio of 0.996, and a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. resp ectiv ely . The trace gas concen tration obtained b y this exp erimen t increases ab out 1.047 times, and the concen trations obtained b y h ydro dynamic and transition o ws increases ab out 1.025 times. Ho w ev er other t w o cases sho w decreases of concen tration ab out 0.99 times. Th us the trace gas concen tration ratio of the exp erimen t results is similar to these cases when the parameters of carrier gas are related to the concen tration ratio of the trace gas. If the factor of 4rc 3hc in all these equations w ere replaced b y transmission probabilit y for b oth gures 4.2.2 and 4.2.3, the concen tration ratio of the trace gas at the exit of the main o w c hannel are somewhat reduced. Therefore it is p ossible to use the ratio of radius and thic kness of mem brane instead of the transmission probabilit y . Impro v ed the theoretical mo dels for all regimes can b e determined b y the mass o w rate. In this study , the n um b er densit y ratio b et w een the pumping c ham b er and main o w c hannel w as replaced as the pressure ratio. Then the parameter did not describ e the prop erties of molecules. In order to impro v e the original theoretical mo dels, the factor ma y include the parameters, collision cross section area of molecule σ or viscosit y µ when the original equations compare with these equations. Ho w ev er the impro v emen t of theoretical mo dels will b e studied later. Finally the exp erimen tal data are compared with the n umerical precitions including the prior theo- 139 (a) (b) Figure 4.2.4: Abundance of trace gas concen tration for the 10nm mem brane. The exp erimen t data ( and) obtained with the pump o (a) and pump on (b). The original equation is used in this study (•), and other data are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.13) from the net ux. Then y -axis is related to the abundance in p ercen t for the exp erimen tal results, and in times for the theoretical results. The co ecien ts for concen tration ratio are a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. 140 (a) (b) Figure 4.2.5: Abundance of trace gas concen tration for the 50nm mem brane. The exp erimen t data ( and) obtained with the pump o (a) and pump on (b). The original equation is used in this study (•), and other data are related to new shap e equations (4.2.6) from the mass o w rate and (4.2.13) from the net ux. Then y -axis is related to the abundance in p ercen t for the exp erimen tal results, and in times for the theoretical results. The co ecien ts for concen tration ratio are a p ore diameter of 10nm, a thic kness of 6µm, and a p ore densit y of 6×10 8 /cm 2 of a mem brane. 141 retical mo del and new theoretical mo dels obtained b y the mass o w rate and net ux as sho wn in Figures 4.2.4 and 4.2.5. With the prior theoretical mo del used in this researc h, the concen trations ratio of trace gas increase around 30 times when the 10nm memrbane and the parameters of shap e equations are used. Otherwise, the parameters of carrier gas are used instead of the parameters for the shap e equation, the concen tration ratio just increase ab out 1 p ercen t. When the 50nm memr- bane and the parameters of shap e equations are used, the concen trations ratio of trace gas increase around 32 times. Otherwise, the parameters of carrier gas are used instead of the parameters for the shap e equation, the concen tration ratio just increase ab out 2 p ercen t. A ccording to new n umerical predictions, all results are smaller than those of the prior theoretical mo del. With regard to these results, the exp erimen tal data and n umerical prediction are still dieren t with the parameters of shap e equation, but it can guess that another case is relativ ely close to eac h other. 4.3 Summary The new t yp e of the preconcen trator prop osed b y Mun tz et al. (Mun tz et al. 2008) assumed that the concen tration ratio of trace gas in a sampled gas, whic h o ws through the main o w c hannel con tin uously , increases at the end of the main o w c hannel when the width of the main o w c hannel is exp onen tially decreased along the length of the main o w c hannel. In general, they considered calculating an increase of concen tration under the conditions suc h that a gas o w sp eed is 5cm/s, a p orosit y is 4.2× 10 −3 , a transmission probabilit y is 0.0066, and a gas densit y ratio b et w een the main o w c hannel and pumping c ham b ers is 0.5. Then the concen tration of xenon gas in a mixture of the helium and xenon gases increases to ab out 37 times at the end of the main o w c hannel. A ccording to the exp erimen tal data, the a v erage pressure dierences b et w een the main o w c hannel and pumping c ham b er are 2.89Torr for the 10nm mem brane, 0.82Torr for the 50nm mem brane, and 0.35Torr for the case with the mem brane remo v ed. And the a v erage gas o w sp eeds are 1.933cm/s, 1.092cm/s, and 1.37cm/s, resp ectiv ely . Ho w ev er the pressure dierences are to o small while the gas o w sp eeds are smaller and close to the consideration unlik e the assumption. The concen tration ratio can again b e calculated with these exp erimen tal data. The concen tration ratio of xenon gas in the mixture of argon and xenon gases increase 1.0468 times for the 10nm mem brane, 1.0228 times for the 50nm mem brane, and 20052 times for the case remo v ed the mem branes, when the shap e equation of main o w c hannel did not c hange and with tho es gas o w sp eed and pressure dierence. Ho w ev er, the concen tration ratio of the xenon gas increases ab out 33 times for the 10nm mem brane, when the shap e equation is reected in the concen tration equation. A ccording to the b oth calculations, 142 eac h n umerical prediction sho ws a dieren t result with eac h mem brane. Ho w ev er these n umerical predictions are dieren t with the exp erimen tal results. The concen tration of xenon gas for the most cases in this exp erimen t decreased appro ximately 10 to 20 p ercen t to the concen tration of xenon gas in an initial sampled gas, and these concen trations increased appro ximately 10 to 20 p ercen t for some exp erimen ts. In order to correct the theoretical mo del and satisfy general cases, another exp erimen t should b e con v erted. Reference Han, Y. L. and M. Y oung, Con tin uous preconcen trator for trace-gas analysis , R e c ent Patents on Me chanic al Engine ering , 2 (2009) : 214 - 227. Hinds, B. J., Aligned m ultiw alled carb on nanotub e mem branes, Scienc e , 303, (2004) : 62 - 65. Mun tz, E. P ., M. Y oung, and Y.-L. Han, Con tin uous lo w p o w er pre-concen trations for distributed microscale trace gas analysis, IMECE 2004 (2004) : 60874 Mun tz, E. P ., Y.-L. Han, and M. Y oung, Pre-concen trator for trace gas analysis, T ec hnical Rep ort, U.S. Patent US2008/01786 , 2008 . Mun tz, E. P ., Y.-L. Han, P erformance analysis of the con tin uous trace gas preconcen trator, Physics of Fluids , 23, 030605 (2011). 143 Chapter 5 Conclusion and F uture W ork 5.1 Conclusion Micro/mesoscale, con tin uous o w-through trace gas preconcen trator devised b y Mun tz et al. (Mun tz et al. 2008, Mun tz et al. 2004, Mun tz et al. 2009) has b een to increase a concen tration of trace gas (for example, from 10ppb to 10ppm), that rarely exists in a sampled gas, with using a mass diusion separation without in terrupting the gas o ws. The con tin uous preconcen trator, whic h can b e useful for detecting real time v ariations in the concen tration of the trace gas, requires less op erational time and oers the p ossibilit y of a higher trace gas concen tration lev el with a smaller size device. More- o v er a newly inno v ated con tin uous preconcen trator, that uses the ph ysical prop erties of molecules instead of c hemical reactions and ro om temp erature instead of using high temp erature to increase the trace gas concen tration, can b e useful to v arious applications in defense, civil en vironmen ts, space science etc. Ho w ev er exp erimen ts that v alidate the prop osed a v ailable n umerical data suc h as concen trations and gas separation ha v e not conducted b ecause of limitation of man ufacturing tec hnique for microscale devices and restriction of separation mem branes. In addition, equations of the shap e of the main o w c hannel and concen tration ratio of the trace gas w ere related to eac h other, so the shap e of the main o w c hannel v aried as comp ositions of sampled gas. This exp erimen tal study w as conducted to compare existing n umerical predictions with the proto- t yp e of preconcen trator. The protot yp e preconcen trator w as scaled up v ariation of the prop osed preconcen trator b y Mun tz et al. (Mun tz et al. 2008, Mun tz et al. 2004, Mun tz et al. 2009), and 144 w as designed as a macroscale device in order to o v ercome the limitation of fabrication. The sizes of main o w c hannel w ere 10cm for the length and en trance width, 0.5cm of the heigh t, and 0.3cm of the exit width, and then the width of the main o w c hannel w as exp onen tially decreased from the en trance to exit. Then, the constan ts for shap e equation of the main o w c hannel w ere that a helium gas o w sp eed w as 5cm/s, a p orosit y F w as 4.2×10 −5 , a transmission probabilit y w as 0.0066 for the p olycarb onate mem brane (6µm in the thic kness, 30nm in the p ore diameter, and 6×10 8 in the p ore densit y), and a densit y ratio is 0.5. In order to obtain the exp erimen tal data, xenon gas w as used as the trace gas and argon gas w as used as the carrier gas with v arious mixture ratios. The argon gas concen trations generally w ere ab out 10 times to 30 times larger than the xenon gas for the 10nm mem brane (GE p olycarb onate mem brane of d c = 10nm of an a v erage p ore diameter), and ab out 10 times to 25 times larger than the xenon gas for the 50nm mem brane (GE p olycarb onate mem brane of d c = 50nm of an a v erage p ore diameter). The exp erimen tal results sho w ed that the concen trations of xenon gas measured at the exit of the main o w c hannel decreased ab out 10 p ercen t from xenon gas concen trations of initial mixed gases, while the concen tration of argon gas decreased more than xenon gas concen tration in the most cases. When the 50nm mem brane w ere attac hed upp er and lo w er surfaces of the main o w c hannel, the concen tration ratio of the xenon gas increased ab out 7 p ercen t ab out the some exp erimen tal data, but the concen tration decreased ab out 10 p ercen t in the most cases. In order to compare the exp erimen tal data with n umerical data, a gas o w sp eed and pressure ratio (or densit y ratio) b et w een the main o w c hannel and pumping c ham b ers should b e obtained from the exp erimen ts. F or the 10nm mem brane, the a v erage gas o w sp eed w as 1.933cm/s, and the a v erage pressure dierence w as 2.89Torr . F or the 50nm mem brane, the a v erage gas o w sp eed w as 1.092cm/s, and the a v erage pressure dierence w as 0.82Torr with the pump on. Then the concen tration ratio of the xenon gas in the mixture of argon and xenon gases b y equation (2.2.12) increased ab out 1.047 times for the 10nm mem brane, and 1.0228 times for the 50nm mem brane, when the equation (2.2.12) w as indep enden t from the parameters related to the shap e of the main o w c hannel. Otherwise the shap e equation w as reected in the equation (2.2.12) and parameters related to the carrier gas w ere not included in the concen tration, the concen tration ratio of the xenon gas increased ab out 33 times for the 10nm mem brane, and 32 times for the 50nm mem brane. The n umerical results w ere similar to exp erimen tal results under the assumption, that the shap e of the 145 main o w c hannel w as not related to the trace gas concen tration. The exp erimen tal results sho w the p ossibilit y that the preconcen trator can b e used to obtain the trace gas within times shorter than 10 seconds ev en though the n umerical and exp erimen tal data sho w somewhat dieren t results. 5.2 Improvement of a Preconcentrator The protot yp e of preconcen trator in this study w as scaled up 10 times larger than the prop osed preconcen trator under the same conditions. A ccording to the n umerical data, the concen tration ratio of the trace gas and shap e of the main o w c hannel are the same with a scale up and scale do wn, so it is not dicult to c hange the scale in order to obtain the same result. The en trance width is only related to the exit width not the shap e of the main o w c hannel and trace gas concen tration, so it can easily extend the size of the exit width to a man ufacturable lev el. In order to obtain the larger concen tration ratio, these are b etter that the heigh t is shorter and the length is longer. Ho w ev er the length is related to the exit width so it can b e determined to a reasonable size. The kind of mem brane whic h can b e used for smaller preconcen trators is still an issue. The GE p olycarb onate mem branes used in this researc h ha v e v arious p ore diameters, but the sizes of p ore diameter are not uniform and p orosities are not distributed constan tly o v er the areas. With a larger size of the main o w c hannel suc h as this researc h, these w ere not problems, but these should b e considered to smaller devices. Nev ertheless, these mem branes giv e imp ortan t information to determine the relationship b et w een the p ore diameter and p orosit y . In order to increase the trace gas concen tration using these mem branes, the p ore densit y will need to b e increased. With regard to the pumping c ham b er, t w o cases w ere discussed. One case w as a size and v olume, and another case w as a pressure. The protot yp e of preconcen trator had a total v olume of t w o pumping c ham b ers larger than a total v olume of the main o w c hannel, b ecause a uniform pressure w as supplied to o v erall the main o w c hannel. Then the total v olume of the main o w c hannel is ab out 13.8cm 3 and one of the pumping c ham b er is ab out 332cm 3 . The unit v olume of pumping c ham b er w as constan t along the length of the main o w c hannel in this study , but the unit v olume of pumping c ham b er prop osed w as v arious along the length. The pressure in the pumping c ham b er w as somewhat smaller than one in the main o w c hannel for the 10nm and 50nm mem branes. In addition, holes of the hole-b o dy attac hed b et w een the pumping c ham b er and separation mem brane 146 had the same diameter and dieren t n um b ers p er segmen t but the hole diameters ha v e dieren t to obtain a similar gas o w sp eed escap ed through eac h hole. In order to shrink the preconcen trator, these assumptions are imp ortan t. The next generation of the protot yp e of preconcen trator will ha v e the follo wing assumptions. The main o w c hannel has 2.5cm of the en trance width and length, 0.125cm of the heigh t, and 0.075cm of the exit width. The pumping c ham b er has a similar v olume with the main o w c hannel, and the hole-b o dy has holes of dieren t diameters. The p ossible separation mem branes, 6µm of a thic kness, w ould require 10nm of a p ore diameter and ab out 10 9 /m 2 of a p ore densit y , 30nm of a p ore diameter and ab out 10 8 /m 2 of a p ore densit y , or 50nm of a p ore diameter and ab out 10 7 /m 2 of a p ore densit y . These tests will b e conducted with the same conditions of the curren t exp erimen t. Moreo v er, easily a v ailable gases in this researc h had a molecular mass ratio that is represen tativ e of t ypical, more complicated molecular structures that are encoun tered in actual situations. Subsequen tly , trace gas mixtures more t ypical of the complicated molecular structures found in hea vy molecules, will b e studied. With regard to the impro v emen t of theoretical mo dels, the mass o w rate ab out all regimes can pro vide a guideline to reinforce the unkno wn parameters. The shap e of the main o w c hannel and concen tration ratio of the trace gas obtained from the h ydro dynamic o w and transition o w w ere relativ ely similar to these equations used for this exp erimen t, but these equations induced from the free molecular o w sho w ed a dieren t result ab out the shap e of the main o w c hannel. Using the net ux ab out all regimes to obtain new theoretical mo dels can still b e an issue, b ecause the equations for h ydro dynamic o w do not satisfy the exp erimen tal results, and it is dicult to get forms for the new equations. Nev ertheless these equations can giv e some idea to impro v e the theoretical mo dels. This curren t researc h w as related to the preconcen trator, one part of analyzer. In order to measure an abundance ratio of eac h gas sp ecies in the sampled gas, a gas c hromatograph/mass sp ectrograph (Agilen t 5975C ) w as used for obtaining the primary exp erimen tal data. Ho w ev er this gas c hromato- graph/mass sp ectrograph (GCMS) is already a nal t yp e of an analyzer, so a detection unit for a new analyzer or gas detector should b e studied. As men tioned in Chapter 2, one of p ossible detection units is to use an electron b eam and sp ectrometer. Then high pressure dierence can o ccur b et w een the en trance and exit of the main o w c hannel, b ecause a high v acuum condition ( ∼ 10 −4 Torr ) is required to generate and main tain the electron b eam. In this case, the gas o w sp eed in the main o w c hannel can b e rapidly increased from the en trance of the main o w c hannel to the en trance 147 of the v acuum c ham b er that is connected with the exit of the main o w c hannel. Therefore the pumping rate of a pump connected with the pumping c ham b ers should b e increased more than curren t pumping rates when the detector is used in natural en vironmen t. 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Elemen ts Helium (He) Air Nitrogen (N2 ) Argon (Ar ) Xenon (Xe) Molecular w eigh t m[U] 4.002602 28.9403 23.0158 39.348 131.293 Densit y [ kg=m 3 ] 0.16353 1.000 0.9998 1.784 5.3954 Diameter d[nm] VHS 0.233 0.419 0.417 0.417 0.574 VSS 0.23 - 0.411 0.411 0.565 Mean thermal sp eed c ′ [m=s] VHS 1259.73 468.4857 525.3331 401.7783 219.9515 (300K ) VSS 1202 454 380 Mean free path [nm] VHS 154.22 47.69 48.15 48.15 25.41 (273K ) VSS 158.27 - 49.57 49.57 26.23 [nm] VHS 169.48 52.408 52.912 52.912 27.925 (300K ) VSS 173.6 58.8 62.6 Viscosit y (Pa·s) 18.65 (273K) 18.27 (291.15K) 17.81 (300K) 21.17 (273K) 21.07 (273K) Viscosities of mixed molecular gases Viscosit y (Pa·s) He/N2 He/Ar He/Xe Air/N2 Air/He Air/Xe ×10 −6 8.167 8.324 5.580 9.953 10.807 9.210 G. A. Bird, Molecular gas dynamics and the direct sim ulation of gas o ws, Oxford engineering science series 42, Oxford science publications,1994 158 T. 2.1. Equations of Mass o w rate and escap ed gas o w sp eed p er assignmen t through the main o w c hannel This table is to describ e the equations of mass o w rate and escap ed gas o w sp eed p er segmen t as sho wn b y equation (4.2.1), (4.2.2), (4.3.3), and (4.3.4) in Chapter 4. P osition Mass o w rate ( g=s) Escap ed gas o w sp eed A t eac h segmen t 2 _ mH(×NH)= _ m fN+1 − _ m fN vH [m=s] 0 (exit) _ m fex =u0wexh f _ m fex - - - 1 _ m f1 =u0w1h f _ m f1 = 2 _ mH1 + _ m fex 2vH ( d H 2 ) 2 ×1 u0h f (w1 −wex) 2 _ m fex wex (w 1 −wex) d 2 H 2 _ m f2 =u0w2h f _ m f2 = 2 _ mH2 + _ m f1 2vH ( d H 2 ) 2 ×1 u0h f (w2 −w1) 2 _ m fex wex (w 2 −w 1 ) d 2 H 3 _ m f3 =u0w3h f _ m f3 = 2 _ mH3 + _ m f2 2vH ( d H 2 ) 2 ×1 u0h f (w3 −w2) 2 _ m fex wex (w 3 −w 2 ) 2 ( d H 2 ) 2 4 _ m f4 =u0w4h f _ m f4 = 2 _ mH4 + _ m f3 2vH ( d H 2 ) 2 ×2 u0h f (w4 −w3) _ 2m fex wex (w 4 −w 3 ) 2d 2 H 5 _ m f5 =u0w5h f _ m f5 = 2 _ mH5 + _ m f4 2vH ( d H 2 ) 2 ×2 u0h f (w5 −w4) 2 _ m fex wex (w 5 −w 4 ) 4 ( d H 2 ) 2 6 _ m f6 =u0w6h f _ m f6 = 2 _ mH6 + _ m f5 2vH ( d H 2 ) 2 ×2 u0h f (w6 −w5) 2 _ m fex wex (w 6 −w 5 ) 2d 2 H 7 _ m f7 =u0w7h f _ m f7 = 2 _ mH7 + _ m f6 2vH ( d H 2 ) 2 ×2 u0h f (w7 −w6) 2 _ m fex wex (w 7 −w 6 ) 2d 2 H 8 _ m f8 =u0w8h f _ m f8 = 2 _ mH8 + _ m f7 2vH ( d H 2 ) 2 ×3 u0h f (w8 −w7) 2 _ m fex wex (w 8 −w 7 ) 3d 2 H 9 _ m f9 =u0w9h f _ m f9 = 2 _ mH9 + _ m f8 2vH ( d H 2 ) 2 ×3 u0h f (w9 −w8) _ 2m fex wex (w 9 −w 8 ) 6 ( d H 2 ) 2 10 _ m f10 =u0w10h f _ m f10 = 2 _ mH10 + _ m f9 2vH ( d H 2 ) 2 ×4 u0h f (w10 −w9) 2 _ m fex wex (w 10 −w 9 ) 4d 2 H 11 _ m f11 =u0w11h f _ m f11 = 2 _ mH11 + _ m f10 2vH ( d H 2 ) 2 ×4 u0h f (w11 −w10) _ 2m fex wex (w 11 −w 10 ) 4d 2 H 12 _ m f12 =u0w12h f _ m f12 = 2 _ mH12 + _ m f11 2vH ( d H 2 ) 2 ×5 u0h f (w12 −w11) 2 _ m fex wex (w 12 −w 11 ) 5d 2 H 13 _ m f13 =u0w13h f _ m f13 = 2 _ mH13 + _ m f12 2vH ( d H 2 ) 2 ×6 u0h f (w13 −w12) 2 _ m fex wex (w 13 −w 12 ) 6d 2 H 14 _ m f14 =u0w14h f _ m f14 = 2 _ mH14 + _ m f13 2vH ( d H 2 ) 2 ×8 u0h f (w14 −w13) 2 _ m fex wex (w 14 −w 13 ) 8d 2 H 15 _ m f15 =u0w15h f _ m f15 = 2 _ mH15 + _ m f14 2vH ( d H 2 ) 2 ×8 u0h f (w15 −w14) 2 _ m fex wex (w 15 −w 14 ) 8d 2 H 16 _ m f16 =u0w16h f _ m f16 = 2 _ mH16 + _ m f15 2vH ( d H 2 ) 2 ×10 u0h f (w16 −w15) 2 _ m fex wex (w 16 −w 15 ) 10d 2 H 17 _ m f17 =u0w17h f _ m f17 = 2 _ mH17 + _ m f16 2vH ( d H 2 ) 2 ×12 u0h f (w17 −w16) _ 2m fex wex (w 17 −w 16 ) 12d 2 H 18 _ m f18 =u0w18h f _ m f18 = 2 _ mH18 + _ m f17 2vH ( d H 2 ) 2 ×14 u0h f (w18 −w17) _ 2m fex wex (w 18 −w 17 ) 14d 2 H 19 _ m f19 =u0w19h f _ m f19 = 2 _ mH19 + _ m f18 2vH ( d H 2 ) 2 ×16 u0h f (w19 −w18) 2 _ m fex wex (w 19 −w 18 ) 16d 2 H 20 (En trance) _ m f20 =u0w20h f _ m f20 = 2 _ mH20 + _ m f19 2vH ( d H 2 ) 2 ×20 u0h f (w20 −w19) _ 2m fex wex (w 20 −w 19 ) 20d 2 H 159 T. 2.2. Equations of Mass o w rate and escap ed gas o w sp eed p er assignmen t through the main o w c hannel This table is to describ e the calculation of mass o w rate and escap ed gas o w sp eed p er segmen t for four single gases as sho wn b y equation (4.2.1), (4.2.2), (4.3.3), and (4.3.4) in Chapter 4. P osition He N2 Ar Xe _ mH (mg=s) vH (cm=s) _ mH (mg=s) vH (cm=s) _ mH (mg=s) vH (cm=s) _ mH (mg=s) vH (cm=s) 0 (exit) 0.059 0.421 505.19 1251.89 21.56(sccm) 25.31(sccm) 17.00(sccm) 13.94(sccm) 1 0.070 0.4837 0.501 0.5665 0.601 0.3811 1.490 0.3123 2 0.083 0.5821 0.597 0.6817 0.717 0.4586 1.777 0.3757 3 0.115 0.6816 0.827 0.8100 0.992 0.5449 2.458 0.4465 4 0.134 0.4121 0.963 0.4826 1.156 0.3247 2.864 0.2660 5 0.157 0.4911 1.125 0.5751 1.350 0.3869 3.347 0.3170 6 0.184 0.5852 1.319 0.6854 1.583 0.4610 3.923 0.3778 7 0.216 0.6974 1.550 0.8167 1.860 0.5494 4.610 0.4502 8 0.255 0.5595 1.828 0.6553 2.194 0.4408 5.437 0.3612 9 0.300 0.6547 2.153 0.7668 2.584 0.5158 6.404 0.4227 10 0.355 0.5901 2.544 0.6911 3.053 0.4649 7.566 0.3809 11 0.420 0.7031 3.010 0.8235 3.612 0.5540 8.951 0.4539 12 0.498 0.6703 3.565 0.7851 4.278 0.5281 10.601 0.4327 13 0.590 0.6657 4.226 0.7797 5.072 0.5245 12.568 0.4298 14 0.702 0.6045 5.026 0.7080 6.033 0.4763 14.949 0.3902 15 0.831 0.6995 5.952 0.8192 7.145 0.5511 17.705 0.4516 16 0.988 0.6759 7.071 0.7916 8.488 0.5325 21.0332 0.4364 17 1.174 0.6713 8.405 0.7861 10.088 0.5288 24.999 0.4333 18 1.396 0.6856 9.993 0.8030 11.996 0.5402 29.726 0.4426 19 1.660 0.7149 11.887 0.8373 14.269 0.5633 35.358 0.4615 20 (En trance) 1.975 0.6816 14.144 0.7982 16.977 0.5370 42.070 0.4400 (0.153) (1.036) (1.459) (4.312) 160 T.3. A v erage v alues calculated b y exp erimen tal data T yp e 10nm mem brane 50nm mem brane No mem brane (dH = 3mm) Mixture Ar−Xe Ar−Xe−N2 −O2 Ar−Xe Ar−Xe−N2 −O2 Ar−Xe Ar−Xe−N2 −O2 Densit y Initial gas 1.906 1.762 1.856 1.707 1.867 1.731 ⟨⟩ No pump 1.919 1.473 1.871 1.386 1.880 1.450 ( kg=m 3 ) With pump 1.912 1.557 1.865 1.461 1.867 1.496 Molecular mass Initial gas 46.60 43.16 45.47 42.14 46.08 43.99 ⟨m⟩ No pump 46.71 36.83 45.68 35.28 45.87 37.78 (U) With pump 46.71 38.55 45.67 36.80 46.36 36.67 Viscosit y ⟨⟩ Initial gas 22.17 21.52 22.18 22.54 22.17 21.53 (Pa·s) No pump 22.17 20.12 22.17 19.81 22.17 20.09 (273K) With pump 22.17 20.50 22.17 20.16 22.17 20.31 Mass o w rate ⟨ _ m⟩ No pump 1.960 1.508 1.451 1.075 0.387 0.308 (mg=s)(in air) With pump 0.556 0.454 0.306 0.240 1.578 1.578 Gas o w sp eed ⟨u0⟩ No pump 6.829 6.829 5.175 5.175 5.635 5.635 (cm=s) With pump 1.933 1.934 1.092 1.092 1.372 1.226 161 F. 1. Kn udsen n um b er based on exit pressures Kn = Lc = 1 √ 2d 2 nLc = kBT √ 2d 2 LcP ; where is the mean free path of gas molecule, d is the v arible hard sphere molecular diameter, kB is the Boltzmann constan t, T is the ro om temp erature, 300K ,P is the v ariable pressure, and Lc is the c haracteristic length, 10nm and 50nm p ore diam ters. T. 4. Ph ysical prop erties of nerv e agen ts Elemen ts m[U] d[nm] c ′ [m=s] [nm] T abun (GA C 5 H 11 N 2 O 2 P ) 162.13 0.93 197.9320 0.0644 Sarin (GB C 4 H 10 FO 2 P ) 140.09 0.99 212.9336 0.0491 Soman (GDC 7 H 16 FO 2 P ) 182.17 1.12 186.7280 0.0531 VX (C 11 H 26 NO 2 PS ) 267.4 (?) 1.38 154.1229 0.0524 DMMP (C 3 H 9 O 3 P ) 124.08 0.83 226.2543 0.0580 DIMP 180 (?) 0.93 (?) 187.8502 0.0394 Mustard (C 4 H 8 Cl 2 S ) 159.08 1.11 199.8205 0.0380 162

Abstract (if available)

Abstract A new type of continuous flow-through trace gas preconcentrator for rarefied trace gas analysis, which has been proposed by Muntz et al. (Muntz et al. 2008, Muntz et al. 2004, Han et al. 2009) has been built and consists of a main flow channel, pumping chambers, and separation membranes between the main flow channel and the pumping chambers. In this case, preconcentration is not from stop, adsorption, and release

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Asset Metadata

Creator Kim, Jihyun (author)

Core Title Experimental development and analysis of a continuous flow-through trace gas preconcentrator

Contributor Electronically uploaded by the author (provenance)

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Aerospace Engineering

Publication Date 08/16/2013

Defense Date 07/30/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag concentration of gas,mass flow rate,OAI-PMH Harvest,preconcentrator,rarefied gas dynamics

Format application/pdf (imt)

Language English

Advisor Muntz, E. Phillip (committee chair), Bickers, Gene (committee member), Shiflett, Geoffrey R. (committee member), Yang, Bingen (Ben) (committee member)

Creator Email jihyunk@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-326099

Unique identifier UC11293543

Identifier etd-KimJihyun-2004.pdf (filename),usctheses-c3-326099 (legacy record id)

Legacy Identifier etd-KimJihyun-2004.pdf

Dmrecord 326099

Document Type Dissertation

Format application/pdf (imt)

Rights Kim, Jihyun

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA