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Rheological behavior of polymer composites containing crosslinked polymers

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Rheological behavior of polymer composites containing crosslinked polymers

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Content RHEOLOGICAL BEHAVIOR OF POLYM ER COM POSITES CONTAINING CROSSLINKED POLYM ERS by Shishir Agarwal A Thesis Presented to the FACULTY OF THE SCHOOL O F ENGINEERING U N IV ER SITY OF SO U TH ERN CALIFORNIA In Partial Fulfillment of the Requirem ents for the Degree M ASTER OF SCIENCE (Chemical Engineering) May 1993 Copyright 1993 Shishir Agarwal UMI Number: EP41841 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP41841 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code uest ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 This thesis, written by Shishir Agarwal under the guidance of his Faculty Committee and approved by all its members, has been presented to and accepted by the School of Engineering in partial fulfillment of the re quirements for the degree of Masters of Science in Chemical Engineering D ate January.. 29y _ _ _ 1993 Faculty Committee D e d ica tio n To m y fath er. A ck n o w led g em en t I would like to express my gratitude to my advisor, Dr. Salovey, for his support and encouragem ent. Working with him was a pleasure and I will always relish this experience. I am also grateful to the faculty members in the Chemical Engineering departm ent, for sharing their knowledge and experiences, fellow students, who were always around when I needed them , and all my friends, for their affection, which m ade my stay at USC a memorable one. Finally, I would like to thank Game and Karen for all the candies, cookies, chit-chat and help. C o n ten ts D ed ica tio n ii A ck n ow led gem en t iii L ist O f T ables vi L ist O f F igu res v ii A b stra ct xi 1 In tro d u ctio n 1 1 .1 Models and Equations Proposed for Rheology of Filled Systems . . . 8 1 .2 Shear R ate Dependence of Viscosity . ........................................................... 1 2 1.3 Time Dependence of V is c o s ity .................................................................... 14 2 E ffect o f C h em ical S tru ctu re on R h eo lo g ica l B eh avior 21 2.1 In tro d u c tio n .........................................................................................................21 2.2 Experim ental D e ta il s ....................................................................................... 23 2 .2 . 1 M aterials........................................................................................................... 23 2 .2 . 2 Synthesis............................................................................................................24 2.2.3 Composite P re p a ra tio n ................................................................................ 25 2.2.4 Characterization .........................................................................................25 2.2.4.1 Differential Scanning C alo rim e try ........................................ 25 2 .2.4.2 Degree of C ro sslin k in g .............................................................25 2.2.4.3 Scanning Electron M icroscopy............................................... 25 2.2.5 Rheology ................................................................................................. 26 2.3 R e s u lts ...................................................................................................................26 2.4 D iscu ssio n ............................................................................................................ 48 2.4.1 Effect of chemical composition of the p a r tic le s .................................51 2.4.2 Effect of molecular weight of the m atrix ...........................................54 2.4.3 Comparison with models for shear dependence of viscosity . . 61 2.5 C o n c lu sio n s .........................................................................................................75 IV 3 T im e D ep en d en t B eh a v io r o f M o d el F illed P o lym ers 80 3.1 In tro d u c tio n .................................................................................................................80 3.2 E x p e r im e n t.................................................................................................................81 3.2.1 M a te r ia l..........................................................................................................81 3.2.2 Synthesis ...................................................................................................... 82 3.2.3 Composite P r e p a ra tio n .............................................................................. 82 3.2.4 Rheology ...................................................................................................... 83 3.3 R e s u lts ...........................................................................................................................83 3.4 D iscu ssio n ....................................................................................................................98 3.4.1 Effect of Chemical Interactions .............................................................99 3.4.2 Effect of Molecular Weight of the M a tr ix ........................................... 101 3.5 C onclusion..................................................................................................................107 4 R h eo lo g ica l B eh avior o f Irrad iated P o ly sty r e n e 111 4.1 In tro d u c tio n .............................................................................................................. I l l 4.2 E x p e rim e n ta l...........................................................................................................115 4.3 R e s u lts ........................................................................................................................ 116 4.4 D iscu ssio n ..................................................................................................................124 4.4.1 Analysis of Rheological M easurem ents with a Power Law . . . 125 4.5 C onclusion..................................................................................................................127 v L ist O f T ables 2.1 Characterization of beads ..................................................................................... 28 2.2 Initial slopes of rheology plots, and apparent yield stresses for P M M A - (Mw = 35,000) and P M M A ( M W = 75,000) matrices filled with crosslinked polymeric p a rtic le s .............................................................................29 2.3 Ree-Eyring param eters for P M M A ( M W = 35, 000) m atrix filled with crosslinked polymeric p a rtic le s .............................................................................65 2.4 Ree-Eyring param eters for P M M A ( M W = 75,000) m atrix filled with crosslinked polymeric p a rtic le s .............................................................................65 2.5 Ree-Eyring param eters for P M M A ( M W = 35,000) m atrix filled with crosslinked polymeric particles, tjn was fixed at 3650 Pa-sec and | at 145 P a - s e c ............................................................................................................65 2.6 Param eters for W ildemuth-W illiams model, for P M M A ( M W — 35,000) and P M M A ( M W = 75,000) com p o sites............................................................69 2.7 Fitted param eters for shear dependence of agglomerate size, for P M M A - (Mw = 35,000) and P M M A ( M W = 75,000) composites, using eq. 2.7 74 L ist O f F igu res 2.1 SEM photograph of PS beads crosslinked with 10% DVB at a mag nification of 2 0 ,0 0 0 X .......................................................................................... 30 2.2 SEM photograph of PM M A beads crosslinked with 10% EGDMA at a magnification of 2 0 ,0 0 0 X ............................................................................... 30 2.3 SEM photograph of PM M A beads crosslinked with 10% DVB at a magnification of 2 0 ,0 0 0 X ................................................................................... 31 2.4 SEM photograph of PS beads crosslinked with 10% DVB at a m ag nification of 2 0 ,0 O 0 X ..............................................................................................31 2.5 SEM photograph of fracture surface of P M M A (M W = 35,000) m a trix filled with DVB-PS particles, at a fracture tem perature of —170° C 32 2.6 SEM photograph of fracture surface of P M M A (M W = 35,000) m a trix filled with EGDM A-PM M A particles, at a fracture tem perature o f — 1 7 0 ° C ...................................................................................................................33 2.7 SEM photograph of fracture surface o iP M M A (M w = 35,000) m atrix filled with DVB-PM MA particles, at a fracture tem perature of — 17§°C 34 2.8 SEM photograph of fracture surface of P M M A (M W = 35,000) m a trix filled with EGDM A-PS particles, at a fracture tem perature of - 1 7 0 ° C ...................................................................................................................... 35 2.9 SEM photograph of fracture surface of P M M A (M W = 35,000) m a trix filled with DVB-PS particles, at a fracture tem perature of — 170°C 36 2.10 SEM photograph of fracture surface of P M M A (M W = 35,000) m a trix filled with EGDM A-PM M A particles, at a fracture tem perature of -1 7 0° C ...................................................................................................................37 2.11 SEM photograph of fracture surface o iP M M A (M W = 35,000) m atrix filled with DVB-PM M A particles, at a fracture tem perature of — 170°C 38 2.12 SEM photograph of fracture surface of P M M A (M W = 35,000) m a trix filled with EGDM A-PS particles, at a fracture tem perature of -170°C ...................................................................................................................... 39 2.13 Log-log plot of viscosity vs. shear rate for P M M A (M W = 35,000) composites at 2 0 0 ° C ............................................................................................... 40 2.14 Log-log plot of storage m odulus(G /) vs. frequency for P M M A ( M W = 35,000) composites at 2 0 0 °C .............................................................................41 2.15 Log-log plot of loss m odulus(G") vs. shear rate for P M M A ( M W = 35.000) composites at 2 0 0 ° C ................................................................................ 42 2.16 Semilog plot of loss factor(tan 8 ) vs., frequency for P M M A ( M W = 35.000) composites at 200° C ................................................................................ 43 2.17 Log-log plot of viscosity vs. shear rate for P M M A ( M W = 75,000) composites at 200° C .............................................................................................. 44 2.18 Log-log plot of storage m odulus(G') vs. frequency for P M M A ( M W = 75.000) composites at 200° C ................................................................................ 45 2.19 Log-log plot of loss m o d u lu s^ " ) vs. shear rate for P M M A ( M W = 75.000) composites at 200° C ................................................................................ 46 2.20 Semilog plot of loss factor(tan^) vs. frequency for P M M A ( M W = 75.000) and composites at 2 0 0 ° C ...................................................................... 47 2.21 Casson plot(plot of vs. 7 ?) for P M M A ( M W = 35,000) and com posites at 2 0 0 °C ........................................................................................................ 49 2.22 Modified Casson plot(plot of 7-2 vs. 7 2 x for P M M A ( M W = 75.000) and composites at 200° C ...................................................................... 50 2.23 Log-log plot of relative viscosity vs. shear rate for PMMA containing DVB-PS particles at 200oC .....................................................................................55 2.24 Log-log plot of relative viscosity vs. shear rate for PMMA containing EGDM A-PM MA particles at 200°C.....................................................................56 2.25 Log-log plot of relative viscosity vs. shear rate for PM M A containing DVB-PMMA particles at 200°C............................................................................57 2.26 Log-log plot of relative viscosity vs. shear rate for PMMA containing EGDMA-PS particles at 200°C............................................................................. 58 2.27 Ree- Eyring plot for P M M A (M W = 35,000) and composites at 200°C 63 2.28 Ree- Eyring plot for P M M A (M W = 75,000) and composites at 200°C 64 2.29 Plot of 1 / 4 > m vs 7 for P M M A ( M W = 35,000) composites at200°C . . 67 2.30 Plot of 1 / < f> M vs 7 for P M M A ( M W = 75,000) composites at200°C . . 6 8 2.31 Plot of agglomerate size vs shear rate P M M A ( M W = 35,000) com posites at 200°G .................................................................................................... 72 2.32 Plot of agglomerate size vs shear rate P M M A ( M W = 75,000) com posites at 2 0 0 ° C .................................................................................................... 73 3.1 Log-log plot of steady shear viscosity vs. aging tim e for P M M A ( M W = 35.000) composites at 200°C ..................................................................................84 3.2 Log-log plot of steady shear viscosity vs. aging tim e for P M M A ( M W = 75.000) composites at 200°C..................................................................................85 3.3 Log-log plot of transient viscosity vs. transient tim e, at various aging times, forP M M A ( M W = 35,000) filled with DVB-PS particles, at 2 0 0 ° <7............................................................................................................................. 8 6 vm 3.4 Log-log plot of transient viscosity vs. transient tim e, at various aging times, forP M M A ( M W = 35,000) filled with EGDM A-PM M A parti cles, at 2 0 0 °C ...............................................................................................................87 3.5 Log-log plot of transient viscosity vs. transient time, at various aging times, fo rPM M A ( M W = 35,000) filled with DVB-PMMA particles, at 2 0 0 °C .........................................................................................................................8 8 3.6 Log-log plot of transient viscosity vs. transient time, at various aging times, io iP M M A (M w = 35,000) filled with EGDM A-PS particles, at 2 0 0 °C ........................................................................................................................ 89 3.7 Log-log plot of transient viscosity vs. transient time, at various aging times, for PM M A (M W = 75,000) filled with DVB-PS particles, at 200°C. 90 3.8 Log-log plot of transient viscosity vs. transient time, at various aging times, for PM M A (M u;=75,000) filled with EGDM A-PM MA particles, at 2 0 0 °C ........................................................................................................................ 91 3.9 Log-log plot of transient viscosity vs. transient time, at various aging times, for PM M A (M W = 75,000) filled with DVB-PMMA particles, at 200°C ..............................................................................................................................92 3.10 Log-log plot of transient viscosity vs. transient time, at various aging times, for PM M A(M u,=75,000) filled w ith EGDM A-PS particles, at 2 0 0 °C ..............................................................................................................................93 3.11 Log-log plot of transient viscosity vs. transient time, without aging, iovPM M A[M w = 35,000) filled with crosslinked particles, at 200°C. . 94 3.12 Log-log plot of transient viscosity vs. transient time, at zero aging times, forP M M A ( M W = 35,000) filled with crosslinked particles, at 200°G..............................................................................................................................95 3.13 Log-log plot of transient viscosity vs. transient time, without aging , for PMMA(Mu, = 75,000) filled with crosslinked particles, at 200°C. . . 96 3.14 Log-log plot of transient viscosity vs. transient time, at zero aging times, for PM M A (M W =75,000) filled with crosslinked particles, at 200°G..............................................................................................................................97 3.15 Log-log plot of relative viscosity vs. aging time for PMMA containing DVB-PS particles at 200°(7...................................................................................1 0 2 3.16 Log-log plot of relative viscosity vs. aging time for PMMA containing EGDM A-PM M A particles at 200°C ..................................................................103 3.17 Log-log plot of relative viscosity vs. aging time for PMMA containing DVB-PM MA particles at 200°C ......................................................................... 104 3.18 Log-log plot of relative viscosity vs. aging time for PMMA containing EGDM A-PS particles at 200°C...........................................................................105 4.1 Steady shear viscosity as a function of shear rate for polystyrene at 2 0 0 ° C ........................................................................................................................ 117 IX 4.2 Storage m odulus(G') as a function of frequency for polystyrene at 2 0 0 ° C ...........................................................................................................................118 4.3 Loss modulus(Cr") as a function of frequency for polystyrene at 200°C.119 4.4 Dynamic viscosity^') as a function of frequency for polystyrene at 200°C...........................................................................................................................120 4.5 Complex viscosity^*) as a function of frequency for polystyrene at 2 0 0 °C ........................................................................................................................... 1 2 1 4.6 Loss factor(tan^) as a function of frequency for polystyrene at 200°C. 122 4.7 Storage m o d u lu s ^ ') and loss m o d u lu s ^ " ) as function of radiation dose at 2 0 0 ° C ......................................................................................................... 123 x A b stra ct The rheology of polym er composites containing crosslinked polym er particles(filler)in a polym er m atrix was studied w ith a W eissenberg rheogoniometer. The chemi cal composition of filler and m atrix was found to have a significant effect on the rheology of the composite. This was attrib u ted to a change in particle structure depending upon interactions between filler and m atrix. Weak particle-m atrix in teractions between a poly m ethylm ethacrylate(PM M A ) m atrix and the surface of polystyrene(PS) particles crosslinked with 10% divinyl benzene(DVB) result in re jection of particles by the m atrix. Therefore, in PM M A composites containing 20% DVB-PS particles, particles tend to cluster, resulting in high shear viscosity at low shear rates and highly non-Newtonian behavior. In dynam ic m echanical analysis, a clustered filler structure yields very small slopes in a log-log plot of dynamic moduli vs. frequency. In contrast, PM M A particles crosslinked w ith 10% ethylene gly col dim ethacrylate(EG D M A ) are well dispersed in PM M A m atrix, due to higher particle-m atrix interactions between polar groups. Therefore, PM M A composites filled w ith EGDM A-PM M A particles do not exhibit large shear thinning, and, in fact, rheological plots of PM M A filled with EGDM A-PM M A particles are parallel to those of pure PM M A m atrix. In order to explore the effects of the chemical com position, we prepared PS and PM M A particles crosslinked w ith DVB and EGDMA. In all cases, we disperse the particles in PMMA m atrix. PS particles crosslinked w ith 10% EGDM A are b etter dispersed in the PM M A m atrix, com pared to DVB-PS particles, due to the com patibilizing effect of EGDM A, and therefore the viscosity, at low shear rates, and shear thinning of PM M A filled with EGDM A-PS p arti cles are smaller than those of PM M A filled w ith DVB-PS particles. Crosslinking PM M A particles with DVB places DVB groups on PM M A particles, and there fore, particle m atrix interactions in DVB-PM MA filled PM M A are smaller than in EGDM A-PM M A filled systems. Therefore, particles tend to agglom erate in PM M A xi composites filled w ith DVB-PM M A particles, especially in a low m olecular weight PM M A m atrix. The molecular weight of the m atrix also affects interactions significantly, higher m olecular weight m atrix having higher particle- m atrix interactions. A dsorption of m atrix molecules onto the surface of filler particles increases w ith an increase in m atrix molecular weight and num ber of polar sites (per molecules). In order to exam ine this effect we com pared PM M A m atrices of molecular weights 35,000 and 75,000. Higher particle-m atrix interaction in high molecular weight m atrix resulted in lower relative viscosities for DVB-PS filled systems, due to b etter dispersion of particles in the m atrix. However, for EGDM A-PM M A filled composites, particles are well dispersed, and higher molecular weight m atrix does not affect the state of dispersion, significantly. Therefore, the relative viscosity of the P M M A ( M W = 75,000) composites filled with EGDM A-PM M A particles are higher than those of P M M A ( M W — 35,000) composites, due to b etter bonding between the filler and m atrix in high molecular weight m atrix. Composites filled w ith PS-EGDM A p arti cles behave similarly to DVB-PS particles, the relative viscosity of high molecular weight composites being lower than for the low molecular weight m atrix, though the difference is smaller compared to DVB-PS filled composites, especially at high shear rates. PM M A composites filled w ith DVB-PM MA particles have a lower relative viscosity w ith the high m olecular weight m atrix at low shear rates, due to better dispersion in the high molecular weight m atrix. However at high shear rates, p arti cles are well dispersed in both P M M A ( M W = 75,000) and P M M A ( M W = 35,000) m atrix and, then, the relative viscosity of the P M M A ( M W = 75,000) composite is higher due to better bonding in the high molecular weight m atrix. Chemical interactions between particles and m atrix also affected the tim e de pendent behavior significantly. W hen sheared at a shear rate of 1.4s- 1 particle agglom erates in PM M A composites filled with DVB-PS particles break down and, therefore, a significant decrease in the viscosity is observed. However, when allowed to rest, clusters are reformed resulting in increase in viscosity w ith tim e. The clus tered structure resulted in significant overshoots in transient viscosity experim ents. In contrast, the relative viscosity of PM M A filled w ith EGDM A-PM M A does not change significantly with shear or ageing tim e, due to absence of large agglomerates. In transient experim ents, this is exhibited by the absence of prom inent overshoot. DVB-PM M A particles form very weak clusters and the viscosity at 0.014s-1 , sub sequent to shearing at high shear rate, is very similar to th a t of EGDM A-PM M A filled systems. However, when allowed to rest DVB-PM M A particles tend to cluster, unlike PM M A particles crosslinked w ith EGDM A, and large increase in viscosity is observed. M olecular weight of the m atrix also affected tim e dependent rheology of com posites, w ith overshoots in transient viscosity m easurem ents being higher for low m olecular weight m atrix, due to the higher degree of agglomeration in low molecu lar weight m atrix. In fact, while an overshoot was absent, even after ageing for 15 hours, for P M M A ( M W = 75,000) filled w ith DVB-PM M A particles, a prom inent overshoot was present in P M M A ( M W = 35,000) composite filled w ith DVB-PM MA particles. Rheological behavior of polystyrene crosslinked by high energy electron radiation was also studied. Steady shear viscosity of the system at higher doses could not be m easured as the gelled polystyrene samples did not flow, when sheared. In dynam ic mechanical analysis higher crosslinking resulted in higher moduli, especially at low frequencies. Increase in storage modulus (G') was sharper than th at in loss m odulus(G /;), w ith increasing radiation dose, and in fact, at higher doses, G' is higher than G". However, crossover of G' and G" occured at different radiation doses for different frequency, and, therefore, crossover of G' and G" was not able to define the gel point. The dynamic moduli obeyed a power law at higher radiation doses, but unlike chemically crosslinked systems, power law behavior was exhibited only at various doses. Power law relaxation of the m odulus over a broad range of radiation doses was attrib u ted to the form ation of structures, which are only locally self similar, due to an inhomogeneous extent of crosslinking in the system , due to the distribution of trace oxygen leading to inhomogeneous crosslinking and scission. C h a p ter 1 In tro d u ctio n The processing of polymer composites is very im portant in industry. The inclusion of filler often results in reduced cost of m aterial and improvement in mechanical, ther mal, electrical, magnetic and physio-chemical properties.However, incorporation of filler also results in complex rheological properties and increased cost of processing. Numerous studies have been carried out to elucidate the effect of filler on the rheo logical behavior of polymers and excellent reviews are available[1-4] . However, due to the complex nature of the problem several aspects are still not well understood and there is need for further investigation. Filled systems with industrial fillers such as carbon black, calcium carbonate, talc and mica have been the focus of m any studies. It has been observed that the presence of filler results in higher steady shear viscosity and dynamic moduli. In steady shear experim ents, inclusion of filler not only results in enhanced viscosity, but also makes the system behave in a highly non-Newtonian m anner and results in shear rate and tim e dependent viscosity. For a sufficiently high filler content, the steady shear viscosity of a system tends to become unbounded at low shear rates, which is often designated a yield phenomenon [5]. In small am plitude oscillatory tests, the presence of filler results in higher dy namic moduli, especially at low frequencies. In fact, for sufficiently high concentra tions of filler, a plateau may appear, in a logarithmic plot of storage m odulus(G ’) as a function of frequency, at low frequencies. This plateau is different from the high frequency plateau corresponding to the suspending medium, and has been found to 1 be related to the phenomenon of yield[6 ]. The effect of filler tends to become smaller at higher frequencies. The basic param eters affecting the rheological behavior of a filled system are a) The content of filler. b) Size and size distribution of filler. c) Shape and surface of the filler. d) Surface composition of the filler. e) Chemical composition of the m atrix. f) Presence of surface modifiers which might affect the chemical interactions between filler particles and between filler and m atrix. The viscosity, as well as the dynamic moduli, of filled systems increases with increasing filler content. For HDPE filled with glass beads, dynamic shear storage modulus increased by almost an order of m agnitude, when the volume fraction of glass spheres was increased from 10% to 50%[7]. O ttani et al. 8 have carried out shear experiments for CaCOz filled LD PE over a wide range of filler loading and have reported an increase in viscosity with filler loading, especially at low shear rates, and the appearence of yield for a CaCOz content of 5%. Rong and Chaffey 9 have reported an increase in dynamic moduli for TiO 2 filled polystyrene, with increase in filler content. Enhancem ent in rheological properties in nonagglomerating systems eg. polymers filled with glass beads, is prim arily due to the presence of high modulus particles and formation of mesophase at the filler-matrix interface. However, in case of agglomerating systems, eg. CaCOz filled polymers, a significant amount of m atrix gets immobilized as it is trapped between the agglomerated filler particles, increasing the effective volume of the filler and, therefore, increasing the viscosity and moduli of the system. Ek et al.[10] have observed a reduction and a shift towards low tem perature of the 7 relaxation peaks and towards higher tem perature of the (3 relaxation peaks, with addition of CaCO 3 in dynamic mechanical analysis of HDPE. The reduction and shift of the (3 peaks have been attributed to a reduction in mobility of the polymer molecules due to adsorption on the filler surface 1 1 . However, it is highly probable that, in systems with agglomerating particles, the reduction in loss factor peak occurs prim arily due to immobilization of m atrix chains trapped within the agglomerate. Li and Masuda[12] have studied the effect of loading, size and rheological history on the dispersion of CaCO 3 particles in polypropylene melts. They reported th at, for 30% loading, composites filled with low diam eter particles(avg. diam eter ~ 0.15^m) show a much higher value of storage modulus((7') in the low frequency region compared to th at filled with large particles(avg. diam eter ~ 4.0//m). Also, the modulus in the low frequency region is affected by shear history, the plateau being absent initially but appearing for repeated m easurements. Particle size also affects the rheological behavior of P S / CaCO 3 system, with a solid content of 30%, smaller particles produce larger increases in steady shear viscosity and a greater decrease in normal stress[13]. However some studies have shown an insignificant effect of particle size on the rheology[14, 15], for a solid content of 20%. Metzner[3] has suggested, th at for dilute suspensions, with solid content upto 2 0 %, modest changes in particle size are of no consequence. However, for very high concentrations of solid, the system must dilate locally to enable one layer of the particle to slide past a layer of skrw moving neighbours, and, then, even modest changes in particle size may affect this motion significantly. Polsinki et al. [ 16] have investigated the effect of filler size distribution using polybutene filled w ith glass spheres of two size ranges of average diam eter 15 and 78/xm. W hen the two sizes were mixed together, a reduction in the relative viscosity, compared to systems filled w ith unimodal sized particles was observed, especially for volume fractions of total solids greater than 0.3%. The inclusion of anisometric fillers may yield higher viscosity[l7] and, stronger non-Newtonan effects depending upon the ratio of the two axes[18]. In fact, due to orientation effects, such suspensions may exhibit anisometric rheological behavior, making the m easured rheological properties dependent on the m ethod of m easurem ent. W hite et al[ 19] have observed significant differences in viscosity curves for PS filled with 20% of glass beads and glass fibers. In contrast, styrene acrylonitrile (SAN) copolymer filled with glass beads and fibers exhibit identical viscosity curves for 35% loading[20]. However the aspect ratio of the short fibers as well as their mechanical stability during the mixing operation in this study were not reported. Surface area of the filler has been reported to have a significant effect on the viscosity and yield stress values for polymers filled with 3 carbon black[2 1 ], as particles with higher surface area possess higher surface energy and, therefore, have a higher tendency to agglomerate. Minagawa and White[22] examined the steady shear viscosity of two low density polyethylenes, two high density polyethylenes and a polystyrene filled with three types of surface treated TiO 2 particles in the size range of 0.18-0.25 fim. The relative influence of AI 2 O3 treated TiO 2 on the five polymers varied inversely to the melt viscosity of the polymers. Also the effect of AI 2 O 3 / S i 0 2 treated T iO 2 particles is higher than AI 2 O3 treated T i 0 2 • Similarity, for suspensions of alum ina particles, in water or in 60% glycerine in aqueous solution, change in pH or in viscosity of the suspending media affected the particle-particle interactions and state of dispersion, and, therefore, significant changes in rheology were observed. Kosinki and Caruther[23] have observed a significant effect of m atrix molecular weight on the stress growth function. W hen the continous phase molecular weight was slightly greater than the entanglem ent molecular weight, significant overshoots were observed. These overshoots were absent for systems where the molecular weight of thecontinous phase was less than or much greater than the entanglem ent molecular weight. Malkin in his review[l] has discussed the effect of molecular weight on the m atrix over the yield stress. It was stated that for a monodisperse m atrix, molecular weight does not have any significant affect. However, going from mono to poly disperse polymer, yield stress changes by tens of times. The surface properties of the filler and the interactions between filler and m atrix also play an im portant role in determ ining the flow characteristics of the filled sys tem. For P P filled with Ca(7 0 3 [ 2 4 , 25], PP filled with mica[26] and P S — CaCO^ systems, surface treatm ent of the filler resulted in better bonding between the filler and the m atrix and a significant reduction of melt viscosity. However for glass beads filled systems, surface treatm ent resulted in enhanced viscosity and dynamic moduli[7, 27]. Similar observations were made for low density polyethylene filled with nonagglomerating stainless steel spherical powder with average diam eter of 15//m[29]. Again, the increase in modulus was dependent on type of surface tre a t ment and method of surface treatm ent application. 4 The type and extent of surface treatm ent does not only determ ine the extent of change in rheology, but can influence the direction of change. Scott et al.[28] have carried out experim ents with CaCOz filled PE systems. Treatm ent of CaCOz by 7 - aminopropyl triethoxysilane(7 -APS) or 7 -methacryloxy propyl trim ethoxy silane(7 - MPS) results in a reduction in dynam ic moduli and increase in tanS compared to the untreated case. However, solution deposition of ethylene propylene diene rub- ber(EPD M ) on the particles resulted in initial increase in dynamic shear modulus upto a specific am ount of rubber and a drastic reduction after th at. EPDM grafted with maleic anhydride(M A) resulted in an decrease in dynamic shear moduli and a subsequent increase with increasing rubber concentration.lt was postulated that surface treatm ent using 7 -APS and 7 -MPS resulted in better dispersion of the par ticles resulting in lower moduli. Small am ounts of EPDM grafting did not influence the dispersion and thus the moduli incresead due to the higher modulus of EPDM . However, at high am ounts of EPD M , the extent of dispersion improved significantly resulting in drastic moduli reduction. However for EPDM-MA grafted system, a significantly better dispersion was achieved for a small amount of grafting resulting in reduced moduli. At high am ounts, the modulus of the composite increases due to a bulk affect. Systems containing industrial fillers are complex and difficult to characterize. Moreover, often various effects are superimposed. To study and quantify these various effects, systems should be designed in such a way that factors like par ticle size,size distribution, shape, surface, m atrix molecualr weight and molecular weight distribution and chemical interactions between particles and between parti cles and the m atrix can be quantified and controlled. Some work has been carried out on model systems eg. glass bead filled systems[7,16,27,30-33], polystyrene par ticle suspensions[33, 34], styrene-divinyl benzene copolymer particles dispersed in solvent or polystyrene solution[35, 76] and polymeric m ethacrylate particles dis persed in silicone fluids and stabilized by an ABA-triblock copolymer consisting of poly(dimethylsiloxane) (PDM S) A-block and PS B-block[37]. A comprehensive un derstanding of the affect of chemical composition of the particles and the m atrix, on the various interactions and thus on the rheology is still lacking, however. 5 Polymeric systems containg monodisperse crosslinked polymer particles, synthe sized in emulsifier free emulsion polym erization[38-40,44], can be used as model filled systems. Since no emulsifier is used, particles are surfactant free and clean. Chemical interactions can be changed and controlled by varying m atrix composition, particle polymer, amount of crosslinker, surface modification and by using compati- bilizers. Characterization techniques for particles and composites included scanning electron microscopy(SEM), differential scanning calorim etry(DSC), crosslinking de term ination by swelling[43], Fourier transform infrared spectroscopy(FTIR ), X-ray photoelectron spectroscopy for the analysis of chemical composition of the beads and therm ogravim etric analysis(TGA) of therm al stability. Therm al stability of the composite was ensured by the addition of 0.3 wt% of antioxidant[42] Previous studies[15, 41] have established that with increased loading, m elt vis cosity and dynamic moduli increase for polystyrene(PS), polym ethyl m ethacry- late(PM M A ) and polybutyl m ethacrylate(PBM A ) matrices. For poly m ethylm etha- crylate m atrix containing 30 wt% of PS particles crosslinked with 2 % divinyl ben- zene(DVB), yield and frequency independent dynamic moduli at low frequencies were also observed. Variation in particle size did not make any significant change in rheological be havior of DVB-PS filled polystyrene. In fact for particle sizes of 0 .2 -0 .8 /L zm , steady shear viscosity and dynamic moduli plots overlap[15]. Crosslinking density also seems to make no significant im pact on rheology. For polystyrene containing DVB- PS particles, crosslinking density variation from l-10% (molar of DVB) did not influ ence the flow characteristics much[l5]. Similar observation was m ade for PS m atrix containing ethylene glycol dim ethacrylate(EGDM A) crosslinked PM M A beads and, PM M A and PBMA matrices containing DVB-PS beads in the crosslinking density range 2-10%[41]. Rheological studies for systems containing beads of varying composition showed different flow characteristics, depending upon the m atrix and bead composition. For polystyrene matrices, beads of different composition are not easily distinguishable Theologically. However, PMMA m atrix filled with 20 wt% of crosslinked polymeric beads show very different flow behavior depending upon bead composition. Com posites containing PMMA beads crosslinked with EGDMA have m elt viscosity curve 6 almost parallel to that of the pure PM M A m atrix and show little shear thinning. PS particles crosslinked with DVB, however, results in highly non-Newtonian systems, viscosity changing by an order of m agnitude for a change in shear rate from 1 0 - 2 s_1 to ~ 5 s-1 . In fact 40%, of such beads resulted in yield and a low frequency plateau in dynamic moduli plots. PBM A m atrix also show different rheological curves for particles with different compositions, though the variations are relatively smaller. It was postulated th at systems containing particles and m atrix of identi cal composition, result in the lowest viscosity enhancem ent at low shear rates and lowest moduli in dynamic mechanical analysis(DM A), while dissimilar compositions of m atrix and filler exhibit highly non-Newtonian behavior. This phenomena was attributed to the state of dispersion of particles in the matrix. Particles identical in composition to the m atrix yielding the most uniform dispersion, while particles differing in composition forming agglom erated structures[41 . The degree of agglomeration can also be varied greatly by small modifications in chemical composition of the particles or by providing a shell, of different polymer, on the particles[45]. Introduction of 5% polyvinyl phenol in PS beads crosslinked with D V B(PSV P beads) makes these beads more compatible with PMMA m atrix resulting in b etter dispersion. Im provem ent in dispersion makes the system behave in a more Newtonian m anner and results in eradication of yield. Similarily a shell of EGDM A-PM M A on DVB-PS beads makes them more compatible with PMMA. Chemical interactions can also be modified by using different crosslinkers or by using compatibilizers. The effect of m olecular weight of the matrix on such inter actions also needs investigation. A full understanding of the shear rate dependence of viscosity which in tu rn is dependent over degree of agglomeration and cluster size, is also lacking. The mechanism and kinetics of destruction of agglomerates under shear and reform ation when allowed to rest, are also very im portant aspects of rheology and need further study. Finally, a model is required which can predict the rheological behavior, taking into account the specific interactions among the particles and, between m atrix and particles. In this study, we attem p t to introduce specific interactions by varying the chem ical composition of filler and m atrix ando analyse the affect of such interactions on rheology. An attem pt has been made to understand the m echanism of form ation and destruction of clusters and to describe the effect of chemical interactions thereupon. 1.1 M o d els and E q u ation s P r o p o se d for R h eo lo g y o f F illed S y stem s Analysis of the rheological behavior of composites is closely related to the rheology of suspensions, as most of the theories predicting viscosity and m oduli of composites have their origin in the theory of the viscosity of suspensions. Einstein[46] proposed the first model to predict the viscosity of dilute suspensions of fing rigid spheres suspended in a Newtonian fluid. The viscosity of a suspension, 77,is related to the viscosity of the suspending medium, 77!, and the volume fraction of the filler, < / > 2, according to: 7 7 = 771(1 + ^ ^ 2 ) (1.1) where fc# is the Einstein coefficient (or intrinsic viscosity) and has a value of 2.5 for dispersed spheres. However, Einstein’s model assumes no interaction between the particles and is valid for very dilute suspensions with noninteracting particles dispersed in a New tonian media. Power series models: 7, = ( 1 .2 ) 71 = 0 where higher order terms represent various interactions, have also been proposed [l]. Equation(1.2) can also be w ritten in a dimensionless form as: VbP= - — = J2 ( L 3) Vo n=1 where rj0 is viscosity of the suspending media. The value of the first coefficient & ! for suspensions containing spherical particles is 2.5. &2 has been associated with hydrodynam ic interaction between the particles and its value varies greatly in the literature, with values ranging from 4.4 to 14.1 in theoretical papers. The most reliable value for spherical particles is 14.1 [47, 48). The value of 63 is even less determ ined and its physical significance is also not understood very well. The concept of a maximum degree of loading, has been introduced. To have any physical meaning, < f} m < 1 . Then, rj8p can be w ritten as a function of reduced (f) concentration < f> r = - — so that as < f> T —> 0 , r j 8p — > k ^ 4 > and as < f> T —> 1, 7}ap — > 0 0. Prn The generalized equation is of the form lisp = Y C n^r" (1-4) 71 — 1 A nother equation proposed by Thom as [49] is of the form 7jgp = -f 10.054 > 2 + Aexp(B<f)) (1-5) where A = 0 .00273, B = 16.6 has been found to be satisfactorily for suspension of spherical particles from 0.1 to 440 fi. However, equations of these forms are not always very convenient to use. More over, predictions using these models are dubious since all the experim ental data can be described by selecting coefficients. Mooney[50] has proposed a one param eter expression : r 2-5^ \ (1 * ■ < Vr= — = exp(- — ) (1.6) TJo 1 (pT where < f> T = s<f>, the coefficient s determ ining th e maximum degree of filling and having values between 1.35-1.91. This formula correctly reduces to rj8p = kE(f> as < f> — > 0 and r]ap — » 00 as c f)r — > 1 By writing M ooney’s equation in an exponential series and ignoring higher terms Eiler’s equation[51] of the form: * = ( 1 + n f x ) ’ 1 8 can be derived. 9 Simha[52] developed a cell model to obtain a theoretical expression for the rela tive viscosity: lim — = - ^ [ -----^ x — ] ( 1 .8 ) where for the spherical particles, is depndent on the type of packing, being 0.52 and 0.74 for cubic and hexagonal packings respectively, f is a semiempirical param eter which depends on the particle size and the volume fraction (f> . A totally different equation was developed by Brinkman[53] and Roscoe[54]: Vr = [1 - < £ ]M where [ 77] is intrinsic viscosity. This equation seems to have physical meaning only in the case of infinite polydispersity, i.e. < j ) m — > 1 , because of the absence of 4 > m term . Krieger and D ougherty[ 6 6 ] and later W ildem uth and W illiam s[72] modified this equation to incorporate the concept of a crowding factor K and a maxim um packing efficiency to get: * = [ T ^ j ¥ = [1 - (1'10) Frankel and Akrivos[56] by a purely hydrodynam ic treatm ent of resistance tof flow through narrow space around spheres, suspended in the liquid, derived, for high filhng range: 9 L Tjr = $ - + < ! ) l i m 7?r = ----------- -—r - (1.11) ■ /r 81 - ( / - ) s v ; Several other equations, empirical or theoretical, for spherical and non-spherical particles, are cited in various reviews[57, 58, 59]. However, only the equations which are pertinent to our analysis, are cited here. Suspensions of particles in non-Newtonian fluids are still more complicated to analyse and model. Rheology of non-interacting spherical particles has been an alyzed theoretically in both power law and second order fluids. A constitutive 10 equation developed by Kaloni and Stastna[60] for dilute suspensions of rigid non interacting spheres in second order fluids predicts an enhancem ent of the normal stress function and no variation in viscosity. Tanaka and White[61] developed a theory for suspensions of interacting particles in a power law fluid, based on the cell theory of Frankel and Acrivos[56]. Particle interactions were incorporated as a linear addition to the equation for noninteracting particles. The final equation thus derived was of the form: 1 = {Y h ) + f W v ° ( 1 -1 2 ) where yield stress, Y, can be expressed in term s of the Hamaker constant, surface potential and dielectric constant. At higher shear rates viscosity is represented by the power law: rl = (B/r) + C"(4>,n)Ki'-1 (1.13) This model also predicts a shear viscosity independent of particle concentration. Jarzebski[62] theory is also an extension of Frankel and Acrivos[56] theory but it predicts a dependence of shear viscosity on particle concentration, with this influence increasing with increasing power law n index of the suspension. The relative viscosity is given by: Vr = ( j )i/ j ( ?^ ) ’ ( T ) - /*7 (1.14) = f* n cos e Sin BM where distance between and J ° ( £ + l - c o s 9) a is the radius of the particle. Sun and Jayaraman[63] have derived for rigid spheres in a second order fluid: Vr = [1 + 2.56 - 6.$36j2i ’io2/v!} (1-15) where r \ 0 and are the m edium viscosity and prim ary norm al stress coefficients respectively. 11 1.2 Shear R a te D e p e n d e n c e o f V isco sity Shear rate dependent viscosity, sometimes accompanied by a yield stress, is often observed for suspensions.Yield stress values can be obtained from extrapolation of the linear part of shear stress-shear rate curve to shear ra te — > 0 . Alternatively an equation, proposed by Casson[64] can be used to estim ate the value of the yield stress: r 1 /2 = k0 + k ^ 1/2 (1-16) However for non-Newtonian suspending media, sometimes, a plot of t * vs 7 ? is not linear and a modified equation has been proposed[65]: t '/* = k„ + (i.i7 ) Vo where rja and T ) 0 are the apparent viscosity and zero shear viscosity of the dispersing medium, respectively. Introduction of shear results in a change in structure, breakup of agglomerates into smaller ones, and is reflected by a change in viscosity. Empirical relationships to describe the shear dependence of viscosity include a power law: 71 = k j ~ n ( 1-18) where n and k a re param eters normally determ ined from experim ental data. Krieger and Dougherty[6 6 ] obtained an equation for the shear dependence for non-agglomerating systems, where only doubiets-to-singlets transform ation takes place, doublet form ation due to Brownian m otion and doublet breakup due to shear stress: 71~ V x = (1 + - ) ' 1 ( 1.19) Vo - Voo To where 7]0 and 77^ are the Newtonian plateau at low and high shear rates respectively,r is the shear stress and r c is a critical shear stress related to Brownian forces. A comparison of this equation with experim ental data yielded empirical equa tions for the zero shear and high shear limits of the viscosity 67. 6 8 Vr„ = (1 - 7.5^) — l'50 ( 1.20 ) 12 ^ = (1 - 1.47*)-1- ” (1.21) For agglomerating particles, agglomerates of a large num ber of particles may form which will breakup into small clusters when shear is applied. Cross[69], using a kinetic argum ent, with the cluster breakup rate proportional to proposed: Vo ~ Voo n 0 0 ^ rl = V~ + r T ^ (1-22) Maron and Pierce[70], assuming the presence of only two types of flow unit in any suspension, one Newtonian and one non-Newtonian, has simplified the generalized Ree-Eyring[71] equation to: Z ifa x 2 sinh_1/?27 , ,sinh_1/327 n 7] = -------- 1 ---------------------- = a 4- o-------------- (1.23) a i a 2 7 7 W ildem uth and W illiams[72] have used the concept of shear rate dependent m ax imum packing fraction, and, based on the kinetic equilibrium between agglomerated and dispersed phase, derived an equation for maximum packing fraction: 1 1 / 1 1 X , , « X = ---------( ------------------) / (1-24) 4>m 4>m0 4>m0 4>Moo where (j> M 0 an(^ ^M oo are the low shear and high shear values of m aximum packing fraction 0 m an-d f is fraction of the total particulates, that exist in dispersed phase. However dependence of f on shear rate is not known and an empirical relation ship, of the type / = ^ ^ , where r is shear stress and A and m are adjustable param eters, has been proposed. Tsenglou[73] has proposed a model, incorporating the size of agglomerate in the viscosity equation. Viscosity and yield stress are evaluated by calculating energy dissipation due to cluster movement and forces acting upon it.T he final equation is of the form: r(< t> > 4 > c ) = V o i [ ^ — }2HN/2) + (L25) 1 — 0 1—0 13 where Yc is the yield stress at the onset of the appearence of yield(i.e. < f> c < 0 ). For (p < C 4> c this equation reduces to V = V o [ ^ — ]2 + W 2 ) (1.26) 1 - 0 1.3 T im e D e p e n d e n c e o f V isc o sity Harris[74] proposed, for the tim e dependent viscosity: V(t) = Vo - f “ t ' ) d i ' I 1-27 ) J — oo with a fading memory: r ^ l e x p [ - ^ ^ ] < i A (1.28) Jo A A W here i2(A) is a viscosity spectrum , A is the relaxation time, l 2^ t is the second invariant of the strain rate tensor and r \ 0 is the undisturbed viscosity. Slibar and Paslay[75] proposed for a m aterial exhibiting yield stress: ^ n @ + / ( = - „ VTo) ( ) where r is the time and deform ation rate dependent yield stress, initial and final values being and r„, rcrit is the value of yield stress at time t and I I d and I I s are the second invariants of deform ation and reduced stress tensor respectively. The m aterial response is given by the constitutive equation: = 0 2 c — Sij f o r \ J T l g < T „ i t (1.30) V 1 Is where d i j and s ^ j are i j th components of deform ation and stress tensors, respectively. Onogi and coworkers [76, 77] have studied the tim e dependent rheology of suspen sions, initially sheared at high shear rate until a steady state is reached Subsequently, the shear rate was dropped to a value much lower than to the initial shear rate and 14 the shearing stress was recorded as a function of tim e. A simple kinetic model gives the shear stress as a function of time: cr(t) — a 0 ta n - 1 -f ta n - 1 — -AA ^ = ^ « ..---- sl (i.3 i) V m - ° o f 4 - tan 1 l - where <j{t) is the tim e dependent shear stress, aQ and am being the initial and final equilibrium stres, t* is the tim e corresponding to m axim um rate of change of shear stress and a is a constant. Ghosh and Bhattacharya[78] have m easured the viscosity of black coal-oil sus pensions, as a function of ageing tim e and proposed an em pirical equation of the type: < j > m = < f> m o + K(1 - exp~at) (1.32) where < j)mo is the m axim um volume fraction for freshly prepared (well dispersed) suspensions and K and a are adjustable param eters. A nother form suggested by M ercer and Weymann[79] predicts th e tim e depen dent viscosity 7 7 (t) to be: r}(t) = A exp[— (£/ti)] + B e x p (—t/T2) + C (1.33) 15 R e fe r e n c e L ist [1] A. Y. M alkin, Rheology of Filled Polym ers, in “Advances in Polym er Sci ence” , 96,70(1990) [2] M. R. K am al and A. M utel, J. Polym. Engg., 5, 393(1985) [3] A. B. M etzner, J. Rheol., 29,739(1985) [4] Yu. G. Yanovsky and G. E. Zaikov, in “Polym er Yearbook” , 5, edited by R. A. Pethrick, Harwood Academic Publishers, New York, pp 61-86(1989) [5] V. M. Lobe and J. L. W hite, Polym. Engg. Sci.,19,617(1979) [6] S. Onogi, T. M atsum oto and Y. 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This is attrib u ted to variations in particle-particle and particle-m atrix interactions w ith modification in chemical com position. It has been postulated th a t particle-particle interactions, stronger th an the particle m atrix interactions, m ay lead to agglomeration or aggregation of particles, the am ount of aggregation increasing w ith the am ount of filler. As the am ount of filler is further increased , ultim ately a filler network may form at a critical degree of loading . The phenom enon of yield has been often associated w ith network form ation[l]. As the size of a filler agglom erate increases, more m atrix molecules are im m obi lized as they become trapped between filler particles. This results in an enhancem ent of effective filler content and yields higher viscosity and moduli. As the shear rate is increased, some agglomerates are broken, and the viscosity of the system decreases. Therefore, filled system s often exhibit shear thinning behavior. A b etter interaction between m atrix and filler tends to increase the viscosity and m oduli as polym er strongly bonded to or adsorbed at the filler surface restricts the m obility of the polym er m atrix. However, a b etter interaction between filler particles and m atrix also reduces interaction between the particles, and thus produces a b etter disper sion. Increased dispersion tends to decrease the viscosity, and therefore, the effect of chemical interaction on the viscosity is very complex. 21 Particle-particle interactions consist of hydrodynam ic and non-hydrodynam ic interactions. Hydrodynam ic interactions result from a change in fluid velocity in the vicinity of other particles. Nonhydrodynam ic interactions may include electri cal forces arising from the charges on the particles, Brownian forces, London-Van der Waals forces and direct chemical interactions between the particles. Leong and Boger[2] have studied suspensions of coal w ith varying surface charge densities and ionic strength. Rheological behavior of such system s changed from low viscosity Newtonian to high viscosity pseudoplastic yield behavior, depending upon the sur face chemistry. Viscosity was found to be least at a point where transition from attractive to repulsive particle interaction takes place. Tsai and Zammourri[3] have studied the rheology of graphite, polystyrene and glass particles suspended in one nonpolar(silicone oil) and two polar liquids (ethylene glycol and glycerol). The Ostwald-de Waale power law was used to characterize the rheology of suspensions and the flow behavior index was found to be related to inter particular Van der Waals attraction forces, quantified in term s of the dimensionless Ham aker constant. Brownian m otion plays an im portant role in determ ining the flow behavior of filled systems of submicroscopic particles. Interparticle attractions and externally imposed forces are opposed by brownian forces. In fact, at nanom eter sizes, brownian motions and interparticle attractions are in dynam ic equilibrium while for m acro scopic sizes hydrodynam ic forces dom inate. Brownian m otion of particles is char acterized by a therm al energy | kT and a tim e 67Tfi0a3/ k T required for a particle to move a distance com parable to its radius. W hether a suspension is in a stable state or in flocculated state depends upon the relative values of dimensionless interaction energy for Brownian forces A / k T , where A and k are Haam aker and Boltzm ann con stants respectively, dimensionless interaction energy of electrostatic forces e^Q 2 a /kT where e and ip0 are dielectric constant and surface potential of the particles respec tively, and dimensionless interaction energy of steric forces ( 1 / 2 — x )« A 2/Vs where X, A and Vs are Flory-Huggins param eter, thickness of adsorbed layer and volume of solvent molecules respectively. W hen A / k T > 1 and e ^ 2akT < 1 or 1 / 2 - X < 0 the suspension is in flocculated state, while if e, ip02akT 1 or 1/2 - X < 0, the suspension is in stable state[4]. 22 Otsubo et al.[5] have observed considerable change in the viscosity of suspen sions of silica in polystyrene solutions, depending upon the heat treatm ent of silica, interpreted as due to differences in the agglomerated structure depending upon the num ber of -OH groups present on the surface. Presence of hydroxyls on the silica surface results in a higher surface energy of silica, and close enough particles tend to agglomerate through hydrogen bonding. Chemical interactions can be varied greatly by making changes in the composition of filler surface or of m atrix. In fact for noninteracting particles, surface treatm ent of the filler with a coupling agent, often results in higher viscosity and moduli[6-8] which is attrib u ted to b etter bond ing between filler and m atrix. The opposite is observed for agglomerating particles, where enhancem ent in com patibility with the m atrix, due to coupling agent results in a better dispersion of the particles. The composition and molecular weight of the m atrix also have a profound effect on rheology. For suspensions containing alum ina or styrene-acrylamide copolymer particles in water, or in an aqueous solution of glycerin, increasing the pH of the suspension resulted in a significant increase in viscosity[9], due to enhancem ent in particle-particle interactions with decrease in absolute value of ( potential. Reducing the viscosity of the m atrix resulted in en hanced relative viscosity[10] and highly shear dependent behavior 9 , as the m atrix viscosity affects the dispersed state and its change with shear rate. For composite polymeric systems, the chemical nature of two phases influences the interactions. 2.2 E x p erim en ta l D eta ils 2.2.1 M aterials Polym ethyl M ethacrylate was obtained from Polysciences. Inc.(Mw 75,000) and Scientific Polym er Products, Inc.(Mw= 35,000). Styrene monom er, and divinyl ben zene and ethylene glycol dim ethacrylate crosslinkers were purchased fron Aldrich Chemical Co. . Styrene is 99% pure and inhibited by 10-15 ppm 4-tertiary butyl- catechol(4-TBC). Divinyl benzene consists of a m ixture of 55% of m eta and para isomers, 42% of ethyl vinyl benzene and 3% dietylbenzene, and inhibited with 1000 23 ppm 4-TBC. Ethylene glycol dim ethacrylate is 98% pure. 25±5 ppm of hydro- quinone inhibitor is also present. All monomers and crosslinkers were stored at — 5°C and were purified, in order to remove the inhibitor, prior to polym erization. Styrene and divinyl benzene were washed w ith an equal volume of an aqeous solution of 10% sodium hydroxide for four tim es[ll], and m ethyl m ethacrylate and ethylene glycol m ethacrylate were purified by bubbling nitrogen for 30 m inutes[12]. Potassium persulfate initiator and sodium hydroxide are certified Fisher Scientific products. Deionized w ater was purchased from Sparklettes, m ethanol from EM Science and dry nitrogen from MG Industries Gas products. 2,6 di-tert-butyl-4-m ethyl-phenol(B H T) antioxidant was supplied by Aldrich Chemicals Co. 2.2.2 S ynthesis Crosslinked monodisperse particles were synthesized in emulsifier free emulsion poly m erization, in an internally stirred reactor according to m ethods drescribedfll, 12]. Polystyrene particles crosslinked w ith divinylbenzene(DVB-PS)and w ith Ethylene glycol dim ethacrylate(E G D M A -PS), as well as poly m ethyl m ethacrylate(PM M A ) particles crosslinked w ith divinylbenzene(DVB-PM M A) and w ith ethylene glycol dim ethacrylate(EG D M A -PM M A ) were synthesized by copolymerizing 10 mole per cent of the crosslinker w ith the monomer. 650 ml. of w ater was placed in an internally stirred reaction flask equipped with a condenser and the flask was placed in a heated water bath, tem perature m ain tained at 80°C. Nitrogen was bubbled through the w ater and flow was continued throughout the reaction. The stirrer speed was set at 350 rpm . After 15 m inutes monomer and crosslinker, free of inhibitors, were added to the flask and allowed to equilibrate for 20 m inutes. 0.16 g of potassium persulfate initiator, dissolved in 30 ml. of w ater was added, and washed in w ith another 20 ml. Reaction was allowed to continue for 4 hours, after which the contents of the flask were poured into a polyethylene bottle and kept at — 15°C for 1 hour and then allowed to m elt. The latex was filtered through glass wool, to remove coagulates, and then was stored at —15°C for 12 hours. After melting, the latex separated into two phases, poly m er beads at the bottom and clear water at the top, and were easily filtered out. 24 Beads were washed repeatedly w ith m ethanol and w ater to remove any unreacted momomer and then dried in a vacuum oven, at 550C , for 24 hours. 2.2.3 C om p osite P reparation M atrix polym er was m elted at 175°C in a brabender plasticorder and 0.3% of antiox idant added to prevent therm al decom position[14]. Powdered polym eric filler was added to the m olten polym er and mixed at 175°C for 15 m inutes, for equal tim e intervals at 50 and 100 rpm . Mixed samples were placed between two alum inium plates, in a concentric circular mold of inner diam eter 5 cm. anthickness 1 mm , and was compression molded at 175°C and 1.5 x 107 P a in a Dake hydraullic press for 15 m inutes and then cooled to room tem perature. 2.2.4 C haracterization 2.2.4.1 Differential Scanning Calorim etry Glass transition tem perature(T 5) of the filler beads was determ ined by differential scanning calorim etry(DSC-4, Perkin Elm er). Samples were heated to 220°C for 2 m inutes, and quenched to 50°C . After 2 minutes samples were heated from 50°C to 220°C at 10°C /m in. Tg was identified as the m idpoint of the endotherm ic displace m ent between linear baselines. 2.2.4.2 D egree of Crosslinking The degree of crosslinking was determ ined by swelling the partcles in toluene as described[13] 2.2.4.3 Scanning E lectron M icroscopy Particle size and fracture surface structure of the composite was exam ined by scan ning electro microscope(SEM ). To determ ine particle size, a latex of polym er beads was diluted w ith an equal am ount of m ethanol, a drop of the m ixture placed on a cover glass and dried in clean air at room tem perature. The cover glass was at- tatched to a alum inum sample holder and coated with about 200A° of gold and 25 palladium using a sputter coater. Samples were examined at magnifications from 103 to 2 x 104. To examine fracture surfaces, composites were annealed, at 200°(7, for 4 hours and 1.5 x 107 Pa in a Dake hydraullic press, in the shape of a strip. The strip was fractured at room tem perature or at liquid nitrogen tem perature and m ounted on the sample holder. The samples were coated with about 200A° of gold and palladium and examined under a electron beam normal to the fractured surface,at magnifications from 103 to 2 x 104. 2.2.5 R h eology Rheological analysis of the m olten composites was carried out in a Weissenberg Rheogoniom eter(R 19) at 200°C, in a cone and plate geometry. The bottom platen is a cone of 5 cm. diam eter and 0.034 rad(2°) cone angle. The top platen is a 5 cm. diam eter flat disk. Experim ents were carried out both in steady shear and oscillatory modes. The shear rate range for steady shear experim ents was 1.4 x 10_3 to 1.4 sec_1 and the shear stress was recorded by measuring the torque in the upper platen generated due to rotating bottom platen. To measure the viscosity accurately shear stress was m easured for both forward and backward shear and average was taken for determ ining viscosity. The frequency for oscillatory experiments ranged from 2 x 10~3 to 20 Hz. The strain am plitude was kept% 5%. The shear generated by the cone in an oscillatory m ode was transm itted, as a torque, via the sample, to the top platen which is constrained by a torsion bar, and oscillates with different am plitude and phase. 2.3 R e su lts M onodisperse spherical beads were prepared in emulsifier free emulsion polymeriza tion. Beads were characterized by SEM, DSC and swelling and results are tabulated in table 2.1. Figures[2.1-2.4] are SEM photographs of the beads. Fracture surfaces of com posites were exam ined by SEM. Fracture at room tem perature for P M M A (M W = 75,000) composites occurs in a ductile m anner and significant deformation of the m atrix was observed. Holes created by pulling out the particles were covered by 26 the resilient m atrix and photographs were difficult to interpret. Therefore, annealed composites were fractured in liquid nitrogen. At liquid nitrogen tem perature, the com posite breaks in a b rittle m anner. SEM photographs of fracture surfaces, for both PM M A m atrices, are shown in fig. [2.5-2.12]. The steady shear viscosity of poly m ethyl m ethacrylate m atrix(M w=35,000), filled w ith 20% by weight of crosslinked particles is illustrated in fig.2.13. Storage m odulus(G /), loss m odulus(G ") and loss factor(tan 6) are plotted as functions of frequency in fig.2.14-2.16. Fig.2.17 contains the steady shear viscosity as a function of shear rate and results of dynam ic me chanical analysis of P M M A { M W = 75,000) composites are plotted in fig.2.18-2.20. The initial slopes of rheology curves for P M M A ( M W = 35,000) composites as well as well as for P M M A ( M W = 75,000) composites are tab u lated in table 2.2. 27 Com position of particles D iam eter Ta XLD (nm .) i°C) (mole percent) 10%DVB-PS 260 nm 166 10.58 10%EGDMA-PMMA 240 nm 140 10%DVB-PMMA 200 nm 163 10%EGDMA-PS 315 nm 147 13.32 Table 2.1: C haracterization of beads 28 M atrix Filler Initial slopes of rheology plots Apparent yield stress(Pa) G' G" V PM M A (Mw = 35,000) PM M A 0.92 1.09 -0.04 DVB - PS 0.16 0.26 -0.77 1036.8 EGDM A - PM M A 0.88 1.01 -0.04 4.8 DVB -PMM A 0.59 0.69 -0.69 204.5 EGDM A - PS 0.44 0.47 -0.73 282.6 PM M A (Mw = 75,000) PM M A 1.33 .97 -0.007 DVB - PS 0.45 0.68 -0.95 981.6 EGDM A - PM M A 1.28 0.97 -0.04 0.3 DVB -PM M A 1.06 0.89 -0.15 45.7 EGDM A - PS 0.0.81 0.85 -0.47 321.5 Table 2.2: Initial slopes of rheology plots, and apparent yield stresses for P M M A - (Mw = 35,000) and P M M A ( M W = 75,000) m atrices filled w ith crosslinked poly meric particles 29 vlc o O O p t = ffl ll' - a . " . I M G - X 2 0 . P S B £ R D S ( X L D 1 0 * B V B > 0 4 /1 r ft* . r *% ^ ^ 4 # K ,r r-. r " f r v. £ ^ v r < * V -^E L FIgaf® % .Is SIM pkotogmpk © £ PS beadi cffossJ B at a magsmi- fWG- X 20.Q K PM QIO3 48i 4 ' L a S E 1 E H T a10.Q K V H i3 P f f f l R ! E f i D S < X L 8 ° ! 5 x E G D H f l > 0 S / 2 8 / 3 1 r % ' _ < *' f f l ^ ■ > r v ^ < v . v ? j c ' P f- O < ! * r > r , <„ V' - - .* • r s € * t ^ r ' - < * r «... S T . _ £ d ! ^ / * 1 * v ™ V . C ^ V ' i v r f c - v - < ‘ ■ r r r .>. ' . , » _ ' f V i o “ f < ‘ . , : . •’ ' r i V - # * y ^ v r r ® ■ v pkotogsapK- of PMMA b<gad§ esossBsiksd witk ,0 i ° « " . ea?°m @ ro PfH a BEfiDSOdtt l i K DVB) 0 4 / 0 8 / 3 2 - ■ '' yp-.iwwp^ w m ? . te su o L s ®£©ii hO 'KV ® B 1 0 m " HAG- X 3 0 . 0 K PHOTO* 4 5 5 8 1 . 0 0 | n t PS BERDSCXLD m E6WWD07. *T% . -$ 5 ^ : "r '’ ^ p r rj , , / : J a , : • ’ # % ' * ; # , . « r ■ ;> 4 * - r - % 5V&%p • '•■.■?'■■* ’ h . • • '•*- ." • SHtlQ6l_f_|ll_m 31 L * S E 1 E H T - 10.0 K M H D - 10 m m / W « X 1.Q0 K P H O T O - 5441 20.0|jm l-- - - - - - - - - - - - - - - - - - - 1 I Pnnfl35K(10XDVB-PS)FR L N 1/21/93 Figure 2.5: SEM photograph of fracture surface of PM M A(M W = 35,000) m atrix filled with DVB-PS particles, at a fracture tem perature of — 170°C (a) at a magnification of 1000X (b) at a magnification of 5000X 0 9 I* SE 1 E H T - 10.0 I C y W D * 10 m m 20. O jo iu |-------------------- p fim ssK c E G D n f t- p n n f l < 5/28/31 > 10/ 12/32 Figure 2.6: SEM photograph of fracture surface of PM M A(M W = 35,000) m atrix filled with EGDM A-PM M A particles, at a fracture tem perature of -170°C (a) at a magnification of 1000X (b) at a m agnification of 5000X 3 3 L - SE1 EHT» 1 0 .0 IC y UD- 1 0 ran 20. O jjm |---------------------1 P nnft35!C C 1O X D U B -P flH F i > F R L N 1/21/33 m atrix 34 L" SEl E H T - 10.0 K V H D ’ 10 5.00pi f -------------— — Pmft35K(10ZDVB-Pfinfi)FR L N 1/21/33 Figure 2.7: SEM photograph of fracture surface of PM M A(M W = 35,000) filled with DVB-PMMA particles, at a fracture tem perature of — 170°C (a) at a magnification of 1000X (b) at a magnification of 5000X I* SE1 EHT- 1 0 .0 K V W D * 10 2 0 .0 u m f - -------------- P FTf1835IC (1 OXEGDf!A- PS ) FR LN 1 /2 1 /3 3 -; v/ • • _ ' - f e t - t Q . L* SEl EHT- 1 0 .0 K V KD- 10 m 5.0Q p> r - - - - - - - - - - - - - - - - - - - - - - - PHnfi35K(10TEGDnfi-P$) FR L N 1 /2 1 /3 3 Figure 2.8: SEM photograph of fracture surface of P M M A (\fw ~ 35,000) m atrix filled with EGDMA-PS particles, at a fracture tem perature of 170°C (a) at a magnification of 1000X (b) at a magnification of 5000X Figure 2.9: SEM photograph of fracture surface of PM M A(M W = 35,000) m atrix filled with DVB-PS particles, at a fracture tem perature of — 170°C (a) at a magnification of 1000X (b) at a magnification of 5000X 3 0 Pflflfl MfiTQOZEGDnfl-Pflttft) FR AT U (a) L - SE1 EHT- 1 0 .0 IC V UD- 1 0 m ' HAG- X 5 .0 0 1^PH O T O -4 7 9 0 5.00(jm ! - - - - - - - - - - - - - - - - - - - - - Pfinfi flflT(lOZEGBflfl-PnnA) FR AT LN Figure 2.10: SEM photograph of fracture surface of PM M A(M W = 35,000) m atrix filled with EGDMA-PMMA particles, at a fracture tem perature of — 170°C (a) at a magnification of 1000X (b) at a magnification of 5000X 0 7 Figure 2.11: SEM photograph of fracture surface of PM M A(M W = 35,000) m atrix filled with DVB-PMMA particles, at a fracture tem perature of — 170°C (a) at a magnification of 1000X (b) at a magnification of 5000X 3 g EHT- 1 0 .0 K V UD« 10 m m 2 0 .0 u m H --------- — —| : EO D fia-PS)5/23/32 F R fiT L N p m fi m u m Figure 2.12: SEM photograph of fracture surface of PM M A (M W = 35,000) m atrix filled with EGDMA-PS particles, at a fracture tem perature of -1 7 0 °C (a) at a magnification of 1000X (b) at a magnification of 5000X 3 9 Shear rate( 1/Sec) Figure 2.13: Log-log plot of viscosity vs. shear rate for P M M A ( M W = 35,000) composites at 200°C. . PM M A m atrix x Composite containing PS particles crosslinked w ith DVB * Com posite containing PM M A particles crosslinked w ith EGDMA o Com posite containing PM M A particles crosslinked w ith DVB + Composite containing PS particles crosslinked w ith EGDM A 40 3 1 0 o O ) Frequency(Hz) Figure 2.14: Log-log plot of storage m odulus((j') vs. frequency for P M M A ( M W = 35,000) composites at 200°(7. Symbols are same as fig.2.13 41 Frequency(Hz) Figure 2.15: Log-log plot of loss m odulus(G? / ') vs. shear rate for P M M A ( M W = 35,000) composites at 200°C. Symbols are same as fig.2.13 42 1 0 ° 1 0 z 1 0 ' 1 1 0 u 1 0 1 1 0 z Frequency(Hz) Figure 2.16: Semilog plot of loss facto r(tan ^) vs. frequency for P M M A ( M W = 35,000) composites at 200°C. Symbols are same as fig.2.13 43 Viscosity(Pascal-Sec) Shear rate( 1/Sec) Figure 2.17: Log-log plot of viscosity vs. shear rate for P M M A ( M W = 75,000) composites at 200°C. Symbols are same as fig.2.13 44 Frequency(Hz) Figure 2.18: Log-log plot of storage m o d u lu s ^ ') vs. frequency for P M M A ( M W = 75,000) composites at 200°C. Symbols are same as fig.2.13 45 o Frequency(Hz) Figure 2.19: Log-log plot of loss modulus(G? //) vs. shear rate for P M M A ( M W = 75,000) composites at 200°C. Symbols are same as fig.2.13 46 Frequency(Hz) Figure 2.20: Semilog plot of loss factor (tan 6 ) vs. frequency for P M M A ( M W = 75,000) and composites at 200°C. Symbols are same as fig.2.13 47 2.4 D isc u ssio n A Newtonian viscosity is exhibited by P M M A ( M W = 35,000) matrix(fig.2.13). In contrast, P M M A ( M W = 75,000) m atrix exhibits a viscosity independent of shear rate at low shear rates(N ew tonian), followed by shear thinning at high shear rates(fig.2.17), which can be attrib u ted to the disentanglem ent of high molecular weight chains at high shear rates[15]. Inclusion of filler resulted in enhancem ent in steady shear viscosity and dynam ic moduli, due to the presence of high modulus particles, as well as due to the form ation of agglomerates of particles due to particle- particle interactions. Also, a reduction, broadening and shift towards higher values is observed in ta n # peaks in a plot of ta n # vs. frequency. Due to the presence of filler a decrease in intensity of ta n # peak is observed. The loss tangent, in general is m ostly due to the m atrix but in systems w ith agglom erated systems, some of the m atrix chains are immobilized, as they are trapped w ithin agglomerates. This results in further decrease in ta n # peak since the immobilized chains, effectively, behave like filler and do not contribute to the loss tangent. Fig.2 . 2 1 contains Casson plots(a plot of T 2 vs. 7 2 )[16] for P M M A ( M W = 35,000) m atrix and composites. A linear relationship is found between T2 and 7 2 and the square of intercepts at y-axis are taken to be apparent yield stress. As can be seen, inclusion of filler results in the appearence of an apparent yield stress, the value of apparent yield stress being highest for DVB-PS filled system and lowest for EGDM A-PM M A system , due to the differences in chemical interactions, which will be discussed in detail later. Due to non-Newtonian nature of P M M A ( M W = 75,000) m atrix, the Casson plot was not able to fit the d ata well, for P M M A ( M W = 75,000) composites. Therefore modified Casson p lo t[17], where, to correct for change in viscosity of the m atrix, is plotted as a function of 7 ^ x (where r ] 0 and r ] 0 0 are the viscosities of the m atrix at the test shear rate and at zero shear rate respectively) and a linear plot was obtained, similar to th a t of P M M A ( M W = 35,000) composites. The apparent yield stress values of P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites are appended to table 2.2. The effect of m atrix molecular weight on the apparent yield stress values of the composites will be discussed later. 48 0.6 0.8 1.2 Figure 2.21: Casson plot(plot of r 2 vs. 7 ^) for P M M A ( M W = 35,000) and com posites at 2 0 0 °C. Symbols are same as fig.2.13 49 250 200 150 100 50 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 2.22: Casson plot(plot of T2 vs. 7 2 ) for P M M A ( M W = 75,000) and com posites at 200°C. Symbols are same as fig.2.13 50 2.4.1 Effect o f chem ical com position o f th e p articles The chemical composition of the filler has a profound effect on the morphology and, therefore, the rheology of filled systems. Surfaces of DVB-PS paricles are not com patible w ith the PM M A m atrix and DVB-PS particles are rejected by the m a trix. Therefore, adhesive failure occurs, at the particle surface for PM M A filled with DVB-PS particles and particle surfaces are clean of m atrix(figs.2.5,2.9). Weak inter actions between particles and m atrix and strong particle-particle interactions lead to the form ation of large agglomerates of particles. In fact, for P M M A ( M W = 35,000) agglomerates connect to each other by chains of particles, exhibiting a tendency to form a network. The highly clustered structure of the composites containing DVB- PS results in highly non-Newtonian behavior(figs.2.13,2.17). Steady shear viscosity is very high at low shear rates due to the presence of an elastic network but is reduced drastically as the shear rate is increased, due to the breakup of clusters. In fact, the slope of the steady shear viscosity vs. shear rate plot on a log-log scale is -0.77 for the com posite in P M M A ( M W = 35,000) m atrix and -0.95 in P M M A ( M W = 75,000) m atrix. In P M M A ( M W = 75,000) m atrix, the non-Newtonian behavior of the m atrix also contributes to the non-Newtonian behavior of the composite and, in fact, two regions of drastic shear thinning are observed(fig.2.17), at low shear rates corresponding to the breakup of agglomerates and at high shear rates correspond ing to the shear thinning of the m atrix. The presence of agglom erated structure also results in very high values of apparent yield stress, obtained from Casson plot. In dynam ic m echanical analysis(DM A) inclusion of DVB-PS particles in PMMA m atrix results in enhancem ent in storage and loss m oduli, and reduction in loss factor(tan S) peak. The enhancem ent in dynamic moduli is higher at low frequen cies and becomes smaller at high frequencies. In fact, for P M M A ( M W = 35,000) filled w ith DVB-PS particles, G' and G" almost become independent of frequency, at low frequencies, and slopes of log-log plots of G' and G" vs. frequency being 0.16 and 0.26, respectively. A plateau at low frequencies, in log-log plots of moduli vs. frequency, is different from high frequency plateau corresponding to the rubbery behavior of the m atrix, and is often attrib u ted to the form ation of a network of particles. Therefore, it is apparent th a t the form ation of agglom erates of particles, whose surfaces are not com patible with the m atrix, connected by chains of particles 51 may lead to the form ation of network. However, 20% loading of DVB-PS particles was not sufficient for network form ation. Therefore, the negative slope of steady shear viscosity of DVB-PS composite in P M M A ( M W = 35,000) m atrix is less than unity, at low shear rates, and G' and G" show slight frequency dependence, at low frequencies. Higher loading of DVB-PS particles in PM M A m atrix m ay lead to network form ation and appearence of yield. Significance of a very high value of neg ative slope(slope=-0.95) in log-log plot of steady shear viscosity vs. shear rate, at low shear rates, in P M M A ( M W = 75,000) m atrix containing 20% DVB-PS particles is not very clear. This is probably due to the fact th at th at P M M A ( M W = 75,000) m atrix itself shows a shear thinning behavior and, shear thinning of the composite involves shear thinning of m atrix as well as breakage of agglomerates of particles. Due to a highly agglomerated structure, a large num ber of m atrix molecules are immobilized, resulting in very low values of loss tangent peaks. Due to a similar chemical struture, surfaces of EGDM A-PM M A particles are com patible w ith PM M A m atrix. In fact, in P M M A ( M W = 75,000) m atrix, high particle-m atrix interaction results in cohesive failure of the m atrix, at —170°C rather th an in adhesive failure at the m atrix-filler interphase during the preparation of fracture surfaces. Such high m atrix-particles interactions overwhelm the particle- particle interactions and, therefore, the particles are well dispersed in the m atrix. Thus, inclusion of EGDM A-PM M A particles does not affect the Newtonian nature of the m atrix and rheology curves are parallel to those of the pure m atrix, though enhancem ent in shear viscosity, as well as dynam ic moduli, due to the bulk effect of high m odulus particles[15] is observed. However, viscosity at low shear rates are much smaller compared to the viscosity of composites filled with DVB-PS particles, due to the absence of large agglomerates in the system. For the same reason, values of apparent shear stress for EGDM A-PM M A filled systems, from Casson plots, are much smaller, compared to DVB-PS composites. Also in DMA experim ents, reduction in loss tangent peak is very small, com pared to the systems filled w ith PS particles. In contrast, at high shear rates particles are well dispersed for both the systems and, due to higher particle-m atrix interactions in EGDM A-PM M A filled compos ites, steady shear viscosities are higher than DVB-PS filled sytems. The presence of 52 10% EGDM A makes the PS particles more com patible w ith the m atrix. In fact in high molecular weight m atrix, some of the m atrix molecules adhere to the surface of EGDM A-PS particles, when fractured at — 170°C, in contrast to DVB-PS particles, where the particle surface is clean of any m atrix molecule. B etter m atrix-particle interactions results, com pared to DVB-PS particles, in b etter dispersion of the par ticles and therefore smaller viscosity at low shear rates. In low molecular weight m atrix, particle-m atrix interactions are weak, and small enhancem ent in particle- m atrix interactions result in large differences in rheological behavior. Therefore, while at low shear rates, viscosity of EGDM A-PS filled P M M A ( M W = 35,000) is much smaller com pared to DVB-PS filld P M M A ( M W = 35,000) viscosity of the two systems is similar at high shear rates. Introduction of 10% DVB affects the com patibility of PM M A particles, and DVB-PM M A particles form agglomer ates, especially in low molecular weight m atrix. Therefore, P M M A ( M W = 35,000) composites containing DVB-PM MA show non-Newtonian behavior, almost identi cal to EGDM A-PS filled P M M A ( M W = 35,000) in steady shear experim ent. How ever, particle-m atrix interactions are stronger in the P M M A ( M W = 75,000) m atrix and therefore, dispersion of the particles is better. Hence, viscosity enhancem ent and shear thinning for P M M A ( M W = 75,000) containing DVB-PM MA particles is much less com pared to th a t of P M M A ( M W = 75,000) containing EGDM A-PS particles. In dynam ic mechnical analysis, storage m odulus of DVB-PM MA filled systems is always smaller than EGDM A-PS filled system , at low frequencies, and the difference diminishes at high frequencies. In contrast, while DVB-PM MA filled systems have a smaller loss m odulus at low frequencies, com pared to EGDM A-PS filled systems, at high frequencies loss m odulus of DVB-PM M A filled systems is higher. Because of enhanced particle-particle interactions, (?', which is an indica tion of the structure of the agglomerates, is higher for the EGDM A-PS system. However Gn, which is an indication of the structure of the fluid, is similar for both EGDM A-PS and DVB-PM M A filled systems. The chemical com patibility of the crosslinker affects the com patibility, of the particle surface w ith m atrix, therefore affecting the dispersed state while the structure of the agglom erate is prim arily de term ined by the particle interactions due to the m ajor constituent of the particles. Therefore while presence of 10% EGDMA in PS particles and 10% DVB in PMMA 53 particles result in similar G” for systems filled with these particles, values of G' for systems filled w ith these particles are very different, as structures of agglom erates for PM M A and PS particles are very different. Similarily, in steady shear experim ents, for P M M A ( M W = 35,000) composites, particle-particle interactions are very strong and rheological behavior is prim arily determ ined by the state of dispersion and, therefore, EGDM A-PS and DVB-PM M A filled systems have similar viscosities(fig.2.13). In contrast, in P M M A ( M W = 75,000) m atrix, particle-particle interactions are not very strong and therefore, the difference in particle-particle in teractions for PS and PM M A particles play a big role in determ ining the viscosity, and, therefore, EGDM A-PS and DVB-PM MA filled P M M A ( M W = 75, 000) com posites have very different viscosities(fig.2.17). 2.4.2 Effect of m olecular w eight o f th e m atrix W hile steady shear viscosity of P M M A ( M W = 35,000) m atrix is alm ost indepen dent of shear rate, shear thinning is observed for P M M A ( M W = 75,000) m atrix. To account for shear thinning, and the difference in the viscosity of the m atrices, relative viscosity^,. = where rj0 is the viscosity of the pure m atrix) was calculated and plotted, as a function of shear rate, for the four fillers in figs.2.23-2.26. 54 10 L • rH C O o o C / 3 * 1— I > 10' 1 0 J I I I I I I I I—— I I I I I I I I I I I I I M i l l , , ________ I---------1 --------1 — I I I I — I I I ■ I III I .1 * » I. ■ I I I I I I ■■ 10"2 lcr1 1(F Shear rate( 1/Sec) 1 0 Figure 2.23: Log-log plot of relative viscosity vs. shear rate for PM M A containing DVB-PS particles at 200°C. x Composites in P M M A ( M W = 35,000) m atrix o Composites in P M M A ( M W = 75,000) m atrix 55 > Shear rate( 1/Sec) Figure 2.24: Log-log plot of relative viscosity vs. shear rate for PM M A containing EGDM A-PM M A particles at 200°C. Symbols are same as fig.2.23 0 < D 1 CO o O CO • rH > Shear rate( 1/Sec) Figure 2.25: Log-log plot of relative viscosity vs. shear rate for PM M A containing DVB-PM M A particles at 200°C. Symbols are same as fig.2.23 0 < D CO 1 o C / 3 Cj Dh C / 1 o O C / 3 > Shear rate( 1/Sec) Figure 2.26: Log-log plot of relative viscosity vs. shear rate for PM M A containing EGDM A-PS particles at 200°C. Symbols are same as fig.2.23 From fig.2.5 we can see th a t large agglomerates are formed when DVB-PS par ticles are included in P M M A ( M W = 35,000) m atrix, in fact forming a network of particles, w ith chains of particles connecting the large agglom erates. The form ation of network results in very high viscosities and highly non-N ew tonian behavior. How ever, in the high molecular weight m atrix, particle-m atrix interactions are stronger, and, therefore, the size of agglomerates formed is smaller. This is m anifested, in rheology , by lower relative viscosities and smaller slopes, at low shear rates, in a log-log plot of steady shear viscosity vs. shear rate. In dynam ic mechanical anal ysis, while a storage m odulus, almost independent of frequency is observed at low frequencies for P M M A ( M W = 35,000) composite, a slope of 0.45 was observed for composites containing P M M A ( M W = 75,000) m atrix. M olecular weight of the m atrix has a similar effect on EGDM A-PS filled systems, w ith a reduction in the agglom erated structure for the high m olecular weight m atrix. In fact, while particle surfaces are clean, in a fracture of P M M A ( M W = 35,000) composites at — 170°C, some m atrix adheres to the particles for P M M A ( M W = 75,000) composites(fig.2.12). Due to an enhancem ent of particle-m atrix interac tions, particle-particle interactions are less im portant and therefore, a smaller rela tive viscosity is observed for high molecular weight m atrix. For DVB-PM M A filled systems, in low m olecular weight m atrix, smaller particle-m atrix interactions were responsible for the presence of clustered structure, in the fracture surf ace (fig. 2 .7) and highly non-Newtonian behavior, in rheology (fig.2.13). However in P M M A ( M W — 75, 000) particle-m atrix interactions are much higher com pared to P M M A ( M W = 35, 000) m atrix, which results in adsorption of polym er molecules on the particle surface(fig.2.11). In fact, at low shear rates, due to presence of larger agglomer ates in P M M A ( M W = 35,000) composites, relative viscosity is much higher for P M M A ( M W = 35,000) m atrix composites compared to P M M A ( M W = 75,000) m atrix. However at high shear rates, most of the agglomerates are destroyed, and therefore the relative viscosity of P M M A ( M W = 75,000) com posite is higher, due to b etter bondig between particles and matrix(fig.2.25). For systems containing EGDM A-PM M A filler, particles are well dispersed in both P M M A ( M W = 35,000) and P M M A ( M W = 75,000) m atrix. However, higher molecular weight of the m atrix results in enhanced particle-m atrix interactions, 59 illustrated by cohesive failure of the m atrix, for high molecular weight m atrix, in contrast to adhesive failure at particle m atrix interphase for P M M A ( M W = 35, 000) m atrix. Therefore, in the higher molecular weight m atrix, we observe higher relative viscosities, due to b etter bonding between m atrix and particles for EGDM A-PM M A filled systems(fig.2.24) Higher m atrix-particle interactions in the high molecular weight PM M A m atrix occurs due to the fact th at at a polymer-solid interphase, adsorption of polym er at the solid surface increases w ith increasing chain length. Theoretically, it has been predicted th at the am ount of polym er adsorbed from bulk polym er is proportional to the square root of chain length[24]. Experim ental data for adsorption of polystyrene onto silica surfaces from solution[25-27] also showed large increases in the am ount of polym er adsorbed w ith increasing molecular weight. Interaction between solid and polym er, polym er and solvent, and concentration of the solution also affected the am ount of polym er adsorbed on the solid surfaces. It is apparent th a t in high m olecular weight PM M A m atrix, the m atrix has a higher tendency to get adsorbed on the particle surface compared to the low molecular m atrix. However, am ount of polym er adsorbed also depends on the interaction between particle surface and m atrix. The mesophase formed due to the adsorption of polym er behaves differently from the particle surface, resulting in b etter interactions between particles and m a trix. Therefore particle-m atrix interactions are improved w ith increase in molecular weight of the m atrix. M alkin in his review[18] has discussed the effect of molecular weight of the m atrix on the yield stress. It was stated th a t for a m onodisperse m atrix, molecular weight does not have any significant affect while for polydisperse polym er, m olecular weight of the m atrix affects yield stress significantly. From table 2.2 we can see th a t for PS particles crosslinked w ith 10% DVB or EGDM A, values of yield stress are not very different for P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites. However, value of yield stress for DVB-PM M A particles filled systems decreased to 25% when the average molecular weight of the m atrix was changed from 35.000 to 75,000. 60 2.4.3 C om parison w ith m odels for shear d ep en dence of viscosity A ttem pts have been m ade to describe the shear rate dependence of viscosity by correlating it w ith the shear rate dependence of the structure of the filled systems. Some of the approaches included the assum ption th a t the flow of filled system con sists of one Newtonian and one non-Newtonian flow u n it[19], th a t the size of clusters, of particles, is dependent on the shear rate[23] and th a t the change in the m axim um packing efficiency of the system changes w ith shear rates (due to reduction in ef fective volume of the filler w ith destruction of agglom erated structure and resultant release of immobilized m atrix molecules) [2 2 ]. M aron and Pierce[19] have simplified the generalized Ree-Eyring[20] model by assuming th at the filled system consists of two distinct flow units, one Newtonian and one non-Newtonian, and th at viscosity of the filled system is given by: , x-sink " 1 ri = rjN - \ - ------------------ :-------- ( 2 . 1 ) a 7 W here, 77at is the viscosity of the Newtonian flow unit and the second term on the right hand side denotes the viscosity of the non-Newtonian flow unit. Viscosities of P M M A ( M W = 35, 000) composites were com pared w ith this model, by a nonlinear optim ization technique and are replotted in fig.2.27. The values of Ree-Eyring param eters is tabulated in table 2.3. It was found th a t value of Newto nian viscosity(t/at) and J is alm ost independent of the type of filler. In fact, the value of tjn is w ithin 5% of the value predicted for suspensions having only hydrodynam ic particle-particle interaction (77 = r)0( 1 + 2.50 + 14.102)) where rfQ is the viscosity of the m edium and 0 the concentration of the filler).Therefore, tjn was fixed at 3650 and 2 was fixed at 145 and the graphs replotted (dashed lines in fig.2.27) and the pa ram eters are tabulated in Table2.5. The free energy of activation of non-Newtonian flow unit(AG') was calculated from the value of /? obtained from eq.2 .1 , w ith fixed 2 and 7/at, from the equation: A G = R T (2 .2 ) h 61 h, k and R are Planck’s, B oltzm ann’s and gas constants, and T is the absolute tem erature. Values of A G are appended to table2.5. f) can be interpreted as the relaxation tim e of the non-Newtonian flow units, A G is a m easure of interparticle interactions. E ither of these param eters can be used to characterize particle-particle interactions. DVB-PS particles are highly incom patible with the m atrix and there fore particle-particle interactions are very strong in DVB-PS filled systems. This is m enifasted by very high value of (3 and A G for DVB-PS filled systems. In con trast, EGDM A-PM M A system yield very small (3 and AG, indicating the absence of strong particle-particle interactions. DVB-PM MA and EGDM A-PM M A filled P M M A ( M W = 35, 000) are interm ediate and have similar values of f3 and AG. Equation 2.1 was used to correlate steady shear viscosity d ata of P M M A ( M W = 75,0 0 0 ) composites also and is plotted in fig.2.28. The corresponding param eters are tabulated in table2.4. Though the viscosity of the Newtonian flow unit rjjsr is of the similar order for all the composites, values of ^ vary greatly. Since the m atrix itself shows non-Newtonian behavior, the system consists of two non-Newtonian and one N ewtonian flow unit, and, therfore models containing one nonlinear param eter fail to describe the flow behavior. 62 rH C /3 Shear rate Figure 2.27: Ree- Eyring plot for P M M A ( M W = 35,000) and composites at 200°C. Symbols are same as fig2.13. Solid lines are for unfixed values of t ]n and ^ while dashed lines indicate the plot w ith t )n fixed at 3650 Pa-sec and J fixed at 145 Pa-sec 63 • rH Shear rate( 1/sec) Figure 2.28: Ree- Eyring plot for P M M A ( M W = 75,000) and composites at 200°C. Symbols are same as fig2.13. Solid lines are for unfixed values of t ]n and J 64 Filler r]N (Pa-sec) x /a (Pa) /? (sec) None 1664 54.55 18 DVB-PS 3091 220.4 2.05 x 104 EGDM A - PM M A 3876 111.9 18 DVB -PM M A 3929 138.3 1543 EGDM A - PS 4020 1 1 0 . 6 3079 Table 2.3: Ree-Eyring param eters for P M M A ( M W = 35,000) m atrix filled with crosslinked polym eric particles Filler m (Pa-sec) x /a (Pa) P (sec) None 0.84 x 104 0.87 x 103 18 DVB - PS 2.3 x 104 0.15 x 103 1.3 x 10y EGDM A - PM M A 2.47 x 104 2.09 x 103 18 DVB -PM M A 2.78 x 104 0.97 x 103 72.1 EGDM A - PS 1.92 xlO4 0.64 x 103 327 Table 2.4: Ree-Eyring param eters for P M M A ( M W = 75,000) m atrix filled w ith crosslinked polym eric particles Filler (Pa-sec) x /a (Pa) P (sec) A G DVB - PS 3650 145 5.24 x 105 173.4 EGDM A - PM M A 3650 145 18 131.1 DVB -PM M A 3650 145 1351 148.6 EGDM A - PS 3650 145 1209 149 Table 2.5: Ree-Eyring param eters for P M M A ( M W = 35,000) m atrix filled w ith crosslinked polym eric particles, tjn was fixed at 3650 Pa-sec and J at 145 Pa-sec 65 W ildem uth and W illiums [22] have proposed a model which takes into account the increase in packing efficiency with increase in shear rate, based on the assum ption th a t the m icrostructure consists of two phases, one corresponding to agglom erated and one corresponding to well dispersed particles. By simple kinetic argum ent they have derived: 4>M 4>M o ^ 4*M o ^ ^ where are m axim um packing efficiency at test shear rate, zero shear rate and m axim um shear rate, respectively, and / is the fraction of total particulates in a dispersed phase. Dependence of / on shear rate is unknown and an equation of the type: f ~ 1 + k j~ m has been suggested, where k and m are fitting param eters which determ ine the shear dependence of viscosity. M axim um packing efficency of P M M A ( M W = 35,000) and P M M A ( M W = 75, 000) filled w ith particles were calculated using Eilers equation: ^ 1 + T ^ 2 ^ The inverse of it is plotted as function of shear rate in fig2.29 and fig2.30 for P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites, respectively.The d ata was fitted using Equation2.3 and equation2.4 and a good fit was obtained. The best fit curves are plotted in fig2.29 and fi.g2.30, by solid lines, and fitted values of param eters feo^M oo and m are tabulated in table2.6. It is apparent th a t values for <j>Mo and <f>Moo are not explainable, physically, for some cases. Also another form of shear dependence of / , f = 1+^m w ith one less fitting param eter was found to fit the experim ental data equally well. 66 Shear rate(l/sec) Figure 2.29: Plot of l/<j)M vs 7 for P M M A ( M W = 35,000) composites at200°C. < / > m was calculated using eq. 2.5. Symbols are same as fig2.13. Solid lines represents a fit of the type / = 67 Shear rate( 1/sec) Figure 2.30: Plot of vs 7 for P M M A ( M W — 75,000) composites at200°C. 4 > m was calculated using eq. 2.5. Symbols are same as fig2.13. Solid lines represents a fit of the type / = 68 M atrix Filler DVB - PS < t> M o 0 . 2 1 < f> M o o 0.48 k 0.64 m -0.87 PM M A EGDM A - PMMA 0.46 0.34 0.61 -0.27 M w = 35,000 DVB -PMM A 0 . 2 0 1.18 0.55 -0.61 EGDM A - PS 0 . 2 0 1.18 1.07 -0.53 DVB - PS 0.19 2.42 0.50 -0.51 PM M A EGDM A - PMMA 0.35 0.33 0.06 -0.74 M w = 75,000 DVB -PMMA 1.62 0.92 -0.79 -0 . 0 2 EGDM A - PS 0.0436 0.14 0.24 0.16 Table 2.6: Param eters for W ildem uth-W illiam s model, for P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites 69 Tsenglou[23] has proposed a model for the rheology of filled systems, incorpo rating the size of agglomerates. According to his model, the relative viscosity of a filled system varies according to: Vr = [1/(1 - ^)]2+W 2> (2.6) where N denotes the size of agglomerates present in th e system. The size of agglom erates(N) was calculated and plotted, as function of shear rate, in fig. 2.31 and fig2.32 for P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites respectively. The size of agglom erate depends stongly over the compostion of the filler, m atrix and shear rate. At low shear rate, large agglomerates are present in composites containing a filler incom patible with m atrix, eg. DVB-PS. However as the shear rate decreases, the size of agglomerates decreases for such a system and at high shear rates, the value of N is smaller th an th a t of filler com patible w ith the m atrix eg. EGDM A-PM M A. Perhaps high m atrix-particle interaction in com patible systems cause m atrix molecules to get adsorbed on more than one molecule simultaneously, giving rise to the form ation of small clustes. Size of these clusters does not change significantly w ith shear rate. High m olecular weight m atrix also improves the particle-m atrix interactions and therefore sm aller agglomerates are formed in high molecular weight m atrix. However for PM M A particles, increased adsorption of the higher molecular weight m atrix leads to high cluster size. The m athem atical representation of the dependence of agglom erate size on shear rate rem ains a question. Log-log plots of agglomerate size vs shear rate can be fitted by a straight line(dashed lines in fig.2.31and fig.2.32), and probably agglomerate size can be represented by an equation of the type N = k ^ . However, this equation does not satisfy the lim iting conditions at 7 — » 0 and 7 — ► 0 0 and the physical significance of the fitting param eters k and /? is also not clear. A nother shear dependent equation can be of the form : where N 0 and N 0 0 are agglom erate size at zero and infinite shear rates respec tively, and k and m are fitting param eters determ ining the shear dependnce of agglom erate size. This equation is more appropriate, since it rightly predicts agglom erate size to be N 0 at zero shear rate, at high shear rate, and a decrease in agglom erate size w ith increasing shear rate. Experim ental d ata was fitted using this equation and is plotted in fig.2.31 and fig.2.32, by solid lines, and the param eters are tabulated in table 2.7. The fitted param eters gave very realistic values of N 0 and Nqq for most of the cases. In fact, except for EGDM A-PM M A filled systems, where N 0 and iV oo are com parable, N 0 Nqq and therefore equation 2.7 can be w ritten as: " ' " • ( ' - T T T R 1 ( 1 S | 71 10 < D N • C/2 0> 3 1 0 < 3 s 0 1 < OB < 10' 10‘ J I I I I II I I I I « I I t I I I _ I I I I- I 1 I 11 ______I ____I I I 1 I 11 '— ...........* -------- -1 . * * * 7 V i o n r W Shear rate(l/sec) 10 Figure 2.31: Plot of agglomerate size vs shear rate for P M M A ( M W = 35,000) composites at 200°C. Agglomerate size was calculated using eq. 2.6. Symbols are same as fig.2.13. Dashed lines are for a fit of type N = k'jP while solid lines represents a fit of the type = 1+k\-m 72 < D N • C /} < D a o ’Sb W) C j 11 i i 11 T Shear rate( 1/sec) Figure 2.32: Plot of agglom erate size vs shear rate for P M M A ( M W = 75,000) composites at 200°C . Agglomerate size was calculated using eq. 2.6. Symbols are same as fig.2.13. Dashed lines are for a fit of type N = k 7 ^ while solid lines represents a fit of the type ~ — -— l+ky-m 73 M atrix Filler N 0 No-Noo k m PM M A M w = 35,000 DVB - PS 63.84 66.33 0.13 0.45 EGDMA - PM M A 16.66 1 2 . 2 -0.06 0.04 DVB -PMM A 51.64 50.94 -0.07 0.26 EGDMA - PS 83.55 83.40 0.06 0.40 PM M A M w = 75,000 DVB - PS 0.34 28.16 -13.27 -0.33 EGDMA - PM M A 4.70 0 . 0 1 -0.09 0.36 DVB-PM MA 23.27 2 2 . 1 1 0.14 0.24 EGDMA -PS 26.58 25.69 0.03 0.7 Table 2.7: F itted param eters for shear dependence of agglom erate size, for P M M A - (Mw = 35,000) and P M M A ( M W = 75,000) composites, using eq. 2.7 74 2.5 C o n clu sio n s The chemical composition of filler and m atrix has a profound effect on the rheology of a composite system. Surfaces of PS particles crosslinked w ith 10%DVB are highly incom patible w ith the PM M A m atrix, and form large agglom erates, resulting in very high viscosity at low shear rates and highly non-Newtonian behavior. The tendency to agglom erate is higher in low molecular weight m atrix, where the presence of a network, of agglomerates connected by chains of particles, resulted in th e appearence of dynam ic moduli, almost independent of frequency, in the low frequency region, and a slope of -0.77 in a log-log plot of steady shear viscosity vs shear rate at low shear rates. PS particles crosslinked with EGDM A are m ore “com patible” w ith the m atrix, due to com patibilizing effect of 10% EG D M A ,and, in fact, some m atrix adheres to the particles when P M M A ( M W = 75,000) filled w ith EGDMA- PS particles is fractured in liquid nitrogen. B etter particle-m atrix interactions result in b etter dispersion of the particles in the m atrix and, therefore, the viscosity and dynam ic moduli of EGDM A-PS filled systems are sm aller com pared to th at of DVB- PS filled systems. The composites containing PM M A particles crosslinked with 10% EGDM A are com patible w ith the m atrix, and therefore are well dispersed. Due to the absence of large agglomerates, EGDM A-PM M A filled systems do not behave in a non-Newtonian m anner and rheology curves are parallel to those of pure m atrix. In fact, in high molecular weight PM M A m atrix, a cohesive failure occurs in the m atrix, when fractured in liquid nitrogen, due to strong adhesion of m atrix on the particle surfaces. Systems filled w ith 10% DVB-PM M A have smaller particle m atrix interactions, com pared to EGDM A-PM M A filler, and therefore tend to form agglomerates. However in P M M A ( M W = 75,000) m atrix, particle- m atrix interactions are strong enough to prevent the form ation of very large agglomerates and, therefore, the system does not exhibit highly non-Newtonian behavior. In P M M A ( M W = 35,000) m atrix particle-m atrix interactions are not strong enough, and large agglomerates are formed, making DVB-PM MA filled system s behave very sim ilar to EGDM A-PS filled systems, rheologically. The molecular weight of the m atrix also has a significant im pact on the particle- m atrix interactions and, therefore, on rheology. W ith increase in molecular weight 75 of the m atrix, the fraction of polym er chains adsorbed on the particle surface in creases and this results in the form ation of a layer of m atrix molecules bonded to the particle surface, which behave differently from the particle surface. This mesophase is more com patible with the m atrix, and therefore particle-m atrix interactions are higher in high molecular weight m atrix. For chemically incom patible systems eg. DVB-PS filled PM M A, enhancem ent in m atrix-particle interactions results in b et ter dispersion of particles and, therefore, the relative viscosity of DVB-PS filled P M M A ( M W = 75,000) is smaller than DVB-PS filled P M M A ( M W = 35,000)in contrast, for chemically com patible system, eg. EGDM A-PM M A filled PM M A, particles are well dispersed and enhancem ent in bonding between particles and m a trix results in increase in relative viscosity. P M M A ( M W = 75,000) containing DVB-PM M A has smaller relative viscosity com pared to P M M A ( M W = 35,000) containing DVB-PM M A particles, at low shear rates, due to the b etter dispersion in high molecular weight m atrix. However at high shear rates, particles are well dispersed in both the m atrices, and relative viscosity of P M M A ( M W = 75,000) com posite is higher due to b etter adhesion between filler and m atrix. Ree-Eyring, W ildem uth-W illium s and Tsenglou models were used to correlate rheological d ata w ith the change in structure of the composites. Ree-Eyring data was found to describe the rheological d ata very well. It was found th a t the viscosity of the N ewtonian unit, in the two unit model, is almost constant for all the fillers and represents viscosity of suspension of noninteracting particles. Sim ilarity for 20% loading, the linear param eter in the non-Newtonian viscosity c o m p o n e n t^ ) is constant for all the fillers and therefore the particle interactions can be described by a single variable param eter(/3). Values of (5 increases with increase in chemical incom patibility of filler and m atrix. However Ree-Eyring model w ith one nonlinear param eter could not describe the rheological behavior of P M M A ( M W = 75,000) filled w ith DVB-PS particles due to the presence of two nonlinear flow units, one corresponding to high molecular weight m atrix and the other corresponding to the agglom erated structure, of very different relaxation times. W ildem uth-W illium s model, based on the shear dependence of m axim um packing efficiency of the system , was found to fit the d ata very well. However, for some systems values of m axim um 76 packing efficiency at infinite shear rate(<^Moo) were more th an 1 and therfore not explainable physically. Tsenglou’s model correlates the steady shear viscosity of the system to the ag glom erate size, in term s of the average num ber of particles in an agglomerate, and it was found to give realistic values of the agglomerate size. It was found th at de pendence of agglom erate size on the shear rate can be correlated, by an empirical equation of the type N = where k and (3 are fitting param eters. However, phys ical m eaning of this equation is doubtful since it does not predict correct values for the lim iting cases of zero and infinite shear rate. In contrast, an equation of the type = 2 _ j _ fcy— m satisfies the boundary conditions and was found to fit the data well. The values obtained for the fitting param eters N 0 and N q q were reasonable for m ost of the cases and the exponent m gives the intensity of particle particle inter actions. It was observed th a t except for non-agglomerating EGDM A-PM M A filler, where N 0 and A ^ are com parable, for chemically incom patible system s N 0 N q q and shear dependence of agglomerate size can be described by N = N 0(l — )• 77 R e fe r e n c e L ist [1] V. M. Lobe and J. L. W hite, Polym. Engg. Sci.,19,617(1979) [2] Y. K. Leong and D. V. Boger, J. Coll. Interface Sci.,136, 249(1990) [3] S. C. Tsai and K. Zammouri, J. Rheol., 32, 737(1988) [4] W . B. Russel, J. Rheol., 24,287(1980) [5] Y. O tsubo, M. Horigozme and K. Umeya, J. Coll. Interface Sci., 83, 240(1981) [6 ] D. M. Bigg, Polym. Engg. Sci.,22, 512(1982) [7] R. E. S. B retas and R. L. Powell, rheol. Acta, 124, 69(1985) [ 8 ] J. D. M iller, H. Ishida and F. H. J. M aurer, Rheol. A cta, 27, 397(1988) [9] T. Ishihara, H. K atsuki and H. Kuno, Rheol. A cta,26, 172(1987) 10] N. M inagawa and J. L. W hite, J. Appl. Polym. Sci., 20 , 501(1976) 11] D. Zou, S. Ma, R. Guan, M. Park, L. Sun, J. J. Aklonis and R. Salovey( no. 5) 1 2 ] D. Zou, J. J. Aklonis and R. Salovey, J. Polym. Sci., P art A: Polym. C hem .,30,2443(1992) 13] Z. Y. Ding, J. J. Aklonis and R. Salovey, J. Polym. Sci., part B: Polym. Phys., 29, pp 1035(1991) 14] K. G andhi, M. Park, L. Sun, D. Zou, C. X. Li, Y. D. Lee, J. J. Aklonis and R. Salovey, J. Polym. Sci., part B:Polym. Phys., 28, 2707(1990) 78 15] J. D. Ferry, Viscoelastic Properties of Polym ers, 3rd ed., John W iley Sz Sons, inc., New York 16] N. Casson, Rheology of Dispersed Systems, P P 84, ed. C. C. Mill, Pergamon Press, London (1959) 17] T. M atsum oto, A. Takashima, T. M asuda and S. Onogi, Trans. Soc. Rheol., 14, 617(1970) 18] A. Y. M alkin, Rheology of Filled Polym ers, in “Advances in Polym er Sci ence” ,96,70(1990) 19] S. H. M aron and P. E. Pierce, J. Colloid Sci., 11,80(1956) 20] T. Ree and H. Eyring, J. Appl. Phys., 26, 7(1955) 21] C. A. Herb and S. Ross, Colloids and Surfaces, 1, 57(1980) 22] C. R. W ildem uth and M. C. W illiams, Rheol. A cta, 23,627(1984) 23] C. Tsenglou, Rheol. Acta, 28,311(1989) 24] G. J. Fleer and J. M. H. M. Scheutjens, Adv. Coll. Interface. Sci., 16, 341(1982) 25] C. Vander Linden and R. Van Leem put, J. Coll. Interface Sci., 67,48(1980) 26] M. Kawaguchi, K. Hayakawa and A. Takahashi, Polym. J., 12,265(1980) 27] G. M. Bristow and W. F. W atson, Trans. Farad. Soc., 54,1742(1958) 79 C h a p ter 3 T im e D e p e n d e n t B eh a v io r o f M o d el F ille d P o ly m e r s 3.1 In tro d u ctio n Polym er composites often exhibit complex tim e dependent rheological behavior, usually referred to as thixotropy and rheopexy[l]. Similar effects occur in pure m acrom olecular systems and are attrib u ted to a variable degree of structure within the system. It is postulated, th a t in a particulate filled system , particles tend to form agglomerates, due to attractive forces such as London-van der W aals attraction and chemical interactions. Degree of agglomeration depends upon the content of filler , size and shape of the particles and the interactions between particles and between particles and m atrix. Particles whose surface molecules are incom patible w ith the m atrix have a higher tendency to form agglomerates, in the shape of chains, spherical aggregates and networks, than those whose surfaces are com patible with the matrix[2]. In fact, for “incom patible” particles, a three dim ensional network may form at a critical concentration. W hen subjected to shear, the stress induced in such systems grows, up to a m axim um , and then reaches a steady state, decay to a steady state being a dynam ic equilibrium between agglom erated and dispersed phases. The breakup of agglomerates due to induced stress include both “erosion” and “rupture” mechanisms, as observed visually for carbon black filled poly(dim ethyl siloxane)[3]. As shear rate is increased,further breakage of agglomerates may result, resulting in a b etter dispersion of particles in the matrix[2]. W hen allowed to rest, dispersed 80 particles may tend to agglomerate, resulting in enhanced viscosity and m oduli[2,4,6- 8] It has been postulated th a t while the shear dependence of the viscosity results from the structure of the fluid, the tim e dependence is a reflection of the rate of deform ation and reconstruction of agglomerates [9]. Techniques used to describe thixotropy have included l)hysteresis loop studies[7], 2)m easuring the transient stress under constant shear rate[2, 10], 3)shearing the m a terial, at high shear rate, until a steady state is reached, and then either m easuring the steady shear viscosity at lower shear ra te [ll] or m easuring the dynam ic m od uli, w ith tim e [ll, 8]. The tim e dependent behavior of a polym er composite is very complex since it it includes both viscoelastic and thixotropic effects[5], which are difficult to distinguish . Complexity of the system is further increased due to the de pendence of the agglom erated structure on past shear history and specific chemical interactions between particles and particles and m atrix. We have designed a system consisting of polym er filled w ith crosslinked polymeric beads, where chemical interactions can be varied and controlled by varying the chem ical composition of the filler and the m atrix. The instrum ent used for this study is a W eissenberg rheogoniometer, which is widely used for rheological measurements[12- 16] and applied to studies on tim e dependent behavior[2, 4, 6, 8, 17, 18]. The response tim e of the rheogoniometer is 0.6 sec[19], which is much smaller than the response tim e of m aterials studied. To avoid the effect of shear rate history, com posites were provided w ith identical and well defined shear treatm ents. 3.2 E x p erim en t 3.2.1 M aterial Polym ethyl M ethacrylate was obtained from Polysciences, Inc. (M ^ =75,000) and Scientific Polym er Products, Inc. (M ^=35,000). Styrene monomer, and divinyl ben zene and ethylene glycol dim ethacrylate crosslinkers were purchased from Aldrich Chemical Co. Styrene is 99% pure and inhibited by 10-15 ppm 4-tertiary butyl- catechol(4-TBC). Divinyl benzene consists of a m ixture of 55% of m eta and para 81 isomers, 42% of ethyl vinyl benzene and 3% dietylbenzene, and inhibited with 1000 ppm 4-TBC. Ethylene glycol dim ethacrylate is 98% pure. 25±5 ppm of hydro- quinone inhibitor is also present. All the monomers and crosslinkers were stored at — 5°C and were purified, in order to remove the inhibitor, prior to polym erization. Styrene and divinyl benzene were washed w ith an equal volume of an aqueous solution of 10% sodium hydroxide for four tim es [20], and m ethyl m ethacrylate and ethylene glycol m ethacrylate was purified by bubbling nitrogen for 30 minutes[21]. Potassium persulfate initiator and sodium hydroxide are certified Fisher Scien tific products. Deionized w ater was purchased from Sparklettes, m ethanol from EM Science and dry nitrogen from MG Industries Gas products. 2,6 di-tert-butyl-4- m ethyl-phenol(BH T) antioxidant was supplied by Aldrich Chemical Co. 3.2.2 Synthesis Crosslinked monodisperse particles were synthesized in emulsifier free emulsion poly m erization, in an internally stirred reactor as described in chapter 2. Polystyrene(PS) and poly m ethylm ethacrylate(PM M A ) particles were crosslinked w ith divinylben- zene(DVB) and w ith ethylene glycol dim ethacrylate(EG D M A ), by copolymerizing 10 mole percent of the crosslinker w ith the polymer. 3.2.3 C om p osite P reparation M atrix polym er was m elted at 175°C in a brabender plasticorder and 0.3% of antiox idant was added to prevent therm al decomposition[22]. Powdered filler was added to the m olten polym er and mixed at 175°C for 15 m inutes, for equal tim e intervals at 50 and 100 rpm .Mixed samples were placed between two alum inium plates, in a concentric circular mold of inner diam eter, 5 cm. thickness 1 mm, and was com pression molded at 175°(7 and 1.5 x 107 P a in a Dake hydraulic press for 15 m inutes and then cooled to room tem perature. 82 3.2.4 R heology The system s studied included P M M A ( M W = 35,000) and P M M A ( M W = 75,000) m atrices and their composites containing DVB-PS, EGDM A-PM M A, DVB-PMMA and EGDM A-PS particles. The tim e dependent rheological analysis of the m olten composites was carried in a W eissenberg Rheogoniom eter(R 19) at 200°(7, in a cone and plate geometry. The bottom platen is a cone of 5 cm. diam eter and 0.034 rad(2° ) cone angle. The top platen is a 5 cm. diam eter flat disk. The experim ents were carried out in a steady shear mode, the samples being subjected to a shear rate of 1.4s-1 for 2 m inutes, till the induced shear stress reached a steady state, and then allowed to rest. For steady shear experim ents, samples were sheared in both forward and backward direction fo 4 m inutes each, and th e average of viscosities was noted down. Transient shear response was recorded by an online com puter(IB M XT). Ageing experim ents involve ageing for tim e specified. These intervals are composed of the following repeated periods: 8 m inutes intervals at a shear rate of 0.014s-1 at which m easurem ents are m ade plus quiescent intervals. 3.3 R e su lts The steady shear viscosity as a function of aging tim e is plotted for P M M A ( M W = 35,000) m atrix and composites in fig.3.1. The aging tim e has been taken to be he tim e between the cessation of shear at 1.4s-1 , and the average of tim es of steady state shear in forward and backward direction at 0.014s-1 . The corresponding plot for P M M A ( M W = 75,000) is illustrated in fig.3.2. The transient viscosities for various systems, at different aging tim es, are illustrated in fig.3.3 through fig.3.10. For transient experim ents, rest tim e denotes the tim e between the cessation of shear at the high shear rate(1.4s-1 ) and inception of shear at the low shear rate(0.014s-1 ). 83 Aging time (Min) Figure 3.1: Log-log plot of steady shear viscosity vs. aging tim e for P M M A ( M W = 35,000) composites at 200°C . PM M A m atrix x Com posite containing PS particles crosslinked w ith DVB * Composite containing PM M A particles crosslinked w ith EGDM A o Composite containing PM M A particles crosslinked w ith DVB -f Composite containing PS particles crosslinked w ith EGDM A 84 0 < D CO 1 > Aging time (Minutes) Figure 3.2: Log-log plot of steady shear viscosity vs. aging tim e for P M M A ( M W = 75,000) composites at 200°C . PM M A m atrix x Com posite containing PS particles crosslinked with DVB * Com posite containing PM M A particles crosslinked with EGDM A o Com posite containing PM M A particles crosslinked with DVB + Com posite containing PS particles crosslinked with EGDMA 85 _ X X ? (X K X X X X X xXKXX^XXXXXXxX X X X X X 5 C » vYx x x x x » c ^ x^ + -> • 1 — I • rH > Time(Sec) Figure 3.3: Log-log plot of transient viscosity vs. transient tim e, at various aging tim es, iovP M M A (M W = 35,000) filled w ith DVB-PS particles, at 200°Cf. Symbols denote different rest times. . 0 M inutes x 10 M inutes * 55 M inutes o 115 M inutes + 195 M inutes - - 435 M inutes - 1170 M inutes 1880 m inutes 86 f t 1 0 3 40 60 80 100 120 140 160 Time(Sec) Figure 3.4: Log-log plot of transient viscosity vs. transient tim e, at various aging tim es, iorP M M A {M w = 35,000) filled w ith EGDM A-PM M A particles, at 200°C. Symbols are the same as fig.3.3 87 10: 0 < D G O 1 H od I 10' C /3 o o C / 3 > 1 0 | ! |. 44-+ + + + l+ l' 1 1 l+f-<^ ^ 4 + + ^ + H -^ 4 + W + + + + x ^ x x ^ x x /x ^ x x x x x x x x x ^ x x x x ' A 0 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.5: Log-log plot of transient viscosity vs. transient tim e, at various ag ing tim es, io rP M M A (M W = 35,000) filled w ith DVB-PM MA particles, at 200°(7. Symbols are same as fig.3.3 88 x T O X x w a x x x x x x x / ^ ^ x x X x x X X X ^ x * x x x x 60 80 100 120 140 160 Time(Sec) Figure 3.6: Log-log plot of transient viscosity vs. transient tim e, at various ag ing tim es, io rP M M A (M w = 35,000) filled w ith EGDM A-PS particles, at 200°C. Symbols are same as fig.3.3 89 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.7: Log-log plot of transient viscosity vs. transient tim e, at various aging tim es, for PM M A(Afw=75,000) filled w ith DVB-PS particles, at 200°C. Symbols denote different rest times. . 0 M inutes * 55 M inutes + 235 M inutes - 1170 M inutes x 10 Minutes o 115 M inutes - - 435 Minutes -. 1880 Minutes 90 10- 0 < D 00 1 o C / D cd O h c /3 O o C /3 > “ S jofrK jc * * * * * * ' .** ^ X x j ^ x x x ^ ^ 10 ‘ 0 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.8: Log-log plot of transient viscosity vs. transient tim e, at various aging tim es, for PM M A(A/U ,=75,000) filled w ith EGDM A-PM M A particles, at 200°C. Symbols are same as fig.3.7 91 v x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ^ x x x x x x x x x x x x ^ . . • . • • ......... 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.9: Log-log plot of transient viscosity vs. transient tim e, at various aging tim es, for PM M A (M W =75,000) filled w ith DVB-PM M A particles, at 200°C. Sym bols are same as fig.3.7 92 10( o 0> co <****** : )!!(el!s(!!^ ^ 4 xXXXXXXXxXxXXXXXXKXXjcxxXXXJ&XX^^ * Y . . • • • • • ........................................................... a • . . .................... 10' 0 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.10: Log-log plot of transient viscosity vs. transient tim e, at various aging tim es, for PM M A (M U ,=75,000) filled with EGDM A-PS particles, at 200°C. Symbols are same as fig.3.7 93 10: 10 ' o 0 C/2 1 ’eS o C/3 O h S 10: o C/3 XXXXX X' xXXx > ? o a x x x ? « x x x ^ 1 0 - 0 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.11: Log-log plot of transient viscosity vs. transient tim e, at zero aging tim es, fo rPM M A ( M W = 35,000) filled w ith crosslinked particles, at 200°C\ Sym bols are the same as in fig.3.1 94 1 0 1 0 1 0 Time(Sec) Figure 3.12: Log-log plot of transient viscosity vs. transient tim e, at equilibrium , forP M M A ( M W = 35,000) filled with crosslinked particles, at 200°C. Symbols are the same as in fig.3.1 95 0 0) C / 5 1 13 o c/5 03 Oh C /5 o o C / 5 • t - H > 10- fX X X X X xX X xX ^' ^xX jo cx x xX x xx x^ ^ + 10' 0 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.13: Log-log plot of transient viscosity vs. transient tim e, at zero aging tim es, for PM M A (M u;=75,000) filled w ith crosslinked particles, at 200°C. Symbols are the same as in fig.3.1 96 1 0 6r o 0 c z > 1 i— H O xn g l t f ■ f H C Z ) o O C Z > • t -H > 10' x xx>kX ^ x x ™ x x x x x ^ ^ * 0 20 40 60 80 100 120 140 160 Time(Sec) Figure 3.14: Log-log plot of transient viscosity vs. transient tim e, at equilibrium , for PMMA(Mu;=75,000) filled w ith crosslinked particles, at 200°C. Symbols are the same as in fig.3.1 97 3 .4 D isc u ssio n From fig.3.1 it is apparent th at the viscosity of pure P M M A ( M W = 35,000) does not increase much, w ith aging tim e, while the viscosity of P M M A ( M W = 75,000) slightly increased w ith time(fig.3.2). This can be attrib u ted to the disentanglem ent of high m olecular weight chains at high shear rate(1.4s-1 ) and their tendency to entangle when allowed to rest. The increase in viscosity with aging tim e for filled systems, subsequent to shear at high shear rate, varies for different systems. W hile for P M M A ( M W = 35,000) filled w ith EGDM A-PM M A particles, changes in vis cosity are small, similar to th at of pure PM M A, enhancem ent in the viscosity of DVB-PM M A filled systems, w ith tim e, is appreciable. P M M A ( M W = 35,000) m a trix filled w ith PS particles also exhibit significant increase in viscosity w ith aging tim e. Composites w ith high molar mass m atrix behave quite differently. Signifi cant increase in steady shear viscosities is shown for all the composites, especially those filled w ith DVB-PM M A and EGDM A-PS, is observed. In fact after 5 m inutes aging tim e composites containing EGDM A-PM M A, DVB-PM M A and EGDM A-PS particles exhibit very similar viscosities, but at equilibrium , their viscosities are different, the viscosity of EGDM A-PS filled system being the highest and th a t of EGDM A-PM M A filled system being the lowest. In transient experim ents, the vis cosity of P M M A ( M W = 35,000) and P M M A ( M W = 75,000) filled w ith DVB-PS filler (fig. 3.3 and fig.3.7 respectively), at short ageing tim es, rises continously w ith tim e. However at longer rest tim es, a m axim um in viscosity is observed, followed by decay to a steady state in viscosity. The value of m axim um viscosity as well as steady shear viscosity increases continously, till the system reaches an equilib rium in about 20 hours. Systems filled w ith EGDM A-PS particles also behave in a sim ilar m anner though the steady shear viscosity and extent of overshoot are sm aller com pared to th at of DVB-PS filled systems(fig.3.6,3.10). In contrast, an increase in viscosity w ith tim e, at short aging tim es, in transient experim ents, and an overshoot at long rest tim es is absent for EGDM A-PM M A filled systems. DVB- PM M A filler, when dispersed in P M M A ( M W = 35,000) m atrix, exhibit an over shoot in transient experim ents, at high aging tim es, while no overshoot is exhibited by P M M A ( M W = 75,000) composites containing the same particles. 98 3.4.1 Effect o f C hem ical Interactions It is apparent th a t the chemical composition of filler and m atrix affects the tim e dependent rheological behavior. Surfaces of EGDM A-PM M A particles are com pat ible w ith the PM M A m atrix and, therefore, are well dispersed in the system. W hen subjected to shear there is no significant change in the state of dispersion, and when allowed to rest, particle-particle interactions are not strong enough to form agglomerates, and, thus, there is no significant increase in viscosity. In transient experim ents, we observe insignificant change in transient viscosity and an absence of overshoot. The presence of DVB molecules in DVB-PM M A particle, makes the DVB- PM M A particles “incom patible” w ith the m atrix, and results in the form ation of agglomerates. However, these agglomerates are weak, and when subjected to shear they break down, resulting in well dispersed systems, which is reflected by a steady shear viscosity very similar to th a t of EGDM A-PM M A filled systems, at low aging tim es. However, as it is allowed to rest for long tim e, agglom erates tend to reform and the viscosity of the system rises. However, interestingly, it can be seen from the steady state shear viscosity, as well as transient experim ents, th at the rate of change in viscosity is not the highest at smallest rest tim es. This seems to be in contrast to a postulate th a t rate of form ation of agglomerates is highest at low rest times and decreases thereafter due to, increase in viscosity of the system and resultant increase in resistance to the agglomeration process[9]. DVB-PS particles, due to incom patibility w ith the PM M A m atrix, are rejected by the m atrix and form large agglomerates(fig.2.5,2.9). W hen subjected to shear these agglomerates break into smaller clusters. At the cessation of shear, agglom erates tend to reform and a significant increase in viscosity w ith tim e is observed. However, for P M M A ( M W = 35,000) filled with DVB-PS particles, the increase in viscosity is not as dram atic as in case of DVB-PM MA filled system , though the vis cosities are much higher in case of DVB-PS filled system , indicating the presence of larger agglomerates. Weak particle-m atrix interactions and strong particle-particle attractions in DVB-PS filled system and when allowed to rest agglomerates much faster than DVB-PM M A filled systen. This is shown by a much higher rate of change of viscosity in transient experim ents at zero rest time(3.11,3.13). In fact, 99 for very high interaction between the particles, resulting from either higher loading, higher surface area of the particles or weaker particle-m atrix interactions, no change in steady state viscosity, w ith increse in aging tim e, may be noticed at m easurable tim es. For silica filled PDMS system[7] hysteresis was absent for systems filled with 4.75% solids while it was prom inantly present for composites containing 3% silica and it was postulated th at recovery of structure is achieved at very short tim es and no change in viscosity is exhibited thereafter. Systems filled w ith EGDM A-PS behave very similarly to those filled w ith DVB- PS, though th e viscosity at any m om ent is much lower com pared to th a t of DVB- PS filled system , due to the lesser degree of agglomeration, as the presence of 10% EGDM A makes the PS particles more com patible with the m atrix. P M M A ( M W — 75,000) filled w ith EGDM A-PS particles has a very low viscosity at low aging times, almost identical to th a t of P M M A ( M W = 75,000) filled w ith, EGDM A-PM M A or DVB-PM M A, particles. However enhancem ent in the viscosity of EGDM A-PS filled system is much higher com pared to EGDM A-PM M A or DVB-PM M A filled systems. Probably when sheared in high molecular weight m atrix, EGDM A-PS par ticles attain a state of dispersion, almost identical to th a t of chemically com patible system containing EGDM A-PM M A. However when allowed to rest, they tend to form agglomerates, though the degree of agglom eration and rate of form ation of agglomerates is much smaller com pared to DVB-PS filled system. In essence, the chemical composition of the particles affect both the kinetics and equilibrium of a composite. Fillers, which are “com patible” w ith the m atrix, agglom erate m uch slower and to a much smaller degree com pared to those incom pat- able w ith the m atrix. fig.3.11and fig.3.13 give the transient viscosity at zero aging tim e for P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites, respec tively, filled w ith various crosslinked polym eric particles. As can be seen, composites containing particles “com patible” w ith the m atrix(eg. EGDM A-PM M A particles) show a much sm aller rate of increase in viscosity, in transient experim ent, com pared to chemically incom patible systems(eg. PM M A filled w ith DVB-PS particles. Sim ilarily transient viscosity at equilibrium is plotted for P M M A ( M W = 35,000) and P M M A ( M W = 75,000) composites in figs. 3.12 and 3.14 respectively and we 1 0 0 observe overshoots in transient viscosity, which is related to yield due to forma tion of a three dimensional network, for incom patible system s of PM M A filled w ith DVB-PS and EGDM A-PS while overshoots are absent for com patible systems eg. EGDM A-PM M A filled PM M A. 3.4.2 Effect of M olecular W eight o f th e M atrix W hile there is a very small change in the viscosity of the P M M A ( M W = 35,000) m atrix fig.3.1, w ith aging tim e, the viscosity of P M M A ( M W = 75,000) m atrix increases w ith aging time(fig.3.2), due to small thixotropic effects exhibited by the high m olecular weight m atrix. Therefore, to study the effect of m olecular weight, relative viscosities, which are the ratio of the viscosity of the composite to th a t of the pure m atrix, of composites in low m olecular weight and high molecular weight m atrices are determ ined and plotted as a function of aging tim e in fig.3.15 through fig.3.18. 1 0 1 > 10 r— I Aging time(Minutes) Figure 3.15: Log-log plot of relative viscosity vs. aging tim e for PM M A containing DVB-PS particles at 200°C. x Composites in P M M A ( M W = 35,000) m atrix o Composites in P M M A ( M W = 75,000) m atrix 102 > < D > Aging time(Minutes) Figure 3.16: Log-log plot of relative viscosity vs. aging tim e for PM M A containing EGDM A-PM M A particles at 200°C. Symbols are the same as fig.3.15 103 > < L > Aging time(Minutes) Figure 3.17: Log-log plot of relative viscosity vs. aging tim e for PM M A containing DVB-PM M A particles at 200°C .Symbols are the same as fig.3.15 104 C / 3 O o C / 3 > < D > Aging time(Minutes) Figure 3.18: Log-log plot of relative viscosity vs. aging tim e for PM M A containing EGDM A-PS particles at 200°C. Symbols are the same as fig.3.15 105 Relative viscosity of P M M A ( M W = 35,000) filled w ith DVB-PS particles is higher com pared to th a t of P M M A ( M W = 75,000) filled w ith same particles, at any m om ent,(fig.3.15) indicating the higher degree of agglom eration in P M M A ( M W — 35, 000) m atrix. However the increase in viscosity, as a function of aging tim e, as well as the transient response, of the two systems is very similar. This is a little surprising because we would have expected a lower rate of aging for P M M A ( M W = 75,000) m atrix due to the higher viscosity of the high molecular weight m atrix and higher resistance to the recovery process henceforth. Probably, for DVB-PS filled system diffusion lim itations are overcome by strong interparticle interactions. EGDMA- PM M A particles are well dispersed in the PMMA m atrix due to interactions of swith the m atrix. However particle- m atrix interactions are higher in the high molecu lar weight m atrix [chapter 2 ] which results in adsorption of th e m atrix molecules on the filler surface. Therefore while relative viscosity of low molecular weight PM M A containing EGDM A-PM M A particles does not change w ith aging tim e, relative viscosity, of systems containing EGDM A-PM M A filler in high molecular weight m atrix, increases, due to desorption of m atrix chains under high shear and their subsequent adsorption on the filler surface when allowed to rest, similar to adsorption and desrption of polyacrylam ide chains, at the surface of filler, in a sus pension of silica in containing polyacrylam ide, glycerine and w ater as suspending media[23]. DVB-PM M A particles, when subjected to high shear, get well dispersed in the m atrix. W hen allowed to rest subsequently,in P M M A ( M W = 35,000) com posite, agglomerates form faster, due to lower viscosity of the system and higher degree of agglom eration is attained at equilibrium , due to higher interparticls at tractions, com pared to P M M A ( M W = 75,000) system. This results in higher rate of increase in relative viscosity and higher relative viscosity, at equilibrium , for com posites w ith low molecular weight m atrix. In fact while P M M A ( M W = 35,000) composites exhibit a prom inent overshoot at high rest tim es, overshoot is absent for P M M A ( M W = 75,000) composite. Molecular weight of the m atrix can influence the degree of dispersion in tim e dependent rheological m easurem ents in a num ber of ways. Higher molecular weight m atrix has lesser particle-particle interactions and therefore a b etter degree of dispersion at equilibrium , when subjected to shear 106 agglom erates break into smaller fragm ents due to higher shear induced in high vis cosity system at same shear ra te (r = £777, where k is a characteristic constant for a system[3]) and rate of form ation of agglomerates is sm aller in high viscosity sys tem due to enhanced resistance to diffusion. In fact while viscosity of EGDM A-PS filled P M M A ( M W = 35,000) is much higher com pared to P M M A ( M W = 35,000) containing EGDM A-PM M A or DVB-PM M A particles, at low aging tim e, for same aging tim es, viscosities of all the three systems with P M M A ( M W — 75, 000) as dispersing m edia, are very similar. Loose flocculates are formed in high molecular weight m atrix due to b etter particle-m atrix interaction, and when subjected to shear at 1.4s" 1 particles get well dispersed in the m atrix for all the three system s, and therefore exhibit similar viscosities. W hen allowed to rest they attain varied degree of dispersion, resulting in significance difference in viscosities at equilibrium . Based on these observations we can postulate th at m olecular weight of the m atrix not only affect the kinetics of the agglom eration form ation, due to viscosity effect, but can also affect the equilibrium structure. This phenom ena can be attrib u ted to the enhancem ent in particle-m atrix interactions w ith increase in m olecular weight of the m atrix. The mechanism for im provem ent in particle-m atrix interactions is not clear, however. 3.5 C o n clu sio n PM M A filled w ith crosslinked polymeric particles exhibit tim e dependent rheological behavior which is greatly influenced by particle composition and m olecular weight of the m atrix. PS particles crosslinked with DVB are highly incom patible with The PM M A m atrix and therefore exhibit a high degree of agglomeration. W hen subjected to shear at 1.4s"1, agglomerates break down into smaller clusters, resulting in decrease in viscosity of the composite. W hen allowed to rest the particles tend to form agglom erate, reflected upon by increase in steady shear viscosity and transient viscosity, at low aging tim es. However, at higher aging tim es, transient response is a reflection of balance between the rate of form ation of agglomerates, due to particle- particle interactions, and destruction of agglomerates, due to shear and Brownian m otion. At sufficiently long aging tim e a three dimensional network is formed which 107 is exhibited by an overshoot in transient response. The extent of overshoot as well as steady shear viscosity increases w ith increasing rest tim e. EGDM A-PS particles are more com patible w ith the PM M A m atrix, due to com- patibilizing effect of 10% EGDM A, and are b etter dispersed com pared to DVB-PS filled systems and this results in lower steady shear viscosities and, smaller over shoots in transient experim ents at high rest times. In fact in P M M A ( M W = 75, 000) m atrix EGDM A-PS particles get well dispersed upon shearing at 1.4s_1. PMMA particles crosslinked w ith EGDM A are com patible w ith the m atrix and, therefore, are well dispersed. Upon shearing at high shear rate there is no significant change in state of dispersion and this is exhibited by insignificant increase in relative viscosity, upon aging, of P M M A ( M W = 35,000) containing EGDM A-PM M A particles. How ever, relative viscosity of P M M A ( M W = 75,000) containing EGDM A-PM M A par ticles increases, due to desorption of m atrix chains, upon shearing at high shear rate, and their subsequent adsorption when allowed to rest. PM M A particles crosslinked w ith DVB form agglomerates in PM M A m atrix, probably due to incom patibility of DVB with PM M A. However, agglomerates are weak and, when subjected to high shear rates, particles get well dispersed in the system. Viscosity of the system in creases appreciably w ith tim e, relative extent of increase as well as rate of increase being higher in P M M A ( M W = 35,000) m atrix com pared to P M M A ( M W = 75, 000) m atrix, due to higher particle-particle interactions and low resistance to the diffu sion of the particles. In fact, while a three dimensional network is formed in low molecular weight m atrix, reflected upon by the presence of prom inent overshoots in transient experim ent, such network is absent in high m olecular weight m atrix. 108 R e fe r e n c e L ist [1] M. R. K am al and A. M utel, J. Polym . Engg., 5, 393(1985) [2] L. Sun, M. Park, J. J. Aklonis and R. Salovey, Polym. Eng. Sci,32,1418(1992) [3] S. P. Rwei and I. Manas-Zloczower, Polym . Eng. Sci.,30,701(1990) [4] N. E. Hudson, M. D. Bayliss and J. Ferguson, Rheol. A cta,17(1978) [5] L. Hellincx and J. Mewis, Rheol. A cta,8,519(1969) [ 6 ] O. C. C. Lin, J. Appl. Polym. Sci.,19, 199(1975) [7] R. S. Ziegelbaur and J. M. C aruthers, J. Non-Newtonian Fluid M ech.,17,45(1985) [ 8 ] J. Mewis and R. De Bleysser, J. Coll. Interface Sci.,40,360(1972) [9] L. E. Kosinki and J. M. C aruthers, Rheol. A cta, 25, 153(1986) [10] S. Onogi, T. M atsom oto and Y. W arashina, Trans. Soc. Rheol., 17, 175(1973) [11] K. Umeya and Y. Otsubo, J. R heol.,24,239(1980) [12] K. Lakdawala and R. Salovey, Polym. Engg. Sci.,27,1035(1987) [13] G. Schoukens and J. Mewis, J. R heol.,22 ,381 (1978) [14] M. Park, K. Gandhi,L. Sun, R. Salovey and J. J. Aklonis, Polym. Engg. Sci., 30, 1158(1990) [15] L. Sun, M. Park, R. Salovey and J. J. Aklonis, Polym. Engg. Sci, 32, 777(1992) 109 [16] L. Sun, J. J. Aklonis and R. Salovey, To be published. [17] Y. De Kee and P. J. Carreau, J. R heol.,28,109(1984 [18] D. Chan, and R. L. Powell, J. Non-Newtonian Fluid M ech., 15, 165 (1984) [19] L. Sun, Ph.D . Thesis, Univ. of South. Cal.(1992) [20] D. Zou, S. Ma, R. Guan, M. Park, L. Sun, J. J. Aklonis and R. Salovey( no. 5) [21] D. Zou, J. J. Aklonis and R. Salovey, J. Polym. Sci., P art A: Polym. Chem .,30,2443(1992) [22] K. G andhi, M. Park, L. Sun, D. Zou, C. X. Li, Y. D. Lee, J. J. Aklonis and R. Salovey, J. Polym. Sci., part B:Polym. Phys., 28, 2707(1990) [23] Y. Otsubo and K. W atanabe, Coll. Surfaces, 41,303(1989) 110 C h a p ter 4 R h e o lo g ic a l B eh a v io r o f Irra d ia ted P o ly sty r e n e Polystyrene discs were crosslinked by irradiation w ith 10 MeV electrons up to a to tal dose of 178 M rad. Rheological studies were carried out using a Weissenberg rheogoniom eter. Dynamic moduli G' and G" were found to obey power law behavior at high crosslinking, the power law exponent for G' being 0.42 and 0.40 at 160 M rad and 178 M rad respectively. Corresponding values for G" were found to be 0.37 and 0.36. It was observed th at the loss fact or (£ cm 6) is highly dependent on frequency for low doses and tends to become independent of frequency as the crosslinking increases, ta n £ values being 0.78 and 0.72 for 160 and 178 M rad doses respectively . However, unlike chemically crosslinked systems, power law behavior is exhibited over a broad range of crosslinking rather than being restricted to the dose where gelation occurs. The difference was attrib u ted to the possibility of form ation of molecular structures which are only locally self similar, due to an inhomogeneous distribution of trace oxygen, and an inhomogeneous extent of scission and crosslinking resulting therefore. 4.1 In tr o d u c tio n The analysis and accurate determ ination of the gel point has been a subject of interest recently [1-11,13-15]. The gel point is defined as the transition of a polymer from a liquid to a solid state. Several theories and analogies have been proposed[l-7] to describe the phenomenon of gelation and to predict the critical extent of reaction for the onset of gelation. The sol-gel transition occurs when at least one of the 111 molecules has grown so big th a t its size reaches the dimension of the macroscopic sam ple[l]. At this point, the steady shear viscosity of the polym er becomes infinite although the equilibrium modulus is still zero. A polym er m ay undergo gelation by physical or chemical means. However, gela tion due to a physical process is reversible and may occur as a sudden transition which is difficult to predict. O ur concern here is w ith perm anent gel form ation, by interm olecular covalent chemical bonds. Various techniques e.g. NMR, R am an, flu orescence polarization, static and dynam ic light scattering and rheology[8 - 1 0 ] have been used to elucidate the nature of the sol-gel transition. Steady shear and dy nam ic m echanical analysis are included in rheological studies. In steady shear, the polym er in a liquid state is subjected to shear flow. The apparent viscosity increases w ith increasing crosslink density. After a specific crosslink density, the polym er can no longer flow and the im position of a stress overloads the instrum ent. The gel point is determ ined by extrapolation of viscosity vs crosslink density as viscosity — > oo. In dynam ic mechanical analysis (DM A), the polym er is subjected to small am pli tude oscillations, and elastic (G') and viscous (G") dynam ic moduli are determ ined. At low crosslink density viscous behavior predom inates. As the crosslink density increases, both G' and G” increase. However, the increase in G' is much larger than the increase in G", and at high crosslink density G' is much higher than G” for all frequencies. Frequently, the intersection of G' and G” ( i.e. the m inim um extent of crosslinking at which G' exceeds G") is used as an indication of the gel p o in t[11,13,14] for chemically crosslinked systems. However, the extent of reaction at which the intersection of G' and G" occurs was found to be a function of frequency in D M A [1 1 , 13] indicating th a t the G* — G” crossover can, at best, approxim ate but not define the actual gel point. It has been found by rheological m easurem ent th a t chemical gels obey a scaling law in the vicinity of the sol-gel transition[4-7,10,ll,13-15]. In this region, it is observed th a t the m odulus((r(£)) relaxes according to a power law, at the critical extent of reaction p = pc, G(t) = S t ~n; (4.1) 112 where t denotes tim e, n is a power law exponent and 5 is a m aterial param eter which is the m easure of the strength of the network at the gel point and depends upon the m obility of chain segments. W inter and Cham bon have suggested[10, 11] the following equation to describe the behavior of gels r(t) = S f 7 (t)(t - t')-ndt' (4.2) J — C O where r is the stress tensor, 7 is the rate of deform ation tensor. This equation is found to apply to a large num ber of chemically or physically crosslinked polym ers[4, 5, 7, 10, 11, 15, 16]. The exponent n varied between 0 and 1 for various systems .Expressions of n in term s of fractal dimensions have been sug gested and relations for monodisperse as well as polydisperse(in m olecular weight) solutions have been derived. A model based on Rouse dynamics for a m onodisperse system predicts 1/3 < n < 1 while percolation theory predicts n = 2/3. An expres sion has been suggested in term s of fractal dimensions and the degree of excluded volume, to take account of swelling of the flexible clusters and dependence on chain length and other compositional variables. Values of n between 0 and 1 are possible for physically acceptable fractal dim ensions(dj) 1 < d/ < 3. O ther models have also been proposed based on the assum ption th a t long tim e relaxation is due to dangling chains attatch ed to the network at only one end[17]. For a long tim e, high energy radiation has been used to modify the properties of polym ers. Irradiation has produced degradation, crosslinking, polym erisation and grafting of various polym ers[18, 19]. The prim ary effect of irradiation on a polym er is the form ation of excited and ionised molecules, which may lead to the rupture of bonds and the production of chemically reactive species. For most polymers rup tu re takes place in the m ain chain or in a side group, resulting in degradation or crosslinking,respectively. O ther effects may include the form ation of small molecular fragm ents and a modification of the molecular structure [2 0 ]. The effect of irradiation on the polym er is highly dependent on the chemical structure, density, molecular configuration, tem perature of irradiation and presence of oxygen[20-23]. Various studies have been carried out to understand irradiation in duced changes in polystyrene and resultant physical properties[24-31]. Polystyrene exhibits highly radiation resistant behavior w ith (G (V ) + G(S)) < 0.1, where G(X) 113 and G(S) denotes crosslinking and scission yields respectively, typical of a polymer containing arom atic groups, which is often attrib u ted to energy transfer w ith sub sequent nondegradative dissipation of energy[32]. The prim ary reactions induced in polystyrene by irradiation are m ain chain scission ( reaction A) and C-H bond dissociation at the tertiary carbon (reaction B)[24] which leads to crosslinking by com bination. Pst - C H 2 - C H + CH 2 - C H ( A ) Ph Ph - C H 2 - C - C H 2 + H Ph ( B ) It has been proposed th at scission and crosslinking take place competitively. In presence of air and at elevated tem peratures, scission(A) predom inates and the m olecular weight of the polym er decreases. It has been reported[26] th a t in vacuum, the ratio of scission to crosslinking, G (S )/G (X ), increased from 0 . 0 2 at 30°(7, to 2 . 8 at 150°C. In the presence of air, chain scission processes are more im portant than crosslinking reactions, at all tem peratures, and result in the form ation of polyene[31] or phenyl ketone[24]. It has been reported[28] th a t at 30°C, the crosslink yield, G(X) decreases from 0.043 in vacuum to 0.022 in air, while the corresponding scission yield, G(S), increases from 0.0086 to 0 .0 2 2 . In the absence of air and at low tem peratures, reaction (B) apeared to be favored over reaction (A) and irradiation results m ainly in crosslinking the polym er. In the absence of air, the m olecular weight of polystyrene increased with increasing doses of 7 -rays[25] and gel was formed at 50 M rad. At doses above 50 M rad, the gel fraction increased reaching 70% at 170 M rad. At the same tim e, the molecular weight of the sol fraction decreased, showing th at both crosslinking and main chain scission take place competitively. The gel doses reported varied from 50-125 M rad depending upon irradiation conditions and sample geometry. It has been proposed th at even in presence of oxygen, gel may form, at higher doses(> lQQMrad), provided G(S) < 114 4(j(X )[33]. However, for systems w ith G(S) > G(X),eve n w ith the use of large radiation doses,the gel fraction was very low[37]. Typically, a relationship is found for crosslinking yield G (X ), M w and radiation dose at the gel point r^[18] G(crosslinks)Mwrg = 0.48 x 107 (4-3) or G(crosslinkedunits)Mwrg = 0.96 x 107 (4-4) (since 1 crosslink= 2 crosslinked units) with rg in kGy and 1 M rad = 1 0 kGy. The molecular weight distribution of irradiated polystyrene chains in solution has also been studied[30]. It has been reported th at irradiation results in an enormous spread of molecular weight, w ith M w/ M n « 2000 and th at for every radiation dose there is a characteristic cut off size above which the concentration of molecules drops dram atically. As the dose increases, the cut off size increases, eventually leading to gel form ation. The size distribution near the gel point was found to obey the scaling law. 4 .2 E x p e r im e n ta l Polystyrene was obtained from the Dow Chemical Company (Dow Styron 685) and has a weight average molecular weight of 250,000 g/m ol and a polydispersity of 2.9 as determ ined by gel perm eation chrom atography in tetrahydrofuron w ith polystyrene standards. Samples were compression moulded into 5cm diam eter discs, 1 m m thick, in a hydraulic press( Preco) at 175°C and 1.5 x 107 Pa for 15 m inutes so th a t trapped air bubbles were removed. Polystyrene discs were irradiated by exposure to 10 Mev electrons from a Linear Accelerator(LINAC) at — 80° C in a nitrogen atm osphere. The LIN AC was set to em it 30 pulses/sec of 13 MeV electrons which were scattered by w ater to yield ~10 MeV electrons. The dose rate approxim ated 24 M rads/hour. Subsequent to irradiation samples were stored on dry ice and then warmed to 25°C in vacuum. 115 Rheological Analysis was carried out in a Rheogoniom eter (W eissenberg , Model R 19) w ith cone and plate geometry( cone angle 0.034 rad, plate radius 2.5 cm). Rheological m easurem ents were made at 200°C. The shear rate range was from 4 x 10~ 3 to 1.4 sec- 1 for steady shear experim ents and the frequency range, 2 x 10~ 3 to 20 Hz for oscillatory shear m easurem ents. Rheological properties m easured included viscosity, rj, at various shear rates,7 , in a steady shear experim ent. Storage m odulus G \ loss m odulus G" and dynam ic viscosity 77' were m easured as functions of frequency in small am plitude(~ 5%) oscillatory shear flow. 4.3 R e su lts The viscosity of irradiated samples as a function of shear rate, for various irradiation doses, up to 80 M rad, is plotted in fig.4.1. A fter doses of 160 and 178 M rad, the sample is no longer able to flow, at 2 0 0 °C , and when subjected to shear, breaks and squeezes out of the cone and plate. Storage m odulus, Gf, and loss modulus, G", were determ ined in oscillatory shear and are plotted as a function of frequency, co, for various doses of irradiation, in figs.4.2,4.3 . Dynamic viscosity(77'), complex dynam ic viscosity (77*) and loss factor(tan^) were calculated from G' and Gn values and are plotted in figs.4.4-4.6 . 116 0 < D G O 1 * c 3 o C /D cd Cl, Shear rate( 1/Sec) Figure 4.1: Steady shear viscosity as a function of shear rate for polystyrene at 200°C . U nirradiated Polystyrene x Irradiated to 32 M rad dose * Irradiated to 80 M rad dose 117 Frequency(Hz) Figure 4.2: Storage modulus(G? /) as a function of frequency for polystyrene at 200°C . . U nirradiated Polystyrene x Irradiated to 32 M rad dose * Irradiated to 80 M rad dose o Irradiated to 160 M rad dose 4- Irradiated to 178 M rad dose 118 Frequency (Hz) Figure 4.3: Loss modulus(Gf//) as a function of frequency for polystyrene at 200°C\ Symbols are same as fig.4.2. 119 CJ 0) CO I 13 CJ C Z 3 Cj Frequency(Hz) Figure 4.4: Dynamic viscosity(7/) as a function for frequency of polystyrene at 200°C. Symbols are same as fig.4.2. 120 Frequency(Hz) Figure 4.5: Complex viscosity^*) as a function for frequency of polystyrene at 200°C'. Symbols are same as fig.4.2. 121 Tan Frequency(Hz) Figure 4.6: Loss factor(tan £) as a function for frequency of polystyrene at 2Q0°C. Symbols are same as fig.4.2. 122 o Q~- a;oiMHz' O.OmHz 0 0 ~-o:r8g#T z - i - : 0 i i 0 .6 H z o X PQ •N #S o X P Q H z Radiation(Mrad) Figure 4.7: Storage m o d u lu s ^ 7 ) and loss m o d u lu s ^ " ) as function of radiation dose at 200°C. To separate the plots for different frequencies both G' and G" are m ultiplied by a separation variable B(io) which is a function of frequency only. Solid and dashed lines denote G' and G' curves respectively. 123 4 .4 D isc u ssio n From fig. 4.1, we can see th at unirradiated polystyrene behaves almost like a New tonian fluid at low shear rate and shows slight shear thinning at higher shear rate. W ith increased irradiation, the viscosity and non-Newtonian characteristics of the flow increase. At 160 M rad dose the sample is no longer able to flow at 200°C In small am plitude oscillatory tests, dynam ic moduli increase sharply w ith fre quency, at low frequency, and tend to flatten out at higher frequencies, typical of N ewtonian fluids and in agreem ent w ith reported experim ents[34]. As the irradiation dose increases, extent of crosslinking increases and an enhancem ent in G' and G" is observed, especially at low frequencies. For increased doses, plots of dynam ic m od uli as functions of frequency on a log-log scale tend to become linear (figs.4.2,4.3). For a dose of 160 M rad, G' vs. frequency on log-log plot is a straight line with slope 0.42. As crosslinking further increases, the slope decreases to 0.40 at 178 Mrad. The G" vs.frequency plot is sim ilar w ith slopes being 0.37 at 160 M rad and 0.36 at 178 M rad. At doses of 160 and 178 M rads, log-log plots of dynam ic viscosity(?/) and complex viscosity^*) vs. frequency are also straight lines(figs.4.4,4.5). Slopes for eta' plots are -0.65 and -0.67 for 160 and 178 M rad, respectively, and for rj* are -0.61 and -0.64 for the same doses. Loss factor (tan £) was highly dependent on frequency for unirradiated and lightly crosslinked polystyrene (fig.4.6). However, as crosslinking increases, ta n £ tends to become independent of frequency. The decrease in loss factor peak can be attrib u ted to the im m obilization of chains w ith increasing crosslinking[35].For a dose of 160 M rad, an alm ost constant value of 0.78 is observed. As the dose increases, tanS rem ains independent of frequency, though a decrease in value to 0.72 at 178 M rad is observed. G' and G” are plotted as function of radiation dose for various frequencies in fig.4.7. For clarity, logB + logG1 and logB -f logG" are plotted, where B = B(co) is an arbitrary separation variable, to separate the plots for different frequencies. As can be seen from fig.4.7, the radiation dose at which G ’ intersects G ” depends on frequency. In fact, for very high frequencies, G' > G” for unirradiated and irradiated polystyrene, typical of m ost polym eric liquids[36]. It can be seen th at for 124 polystyrene, the intersection of G' and G" is not a satisfactory m easure of the gel point. 4.4.1 A n alysis o f R heological M easurem ents w ith a Pow er Law The gel equation ( eq.(4.2)) applies to small strains only. For small dynam ic strains of the form 7 = q 0 sincot, at the gel point (p = pc),equation (4.2) takes the form : G*(u,pc) = T(l-n)S(iu> )n (4.5) W here G*(u>) denotes the complex modulus at frequency uo and critical extent of crosslinking pc. W hence, G’ = SujnT(l — n) cos mr/ 2 (4*6) G" = S u nT(l - n) sin mr/ 2 (4.7) and tan S = G"/G' = tan mr/ 2 (4-8) Therefore the storage and the loss modulii are related by G'iuo) = Gn(uj)l ta n (n 7r / 2 ) = T(1 — n) cos(nx /2 )Ston (4-9) And the dynam ic viscosity (77* = yj(G‘ /a ; ) 2 + (G"Iw)2) becomes 77* = S T (1 - n ) u ? ~ n (4.10) Equations 4.6 and 4.7 predict th at at the gel point, a plot of G' and G" as a function of frequency on a log-log scale will be a straight line w ith slope n. Indeed the plot of G' gives a straight line w ith a slope of 0.42 for 160 M rad dose and 0.40 for 178 Mrad(fig.[4.2]). Also equation 4.8 predicts th at tan 6 is independent of frequency and gives a constant v alu e= tan (n 7r / 2 ). From fig. 4.6, an almost constant value of 125 0.78 is obtained for 160 M rad and 0.72 for 178 M rad. Corresponding values of n are 0.42 and 0.40. Therefore, it is apparent th a t irradiated polystyrene shows scaling behavior over a range of crosslinking and not only close to the gel point as observed in case of chemically crosslinked gels. So for irradiation it is difficult to determ ine the exact gelation dose by rheological m ethods only. The value of the exponent is highly dependent on the crosslinking m ethod and the composition, n varied from 0.19 to 0.92 depending upon stoichiom etry, chain length and concentration for end linked poly(dimethylsiloxane)[39]. For end linking networks w ith balanced stoichiometry, an n of 0.5 was able to fit the d ata w ell[ll, 12]. Also, for such systems at the gel point, Gr ~ G”, and thus the intersection of G' and G" defines the gel point quite correctly. However, n > 0.5 is observed for system s such as end linking networks, w ith im balanced stoichiom etry(n — 0.5 — 0.7)[10], bulk condensation of polyester(n « 0.69)[6], epoxies(n « 0.7)[5] and PVC plastisol[38](n « 0.8) and the gel point occurs earlier th an the G1 and G" crossover. For our system (irradiated polystyrene) and for irradiated polyethylene[40] n < 0.5, and th e gel point occurs beyond the crossover. The rheological behavior should be directly related to the structure of the m a terial. Theories of gelation predict a power law cluster num ber distribution at the gel point in term s of cluster mass M N m ~ Af T (4.11) W here r is a m easure of the polydispersity in the size of clusters in the system. Power law mechanical behavior has been attrib u ted to the fractal structure (i.e. structural self sim ilarity) which evolves during th e crosslinking[39]. The m echanism of irradiation induced gelation is very different from chemicaly crosslinking. In the case of chemicaly crosslinked systems, only crosslinking takes place and the molecular weight of the whole system rises with increasing crosslinking. For radiation cured systems, crosslinking and scission often take place sim ultane ously, resulting in an enormous spread of the m olecular weight. In fact while the m olecular weight of the gel fraction, of polystyrene in cyclopentane, rises w ith in creased dose, th a t of the sol fraction decreases[30]. The relative am ount of scission 126 and crosslinking is highly dependent on the presence of oxygen. For polystyrene irradiated in vacuum at 20 — 40°C, the ratio G (S)/G (X) can vary between 0 and 2.0[28] depending upon the sample geometry, m ethod of preparation, radiation dose, tem perature and efficiency of evacuation. Depending upon the sample geometry, in homogeneous distribution of trace amounts of oxygen is possible. Inhomogeneity during irradiation may result in regions which are only locally self similar, and dif ferent parts of the sample may undergo gelation at different times. Scanlan and Winter[39] have observed the effect of tem perature inhomogeneity on the gelation of PDMS and have reported on the impossibility of determ ining an instant of self similarity for the whole sample. Nemirovski et al.[16] have studied the rheology of blends of pure polystyrene and polystyrene crosslinked with divinylbenzene(XPS). For physically blended systems, power law relaxation was observed for XPS contents beyond 60%. Though the goodness of the model is enhanced at 80% and 100% XPS, at 60% XPS the correlation is reasonably good. Samples with lower XPS content do not exhibit power law behavior. This indicates th at, probably, for heterogeneously crosslinked systems, the m aterial relaxes according to a power law over a wide range of crosslink content. For our system , as well as for irradiated polyethylene[40], due to an inhomogeneous distribution of oxygen, probably, radiation resulted in locally self similar structure in different parts, which may undergo gelation at different ex tent of reaction.Therefore, the system exhibits power law relaxation behavior over a broad range of irradiation dose. Probably the instant when the first insoluble molecule (gel) is formed is given by the first instant when the modulus follows the scaling law. 4.5 C on clu sion Irradiation of polystyrene resulted primarily in crosslinking as, indicated by an en hancement in steady shear viscosity and dynamic moduli. At doses above 160 M rad, irradiated polystyrene is not able to flow, at 200°C, due to gel form ation. The in stant of gelation is difficult to determ ine, directly, from steady shear experiments and dynamic mechanical m ethods were employed. However, the crossover of G' and 127 G" is found to be dependent on the frequency and thus was inadequate to deter m ine the gel point. The dynam ic m oduli were found to obey a power law at high crosslinking, the slopes, on a log-log plot of moduli vs. frequency, being, 0.42 for G' at 160 M rad and 0.40 at 178 M rad, and 0.37 for G" at 160 M rad and 0.36 at 178 M rad. Loss fact or (tan < 5 ) becomes independent of frequency, at high irradiation doses, values being 0.78 for 160 M rad and 0.72 for 178 M rad. However, unlike chemi cally crosslinked systems where the system exhibits power law relaxation only at the instant of gelation, irradiated polystyrene exhibits power law relaxation over a range of crosslinking doses. This difference is probably due to the heterogeneous structure th a t emerges during crosslinking of polystyrene with irradiation, due to scission and crosslinking reactions taking place sim ultaneously w ith the effect of a heterogeneous distribution of trace oxygen superposed. However a further investigation involv ing polystyrene molded in an inert atm osphere, to elim inate the presence of trace oxygen, as well as comparison w ith other techniques of gel point determ ination, is required to substantiate it. 128 R efe r e n c e L ist [1] D. Stauffer, A. Coniglio and M. A dam , Adv. Polym. Sci. , 44, 103, (1982) [2] P.-G. de Gennes, Scaling Concepts in Polym er Physics, (Cornell, Ithaca, New York, 1979) [3] M. M uthukum ar, J. Chem. Phys., 83, 3161, (1985) [4] D. D urand, M. D elsanti, M. Adam, J. M. Luck, Europhys. L ett., 3, 297, (1987) [5] J. M. M artin, D. Adolf and J. P. W ilcoxon,Polym. Prepr. Am. Chem. Soc. Div. Polym . Chem ., 30, 83, (1989) [6] M. R ubinstein, R. H. Colby and J. R. Gilm or,Polym . Prep. Am. Chem. Soc. Div. Polym. Chem, 30,81,(1989) [7] F. Cham bon and H. H. W inter, J. Rheol., 31, 683, (1987) [8] R. W inter, D. W. Hua, X. Song, W. M antulin and J. Jones, J. Phys. Chem., 94, 2706, (1990) [9] E. W. Hansen and T. Lund, J. Phys. Chem ., 95,341, (1991) [10] F. Cham bon and H. H. W inter, J. Rheol., 31,683,(1987) [11] H. H. W inter and F. Cham bon, J. Rheol., 30,367, (1986) [12] F. Cham bon, Z. S. Petrovic, W. J. M acKnight and H. H. W inter, M acrom., 19, 2146, (1986) [13] L. M atejka, Polym. Bull., 26, 109, (1986) 129 [14] H. H. W inter, Polym. Eng. Sci., 27, 1698, (1987) [15] H. H. W inter, ”Gel Point” in Encyclopedia of Polym. Sci. and Eng., Editors H. F. M ark, N. M. Bikales, C. G. Overberger and G. Menges, 2nd Ed., Suppl. Vol., 343, Wiley, (1989). [16] N. Nemirovski, M. Narkis and R. Salovey, ’ ’The Structure of Polystyrene Blends” (To be published) [17] J. G. Curro, D. S. Pearson, E. Helfand, Macromol., 18, 1157, (1985) [18] A. Charlesby, ”The Effect of Ionising radiation on Polym ers” , in Irradiation Effects on Polym ers, Edited by D. W. Clegg and A. A. Colleyer, Elseveir Applied Science, 39, (1991) [19] A. Charlesby, R adiat. Phys. Chem., 9, 17, (1977) [20] F. A. Makhlis, R adiation Physics and Chem istry of Polym ers, Wiley, New York,(1975) [21] A. Chapiro, R adiation C hem istry of Polym eric Systems, Interscience, Lon don,(1962) [22] R. W. G arrett, D. J. T. Hill, T. T. Le, K. A. Milne, J. H. O ’Donnell, S. M. C. Perera,P. J. Pomery, ’ ’Tem perature Dependence of the R adiation Chem istry of Polym ers” , Radiation Effects on Polymers, E dited by R. L. Clough, S. W . Shalaby, Am erican Chemical Society, W ashington,D C,(1991) [23] E. S. Kem pner, R. Wood and R. Salovey, J. Polym. Sc., Polym. Phys., 24, 2337, (1986) [24] T. Ogawa, S. Nishimoto and T. Kagiya, Polym. Degrad. Stab., 15, 291, (1986) [25] C. Brinkinshaw and M. Buggy, J. Appl. Polym. Sci., 41, 1913, (1990) [26] T. N. Bowner and J. H. O ’Donnell, J. Polym. Sci., Polym . Chem. E d .,19,1167, (1981) 130 [27] T. N. Bowner, L. K. Cowen, J. H. O ’Donnell and D. J. W inzor, J. Appl. Polym. Sci., 24, 425, (1979) [28] J. H. O ’Donnell , N. P. Rahm an and C. A. Sm ith, J. Polym. Sci., Polym. Chem. Ed., 17, 4081, (1979) [29] E. Egusa, K. Ishigure and Y. T abata, M acrom., 13, 171, (1980) [30] L. Leiblcr and F. Schosseler, Phys. Rev. L ett., 55, 1110, (1985) [31] G. Geuskens, D. Baeyens-Vomant, G. Delamaunois, Q. Lu-Vinh, W. P iret and C. David, Eur. Polym. J., 14, 291, (1978) [32] R. H. P artridge,”Energy Transfer in Polym ers” ,The R adiation C hem istry of M acromolecules, V ol.l, Edited by M.Dole, Academic Press, New York ,(1972) [33] O. Saito,The R adiation Chem istry of M acrom olecules,V ol.l,Edited by M. Dole,Academic Press, New York,(1972) [34] M Park. K. Gandhi, L. Sun, J. J. Aklonis and R. Salovey, Polym. Eng. and Sci., 30,1158, (1990) [35] T. 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Creator Agarwal, Shishir (author)

Core Title Rheological behavior of polymer composites containing crosslinked polymers

Degree Master of Science

Degree Program Chemical Engineering

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

Tag chemistry, polymer,engineering, chemical,OAI-PMH Harvest

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Advisor Salovey, Ronald (committee chair), Shing, Katherine S. (committee member), Yortsos, Yanis C. (committee member)

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