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The determination of differential diffusion coefficients of radioactive ions

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The determination of differential diffusion coefficients of radioactive ions

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Content THE DETERMINATION OF DIFFERENTIAL DIFFUSION COEFFICIENTS OF RADIOACTIVE IONS A Thesis Presented to the Faculty of the Department of Chemistry University of Southern California In Partial Fulfillment of the Requirements for the Degree Master of Science by Fames. W. Cobble June 1949 UMI Number: EP41572 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 EP41572 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 ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6- 1346 ' 5 0 C & 5 - ? This thesis, written by ^.•..Se^B^^PpbbX^,,,.,............. under the guidance of h^.f.... Faculty Committee, and approved by all its members, has been presented to and accepted by the Council on Graduate Study and Research in partial fu lfill ment of the requirements for the degree of Master of Selence Emory...S..„Bpg<^dus.......... Dean D ate ....... Faculty Committee jCL 6 Chairman ... TABLE OF GONTBSTS CHAPTER PAGE I. INTRODUCTION ................... I II. THEORY OF ELECTROLYTE DIFFUSION ........ 10 Diffusion of a single ion species ...... 10 Diffusion of an electrolyte....................14 The limiting law of diffusion for a t single ion................ ................. 16 Previous experimental results ........ 18 III. THE DETERMINATION OF DIFFUSION COEFFICIENTS BY MEANS OF THE DIAPHRAGM CELL............. 80 Description of the apparatus ......... 80 The oaloulation of the diffusion coefficient . 83 Determination of the oell constant.............. 35 IV. EXPERIMENTAL PROCEDURES.......................... 87 V. EXPERIMENTAL RESULTS............. 30 Diffusion coefficients for Na+ at 35°C. . . . 30 Diffusion coefficients for Na* at 35°C. . . . 37 VI. DISCUSSION ........................' . . 48 Conclusion........................... 47 BIBLIOGRAPHY................................ 49 APPENDIX .................... 51 LIST OF TABLES TABLE I. II. III. IY. % Differential Diffusion Coefficients of Sodium Ion in Sodium Chloride Solutions, 25°C»« Unstirred .... ................. Differehtial Diffusion Coefficients of Sodium Ion in Sodium Chloride Solutions, 25°C. , Stirred......... . ......... • . . . Differential Diffusion Coefficients of Sodium Ion in Sodium Chloride Solutions, 35°C.„ Stirred . A Sample Coincidence Correction ...... PAGE . 31 . 32 . 38 . 53 LIST 01? FIGURES FIGURE PAGE 1. The Glass Diaphragm Diffusion Cell........... 21 2. Diffusion Coefficients of Sodium Ion in Sodium Chloride Solutions. 25°C. ...... 33 3. Diffusion Coefficients of Sodium Ion in Sodium Chloride Solutions. 35°C............ 39 4. Coincidence Corrections of a Glass Solution Geiger-Counter Tube ............... 54 5. Neutron Bombarded Sodium Carbonate Decay Curve .......................... 56 CHAPTER I INTRODUCTION Any historical development of the diffusion of electro lytes in solution must begin with the theoretical work of Adolf Pick**' and the experimental work of Thomas Graham2. Pick's research led to one of the basio laws of diffusion. Pick's First Law: S represents the amount of material diffusing through a unit area in a given plane in unit time, is the concentration o X gradient, and D is the proportionality constant, called the diffusion coefficient. The work of Graham led to the differ entiation of solutes into colloids and crystalloids, and the subsequent discovery of the phenomena of dialysis. Equation (1) is essentially'the defining equation for the diffusion coefficient, D . It has been found experimen tally that this coefficient is dependent upon the nature of the solute, the type of solvent used, the temperature of the solution, and the concentration of the solution. Qualita tively* electrolytes which have large values for diffusion A. Fiok, Pogg. Ann, 94, 59 (1855). 2 T* Graham, Phil. Trans., 140, 438 (1851); 144, 177 (1854); 151, 183 (1861). coefficients are transported in a solution at a faster rate than other electrolytes having smaller values of D * under the same conditions. The determination of the diffusion coefficients of electrolytes In solution has long been a difficult and perplex ing problem. Experimentally* these determinations consist ©f evaluating the terms in equation (1)* the permeation rate* S , and the concentration gradient. By a change of variables, expression (1) may be rewritten as: & - D - & (8) whioh allows an alternate way to determine D , by measurement of the change of concentration with time at some point* as well as the concentration gradient existing there. Most of the experimental methods employed have required that finite concentration changes occur during diffusion to allow accurate analysis of the material transported. A diffu sion coefficient obtained by this method represents an average coefficient over the range of the concentration change. This coefficient is called an integral diffusion coefficient and is some average of differential diffusion coefficients represent ing the rate of diffusion in a single concentration. Equations (1) and (2) sore differential equations having general solutions* but whose specific solution will depend upon the particular boundary conditions imposed. These boundary conditions will be determined by the type of experi ment and apparatus used to study diffusion* and oan be divided into two general Glasses. These two classes are free diffu sion and restricted diffusion. In free diffusion* the apparatus usually eonsists of a long vertical tube with pure electrolyte or a solution at the bottom* and with pure solvent, or a less concentrated solu tion on top of the other. The sharp interface originally formed will gradually become diffuse* due to the fact that material is diffusing from the concentrated region into the more dilute region. To meet the requirements of free diffu sion* the tube must be infinitely long so that the concentra tions at both ends will not change. Practically this is ac complished by using a tube of finite length* and allowing the diffusion process to take place for times short enough so that there will be no appreciable concentration changes at the extremities of the apparatus. The problem essentially reduces itself to determining two of three factors: the permeation rate* the concentration gradient* or the change of concentration with time at some point in the solution. Various investigators have attempted to solve this problem in a variety of ways. Clack3 approximated the free diffusion prooess by hav ing two large reservoirs of different concentrations connec ted by a tube* and measuring the amount of material trans ported from one reservoir to the other In a given time. 3 B. W. Clack, Proo. Roy. Soc..1 2^. 374 (1908). Since the concentrations of the two reservoirs were not too different* and were large enough so that the concentration change was small, this method approximated the conditions necessary for determining differential diffusion coefficients. The sehleiren optical method of scanning a concentration gradient set up in a tube has found wide use in studies of the diffusion of non-eleotrolytea, and some use in electro lyte diffusion.4,5 The restricted type of diffusion apparatus is similar to the free diffusion type except that the diffusion tube is much shorter, and during the diffusion run appreciable con centration changes may take place at the extremities of the apparatus. If the diffusion coefficient were independent of the concentration this v/ould not make any difference, but this is not generally the case. If the time of diffusion is made so small so that the concentration change is small, then the errors in determining the exaot change are very large. Ap proximations have been made by slicing the diffusion tube into oompartments after the diffusion run, and analyzing each separate compartment for concentration changes.6,7 Such dif fusion coefficients are rather difficult to interpret, how- 4 D. Wiener, Ann. Physik., 49, 105 (1893). 5 L. G. Longsworth and D. A. Maclnnes, J. Am. Chem. Soo., 62, 705 (1940). 6 S. Cohen and H. R. Bruins, Zeit. phys. Cham., 103, 337 (1923). 7 L. W. Oholm, Zeit. phys. Gham., 50, 309 (1905). 5 ever* since they do not correspond strictly to either differ ential or integral coefficients. Hamad and French® have recently used a two compart ment oell in which they allow diffusion to take place for a short time* and by means of oonductimetrie analysis in situ were able to determine differential coefficients. All of the above methods suffer in one respect# and that is in the difficulty in trying to establish and maintain a concentration boundary in a diffusion tube which is free from thermal convection and vibration currents. This is most easily accomplished when there are large concentration and hence, density, differences. However, these are usually exactly the conditions one tries to avoid in seeking differ ential coefficients. It is also practically impossible to study diffusion in very dilute solutions for the same reason. The diaphragm cell, developed by Northrop and Anson9, and McBaln and Liui0# attempts to overcome the difficulties of undesirable stirring by separating two compartments by a porous membrane in which the solution is immobilized by the capillary action of the small pores. However, it still suf fers from the respect that one must allow enough material to y P, —, ^ rr ,-- r - i ® H. S. Harned and D. M. French, Annal, N. Y. Acad. 3oi* , 46, 367 (1945). ® J. N. Northrop and M. L. Anson, J. Gen. Physiol., 12. 543 (1938). J. W. MoBaln and T. H. Liu* «T. Am* Chem. See., 53, 59 (1931). / f - diffuse through the membrane or diaphra^a to accurately determine the concentration change analytically. This means that there must be a finite concentration difference between the two compartments, and a finite concentration change dur ing diffusion. For this reason, one obtains integral co efficients from this apparatus, too, and it is also not possible to study the very dilute concentration range. It is not surprising therefore, considering the variety of apparatus used, and the various diffusion coefficients ob tained, that comparison and correlation of the data of sepa rate workers lias often been impossible. A large part of this is undoubtedly due to experimental difficulties. However, the failure of the earlier workers to realize that the type of diffusion coefficient obtained was dependent upon the ex perimental conditions has also complicated the situation. This can best be Illustrated by the fact that even though Graham first reported diffusion experiments in 1805, probably the only electrolyte whose diffusion behavior Is adequately known in all concentration ranges is potassium chloride. *^2 In the diffusion of electrolytes into water or into a less concentrated solution, the diffusion rates of both ions are by necessity the same, because of the requirement that the solution remain electrically neutral. This mean diffu sion rate for the electrolyte has a value somewhere In . ^ H. S. Harned, Chem. Bev.• 40, 463 (1947). IP H. S. Harned and R. L. Nutall, J. Am. Chem. Soo., 71, 1460 (1949). — 7 between the values for the Individual ions. Of more theoretical interest would be the individual rates of diffusion of the single ions in solution. The work of Jehle13 in 1938 on the ionic self diffusion coefficients of radioactive sodium and chloride ions in sodium chloride solutions initiated a new method of investigating the proper ties of individual ions in solution. The progress of diffu sion can be followed by means of the radioactivity of a single ion species, thereby eliminating the need for finite concen tration gradients formerly used. The use of radioactive isotopes permits measurements to be made directly at a given concentration, and the requirement that the cations and anions move at the same rate is removed. This allows the direct study of individual ionic behavior, and the subsequent determination of the differential diffusion coefficients at a given concentration. It also makes possible the extension of the study of diffusion behavior to extremely low concentra tions. Jehle’a method is a free diffusion method, and is dif ficult to use because of maintaining the diffusion tube free from thermal convection currents and vibration stirring. Adamson14, by combining the advantages of the diaphragm oell* in which these stirring effects are negligible, and the 13 L. P. Jehle, Ph. D. Dissertation, Univ. of Calif. at Berkeley, (1938), 14 A. W. Adamson, J. Phys. Chem.# JJ5# 176 (1947). 8 advantages of the Jehle method of following the individual lonio diffusion* was able to obtain direotly differential diffusion coefficients using very simple apparatus. It is this method which has been used to obtain the data of this research. The study of the diffusion coefficients of single ions is one of the few methods of studying the behavior of indi vidual ions direotly. Because the diffusion of an ion in solution is determined by the charge on the ion, the size of the ion, and amount of hydration, and the concentration of the solution* it should be possible to study each of these physical effects for single ion species. The availability of isotopes from the Atomic Energy Commission for practically every element will facilitate such studies. Theoretical equations have been developed by Nemst^®, and Onsager and Fuoss16, for the diffusion of electrolytes. Their expressions are only valid for dilute solutions, and have been difficult to test by previous methods, Sinoe radioactive isotopes are available in high specific activity in many oases, it will be possible to study ion behavior at extremely high dilutions where direct comparison with theory without resorting to extrapolation will be possible. It should be stated that the oompleta program outline# 15 w. Nerost, Zeit. phys. Chem., 2. 615 (1888). L. Onsager and R. M. Fuoss, J. Phys. Chem., 36, 8689 (1932). 9 above is beyond the scope of this thesis. The main objectives of this research are to investigate the method of obtaining differential diffusion coefficients for radioactive ions in the MoBain type diaphragm cell, and if possible to correlate such measurements with existing theory. CHAPTER II THEORY OF ELECTROLYTE DIFFUSION I. Diffusion of a single ion species Expression (1), Flak’s first law* is merely the defin ing expression for the diffusion coefficient, and does not reveal any information as to the theory of the forces causing the diffusion process. Nernst-1 - proposed that the velocity of an ion in solution could be assumed to be proportional to the chemical potential gradient and eleotrioal potential gradient existing at that point in the solution. His exact expression is: V = -CJ(du/cU v dE/dx) J (3) where (d is the mobility of ion, and v is its velocity. In the absenoe of an external electrical field, &E/4x becomes zero, and we have the expression: ; V = ■ -£J(du/dx). (4) The number of ions which are diffusing per unit area per unit time is equal to S = CV (5) where c is the concentration of the ion. On combining (3) and (4) we obtain ! S s ~cU) d u/dX . . ) If we replace the chemical potential by its definition at high dilutions, i.e., ^ ¥. Nernst, Zeit. phys. Chem., 2, 613 (1888). 11 U s u* + RTlnc {7) which becomes on differentiation du/dx = ■ RT dlr>c/dx, (8) we obtain, S = -cURTdlnc/dx, (9) or S r -cCJRT jl djkj (10) which reduces to: S s-"R T ^ (i d Substituting (1) in (11) gives D = U H T (12) which is the Nernst limiting value of D for a single ion. The mobility of an ion can be written as: (J = — 300 A ... 96,500 {21 e (13) where A is the ionic conductance, t the number of e charges on the ion. Expression (12) reduces, then, for a single ion at infinite dilution to: D = ,t.TA (i*) where k has a value of 7.75 x 10“®, D being expressed in om2/day. If we consider a more concentrated solution, then the chemical potential of an ion is no longer proportional to the 12 t concentration, but to the activity of that ion. Equation (7) than becomes A similar treatment with this equation gives' the final expression which is equivalent to (14) except that it contains a term correcting for the activity at finite concentrations. Ac cording to the theory, this equation is valid at any concen tration, and would allow the calculation of the diffusion coefficient over the entire concentration range, if the ionic conductances and ionic activity coefficients are known. Since ionic activity coefficients are not available, it is of more interest to oalculate them from the diffusion coeffi cients, which will be experimentally obtainable. Indeed, this method seems to be the only one available for such cal culations, assuming that the original theory is correct. - ft0 + R T In a (15) (16) We can rearrange expression (16) as follows: 0 c din# d c K/Z A T (17) and further. (18) and Integrate, 13 (19) so that w,e obtain: i (O.c) = .In * J 0 (SO) The left hand side of the equation can be Integrated either graphically or by plotting f(D.o) against c, and taking the area under the curve , or analytically by express ing f(D.o) as a function of e. Such an area will give a value of lh K Although it may seem that the function f(D.o) becomes infinite at c equal to zero, this is not necessarily so. sinoe'D equals under this condition as seen from (14). By definition the activity coefficient of an ion is unity at o equal to zero. and In * becomes zero, as well as the function. 14 II. Diffusion of an electrolyte In the previous section we were dealing with the case of the diffusion of an ion in a solution of a single concen tration. The work of Jehle2 and Adamson® was of this type, ahd is the manner in which this research was also carried out. However, the hulk of the diffusion data has heen oh- / tained through the study of the diffusion of an electrolyte along a concentration gradient, and as was pointed out, the cations and anions are restrained or accelerated so as to move at the same velocity in order to maintain the electro- . neutrality of the solution. On introducing this fact as*. V4 = V- (SI) one can derive equations for molecules (combinations of ions) similar to those for ions alone. The Hernst expression, for example, then becomes: 0 ' - ( t . * t . ) R T ( i t m The problem becomes more involved at finite concentrations, since we have effects present besides the change of activity with concentration. As the electrolyte of one concentration diffuses into one less concentrated, there is a change in the partial molal volumes involved,, and a term must be introduced for this correction. Since the dragging effect of the cation 2 L. P. Jehle, Ph. D. Dissertation, Univ. of Calif, at Berkeley, (1937). ® A. W. Adamson, J. Chem. Phys.* 15, 176 (1947). IS on the anion is dependent upon the ionic atmosphere effects, the situation is further complicated. The theory of Onsager and Fuoss4 has attempted to handle these effects, and they have derived the following equation: [)= k T ( I + C d. ) c V d c / where 11 is given by: I ,n *o f) . 1.0748 /A ” , A°-)_ 0 J 404. /A V A ° - \!L S — ,2 where a0 is tlje mean distance of approach of the ions in angstroms, Y \ 0 is the viscosity of the pure solvent, ti? is the equivalent conductance, and Ka = A where A = * • 0 is the dielectric constant of the solvent. (0 t ) 1 / 1 Values of the function and (Ka)4^K<x have been calculated and recorded.® 4 L. Onsager and B, M. Fuoss, J. Phys. Chem., 36, 3669 (1933). ® H. S, Harned and B. B. Owen, Phys, Chem. of Electrolytic Solutions, Beinhold Pub. Co.,N. Y. (1943), " * III. The limiting law of diffusion for a single ion In section I, equation (14) first derived by Nernst**, is an expression for the limiting value of the diffusion coefficient at infinite dilution. It is also of interest to determine the change of the diffusion coefficient with con centration, or the limiting slope as it is sometimes called* This &j$ done by expressing the activity coefficient and ionic conductances In terms of the respective limiting laws. If we limit ourselves to that concentration range over which the Debye-Huekel theory is valid, then the activity coefficient of the ion is5 log J f , = - 0.507 EC 2 at 25°C. On taking the derivative of (35) with respect to concentration, we obtain: d log y c"Vz _fe— - = -0. 253 2 c m ) a C One can further write the equivalent conductance by means of the Onsager® relation for a 1:1 electrolyte: z\ = A 0 - [o .2 2 l A* + 2 9. 9 c.> / z ]. (2 7 ) This equation, derived theoretically by Onsager in 1937, is valid over about the same concentration range as the Debye- Huokel theory. If we substitute (2d) and (27) in (16), and neglect all powers of c higher than e^» we obtain the limit ing relation for a single Ion. For sodium chloride, for 6 L. Onsager, Physik. felt., 28, 277 (1927) 17 example» this expression is: £:= i.is [I 4/c ' 2] 25°C: or D = 1.41 [\ - I . 43 at 35° C. £ in- these expressions is given in cm2/day. (28) (29) I 18 17. Previous experimental results When' Onsager and JPuoss attempted in 1932 to find experimental evidence to confirm their theoretically derived equations, they were unable to find data of sufficient ac curacy or in dilute enough solutions to do so. At the present time, only the work of Harned and Nuttall7 with potassium chloride in water has verified the theoretical expressions. On the other hand, James, Holllngshead, and Gordon® have shown that if the Nernst equation were valid for KG1 it could not be valid for HC1 or HgSO^ on the basis of their diaphragm oell data. The HOI appeared to extrapolate to a value of P at infinite dilution 6$ lower than required by the Nernst equation, but D for H&SO4 was some 12$ higher. Similarly, Adamson9 has reported that the limiting value for sodium ion diffusion in Nal solutions is 7$ greater than the theory would predict, although the slope of the diffusion coefficient is in good agreement with the Onsager- Fuoss theory. The data in this case were also obtained by the diaphragm method. The observations with diaphragm cell data might tend to make one suspect this method of measuring diffusion coefficients, but Jehle10 also found values for 7 H. S. Harned and B. L. Nuttall, J. Am. Chem. Sod., 1460 (1949). ® W. A. James, E. A. Holllngshead, and A. R. Gordon, J. Chem, Phys., 7, 89 (1939). 9 A. W. Adamson, loc. clt. 10 L. P. Jehle, loc. oit. 19 sodium Ion and chloride ion diffusion coefficients higher than the limiting value would require * and moreover, the limiting slopes were not in agreement with theory. Oholm^ using a layer-analysls free diffusion cell found that the Integral coefficients for KOI, HaCl♦ LiGl* and KI in 0.01 N solutions diffusing Into water were already as large as the Nernst limiting values, when they should have been a few per cent lower to allow for an increase.on dilu tion. However, with HOI, KOH, and NaQH, the results were from six to ten per cent lower than the limiting values. It can be,seen that in the light of these marked differences. In 3ome cases, that the experimental basis for the limiting laws Is rather inconclusive, if indeed, it exists at all. ^ L. I, 5holm, Zeit. phys. Chem., §0, 309 (1905). CHAPTER III THE DETERMINATION OF DIFFUSION COEFFICIENTS BY MEANS OF THE DIAPHRAGM CELL I. Description of the apparatus It has been pointed out in an earlier section of this thesis that the diaphragm cell method of determining diffu sion coefficients has the distinct advantage of simplifying the apparatus needed, and the effeots of thermal and vibrational stirring are considerably reduced. By using the tracer method of following the movement of radioactive ions across the diaphragm in a solution of a single concentration, one is able to calculate directly the differential diffusion coefficient for the particular ion at that concentration. It is this method whioh Adamson used, and was employed in this research. In its simplest form, the diaphragm cell consists of a hollow cylindrical tube with a sintered glass membrane in the middle dividing the tube into two compartments. The particular design of cell used is shown in Figure 1. The volumes of the compartments are about 30 oc., the sintered glass membranes being constructed from Pyrex brand sintered glass filtering funnels of medium porosity. The flow rates of the diaphragms for water were approximately 10 cc./min. for a one p.s.i. head. Modifications of this type of MoBain- I FIGURE I THE GLASS DIAPHRAGM CELL (ACTUAL SIZE) Northrop oell have been used^*^*^*4 by various investigators. ^ J. N. Northrop and M. L. Anson, J. Gen. Physiol.Id* 543 (1938). ® J. W. MoBain and T. H. Liu, J. Am. Chem. Soo.* 53. 59 (1931). 3 G. S. Hartley and D. P. Runnicles, Proo. Roy. Soc., A168, 401 (1938). 4 H. Mouquin and ¥. H. Cathoart, J. Am. Chem. Soo.* 57* 1791 (1935). ' 23 II. The calculation of the diffusion coefficient If C, and C2 represent the ooncentrations of tracer in the two compartments of the cell at some instant of the diffusion, the concentration gradient will be C,-c2 /X If the quantity d cj of radioactive ion diffuses in the time d t , then represents the flow of tracer from one compartment to the other, being the area to thickness ratio for the glass dia phragm. All of the factors in the above equation can be directly measured, except the cell constant, A/%, The procedure which has been used consists of measuring the rate of transport of some material whose diffusion coefficient is known, thereby standardizing the cell. Since the change in the quantity of radioactive ion in one compartment must equal the change In the other, we may write: On subtracting the lower equation from the upper, and writing &C for C,~CZ , we obtain: - d <1 = (c,- t2) dt (30) dc * (°A )fc,-e2) dt o \/z dc * ( Q A 'j t t z ~ci) d* - 0 (31) d + K O dt - o A c (33) 24 where K . the cell factor is given by ^ 2.3o~3 X ( V’ V* ) (33) This expression can be integrated between the initial and final concentrations, and we obtain: log AC£ = - K Dt. (34) A c f Since the amount of radioactive ions in one compart ment at the beginning of the diffusion must e<jual the total number in both compartments after diffusion has taken place (assuming no decay), we may rewrite (34) as: 0 = £ r log f C| ~ C l (35) K t l c,-cz -> where D is given in cm2/day. 25 III. Determination of the cell constant The cell constant cannot by directly measured for glass diaphragms, and must be obtained by studying the dif fusion of a substance whose diffusion coefficient is known from independent measurements by other means. The substance commonly employed for this purpose is potassium chloride. Gordon5 has discussed the problem of cell calibration, and concluded that for the diffusion of 0.1 N KC1 into water ’ with a concentration change of 25$, the value of 1.58 cm^/day for D seem to be the best value available. This procedure enables one to determine a cell con stant, so that the diffusion coefficients obtained for KOI in more dilute solutions extrapolate to the Nernst limiting value at infinite dilution. However, the diffusion coeffi cients obtained in diaphragm cells under these conditions are more like integral coefficients than differential values, and probably infinite dilution extrapolations are only fair ap proximations at the 'best. We can see that equation {34} is valid only if D is independent of the concentration so as to allow integration of the previous expressions. This obvi ously Is not true, although in some concentration ranges it is not a bad approximation. It may also be true that bound layers of ions at the glass-solution Interface may increase the effective thickness of the interface, and that this 3 A. R, Gordon, Annal. N. Y, Acad. Sol., 46, 285 (1945). t : % 26 effect may change with concentration. Moreover, it is difficult to test these effects due to the scarcity of diffu sion data in other types of cells. For these reasons, it Is not at all apparent that the above scheme will properly calibrate the diffusion cell for subsequent ionic differential diffusion coefficient measurements over a wide range of con centration. However, it was the best one available at the time the diffusion work was begun. It leaves much to be desired though, for a good calibration scheme, and attempts to circumvent this difficulty will be discussed in a later section of this thesis. GHAPTEB XV EXPMIMSNTAL PROCEDURES The solution of a given concentration to be studied is made up either directly, or by dilution of a more concen trated one. No attempt was made to make up the solutions beyond an accuracy of 0.5%. The solutions were degassed by a water aspirator and divided into three portions. One was placed on one side of the diaphragm. To the other, a small amount of radioactive tracer was added, and this solution was placed on the other side of the diaphragm. Care was taken to exclude air bubbles frora the diaphragm by forcing the non-radioactive solution through the diaphragm. Oc casionally* erratic results indicate that either bubbles were left In the diaphragm, or formed during the run, and these results were discarded. The cells were suspended in a thermostat at the desired temperature, which was known to + 0.01°C. After about three hours, the non-radioactive solution was replaced by fresh solution. The purpose of this short preliminary diffusion was to allow a concentration gradient to be established in the diaphragm. After about three days (two days at 359C.), the solutions were removed and stored in test-tubes until they could be counted, or in the case of non-radioactive runs for calibration, until they could be analyzed. In potassium chloride calibration runs, the concentrations of potassium chloride were determined by 28 titration with silver nitrate* using potassium chromate as an indicator. The radioactive analysis was made by counting the solutions in a glass-jacketed glass-walled solution counting tube. The original counting tube from which it was con- ’ structed is the type manufactured by the Eck and Krebbs Com pany* New York. The sensitive counting volume inside the geiger tube was filled with at 10$ alcohol* 90$ argon mixture with a total pressure of 10 cm. This tube operated at about 1000 volts, and had a normal background of about 75 counts per minute. Since the volumes of the solutions from the two com partments whioh were counted were the same, and were counted with the same counting apparatus, the counts per minute oould be substituted in equation (35) after corrections for coinci dence and background were made. In some cases, as when the * short-lived isotope Na24 was used, a further decay correction was also necessary. These corrections are discussed in more detail in the appendix. Two radioactive isotopes of sodium were used in this research; Na22 (3 yr. half-life) and Ha24 (14.8 hr. half-life). The Na22 was obtained from the Carnegie Institute of Terres- tial Magnetism, and was prepared by deuteron bombardment of magnesium. It was obtained essentially carrier free, i.e., of high specific activity. The Na24 was obtained from the Atomic Energy Commission Oak Bidge National Laboratories, and 29 was prepared toy the neutron bombardment of sodium carbonate. There was no report in the Project literature of any other f activities, but a subsequent check on the decay of this mate rial indicated that some radioactive impurities were present. This was verified by recent communications with the Oak Ridge laboratories. The actual decay of the material is shown in Figure 5, appendix. The electronic counter which was employed was the Geiger-Mueller Counter* Type A, which is manufactured by the Cyclotron Specialties Company* of Moranga* California. It has an external Neher-Harper quenching circuit, and is equipped with'a mechanical recorder. It is a scale-of-eight type counter* recording every eight impulses on the meohani- eal recorder, with a meter-type interpolation device. The counting apparatus had sufficient stability so that a standard sample-counted before and after the counting runs gave the same corrected aotivity. Since the solutions from the two compartments of the diffusion eell were always counted within an hour of each other, no correction had to be made for counter-drift. CHAPTER T EXPERIMENTAL RESULTS I. Diffusion coefficients for Ha* at 25°C. Diffusion coefficients for radioactive sodium ions in sodium chloride at 25°C. are given in tables 1 and 2* and are plotted in Figure 2. The lower curve represents data ob tained merely by suspending the diffusion cell vertically in the thermostat. The straight line represents the Qnaager- Fuoss limiting law* with the Hernst limiting value of 1.15 cm2/day at infinite dilution. Most investigators using the MoBain Northrop diffusion cell have found that stirring the solutions In the two com partments has not been necessary. However, previous experi ments were always carried out with macro concentration and hence, density, differences across the diaphragm. Apparently as the salt diffuses through the membrane, the change in density of the solution near the diaphragm produces density stirring throughout the cell which Is sufficient to keep the solutions of uniform concentration throughout each compart ment. In the case of tracer diffusion, however, there are no macro concentration gradients, and one cannot rely upon density stirring to keep the solutions homogeneous, although there are undoubtedly temperature gradients existing even in 1 A. B. Gordon, Annal. N. Y. Acad. Sci. , 4§_, 285 (1945). 31 TABLl? I Differential Diffusion Coefficients of Sodium Ion in Sodium Chloride Solutions 35°C. Unstirred Cell Cone. KD K M £av. I 10"®(ea) 0.0858 0.0759 1.13 1.16 cm2/day II * ♦ 0.0727 0.0611 1.19 1 0.000689 0.0765 0.0750 1.02 1.02 om2/day a 0.00293 0.0770 0.0762 1.01 1.01 om2/day l w 0.0776 0.0753 1.03 3 n 0.0784 0.0776 1.00 I 0.0100 0.0736 0.0759 0.97 0.97 om2/day II » f 0.0593 0.0611 0.97 2 0.0285 0.0777 0.0762 1.02 1.01 om2/day 1 « 0.0770 0.0762 1.01 2 0.0563 0.0774 0.0759 1.02 1.00 cm2/ day 1 « » 0.0735 0.0750 0.98 33 TABLE II Differential Diffusion Coefficients of Sodium Ion in Sodium eWorld© Solutions 35*0. Stirred Cell Cone. ££ £ D Ejav. II 10“6(ca) 0.0934 0.0612 1.51 1,46 cm2/day I n 0.1108 0.0759 1.46 I n 0,1061 0.0759 1.40 I 0.000344 0.0961 0.0763 1.26 1.25 cm2/day II I f 0.0758 0*0611 1.24 II 0.00293 0.0690 0.0611 1.13 1.13 cm2/day I 0.293 0.0821 0.0763 1.08 1.08 cm2/ day III 0.683 0.0794 0.0731 1.09 1.09 cm2/day II 0.0665 0.0611 1.09 II 0.103 0.0643 0.0611 1.05 1.11 cm2/day I i t 0.0877 0.0763 1,15 I i t 0.0839 0*0763 1. lo II n 0.0690 0.0611 1.13 II 1.115 . 0.0647 0.0611 1.06 1.06 cm2/day IV 2,026 0.0828 0.0777 1.07 1.07 cms/day (c m 2/day) INITIAL SLOPES (I) D = 1.46 (I - 6 .6 4 c l/2) Q (I) (STIRRED) ■O- ° D (UNSTIRRED) 1.00 Fa FIGURE 2 (2) (THEORY) DIFFUSION COEFFICIENTS OF SODIUM ION 0.80 IN SODIUM CHLORIDE SOLUTIONS, 25°C . 2.00 1.00 0.50 1/2 34 a well-oontrolled thermostat* and certainly some vibration stirring. Adamson^ had made teats by stirring the solutions in his diaphragm cells and found that the diffusion coefficients calculated with and without stirring at one concentration agreed within experimental error, The need for stirring will depend upon the thermal and vibrational mixing present and this way will be a function of the particular arrangements of apparatus used. This may explain the fact that stirring was found to be necessary in the present work* but apparently not so in Adamson's experiments. The upper curve represents data obtained in the same manner as before, except that in this case the cells were sus- pended horizontally in a saddle arrangement, and were rotated about their central axis. The stirring arrangement was such that the cells were rotated in one direction for about 4-5 revolutions and then reversed and rotated in the other direc- « tion for the same number of turns. The complete cycle required one minute. Various stirring rates were tried; those of a few less and of more revolutions per minute had no effeet on the observed diffusion coefficient. However, when the stirring rate was considerably reduced, to about 3-4 revolutions per minute, the observed diffusion coefficient decreased appreciably. A similar effect has been found by 2 A. ¥. Adamson, Private Communication. 35 Nielsen3, working in this laboratory. Visual observation on an injected solution of a very dilute potassium permanganate solution showed that the stir ring procedure used was adequate to completely stir the solution in ten minutes; to produce a one per cent difference in the diffusion coefficient, the stirring could have taken almost twenty minutes. Because of the observed differences between^ the stirred and non-stlrred runs, it was decided to use the stirring procedure in all of the subsequent diffusion studies. It can be seen that the theoretical value for the limiting diffusion coefficient and the experimental value do not agree. The Nernst limiting value is 1.15 ca^/day; that obtained was 1.46 cm2/day» which is some Z0% higher. It has been pointed out, however, that thl3 seems to be the general case, rather than the exception. Of course, there is the possibility that the calibration procedure has not properly calibrated the cell. This point will be discussed In more detail later. It can also be seen that the limiting slope of the dif fusion coefficient does not agree with that predicted by the Onsager-Fuoss theory. The actual diffusion coefficients change more rapidly in the dilute solutions after which B remains constant over a considerable change In concentration. These facts are rather surprising In light of the general «T. M. Nielsen, Private Communication. 36 shape of electrolyte diffusion curves, which generally go through a minimum. This behavior was also found by Adamson^ using diaphragm cells, but is different from that observed by Jehle^ with free diffusion measurements. It should be mentioned that Adamson found satisfactory agreement with his data and the Qnsager-Fuoss limiting slope. However, it is not certain whether this conclusion is entirely valid due to the fact that mechanical stirring was not used in his experiments. It would seem from the ionic diaphragn studies* that there is some property of the diaphragm cell whioh is distort ing the shape of the diffusion curves, and the data suggest that some other mechanism is available for the transport of ions besides that of Brownian movement through the solution. This effect could not be entirely due to calibration, sin^e this would only change the absolute values of the diffusion coefficients, but not the shape of the curve. 4 A. W. Adamson, J. Chem. Phys. 16, 176 (1947). ® L. P. Jehle, Ph. D. Dissertation, Univ. of Calif, at Berkeley (1937). 37 II. Diffusion coefficients of Na* at 35®C. It was decided to obtain diffusion coefficients at 35°C. in order to be able to compare quantitatively the dia phragm cell data with free diffusion data. This was desir able for two reasons. First, it would be possible to see If the leveling off effect of the diffusion coefficient in more concentrated solutions was present«at 35®C., and in general, if the shapes of the two curves were at all similar. Sec ondly, it would be possible to es.tabllsh an Independent calibration system if the curves differed from each other at all concentrations by a constant factor. This would Indicate that the value chosen for the KOI diffusion which was used for calibration was In error and could be corrected. The data obtained, in stirred diaphragm cells at 35®G. for sodium ion in sodium chloride solutions are given in table 3, and plotted along withJehle’s free diffusion data in Figure 3. It can be seen that, qualitatively, the 35®C. curve resembles the 35®0. closely. What is more important is the fact that the free diffusion curve and the diaphragm dlf- ' filSMh curve do not appear to be simply related at all. The leveling out effect, apparent In the 35®C. data. Is also present in the 35°0. diffusion coefficients. This is not present in the free diffusion data, which go through a mini mum. If the effect of the diaphragm was merely one of physically blocking some of the space between the two com partments, this is certainly not the behavior one would pre- 3 8 TABLE III Differential Diffusion Coeffioients of Sodium Ion in Sodium Chloride Solutions 35°C. Stirred Cell Cono HD K D Dav. III 10~6(Qa) 0.1135 0.0612 1.84 1.78 cm2/day III « 0.1063 0.0613 1.74 IT n 0.1479 0.0777 1.90 IV n 0.1391 0.0777 1.79 IV 0.001 0.1269 0.0777 1.64 1.64 cm2/ day II 0.010 0.0915 0.0612 1.49 1.50 cm2/day IIIA w 0.0688 0.0588 1.51 III 0.100 • 0.1033 0.0731 1.40 1.46 cm2/day IV f t 0.1169 0.0777 1.50 III « 0.1051 0.0731 1. 44 IV n 0.1153 0.0777 1.48 I 1.000 0,1103 0.0759 1.45 1.49 cm2/day II r t 0.0948 0.0612 1.54 INITIAL SLOPES (1) D = l.8 0 (l-0 .7 8 c '* ) (2) D = 1.80 (I -3 .0 0 c l/2) (3) D = 1.47(1- l.4 3 c l/2) JEHLE (2) THIS RESEARCH FIGURE 3 DIFFUSION COEFFICIENTS OF SODIUM ION IN SODIUM CHLORIDE SOLUTIONS, 35°C. 0.75 .00 1/2 40 diet. If we accept Jehle's data, then there is obviously some other function being exercised by the diaphragm merely than one of occupying volume* It is, of course, possible that Jehle’s data are in error. It has already been pointed out that there Is con siderable difficulty in forming and maintaining a convection free boundary in free diffusion apparatus, iehle tested $ this effect by using a very weak dye solution and seeing If the boundary could be maintained in his thermostat. It might be argued that the presence of the minute density difference of the dye solution and of the pure water used in’ his test helped minimise this effect. However, this is exactly the situation that existed In his study of the motion of the 24 radioactive ions. The tracers I©hie employed were Ha and 0138. rpkQ sodium Isotope cannot be prepared in extremely high specific activities, and the inactive sodium chloride present undoubtedly changed the concentration of the tracer compartment of his diffusion apparatus minutely. One might suspect that such concentration gradients, although small, might have a large effect upon the observed diffusion coefficient, since the electrolyte flow might even be in a different direction than the ionic flow. However, a calculation of the effect of a 0.1$ concentration gradient across the boundary shows that the effect upon the observed D is considerably less than one per cent. In actual practice, the concentration gradient was probably much less than this. 41 Because of the short half-life of Cl®® (38.5 min.)» Jehla could not allow the diffusion to take place for too long a period of time, for then he would have been unable to determine the radioactivity of the chloride ions with any accuracy at all. In fact, even with (half-life: 14.8 hrs.), he was limited practically to a day or so. In these short diffusions, especially with the chloride ion, the stirring'effects are also minimized. These reasons, plus the fact that the data plot on a very smooth curve, provide some justification to the acceptance of Jehle’s data. CHAPTER VI DISCUSSION The only previously published data on the diffusion coefficients of individual ions obtained with glass diaphragms is that of Adamson-*-, and Brady arid Salley.® The later study was concerned with the diffusion of radioactive sodium Ions in colloidal electrolytes and will not be considered here. Adamson first utilized the tracer technique of lehle, plus the advantages of the McBain type diaphragm cell. However, sinoe the effects of stirring upon his experimental apparatus were not fully investigated, this work is more of an explora tory nature. Our data certainly indicate that stirring of the solutions in the cells is necessary to insure that the composition at any instant is oonstaat throughout the com partment. The stirring method devised has the advantages of simplicity over previously reported stirring mechanisms which require the Introduction of glass rods or spheres inside the cell compartments.® At both 25°C. and 35®C., the diffusion coefficients obtained do not agree with theory. This corroborates the tentative conclusions of other investigators who determined A. W. Adamson, I. Chem. Phys., 15, 176 (1947). ® A. P. Brady and D. J. Salley, *T. Am. Chem. Soo.* 70, 914 (1948). ® Gr. S. Hartley and D. P. Runnicles, Proe. Roy. Soo., A168, 401 (1938). mean diffusion coefficients in the glass diaphragm cells. The situation may be altered somewhat by the fact that the absolute values of the diffusion coefficient depend upon th® calibration procedure, and th© diffusion coefficients reported in this thesis may have to be later multiplied by a constant representing taking a new value for the diffusion coefficient of the electrolyte used for calibration. Since the diffusion coefficient of sodium ion at 55®C. at infinite dilution obtained in the diaphragm cell agrees well with that obtained by Iahle, the calibration procedure is probably adequate as a first approximation. This assumes, of course, the validity of Jehlefs data. It would be possible to obtain the Nernst limiting value by choosing another calibration value, although at the present time there is no justification for doing so. However, even multiplying the diffusion coefficients by a constant factor would not change their relative positions, and the limiting slope x^ould still be incorreot. There is another explanation that would account for the non-agreement with theory of the data. By comparing the dif fusion coefficients with Jehle’s free diffusion data, it was seen that the shapes of the curves indicated that the glass diaphragm had some effect besides that of merely occupying space. This was also evident from the B5°C. studies. We have made the assumption throughout that the ions diffuse from on© compartment to th© other through the interstitial AA * Z r S S solution. Another transport mechanism would be surface dif fusion along the capillary walls. It is a well known fact that there is appreciable adsorption of electrolytes upon glass surfaces. In most situations* the ratio of the surface area to the volume of solution is small, and such effects are of minor importance, s In the case of the glass porous diaphragms* this is not the case. The glass diaphragms are constructed by sintering powdered glass together to form a porous mass, which consists of a disordered network of small capillaries and interstices. With a large surface to volume ratio, It is not unlikely that adsorbed layers of ions could provide another path for the diffusion of ionic material through the membrane. If this is true, one would not a priori expect the surface rate of transport to be the same as the solution rate. Since the adsorption of material on the glass surfaces is a function of concentration, this effect might well lead to a distortion of the shape of the.observed slope, and give rise to apparent diffusion coefficients not in agreement with theory. The possibility of surface transport has received little attention in previous studies on diffusion in diaphragm cells* the only investigation being made by McBain and Liu.® They showed that there Is no apparent drift in the diffusion coefficient ratio from two solutes passing from a more porous $ I. W. McBain and T. H. Liu. J. Am. Chem. Boo.* 53, 59 (1931). 45 to a less porous diaphragm, or from a glass diaphragm to an alundum one. If surface transport were prominent, they reasoned that one would expect the ratio to be dependent on the nature and magnitude of the surface in the pores* This single test has been universally accepted, but it should be pointed out that MoBain and Liu studied this effect in electrolytic solutions which were greater than 0.05 N* From the general shape of adsorption isotherms* one would conclude that the greatest change in adsorption* and hence the effect upon the diffusion rates, takes place, in more dilute solu tions. It is quite possible* then, that In the concentration range studied by MeBain and Liu that the adsorption sites were already completely filled* and the effect of surface transport in the more concentrated solutions entirely masked. For this reason, it does not seem that the tests are adequate, and certainly do not rule out the possibility of surface transport in diaphra^n cells. On the other hand, there is some evidence that such effeots are real. Mysels4 has compared the conductivity of two solutions of differing concentrations in a normal cell and in one whioh contained a glass diaphragm, and found a dis crepancy in the ratios of their conductivity of the order of 10%. If the diaphragm did not help in the transport of ions in solution, then one would expect the ratios to be the same, 4 K. J. Myseis and J. W. MoBain* J. Coll. Sci., 3, 45 (1948). independent of the concentration. Due to these previously unoonsidered effects of surface transport* it should be pointed out that all of the previous diffusion data collected in dilute solutions by other workers is subject to considerable doubt as a result of this investi gation. It is rather surprising that very little attention has been given to the possibility of surface transport, con sidering its probable importance in the diaphragm cell. One milhbd ^whioh could be used to eliminate this ef fect of surface transport is to use metallic porous membranes to separate the two compartments. It is very probable that sorption of ions upon metallic surfaces would be very slight, and this would largely eliminate the undesired transport. It should be possible to determine the quantitative effect of the diaphragm. studying the conductivity of solu- V ? tions in the dilute region across the diaphragm. This would enable one to obtain the cell constant as a function of con centration, which could then be used to evaluate subsequent diffusion data at that concentration. The assumption would have to be made that the mechanism of conductivity through the diaphragm Is the same as diffusion, and that the relative effects of the surfaces are the same. Conclusion The theoretical basis for diffusion has been discussed in terms of existing theories; it has been shown how &rom the present theory it is possible to compute individual ion activity coefficients. A procedure has been developed for obtaining differ ential diffusion coefficients in the McBain-Northrop type of glass diaphragm diffusion cells. By following the diffusion of a radioactive speoies, the necessity of having salt con centration gradients was eliminated, making it possible to directly determine differential coefficients. The method is extremely well suited to studies at very low concentrations. The diffusion coefficients of sodium ion at 25°C. and 35®C. have been determined over a wide concentration range. The observed diffusion coefficients do not agree with the Kernst limiting value, or the Onsager-Fuoss limiting law. It has been shown that this is roost likely due to adsorption of electrolyte by the glass membrane rather than to a calibration error. By comparison of the 35®C. data with that obtained by Jehle in a free diffusion cell, the effect of the diaphragm is' evident in distorting the shape of the diffusion curve. This effect is also evident at 25°C. It is suggested that the effect of the diaphragm is one of surface conduction of material along the adsorbed ions on the glass surfaces. This is supported by published conductivity work. 48 Two methods have been outlined which should allow the diffusion coefficients to be determined without the complica tions of the surface effects. BIBLIOGRAPHY 49 BOOKS H. S. Earned and B. B. Owen* The Physical Chemistry of Bleo- trolytio Solutions (Reinhold Publishing Company), 1943. PERIODICALS A. W. Adamson, J. Chem. Phya., 1£, 176 (1947). A. P. Brady and D. J. Salley, I. Am. Chem. Soo., 70, 914 (1948). B, W. Glaek, Proe. Roy. Soo., 81, 374 (1908). I. Cohen and H. R. Bruins, Zeit. phys. Chem., 103, 337 (1923). A. Pick, Pogg. Ann., 94* 59 (1855). A. R. Gordon, Annal. N. Y. Aoad. Soi., 46, 285 (1945). T. Graham, Phi11 Trans., 140, 438 (1851)] 144, 177 (1854); 151. 183 (1861). H. S. Harned, Chem. Rev., 40, 463 (1947). H. S. Harned and D. M. French, Annal. N. Y. Acad. Soi., 46, 267 (1945). v H. S, Earned and R. L. Huttall, I. Am. Chem. Soo., 71, 1460 (1949) G. S. Hartley and D. F. Runnioles, Proo. Roy. Soo., A168, 401 (1938). W. A. James, E. A. Ho1lingshead, and A. R. Gordon, J. Chem. Phys.. 7, 89 (1939). L. G* Longsworth and D. A. Maolnnea, J. Am. Chem. Soo., 62, 705 (1940). J. W. MoBain and T. H. Liu, J. Am. Chem. Soo., 5^, 59 (1931). H. Mouq.uin and ¥. H. Cathcart, J. Am. Chem. Soo. , 57, 1791 (1935). 50 K. J. Mysels and J. W. McBain, J. Coll. Sci.» 3. 45 (1948). W. Nemst, Zeit. phys. Chem., 2, 613 (1888). J. W. Northrop and M. L. Anson* *T. Gen* Physiol.* 12* 543 (19|f8). ~ ” L. W. Oholm, &©it. phys. Chem., 50* 309 (1905). L. Onsager, Fhysik. £eit., 28, 277 (1927). L. Onsager and R. M. Fuoss* J. Phys. Chem., 36* 2689 (1938). D. Wiener, Ann. Physlk., 49* 105 (1893). UNPUBLISHED MATERIALS A. W. Adamson, Private Communication. L. P. Jehle, Ph. D. Dissertation, Univ. of California at Berkeley, 1938. T. P. Kohman, A General Method for Determining Coincidence Corrections, U. S. Atomic Energy Commission Document, MdDC-905. J. M. Nielsen, Private Communication. AFPMDIX 51 In determining th© activity of a radioactive sample » various corrections must be made to the observed counting rate to obtain the true counting rate. The corrected count can be expressed as: N t = (N0 a- b) cd (1) where is the true count* N0 is the observed count, a is the coincidence correction, b is the background correc tion, C is the decay correction, and d is the geometry and scattering correction. The factor d is only important when the counting of samples Is made under different conditions. In the present research, the activities of the two compart ments were determined with the same geiger tube under the same conditions, and the factor d does not need to be considered. The coincidence factor, <X » oorreots for the fact that if two particles enter the geiger tube too close together, the tube will only register the presence of one particle. This effect becomes tpiite important at high counting rates, but Is appreciable even at lower rates. To determine this last correction, one assumes that the actual counting rate can b© expressed as a power series of the recorded value: R' s R * t R* * v R* * ......... <3) For low counting rates, we need only to consider the first 53 two terms of this equation. In this resulting equation, t is called the "dead time" of the counting apparatus, and cor responds to the minimum response time of the counting equipment: R' = R + t Re . (3) By counting two different sources separately, and then together, under similar geometry conditions (to eliminate the geometry correction effect), one can determine the correction factor, C L . To do this we make the assumption that the true count of both samples together la equal to the sum of the individual counts of the separate samples. It can be shown-*- that the factor t is given by the expression t - Ra + Ra - Rc ~ k R ‘ - R ? - R ! = 'E (4) where R A and Rg refer to the observed counting rate of two individual samples, Rc the rate when both samples are counted together, and b is the background correction. A sample cal culation is given below for three ranges of counting rates: T. P. Kohman, A general Method for Determining Coincidence Corrections, U. S. Atomic Unergy Commission Document, MDDC-905. 53 TABLE m A Sample Coin©idenoe Correction R a 1853 2766 3797 ft 8 1605 2317 5637 Rc 3385 4976 9173 b 45 47 48 D 30 60 813 f V VO 1 o X 3.43 7.651 1.442 V Vo 1 o X 2.576 5.369 3.178 Rc* n,6 X io 11.46 24. 76 8#«14 C X io~6 ■ Iw 5.45 11.74 37.95 t - - DIE 5.51 5.11 5.61 ^average1 5.4 x 10~6 min. Therefore: R 1 = R 5. 4 k <0* R This can be expressed further as a certain percentage correction per thousand counts, and in the case given is 0*54$ per thousand counts. It Is also common practice to plot the number of counts correction against the total ob served count, and this is done in Figure 4. The background correction, b , is determined before and after counting by determining the reading that the counting apparatus records when the solution counted is filled with water alone. CORRECTION (c o u n t s/min. ) 60 50 RECORDED FIGURE 4 SAMPLE COINCIDENCE CURVE 2000 3000 RATE (COUNTS/MIN.) 55 For isotopes of long half-lifes the decay correction, C » is not important* However, in this research it was necessary to use some Ha24 which has a half-life of 14.8 hours, and appreciably decays in an hour or so, the length of time usually consumed in taking a count. The Na24 was ob tained from the Qak Ridge neutron pile, and was prepared by neutron bombardment - of sodium carbonate. If impurities were present in the sodium carbonate, then the resulting bombarded product might contain more than one activity, and the correc tion factor could not be determined by merely .assuming a 14,8 hour half-life. What was actually done was to follow the decay of a sample of the original sodium earbonate in an automatic recording apparatus, and make corrections from a plot of the observed decay. Such a plot is shown in Figure 5, which clearly indicates the presence of radioactive impuni ties. Such a plot not only enables one to make the true decay correction, but also showed that after a certain time, appreciable impurities were present to invalidate certain runs. 14.8 HR. TOTAL ACTIVITY 26 HR. FIGURE NEUTRON BOMBARDED SODIUM CARBONATE DECAY CURVE 500 600 0 400 300 100 200 HOURS

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Creator Cobble, James Wikle (author)

Core Title The determination of differential diffusion coefficients of radioactive ions

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