1414
R. ARNOLD
Temperature Dependence of Electroosmotic Water Transport through Cation-Exchange Membranes. The Effect of Proton Jumping by R. Arnold Dieision of d4incrol Chemistry, CSIRO, Port Melbourne, Victoria 6 2 0 7 . Australia
(Received October 7, 1 9 6 8 )
The effect of temperature on electroosmotic water transference through cation-exchange membranes in the hydrogen ion form has been measured in 1 and 5 N sulfuric acid. Some measurements are also reported for the potassium form of these membranes in 1 N potassium hydroxide. In the hydrogen ion form the water transference numbers rise with temperature, whereas there is a slight decrease with temperature in the amount of water transferred per potassium ion. The rise in water transference number with temperature for the hydrogen ion is attribbted to a decrease in the fraction of current carried by proton jumping. A t room temperature about 75% of the current is carried by proton jumping, and the results are also consistent with the activation energy for the proton jumping mechanism being 1 to 1.5 kcal/mol less than that for ordinary migration. In 5 N acid solutions some additional effectsuch as a decrease in acid dissociation may aIso be operative.
Introduction Although electroosmosis through ion-exchange membranes has been studied fairly extensively,’ most of the work has concerned the transport of water caused by the more common metallic cations. Very little is known about the electroosmotic effects which result when hydrogen or hydroxyl ions are the conducting species. A convenient measure of electroosmosis is the transference number lw, expressed in moles of water per faraday. This quantity falls with increasing electrolyte concentration, and in the case of membranes of low water content it has been that a lower limit is reached. In general this lower limiting value should correspond to the primary hydration- number of the counterion concerned. In the case of the hydrogen ion, however, the lower limiting value of fw a t 25” is only about 1.0 mol/F, and this low value has been attributed2 to the fact that most of the current is carried by the proton jumping mechanism6 without any net transference of water molecules. In the present work, measurements are reported of the effect of temperature on electroosmosis in cationexchange membranes in acid solution. The main aim was to gain some further insight into the processes involved, but the measurements were also of interest in connection with the use of these membranes in a fuel cell. The effect of temperature on electroosmosis is uncertain, even when hydrogen ions are not involved. An equation due to Oda and Yawatayaa in modified form2 expresses the electroosmotic transference number as
where h+ and h- are the hydration numbers of cation The Journal of Physical Chemistry
and anion, E+ and L are the ionic transport numbers in the membrane, f is the number of moles of free water per ion-exchange site, s is the amount of sorbed electroIyte in equivalents per ion-exchange site, h is the sum of the hydration numbers of the invading anions and cations, and ti+ and tis are the mobilities of the counterion and the free water, respectively, in the membrane. It seems unlikely that the hydration numbers h+, h-, and h would be affected by small changes in temperature, since primary hydration water is usually held very strongly by ions. Variations in I+ and s with temperature are expected to be small and in any case are easily measured and will be accounted for in the present work. Hence the main question is the effect of temperature on the “slip factor” ti,/ti+ and on the amount of free water, f . Since increasing temperature generally causes a decrease of interactions and in particular a breaking up of the structure of water, the‘ factor %/ti+ should decrease with temperature, causing a fall in lw. On the other hand, there might, for similar reasons, be an increase in the amount of free water, if raising the temperature causes a loosening of water molecules attached to the molecules which form the membrane. The same considerations emerge if the electrokinetic coefficient corresponding to tw is expressed in terms of friction coefficients.6 As might be expected, (1) For review see N. Lakshminarayanaiah, Chem. Rev., 6 5 , 491 (1965). (2) R. Arnold and D. A. Swift, Aust. J. Chem., 2 0 , 2575 (1967). (3) Y. Oda and T. Yawataya, Bull. Chem. SOC.J a p . , 3 0 , 213 (1957). (4) A. S. Tombaiakian, H. J. Barton, and W. F. Graydon, J. Phys. Chem., 6 6 , 1006 (1962). (5) For a detailed discussion of proton transfer processes see, e.g. (a) B. E. Conway in “Modern Aspects of Electrochemistry,” No. 3, J. O’M. Bockris and B. E. Conway, Ed., Butterworth and 00.Ltd., London, 1964. Chapter 2; (b) M. Eigen and L. de Maeyer in “The Structure of Electrolytic Solutions,” W. J. Hamer. Ed., John Wiley and Sons Inc., New York, N. Y., 1959, Chapter 5. (6) See, e.g., A. Katchalsky and P. F. Curran, “Non-equilibrium Thermodynamics In Biophysics,” Harvard University Press, Cambridge, Mass., 1965, p 172.
1415
THEEFFECT OF PROTON JUMPING the relevant expression involves the ratio f i w l f w m , where jiw andf,, are the coefficients of friction between the counterion and water and between water and the membrane. An increase in temperature should decrease both friction terms, and this might lead to a fall in the electroosmotic transference number in membranes of high water content where the ion-water interaction would be more important. In general, however, it is not obvious what the effect of temperature on Zw would be. Experimentally, very little work has been done on the effect of temperature on electroosmosis. George and Courant7 carried out measurements at 10, 25, and 40” on an “Ionics” cation-exchange membrane in a number of different ionic forms (but not the hydrogen ion form). A small decrease in water transference number with temperature was found. The membranes were in the “leached” form, however, and the results varied with the current density employed; one cannot be sure, therefore, that the temperature effects were not due to changes in polarization. Leitea reported that the “electro-osmotic water transport ratios” were “essentially unchanged” by temperature increase to 65 and 82” for “Ionics” cation-exchange membranes (presumably in the sodium form). On the other hand, a rather remarkable increase is reported by Bejerano, Forgacs, and Rabinowitzg for the total water transference by sodium and chloride ions in electrodialysis cells over the range 30-90”. The exact conditions and methods for separating the electroosmosis from diffusive transport were not stated. The effect of temperature on electroosmosis is clearly uncertain even for ordinary ions and therefore, although the main interest has been in the behavior of membranes in sulfuric acid solutions, some measurements were included with membranes in the potassium form in potassium hydroxide solutions. For membranes in the hydrogen ion form the only reference to the effect of temperature appears to be a single measurement of Boyacklo for a cation-exchange membrane. This showed a very marked rise in transference number on raising the temperature from 25 to 40”.
Experimental Section The three membranes used were all based essentially on cross-linked polystyrenesulfonic acid. In two of them, referred to as AZG and DYG (Ionics Inc., Watertown, Mass.), the cation exchanger material is supported on a mesh of glass fiber. As far as is known these two membranes differ only in the degree of crosslinking of the ion-exchange material; the capacities and saturation water contents found were (referred to the H form) : AZG 1.6 mg-equiv per dry g, 0.47 g of water per dry g; DYG 1.99 mg-equiv per dry g, 0.38 g of water per dry g. The third membrane, referred to as ACI (Asahi Chemical Industries, Japan) is of the holriogeneous type and contains no supporting mesh
(capacity 2.83 mg-equiv per dry g; water uptake 0.95 g per dry g). The water transference numbers were determined by the gravimetric method. The construction of the cell and details of the procedure are described in the previous publication.2 I n brief, the method consists in adding a known amount (about l o g ) of sulfuric acid solution to a receiver compartment on one side of the membrane, the other side being in contact with a flowing solution of similar composition. Using platinum electrodes a constant current was passed for a measured time such that about 0.5-1.0 g of water was transferred across the membrane. To compensate for backdiffusion the concentration of the acid initially added to the receiver was adjusted so that the average of the initial and final concentrations would be approximately equal to that of the flowing solution on the other side.l’ A t the end of the experiments the weights of acid and of water in the receiver were determined. The exposed area of the membrane was 4cm2 and the current densities ranged from 12 to 100 mA/cm2. No dependence of the results on current density was detected. Acid concentrations of 1 and 5 N were used. Using sulfuric acid, for every l+equivalents of hydrogen ion which pass through the membrane into the cathode compartment, one equivalent is removed a t the cathode. The change in the amount of acid in the compartment enables Z+ to be calculated; these changes are very small since t+ is close to unity for hydrogen ions in these membranes. To determine the electroosmotic transference due to potassium ions 1 N potassium hydroxide was used; the electrodes were again of platinum. In this case, the reaction at the cathode is
2H20
+ 2e
---f
20H-
+ HI
Hence the passage of one faraday causes the amount of potassium hydroxide in the cathode compartment to increase by 2; equivalents whereas the water content increases by only (lw - 1). In these experiments therefore the amount of electricity passed was restricted in order to avoid large changes in concentration across the membrane since it was thought that these might introduce diffusion effects too large to be overcome by the compensation method. The amounts of water transferred were therefore about 0.3 g and the values of the transference number are less accurate than those found using the acid solutions. (7) J. H. B. George and R. A. Courant, J . Phys. Chem., 71, 246 (1967). (8) F. B. Leitz, Abstract 228, Boston Meeting, Electrochemical Society; J. Electrochem. Soc., 115, 8 6 0 (1968). (9) T. Bejerano. Ch. Forgacs, and J. Rabinowitz, Desalination, 3 , 129 (1967). (10) General Electric, Final Technical Report on Contract No. DA-36-039-AMC-O0095(E) ; Sept 1963; (ARPA Order No. 8 0 ) . (11) A. G. Winper, R . Ferguson, and R. Kunin, J. Phys. Chem., 6 0 , 656 (1956). Volume YS,Number 6 M a y I969
1416
R. ARNOLD
The receiver compartment was normally stirred but the results did not appear to be affected by the rate of stirring or even by omitting stirring altogether. Accordingly, in some of the experiments above room temperature stirring was omitted, the stirrer inlet stoppered, and a water condenser fitted to the gas outlet of the receiver compartment. The water thus trapped was weighed and used as a correction. In this way the evaporation error was reduced to a minor level at 40'. At still higher temperatures evaporation was appreciable, most of the loss occurring when filling and sampling the cell. This error was reduced (a) by determining the water lost using zero current and using this as a correction, and (b) in the experiments with DYG a t 55", by alternately making the receiver the cathode compartment and the anode compartment. Since the evaporation error has opposite sign in the two cases, the mean should be reliable. The effect of temperature on acid and water absorption was also measured. The usual methods for determining these quantities12 were used.
Results A . Membrane in the H+ Form in HtS04 Solution. The electroosmotic transference numbers obtained in acid solutions are shown as a function of temperature in Figures 1 and 2. The points are in nearly all cases the mean of several determinations, the line height
~~~
0
~~~
20
IO
IO
20
30
40
40
50
60
Temp, 'C.
Figure 2. Electroosmotic transference numbers for membranes in 5 N HzSO~.
indicating the average deviation from the mean. Two different samples of DYG membrane were used in 1 N acid. It will be seen that there is in each case a definite rise in the transference number with temperature. I n the case of DYG membrane in 5 N acid, & falls well below 1.0 mol/F, the extrapolated value a t 0" being 0.92 mol/F. Hence the apparently integral value of 1.0 which was obtained as lower limit in the work2 at 25' has no particular significance. Average values of the hydrogen ion transport number are shown for a number of interpolated temperatures in Table I. It will be seen that there is a definite decrease in cationic transport number with temperature. (This is no doubt due to the increased acid absorption reported below.) Before interpreting the electroosmotic results, therefore, it will be necessary to consider the likely effects due to anionic migration. The quantity of real interest is the number of moles of water transported per hydrogen ion. If this quantity is denoted by T,, the observed transport number can be written
fw
-
30
=
f+T, - L h -
(2)
where h- is the primary hydration number (per equivalent) of the anion. For the sulfate ion, those hydration numbers in the literature13 which appear to apply to primary hydration, range from 1 to 2.4mol/ equiv. There does not appear to be any information on the hydration number of the bisulfate ion. Using a value of 2 for h- and the experimental values of f+, T , has been calculated using eq 2 for the measurements in 5 N acid; the results are in Table 11. It will be seen that these corrections, although significant, do not affect the general pattern of the results. In 1 N acid
Temp, 'C.
Figure 1. Electroosmotic transference numbers for membranes in 1N HzSOa. The Journal of Physical Chemistry
(12) R . Arnold and D. F. A. Koch, Amt. J. Chem.. 19, 1299 (1966). (13) "Gmelins Handbuch der Anorganische Chemie," Vol. 9. Part B, Verlag Chemie, Weinheim, 1960. p 756.
1417
THEEFFECT OF PROTON JUMPING ~~
Table I: Effect of Temperature on Hydrogen-Ion Transport Numbers (Smoothed Results) Mem-
Acid
brane
normality
AZG DYG ACI ACI DYG
1 1 1 5 5
-Transport
~
Table 111: Effect of Temperature on Acid and Water Absorption
Ionios AZG
numbers f--+
5”
25’
40’
0.9915 0.999 0.998 0.990 0.995
0.992 0.9995 0.998 0.987 0.995
0.992 0.9997 0.998 0.982 0.992
550
N acd i--
-1
-
N acid-
-Temp,-6.1
O C
Wa
0.978 0.986
P
5 25 47 18.8 19.3 19.3 0.158 0.166 0.166
4 18.2 1.05
25 17.8 1.08
40 17.5 1.09
Ionics DYG N acid-----
-1
E,
may be taken as numerically equal to T, within the experimental error. Table I11 shows the effect of temperature on the absorption of water and acid by the membranes. With rising temperature a small shrinkage or loss of water occilrs but at the same time a small but definite increase in acid absorption occurs. This may be due to the decrease with temperature in both the first14and second16 dissociation constants of sulfuric acid. Un-ionized sulfuric acid molecules are not subject to Donnan exclusion, and since the Donnan effect is less marked for a monovalent eo-ion than for a divalent eo-ion, absorption should also be increased by conversion of sulfate to bisulfate ions. In the case of the ACI membrane the amount of acid absorbed goes through a maximum and decreases at higher temperatures; this membrane shrinks more extensively with temperature and concentration and in fact the internal acid concentration does not show the maximum but’ continues to increase with temperature. B. Membrane in the Potassium Form in Potassium Hydroxide Solution. The results obtained using the membranes in the potassium form are reported in Table IV. As explained in the Experimental Section, the errors in these transference number measurements are greater than those affecting the determinations using the hydrogen ion form. Each result is the mean of three or four determinations and the range shown is the mean deviation. While the results for the transference numbers show little variation with temperature, there is a definite rise in the cationic transport number. As a result of this the values of T,, the number of moles of water carried per equivalent of potassium ion, show a small but significant fall with temperature. The ~
membrane-
-DYG
5 25 43 10.6 10.36 10.7 0.031 0.035 0.035
.
6 9.94 0.315
1N
Temp,
tw,
Tw
mol/F
Temp,
O C
mol/equiv
OC
mol/F
mol/equiv
1.5 3.4 24 40 55
0.98 1.00 1.02 1.10 1.2
1.01 1.03 1.06 1.16 1.27
2.6 15 25 39 54
0.92 0.96 1.01 1.10 1.22
0.94 0.97 1.04 1.12 1.27
T W
-
acid-
25 40 9.54 9.65 0.325 0.333
ACI 1N
W S a
acid
6N
r-
Temp, OC
25 18 0.09
4 15.1 0.64
22 14.9 0.67
-
acid 40 14.1 0.63
?
50
0.575
W = water content in moles per equivalent of membrane.
8 = acid content in equivalents per equivalent of membrane.
detailed method of calculating T, will be discussed more fully below.
Discussion The number of moles of water transferred per equivalent of cation is given by eq 2 as Tw = (Ew
+ kh-)/t+
and this combined with eq 1 gives
(3) For the particular case of the hydrogen ion, however, most of the current is carried by proton jumping, a process which involves no water transport, and only the fraction carried by ordinary migration is responsible for the water transport. Calling this fraction p, and for simplicity writing the last term of eq 3 asf’, we have
B
membrane-----. lw
s
6
Tw = (h++f’)P It is assumed that the fraction p is given by
~~~
Table 11: Electroosmotic Transference Numbers in 5 N H2SOd Corrected for Anionic Transport -AD1
W
7
Temp, O C
= Xm/(L
+
Xj)
(4) (5)
where A,, and X j are the mobilities displayed by the hydrogen ion in migration and in proton jumping, respectively. The effect of temperature on this (14) N. R . Rao, Current Sci., 11, 429 (1942). (16) H. S. Harned and B. B. Owen, “The
Physical Chemistry of Electrolyte Solutions,” 3rd ed, Reinhold Publishing Corp.. New York, N. Y . , 1958, p 755. Volume 73,Number 6 May 1969
1418
R. ARNOLD
Table IV: Electroosmotic Transference Numbers and Cationic Transport Numbers for Membranes in 1 N KOH Solution
Table V: Migrational Water Transference Values ( h f') and Activation Energy Differences AE Calculated from the Experimental Results
+
Temp, Membrane
'0
tc
t,, mol/F
T,, mol/equiv
Acid normality
(h +f'),
Membrane
mol
AE, kcal/mol
AZG AZG DYG DYG
1.4 24.6 2.4 24.9
0.63 0.65 0.92 0.94
5.16h0.14 5.19 ==! 0.19 3.98h0.11 3.88 & 0.08
8.55h0.22 8.31 f0.29 4.38 A0.12 4.17 f0.09
DYG ACI DYG ACI AZG
5 5 1 1 1
4.0 4.2 4.2 5.8 9.0
1 .O (3-24"),1.9 (24-54') 0.3 (1.5-24'), 1.6 (24-55") 0.8 1.4 0.9
quantity P must be determined by the difference AE between the activation energies of the two processes of migration and proton jumping; Le.
In (Xj/Xm)
= In ( 1
-P)/P
=
constant
+ (aE/RT)
of the activation energy difference AE are in keeping with estimates from conductivity data. For this purpose eq 5 for @ may be combined with the equation AH = P X m
(6)
It is now assumed, as before,2 that the limiting low values of T , correspond to zero values off' (as indicated by eq 3 for high s and low f ) ; i.e., only primary hydration water is carried. It is further assumed that the primary hydration number is 4, corresponding to the ion Hs04+, and that this is independent of temperature. Equation 4 then becomes simply, T , = 4P, and this is applied to the case where the lowest values of T , were observed, i.e., DYG in 5 N acid. This gives p = 0.259 at 25", and furthermore enables a set of values of P at different temperatures to be obtained from the experimental results for this membrane and solution. To apply this sort of treatment to the other cases where higher water transference numbers were obtained requires some further assumptions which are less reliable but nevertheless worth testing. It is assumed that the value of p found for DYG in 5 N acid at 20" by the above method ( i . e , , taking T , = 4 8 ) applies at 20' to all cases. Using this value of P an estimate of the water term (h, f') can be estimated by eq 4 for each membrane-solution combination. (This quantity is in effect an estimate of the value T , would have if there were no proton jumping.) This value of (h+ +f')is then assumed not to vary with temperature, and is used to calculate values of P from the experimental values of T , at different temperatures. In each case graphs of log ( 1 - P ) / B against 1/T were drawn in order to calculate values of AE by means of eq 6. The resultant graphs were reasonably straight lines for the measurements in 1N acid, corresponding to single values of AE in the range 0.8-1.4 kcal/mol. For the measurements in 5 N acid the graphs were not linear but corresponded to a rather marked increase of AE with temperature; hence only approximate values for the high- and low-temperature ranges could be estimated. The results are reported in Table V, together with the estimates used for ( h +f'),the number of moles of water per migrating ion. It is next necessary to see whether the values of and
+
The Journal of Physical Chemistw
+ (1 - P ) X j
(7)
where AH is the observed conductivity of the hydrogen ion. Since the value of A, is not known, the equations can only be solved for @ if we assume that the migrating hydrogen ion moves with about the same mobility as a potassium or sodium ion. Thus replacing Xmby XK or ha,eq 5 and 7 have been solved using data in the literature16for infinite dilution. From the values of /3 found at different temperatures the difference in activation energy may be obtained using eq 6. The results of these calculations are given in Table VI. Data for both potassium and sodium have been used. According to Conway,17 the potassium ion is the better model of the migrating hydrogen ion. There is a very slight curvature in the activation energy graph for the sodium ion data and an inflection in that derived from the potassium data. In each case, therefore, separate activation energies are given for the higher and lower temperature range. It will be seen that the activation energies found agree not
Table VI: Estimates from Conductivity Datal6 of the Fraction of Hydrogen Ion Migration and of the Activation Energy Difference, AE Temp,
O C
0 5 15 18 25 35 45 55 100
,5 from K + data
0.138 0.142 0.149 0.151 0.154 0.161 0.168 0.175 0.206
AE, kcal/mol
0'91
0.99
,5 from N a + data
0.095 0.099 0.107 0.109 0.114 0.122 0.128 0.137 0.163
kcal/mol AG
1.23
1.39
(16) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworth and 00.Ltd., London, 1959. p 465. (17) Reference Sa, p 85.
1419
THE EFFECT OF PROTON JUMPING unreasonably with those in Table V found from the electroosmotic experiments in the low-temperature range.18 There is also a rise in AE with temperature, but this is much smaller than that found from the electroosmotic results in 5 N solution. On the other hand, the values of fl estimated from the conductivity data are much lower than the values estimated (0.259 at 25') for the membranes. The results in Table V are based on measurements in membranes in which the internal electrolyte concentration is 3-7 equiv/1000g of water, whereas those in Table VI are derived from results referred to infinite dilution. The approximate agreement of the activation energy difference suggests that the same processes are rate determining in each case. Calculations by Horne and Courant1s give the activation energy for conduction in HC1 solutions at 10' as 2.98 kcal/mol in 1.0 N HC1 and 3.12 kcal/mol at infinite dilution. A very similar concentration dependence is shown for the conduction of NaCl in calculations by Horne and Birkett,lg the activation energy falling about 0.1 kcal between 0 and 1N. These results support the idea that the value of 6E does not change markedly with concentration. The fact that the values of p derived from conductivity data do not agree with those estimated from the measurements on membranes must then be attributed to changes in the entropy of activation for conduction on passing from dilute solutions to the conditions prevailing in the membrane. Such changes would result from the breakdown of the water structure which must occur in the concentrated interior of the membrane. The marked upward curvature in the electroosmotic results found in 5 N acid solutions (Figure 2) does not find any explanation in this examination of the conductivity data. It is probable that under these conditions it is not correct to assume that the free water term f' is independent of temperature. As pointed out earlier, the dissociation of sulfuric acid decreases with temperature, particularly at higher concentration^.'^ In view of the similarity in structure, and since the dissociation of moderately strong acids usually decreases with temperature,16 it seems probable that the sulfonic acid groups on the membrane itself would behave similarly. Thus a rise in temperature in the concentrated system would result in a lowering of the concentration of ions. and a consequent liberation of water molecules. The amount of free water (f in eq 1) would then increase. The assumption that the amount of water carried per migrating ion is independent of temperature may be examined using the electroosmotic data obtained in KOH solution. It is first necessary to correct for the effect of the anionic migration and calculate T,, the number of moles of water transferred per potassium ion. Since the anion in this case is the hydroxyl ion which also travels to a large extent,by proton jumping, eq
2 has to be modified to
,Tw
=
,T+T, - fl'f-h-
(8)
where p' is the fraction of the hydroxyl ion transport which takes place by migration. Values of p' may be estimated by means of equations analogous to ( 5 ) and (7) using conductivity data for OH- and F- ions. When such calculations were carried out an unexpected result was obtained; p' is independent of temperature over the range 0-25". The same result is obtained if chloride is used instead of fluoride as model for the migrating hydroxyl ion; in other words, the activation energies for conduction by OH-, F-, and C1- are all the same in spite of the very different mechanism involved in the case of the OH- ion. According to Conway,20the rate-determining step in the proton-jumping mechanism for conduction is rotation of a water molecule. In acid solutions this rotation is assisted by the repulsion between two spatially opposed -OH groups. In alkaline solutions where there is a proton defect one of these hydrogen atoms is absent and the repulsive force is much reduced. Rotation in alkaline solutions is then more dependent on thermal forces and this may explain the equality of the activation energies for the two types of conduction. The values found for p' were 0.19 from the fluoride data and 0.243 from the chloride data. For the calculations fl' was taken as 0.2 and h- as 3. The latter value assumes that the ion H,04- would be the main species involved,21corresponding to Hs04+which was taken as the migrating form of the hydrogen ion. The arguments are not, however, affected by the exact values of 0' and h- since the main effect in calculating T , from fv by eq 8 results from dividing by the experimental value of ,T+. The calculated values of T, are in the last column of Table IV. In each case there is a fall of about 0.2 mol of water per equivalent on raising the temperature from 2 to 25'; this is about equal to the experimental error in the results for AZG but is greater than the error for DYG. (This is unexpected since with DYG the water transported is mainly confined to the primary hydration water; if anything, a more definite effect would have been expected in the case of AZG). It is likely, therefore, that the assumption of ( h f') values independent of temperature (eq 4) was not
+
(18) R. A. Home and R. A. Courant (J.P h y s . Chem., 69, 2224, (1965)) assumed the fraction of conduction by proton jumping to be inversely proportional to the activation energy, and hence obtained from the conductance data an estimate of 3.00 kcal/mol for the activation energy of conduction by proton mobility in HC1. For KC1 they found an activation energy of 4.20 kcal/mol; hence from their flgures A E = 1.2 kcal/mol. (19) R. A. Horne and J. D. Birkett, Electrochim. Acta. 12, I163 (1967). (20) Reference 5a, especially p 115. (21) A. M. Azzam, Z. Phys. Chem. (Frankfurt am Main) 32, 809 (1962). Volume 73,Number 6 Maa, 1960
R. FERN~NDEZ-PRINI, E. BAUMGARTNER, S. LIBERMAN, AND A. E. LAGOB
1420
quite correct and that p increases more with temperature than suggested by the first estimate on which the results in Table IV are based. If allowance is made for a decrease in T, with temperature of about the same magnitude as that found for the potassium ion, the estimates of the activation energy difference AE are increased by 0.2 to 0.5 kcal/mol; this would bring the values closer to those found from the conductivity data (Table VI) based on the sodium ion. The values of T, for the migrating potassium ion at 25’ are 4.2 and 8.3 mol/equiv for DYG and AZG membranes, respectively. These may be compared with the values of 4.2 and 9.0 mol/equiv for ( h +f’) for the same two membranes in 1 N H2S04. Since the quanis an estimate of the amount of water tity ( h +f’) which would be transferred per hydrogen ion in the
absence of proton jumping, the approximate agreement: is encouraging, It may be concluded from this investigation that for the hydrogen ion the effect of temperature on the water transference number is mainly due to the reduction in the proportion of current carried by proton jumping.22 Other factors such as a reduction in the amount of water dragged by the migrating ion and, especially in concentrated solutions, a reduction in the acid dissociation may be contributing factors to the effects observed. (22) Recently, Schtinborn and Woermann (Ber. Bunsenges. Phys. Chem., 71, 843 (1967)) have concluded, on the basis of a n analysis of reflection coefRcients. that the proton jumping mechanism must be largely inhibited in the interior of cation exchange membranes. The present work does not support this conclusion.
Tracer Diffusion and Activity Coefficients of Counterions in Aqueous Solutions of Polyelectrolytes by R. Fern6ndez-Prini,la E. Baumgartner, Citedra de Fisdcoqutmica, Ftd. de Qulmica g Farmacia, Universidad de Chile, Santiago, Chile
S. Liberman,’b and A. E. LagOslo Departamento de Qutmica Inorgdnica, Ftd. Ciencias Exactas 21 Naturales, Universidad de Buenos Aires, Argentina (Received October 7 , 1 9 8 8 )
Tracer diffusion coefficients of Ag+ in silver polystyrenesulfonate and counterion activity coefficients of sodium and silver polystyrenesulfonates have been determined at different concentrations. The results have been analyzed using a simple electrostatic model which assumes the polyions to be parallel sheets of uniform charge density distributed in the volume of the solution. This model enabled the derivation of a relationship between tracer diffusion and activity coefficients of counterions. Data for sodium dodecyl sulfate and partially neutralized polyacrylic acid were also examined. The activity coefficients of the counterions in the polyelectrolyte solutions were calculated from the theoretical relationship between activity and tracer diffusion coefficients, with the experimental values for the tracer diffusion coefficients. According to the model employed, if the distance between adjacent charged groups on the chain is constant, activity and tracer diffusion coefficients should be independent of concentration. It was possible to explain satisfactorily the low values and similar behavior of activity and tracer diffusion coefficients for a given counterion as concentration varied. The model is, however, more useful when dealing with properties of polyelectrolytes having different degree of ionization.
Introduction Transport and thermodynamic properties of counterions in polyelectrolyte solutions are abnormally low when compared to the same -properties in solutions of simple electrolytes; this phenomenon has often been attributed to counterion binding.2 It is recognized that this behavior is due to interactions between the polyion and the counterions. The Journal of Physical Chemistry
These interactions may arise from the localized effect of each charged site on the polyion chain, i.e., sitebinding, or from the overall charge density on the chains. Recently, the low tracer diffusion coefficients (1) (a) To whom all correspondence should be addressed. (b) Department of Chemistry, Massachusetts Institute of Technology, Cambridge. Mass. (c) Electrochlor 8. A.. Buenos Aires, Argentina. (2) 8. A. Rice and M. Nagasawa, “Polyelectrolyte solutions,” Academic press IW, N ~ WYork, N. Y., 1961, Chapter 9.
