4268
A. SCHWARZ AND G. E. BOYD
Measurement of the lines arising from the mesomorphic phases under the condition v, >> 7AH produces a line width which is very sensitive to changes in the systems and, in addition, removes the artificial line broadening produced by the modulation field H,. All known phase transitions in the temperature range covered in this investigation have been detected. In addition, in sodium myristate an apparent transition
at 162" has been detected. This transition has not previously been reported. Acknowledgments. The authors wish to express their appreciation to their associates who aided in this investigation. Special thanks are due to M. C. Beisner for recording the spectra, to R. G. Folzenlogen for preparing the acids, and finally to A. J. Mabis and F. B. Rosevear for instructive advice and criticism.
Thermodynamics of the Exchange of Tetramethylammonium with Sodium Ions in Cross-Linked Polystyrene Sulfonates at 25"'
by A. Schwarz and G . E. Boyd Oak Ridge National LabOTatOTy, Oak Raga, Tennessee 87881 (Received J u l y I d , 1966)
A thermodynamic computation of the selectivity coefficient for the ion-exchange equilibrium between tetramethylammonium (TMA) and sodium ion in dilute aqueous mixtures and cross-linked polystyrene sulfonates was carried out by applying the GibbsDonnan equation to measurements of equivalent water contents and volumes on lightly cross-linked preparations. A comparison of the experimentally determined selectivity coefficientswith those computed showed satisfactory agreement within the errors involved. The configurational free energy increase in the molecular network of the ion exchanger when the relatively large TMA cation wa8 taken up was shown to be an important factor in determining the observed strong inversion in the seIectivity coefficient as the cross linking was increased. Indirect indication of "site binding'' of Na+ ion in the more highly crosslinked preparations was obtained from the calculated behavior of the activity coefficient ratio for sodium and TMA ions in the exchanger.
Ion-exchange reactions involving the quaternary ammonium ions in aqueous solutions are of interest because studies with them serve to shed light on the role of size and hydration in determining the selective uptake of cations by cross-linked organic ion exchangers. In previous work,2&*b a quantitative description of the dependence of the mass law concentration product ratio for ion-exchange equilibria on exchanger cross linking and ionic composition was achieved with the Gibbs-Donnan equation. This equation, which may be written as The Journal of Physical Chemistry
log K , = PAV/2.3RT
(1)
relates the thermodynamic equilibrium constant, K,, for an exchange reaction to the configurational (1) Presented before the Division of Physical Chemistry, 160th National Meeting of the American Chemical Society, Atlantic City, N. J., Sept. 1966. Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) (a) G. E.Myers and G. E. Boyd, J . Phy8. Chem., 60,521 (1966); (b) G. E. Boyd, S. Lindenbaum, and G. E. Myers, ibid., 65, 677 (1961). (3) F. G. Donnan and E. A. Guggenheim, 2. physik Chem.. 162A, 346 (1932).
IONEXCHANGE IN CROSS-LINKED POLYSTYRENE SULFONATES
free energy change in the molecular network of the ion exchanger, which may be expressed as a product of a pressure and a partial molal volume change. A method for estimating the mass law concentration product ratio, or selectivity coefficient, D,can be based on eq. 1. Thus, the selectivity coefficient for the exchange of singly charged cations, 1 and 2, with 2, the preferred ion, isza log Di2 = P(gi
- gz)/2.3RT log
f
(n/rz)r
- 2 log (r1lrz>Tv (2)
When the quantity P in eq. 2 is large, as with highly cross-linked exchangers, and/or when (e1 - &) is large, as in exchange reactions with large cations, neglect of the first term on the right-hand side of eq. 2 may lead to large errors. For example, in the exchange of tetraalkylammonium ion with Na+ ion, the quantity PAs/ 2.3RT may be more important in setting the value of log D12 than the term log ( r ~~ /2 ) ~ I.n our earlier investigations*&on the exchange of H+, Li+, K+, and Csf ions with Ka+ ion, the term log (y1/72)~was dominant. This paper reports a study of the exchange of tetramethylammonium ion (TMA) with Na+ ion in several cross-linked polystyrene sulfonates. Each of the terms on the right-hand side of eq. 2 will be computed, arid their sum will be compared with values of log Ox2measured in equilibrium distribution experiments at 25".
Experimental Section Materials. Four polystyrene sulfonate exchangers nominally cross linked with 0.5, 2, 4, and 8% divinylbenzene (DVB) were used. These preparations were obtained from the Dow Chemical Co. and were designated as Dowex 50W. Their exchange capacities, measured by electrometric pH titrations in 2 N aqueous salt solutions, were 5.46, 5.20, 5.32, and 5.19 mequiv./g. of dry 11-form, re~pectively.~The exchange capacity for tetramethylammonium ion (TMA), which was determined by self-exchange with 14Clabeled TMA and by elution of an aliquot of exchanger in the 14C-labeledTMA form with HC1, was the same as for sodium ion within experimental error for all but the 8% DVB preparations where a value of 5.01 (96.6% of full capacity) was found. After pretreatment to remove metallic impurities and linear polyelectrolyte, a bed of exchanger in the Naform was piaced in a jacketed column maintained at 25", and an excess of solution of the desired composition was passed until equilibrium was reached. After removing the solution from the bed, the exchanger was washed and stored in a closed vessel over saturated MgClz solution a t room temperature. The water content of an aliquot was determined by drying to a con-
4269
stant weight under vacuum trapped with liquid nitrogen. These preparations of varying ionic composition5 and cross linking were employed in the measurements of selectivity coefficients and in the equivalent water and equivalent volume determinations described below. Reagent grade chemicals were used as received except for the tetramethylammonium chloride, which was purified additionally by recrystallization from methanol-weter. Selectivity CoeBczent Measurements. Determinations of the equilibrium selectivity coefficients, D N were performed with mixed aqueous electrolyte solutions a t an ionic strength, p = 0.1, except with the 0.5% DVB exchanger where p = 0.01. Carbon-14labeled TINAe and 14.8-hr. 24Na were employed as tracers, Further purification of the TN'A 14C was achieved by heating the compound under reduced pressure (2-3 mm.) at 50" and collecting the volatile impurities in a liquid nitrogen-chilled trap. This operation was repeated until negligibly small amounts of I4C activity (4-5 times background) were condensed. Proof of the purity of the TMA 14C employed was obtained by eluting a small sample from the top of a columnar ion-exchange bed (Dowex 50W-8, Na form) with 0.1 M NaC1. The elution curve showed but a single peak whose area was equal to the initial activity placed on the bed. Additionally, the weight distribution coefficient computed from the column parameters was in agreement with that estimated from other exp eriments. Assays of the y-ray emitting 24Nawere performed with a well-type thalliated NaI crystal scintillation counter. Carbon-14 was measured by liquid scintillation methods; however, it was necessary to count aqueous electrolyte solutions so that the more highly efficient toluene-base counting mixture could not be used. The following mixture gave a 47% counting yield (including instrument losses) without phase separation when l ml. of 0.1 M neutral aqueous electrolyte was dissolved in 15 ml.: (a) 3000 ml. of p-dioxane (Matheson Coleman and Bell) ; (b) 300 g. of naphthalene recrystallized from alcohol (Eastman Organic Chemical Go.) ; 28.0 g. of 2,5-diphenyloxazole, PPO (Packard Instrument Go.); (d) 1.0 g. of 1,4-bis-2(8phenyloxazolyl)benzene, POPOP (Packard Instrument Co.); (e) 200.0 g. of deionized water. A Model (4)Analyses for the sulfur content of the exchangers were in agreement with these exchange capacity values. ( 5 ) Ionic composition was expressed as equivdent fraction of TMA, WXA.
(6) Nuclear Chicago Co., Des Plaines, Ill. Specific activity = 1.5 mcuries/mmole ; radiochemical purity 99% by dilution analysk.
Volume 69, Number 12 December 1966
~
~
4270
314 EX Tri-Carb liquid scintillation counting system was employed. A rate study was conducted to determine the time necessary for the attainment of ion-exchange equilibrium. The homoionic 14C-labeledTMA salt of the 8% DVB cross-linked exchanger was caused to exchange with TMA in aqueous solution in a “finite bath” experiment. Eighty per cent of equilibrium was reached in 2.0 min. ; a 24-hr. period, accordingly, was considered sufficient for the establishment of an isotopic redistribution. The possibilities that I4C in the TMA might exchange with the ion-exchange copolymer or that not all of the labeled TMA is removed from the exchanger when it was eluted with 1 M HCP were investigated. A 14C-labeledTMA salt of the 8% DVB exchanger was prepared and allowed to stand. The exchanger was then converted to the H form by treatment with an excess of 1.0 M HC1. Approximately 1.6 g. was dissolved in 100 ml. of 601, H202containing 150 mg. of FeS04.7H20 and the gases evolved were collected in 0.1 M NaOH. Virtually no 14C activity was found in either the aqueous solution or in the base, indicating that the amount of I4C that might have entered the structure of the exchanger or remained attached to exchange sites was negligible. Self-exchange reactions with 14C-labeled TMA and 24Nawere employed in the selectivity coefficient determinations. Aliquots of pre-equilibrated exchanger whose preparation was described above were placed in contact with solution identical in composition with that with which it had been brought to equilibrium but containing 24Naand TMA-W tracers. After mixing in a thermostated bath at 25.0” for 24 hr., the phases were separated and the exchanger was regenerated with 1.0 M HC1. The 24Na y-ray activity in an aliquot of the eluate was counted with a well-type crystal scintillation counter setting the discriminator level high enough to exclude pulses from 14Cbremmstrahlen. The Z4Na half-life and y-ray spectrum were compared with standards ‘to establish the purity of the tracer. The ratio of y-activity in the exchanger to that in the aqueous phase was observed not to change with time, indicating that an isotope of constant half-life was measured in both phases. On several occasions in self-exchange experiments where XTMA = 1.00 the aqueous phase was analyzed for sodium by flame photometry. The amount of Na found was close to the limit of detection of the method and, hence, was vanishingly small. The absence of sodium confirmed the assumption that a valid self-exchange experiment had been performed. The l4C-labeled TMA in the 1 M HC1 eluate8 was The Journal of Physical Chemistry
A. SCHWARZ AND G. E. BOYD
measured after a lapse of at least 12 half-lives of the 24Na. The activity of the latter was found to have decreased to background after this time when measured either with a multichannel analyzer or by an integral count rate determination. As an additional check, the P activities of two samples, one of which had had 24Naadded, were compared with a liquid scintillation counter. There was no interference by the 24Nawith the 14Cactivity measurement after a decay of 7 days. Numerical values for the selectivity coefficient for the uptake of the preferred TMA iong were derived from measurements of the radioactivities of the TMA and Naf ions in the exchanger and in the aqueous phase, respectively
DNaTMA = [(TMA),/(TMA) , I/ [(Na+)r/(Na+)Nl (3) The equivalent fraction of TMA in the exchanger, was obtained from
XTMA, xTMA
=
DN~T~*(xTMA),/
+(
D - 1)(XTMA)w] ~ ~ (4) ~ where (XTMA), is the aqueous phase equivalent fraction. An activity balance was made in each experiment to reduce the possibility of systematic errors caused by adsorption losses, etc. The fact that only 96.6% of the exchange capacity of the 8% DVB preparation was available for the TMA ~A ion (see above) made it necessary to correct D NT M for the unavailable exchange sites. The selectivity coefficients reported for this preparation, therefore, must be considered less accurate than with the other preparations because they have been based on capacity rather than on counting ratio determinations. Equivalent Water Content Measurements. The isopiestic vapor pressure comparison procedure for the measurement of the equivalent water contents, xN, of the various ion exchanger preparations as a function of water activity, a,, has been described.lo Saturated salt solutions of accurately known a, were used as referencesll when available; otherwise, NaCl solutions [I
(7) Micro amounts of tetraethylammonium ion were found by D. K. Hale, D. I. Packham, and K. W. Pepper, J. Chem. Soc., 844 (1953), to be taken up strongly by the H-form of a 15% DVB cross-linked polystyrene sulfonate. (8) The presence of acid or salts at concentrations above 0.1 m caused an appreciable lowering in the efficiency for counting TMAIC!. Unsuccessful attempts were made to overcome this “chemical quenching.” The procedure finally used was t o adjust the counting mixtures prepared from the aqueous and eluent phases, respectively, to the same composition. (9) The “preferred ion” was defined as that ion which is selectively extracted by the most weakly cross-linked exchanger (Le., the 0.5% DVB preparation). (10) 8. Lindenbaum and G. E. Boyd, J . Phys. Chem., 6 8 , 911 (1964). (11) R. H. Stokes and R. A. Robinson, Ind. Eng. Chem., 41, 2013 (1949).
~
4271
IONEXCHANGE IN CROSS-LINKED POLYSTYRENE SULFONATES
were employed. These latter solutions were analyzed for C1- ion by potentiometric titration when vapor pressure equilibrium had been attained. Isopiestic equilibrium with the exchangers was approached from both directions (Le.) by the uptake or loss of water), and measurements were conducted in duplicate on the 0.5, 2, and 8% DVB exchangers. Water contents of the 4% DVB preparation in equilibrium with 0.1 m electrolyte solutions were found by measuring the increase in concentration of a 82P-taggedhigh molecular weight polyphosphate solution when partially dried exchanger was immersed in it and osmotic equilibrium was established. Equivalent Volume Measurements. Varying compositions (Le., XTMA) of the 2% DVB exchanger in equilibrium with various known water activities were employed in the equivalent volume measurements. Dry n-octane (synthetic, Matheson Coleman and Bell) was used as a displacement liquid in a pycnometric technique described elsewhere.2b The n-octane was dried by passing it though a deep bed of Linde 4A molecular sieve. The density of the dried liquid was found in good agreement with the literature value.
I
0.4
Experimental Results and Treatment of Data The variation of the selectivity coefficient, DNaTMA for the uptake of TMA with exchanger cross linking and composition is shown in Figure 1. The curves drawn through the experimental points shown represent a least-squares fit to a quadratic equation in XTMA. An unusual feature is the strong selectivity reversal as the cross linking of the polystyrene sulfonate increased. With the 0.5% DVB exchanger, tetramethylammonium ion was preferred for all compositions; with the 8% DVB exchanger, Na+ ion was preferred for all compositions.l2 This behavior contrasts with the selective uptake of Cs+ ion by the sodium form of polystyrene sulfonates where D N+"'~ was observed to increase with cross linking.2a The measurements of the equivalent water contents, xw, are given in Table I as a function of water activity (Le,, -log a,) and ionic composition for the 0.5 and 2% DVB preparations. These data, and those for the 8% DVB exchanger which are not listed, were converted to weight normalities by the relation N , = lOOO/z, and fitted by least squares to a polynomial in -log
I
I
I
I
I
I
I
0.2 0.3 0.4 0.5 0.6 0.7 0.8 EQUIVALENT FRACTION OF TMA
I
0.9
Figure 1. Equilibrium selectivity coefficients a t 25' for the exchange of tetramethylammonium with sodium ions on variously cross-linked polystyrene aulfonate; (1.1 = 0.10).
side of eq. 2. I n the estimation of the configurational free energy, the quantity P is computed from14
P
=
(RT/&J In (aw'/uw)
(Nm
constant)
(6)
where 5, is the partial molal volume of water in the exchanger and a,' and a, are the water activities in a cross-linked preparation and in a chemically identical exchanger so lightly cross linked that P = 0, respectively. The data of Table I also were employed in the evaluation of the activity coefficient ratio, log (')"a/YTMA)r, by means of the equation2a log
(?"a/?'TMA)r
log
(YNa*/'YTMA*)r
- 0.055511~ (7a)
where the integral, IR,is defined by
aw13
Nm
=
+ P(--logaw) + y(--log~w)~ (XTMA
constant)
(12) A pronounced reversal in the selectivity coefficient with cross
(5)
Equation 5 was applied in several ways in the computation of the first and second terms on the right-hand
k k h g in polystyrene sulfonate ezchangers also has been observed
in the exchange of tetramethylammonium ion with potassium ion by H. P. Gregor and J. I. Bregman, J. CoZZoid 8ci., 6 , 323 (1961). (13) The constants a, B, and y in eq. 6 will be supplied on request. (14) G. E. Boyd and B. A. Soldano, 2. EZektrochenz., 57, 162 (1963).
Volume 69,Number I8 December 1966
4272
A. SCHWARZ AND G. E. BOYD
S,
-log aw
IR
=
-
u3
( ~ x ~ / ~ x T M d( A ) ~ log ~
m A
a,)
(XTMA
constant)
: (7b)
The quantity, log (YN,*/YTMA*)~, was obtained from measurements of the selectivity coefficient, D*,on the 0.5% DVB preparation in equilibrium with highly dilute aqueous electrolyte mixtures. I n this case the first and third terms on the right-hand side of eq. 2 become negligibly small, and log D* = log
(YN~*/YTMA*)~
(8)
The required values of the coefficient, ( ~ X , / ~ X T M A ) ~ ~ , which is a function of -log a, and XTMA, were found by computing X, for chosen values of XTMA and -log a, from eq. 5. These interpolated X, values were fitted by least-squares methods to an empirical equation of the form X, = a
+
+
~XTMA
h
3 h N. 0 d
0 m 0
: m
h
m
2 0
N n
n
3 N
0
h
0
m n
x
W n
x
CXTMA'
(-log a, constant)
(9)
A plot of the derived ( ~ x ~ / ~ z T M values A ) ~ ~ as a function of -log a, = y for the 0.5% DVB and 2% DVB exchangers with XTMA = 0.0, 0.5, and 1.0 is given in Figure 2. The curves shown were computed from the "least-squares" equation (~X,/~ZTMA)= ~ ~ Ale-Azv
+ A3e-A4v
(10)
This equation was employed because of the unsymmetric maxima observed in Figure 2. The appropriate values of -log a, for the upper limit of the integral in eq. 7b were obtained by substituting the xWvalues for the more highly cross-linked exchangers in eq. 5 for the 0.5% DVB preparation and solving the quadratic. It is evident from Figure 2 that the quantity IR is positive over a wide range in -log a,. The measured equivalent volumes, Ve, were employed to compute the quantity (zj~, - %MA), also required to estimate the configurational free energy of the copolymer molecular network. The experimental Ve (ml. equiv.-') for XTMA = 0.00, 0.342, 0.569, 0.800, and 1.00 taken on the 2% DVB exchanger with varying z, (g. of H20 equiv.-') were fitted to the empirical equationzb V , = V , 1.00298~,~/(bf x,) (11)
+
where 8, is the equivalent volume of the anhydrous exchanger and b is the fractional molar volume defect (Table 11). Values of 142.0 and 221.0 ml. equiv.-l were observed experimentally for V , for the sodium and tetramethylammonium forms, respectively. The computation of the difference in the partial molal volumes of these forms was based on the equation2" The Journal of Physical Chemistry
8 $
f
8 u1
m 05 N)
8 u3
m
3 d
9 0 (D
h 3 d
8
P - .
.?Y
g : :M AM8 m
f: m
0
9
0
m m 3 0
x
m
59
0
(0 0
8
8 3
m
0 3
8
.. .. .. .. .. . . . . .
4273
ION EXCHANGE IN CROSS-LINKED POLYSTYRENE SULFONATES
(UNP,- UTMA) = Ahv,
-
&r
w
(&/bZTMA)s,dZw (zTMA constant)
- 94
I
-82’
h 4
I
I
I
I
I
4’0 1: 16 WEIGHT NORMALITY, Nm
1’8
20
I
I
I
I
(12)
The required values of the partial molal volume of water, ow = (dVe/b~w)mMA, were computed from eq. 11and fitted to the empirical equation 8, =
a
+
~zTMA
4-CZTMA’
(zWconstant)
(13)
from which ( i % w / b ~ ~ ~values ~ ) z wwere computed. These differential coefficients were fitted to empirical equations which were used to evaluate the integral
e
2
‘
I 40-
-$
20 -
-40F
Nominal 2% DVB
I
I
I
0.01
0.02
0.03 -log a,
,
I
0.04
0.05
,
0.0
Table 11: Least-Squares Parameters for the Variation of Equivalent Volumes (ml. 1 of Tetramethylammonium-Sodium Salt Forms with Equivalent Water Content (g. equiv.-l) According t o Eq. 11
v.
b
0.000 0.342 0,569 0.800 1.ooo
144.8 168.4 187.7 203.9 219.2
25.1 21.4 17.3 13.7 12.6
A
Figure 3. Variation of partial molal volume difference of tetramethylammonium and sodium resinate with weight normality.
log ( Y N ~ C I I Y T Y=A C ~ ) ~
1%
Figure 2. Variation of ( & T ~ / ~ Z T M A ) ~with , -log aw for cross-linked polystyrene sulfonate.
XTXA
A A
in eq. 12. The results of the calculations based on eq. 12 are shown in Figure 3 where it may be seen that the difference, - ~ T M A ) , is relatively quite large. For example, the difference, (@Na- 8 ~ was ~ )but -18 ml. equiv.-l, approximately.2a Recent measurementsLs of the partial molal volumes of tetramethylammonium bromide in aqueous solutions allow a calculation , is shown in of the difference, (8NaBr - ~ T M A B ~ )which Figure 3 for purposes of comparison.16 It is seen that a fair concordance between the two sets of measurements exists as would be expected; this fact suggests that V , values measured on the 2% DVB exchanger are reliable. 1 The third term on the right-hand side of eq. 2, -2 log ( Y N ~ C ~ / Y T M A C ~ )is~ , a measure of the ionic interactions in the dilute aqueous electrolyte mixture in equilibrium with the ion exchanger. The contribution of this term for a 0.1 m solution is expected to be small. Its evaluation was accomplished by applying Harned’s rule and estimating a with a procedureL7suggested by Guggenheim. The equation was
-20H
4
k
(YNESI(O)/YTMACI(O))
-
(b‘NsCl
- b’TMAC1)m
(14)
where YNaCl(0) and YTMACI(O) are the activity coefficients of pure NaCl and TMACl solutions at molality, m, and the quantities b’ are obtained from the relation b’ = 0.4342 (104 9.19), where 4 is the molal osmotic coefficient at m. The derived value of 2 log ( y N a c l / Y T M A C ~ ) was ~ 0.0210 when m = 0.1, independent of the equivalent fraction of TMACl in the mixed
-
Range of zw
0.1-385.9 0.1-395.3 0.1-420.1 0.1-373.7 0.1-408.3
(16) W. Y. Wen and 8. Saito, J. Phys. Chem., 68, 2639 (1964). (16) Values for V N ~ B&a~ a function of concentration were computed with the equations and values of .$vo and S, given by H. 8. Harned and €3. B. Owen, “Physical Chemistry of Electrolyte Solutions,” Reinhold Publishing Corp., New York, N. Y., 1959,p. 361. (17) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co. Ltd., London, 1955, p. 440.
Volume 69, Number 12 December 1966
4274
A. SCHWARZ AND G. E. BOYD
Table I11 : Computation of the Equilibrium Selectivity Coefficient, DNaTMA, for the Exchange of Tetramethylammonium with Sodium Ion for Various Ionic Compositions of Nominal 2, 4, and 8% DVB Cross-Linked Polystyrene Sulfonate" log D N , =~PAD/2.3RT ~ ~ f log (YNJYTMA)~
a
- 0.0210
2
0.00 0.50 1.00
503 497 486
0.0077 0.0084 0.0099
0.2058 0.1830 0.1408
0.0136 0.0192 0.0410
0.1922 0.1638 0.0998
20 22 26
91.9 90.6 89.3
0.0317 0.0350 0.0417
1.38 1.28 1.09
0.97 0.88 0.86
4
0.00 0.50 1.00
310 249 190
0.0157 0.0266 0.0467
0.2058 0.1830 0.1408
0.0557 0.0854 0.1330
0.1501 0.0976 0.0078
45 79 141
91.2 89.8 88.4
0.0721 0.1251 0.2215
1.14 0.89 0.58
1.08 0.97 1.03
8
0.00 0.50 1.00
192 180 174
0.0306 0.0431 0.0529
0.2058 0.1830 0.1408
0.1300 0.1390 0.1430
0.0758 0.0440 -0.0022
91 130 161
90.1 89.2 88.3
0.1451 0.2058 0.2517
0.81 0.66 0.53
1.13 0.88 0.91
Based on the 0.5% DVB exchanger.
Table IV : Computation of the Equilibrium Selectivity Coefficient, DNaTMA, for the Exchange of Tetramethylammonium with Sodium Ion for Various Ionic Compositions of Nominal 4 and 8% DVB Cross-Linked Polystyrene Sulfonate" log D N , ~= ~PAij/2.3RT ~ , %
Iog
a,
(YNa*/YTMA*)r
ZTMA
Zw
4
0.00 0.50 1.00
310 249 190
0.0114 0.0214 0.0416
0.1801 0.1047 0.0349
8
0.00 0.50 1.00
193 180 174
0.0295 0.0390 0.0486
0.1801 0.1047 0.0349
YN*/YTMA)~
- 0.0210
('YNdYTMA)r
P
- A5
-2.3RT PAV
0.0145 0.0263 0.0505
0,1656 0.0784 -0.0156
45 79 141
91.2 89.8 88.4
0.0721 0.1251 0.2215
0.86 0.55
1.04 1.01 1.08
0.0593 0.0614 0.0645
0.1208 0.0433 -0.0296
91 130 161
90.1 89.2 88.3
0.1451 0.2058 0.2517
0.90 0.66 0.50
0.88 0.97
log
-log
DVB
+ log (
0.055511~
Daalcd
1.18
Dobad/ Dcslod
1.01
Based on the 2.001, DVB exchanger corrected to P = 0 and p = 0.01.
electrolyte. The values for YTMACI(O) and 0.1 m were taken from a recent publication.'O
~ T M A Cat ~
Discussion and Conclusions A summary of the calculations of the selectivity co~ ~ of, the cross linking and efficient, D N ~as a~ function ionic composition of the exchanger is afforded by Table 111. These calculations were based on the measured properties of the most lightly cross-linked preparation (e.g., 0.5% DVB) which was taken as the reference exchanger. In principle, the thermodynamic procedure described above allows the calculation of the selectivity coefficient for any cross-linked exchanger relative to the properties of a more lightly cross-linked one, This point is illustrated by Table IV, where the 2% DVB exchanger was taken as the reference. The calculated DNsTMA values in Tables I11 and IV are believed to show a satisfactory agreement with the experimentally measured values. The agreement is The Journal of Phvsical Chemistry
better with the 2% DVB cross-linked exchanger as the reference principally because of the greater accuracy with which its equivalent water content was measured for small values of -log G. However, an additional cause was the fact that the equivalent weight of the 2% DVB exchanger (192.1) was much closer to that for the 4% (188.1) and for the 8% (192.6) preparations than was the equivalent weight of the 0.5% DVB exchanger (183.0). The thermodynamic calculations were based on the assumptions that: (a) the ion exchangers may be regarded as homogeneous, ternary mixtures of tetramethyl resinate, sodium resinate, and water, and (b) the lightly cross-linked reference exchangers are chemically identical with the more highly cross-linked exchangers. Assumption b especially breaks down for preparations with 8% DVB and greater because of the increased organic content of these exchangers, and because of the increasing number of suIfonate groups on the cross links. The importance
4275
IONEXCHANGE IN CROSS-LINKED POLYSTYRENE SULFONATES
of such changes in composition and structure have been elucidated in the extensive research of Banner'* with aqueous solutions of “model” compounds. It may be concluded from these investigations that an increase in selectivity coefficient should accompany an increase in the equivalent weight of an exchanger, and it is of interest to note that the differences between the experimental and calculated selectivity coefficients given in Table I11 are in this direction. The relative contributions of the various terms in for varying water content eq. 2 to log DNaTMA (and, hence, cross linking) when ZTMA = 0.0 are shown in Figure 4. It is evident that an important cause of the large decrease in the selective uptake of tetramethylammonium ion with increasing cross linking is the large increase in the configurational free energy (Le., the PAar?/2.3RT term) of the polymer molecular network when the large quaternary ammonium ion enters the exchanger. The magnitude of the selectivity coefficient reversal is accounted for quantitatively by the right-hand side of eq. 2, and this fact greatly increases our confidence in the essential correctness of the model on which the thermodynamic derivation of eq. 1 was based, The observed selectivity coefficient decrease, as the fraction of TMA in all the exchangers was increased (Figure l), and the reversal found with the 4% DVB exchanger also were reflected in the thermodynamic calculations (cf. Tables 111and IV). It is of further interest to note that the ionic interactions in the exchanger, which are reflected by the term log ( Y N ~ / Y T M A ) ~ , were such as to decrease the selectivity for tetramethylammonium ion with increased cross linking. This behavior, of course, indicates that the activity coefficient for Na+ ion in the exchanger decreases more rapidly with increased M, than does YTMA, and it suggests that possibly “site binding” of Na + ion becomes increasingly important as the water content of the exchanger decreases. The TMA ion is believed to be only slightly hydrated,lg and the mechanism of its interaction with the sulfonate groups probably does not change significantly as xw is decreased. This difference in the interaction of TMA and sodium ions with the sulfonate group also manifests itself in aqueous solutions. Recent measurementsZ0of thermodynamic activity coefficients of the sodium and tetramethylammonium salts of ethanesulfonic acid have shown that T& for the latter salt a t small concentrations is less than that for the Na salt, but that when m > 1.5 the reverse is true. The selective uptake of the tetramethylammonium cation by the most lightly cross-linked exchanger may be regarded as a consequence of water-water interac-
I
-0.2
’
I
’
I
’
I
’
I
’
-
--0.4 O ‘ I /-
0
2
4 6 8 10 WEIGHT NORMALITY, N, = 1000/Xw
12
Figure 4. Comparison of terms contributing to calculated log D for the tetramethylammonium-sodium exchange on variously cross-linked Dowex 50 at 25’; ZTMA = 0.0.
tions which act to force large unhydrated ions from their aqueous solutions. This type of an effect has been proposed21 to explain the large selectivity coefficients shown by strong-base anion exchangers for large, unhydrated anions such as C104-, Re04, I-, ions, etc., and for the uptake of quaternary ammonium ions by cation exchangers in which “structure-enforced ion pairs”22 in the exchanger presumably are formed. It seems unlikely, however, that such ion pairs even if they are formed with polystyrene sulfonates can be very stable because of the strong hydration of the sulfonate group. When the cross linking is increased, these pairs become progressively more unstable and strong selectivity reversals occur. The conclusion from this research is that both ionic size and hydration are important in determining the uptake of tetramethylammonium ion by cross-linked polysulfonate cation exchangers. Acknowledgment. It is a pleasure to acknowledge the interest and help given during the course of this research by our colleague, Dr. 8. Lindenbaum. (18) 0. D. Bonner and 0. C. Rogers, J. Phys. Chem., 64, 1499 (1960); 65, 981 (1961); 0. D. Bonner and J. R. Overton, ibid., 67, 1035 (1963). (19) E. R. Nightingale, Jr., ibid., 66, 894 (1962), on the basis of
viscosity measurements has described the (CHs)eN+ ion as weakly perisurface hydrated. (20) H. P. Gregor, M. Rothenberg, and N. Fine, ibid., 67, 1110 (1963). (21) B. Chu, D. C. Whitney, and R. M. Diamond, J . Inorg. Nucl. Chem., 24, 1405 (1962). (22) R. M. Diamond, J. Phys. Chem., 67, 2513 (1963).
Volume 69, Number 18 December 1966
