CATIONINTERCHANGE ACROSS ION-EXCHANGE MEMBRANES
883
Cation Interchange across Ion-Exchange Membranes
by M. Worsely, A. S. Tombalakian,' and W. F. Graydon Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Canada (Received September 3, 1964)
The possibility of preparing polystyrenesulfonic acid ion-exchange membranes having various degrees of porosity by changing the alcohol group in the ester mononier was investigated. Polystyrenesulforiic acid ion-exchange inenibranes were formed using the methyl, ethyl, n-propyl, n-hexyl, and n-octyl esters of p-styrenesulfonic acid. The membranes were found to exhibit an increase in permeability with increase in the size of the alcohol group of the ester monomer. S o preferential ion screening or sieve effect was observed as successively larger univalent inorganic and organic cations were used to interchange with hydrogen ion. The dependence of the membrane interdiffusion coefficient on the single ion diffusion coefficients of the interchanging ion species in the membrane for various conditions of the membrane diffusion was determined. Good agreement was found between the observed interdiffusion coefficients and values calculated using single ion diffusion coefficients of hydrogen in the membrane and limiting ionic mobility ratios in water.
Introduction The swelling and transfer behavior of polystyrenesulfonic acid ion-exchange membranes formed by the bulk copolyniclrization of the n-propyl ester of pstyrenesulfonic acid with styrene and divinylbenzene have been invc:~tigated.~-~The effects of membrane exchange capacity and cross linking, solution concentration, temperature, counterion valence, and size on niasstransfer rates have beeti recently reported.' The results of measurenierits of membrane nioisture contents in various ionic forms and rates of ion transfer during the in1 erchange of hydrogen with univalent inorganic and organic cations across membranes formed from the methyl, ethyl, n-propyl, n-hexyl, and noctyl esters of p-styrenesulfonic acid are given in this report. The effects of variation of the alcohol group in the ester monomer on the structure and permeability of the membranes formed have been determined. Experimental ( A ) Preparation of Monomers. The methyl, ethyl, n-propyl, n-hexyl, and n-octyl esters of p-styrenesulfonic acid were prepared from p-phenyl ethyl bromide by a sequence of sulfochlorination, esterification, and dehydrobroniination react ions.* ( B ) Membranes. The membranes used in this work were prepared by the bulk copolymerization of
the esters of p-styrenesulfonic acid with styrene, divinylbenzene, and benzoyl peroxide as catalyst and subsequent hydrqlysis in 5% caustic soda solution to produce polystyrenesulforiic acid. 2 ~ 8 , 9 The membranes were formed a t 110-120° in 2 hr. A mass balance on a menibrane formed from the npropyl ester of p-styrenesulfonic acid showed a loss i n weight of about 4% during polymerization and of a further 3% during the hydrolysis. The methods used for the determination of niembrarie nioisture content, exchange capacity, and thickness have been described p r e v i ~ u s l y . ~In Table I are given the characteristics of the menibranes used in this work and the membrane moisture contents in various ionic forms in contact with pure water at 23'. (1) Depnrtnient of Chemistry a n d Engineering, Lnurentian University of Sudhur?,, S u d b u r y , Ontario, C a n a d a .
(2) W. F. Graydon and R. J. Stewart, J . P h y s . Chem., 59, 86 (1955). (3) R. J. S t e w a r t a n d W. F. G r a y d o n , ibid., 6 0 , 750 (1956). (4) R. J. Stewart and W. F. Graydon, ibid., 61, 164 (1957). ( 5 ) A. S. Tonibnlakian, H. J. Barton, a n d W. F.Graydon, ibid., 6 6 , 1006 (1962).
(6) J. Ciric and W. F. Graydon, ibid., 66, 1549 (1962). (7) A. S. Tomb:ilnkian, C. Y. T e h , and R . F. G r a y d o n , Can. J . Chem. Eng.. 42, 61 (1964). ( 8 ) I. H. Spinner, J. Ciric, and W. F. G r a y d o n , Can. J . Chem., 32, 143 (1954). (9) W. F. Graydon, I!. S. Pntent 2,877,191 ( M a r c h 10, 1959).
Volume R 9 , .\-umber
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March 1.96.5
M. WORSELY,A. S. TOMBALAKIAN, AND W. F. GRAYDOS
884
Table I : Membrane Characteristics Membrane no.
1 2 3 4 5 6 7 8 9 10 11
7;D V B
Capacity, mequiv./g. of dry resin, H form
Ester form
6 6 6 6 6 4 4 4 2 6 6
1.93 2 56 2.49 2 29 2.24 1.79 2 54 2.47 1 97 1.60 2.31
Methyl Ethyl n-Propyl n-Hexyl n-Octyl Methyl Ethyl n-Propyl Ethyl %-Propyl n-Propyl
Mole
Moisture content, moles of HzO/equivalent-------Na H+ Li + (CHa),N
K+
+
18.9 19.7 22.2 25.9 27.3 23.1 25.1 28.5
20.0 21.4 23.9 28.3 30.5 24.3 30.1 30.4 33,7 10.8 23.1
10.4
20.3 22.6 24.3 29.1 31.0 24.7 30.4 31.2
20.5 22.8 25.0 30.1 32 2 25.0 30 9 31.6
17.5 20.5 22.4 25 3 26.4 21 3 27.5 28.4
11.3
11.7
9.2
+
(CtHa)pN
18.6 21.0 23.3 23 8 26 9 24.3 29.0 29.3
Thickness, cm. (-0.0002)
0.1392 0.1612 0 1573 0 1460 0 1040 0 1335 0 1402 0.1440 0.0762 0 0712 0.0688
Table I1 : Cation Interchange, Various Ion-Pair Exchange Systems a t 25.0’
System
--Membranes-No. Ester form
-Initial 0 1 N
KC1-HC1
NaCl-HCl
LiCI-HCI
( C~H,)nNCl-HCl
exchange flux, g. equiv./cm.l h r . X 10‘05N LON 2 0 N 3 0 N
1 2 3 4 5
Methyl Ethyl n-Propyl n-Hexyl n-Octyl
18 20 23 25 30
9 9 5 4 7
1
2 3 4 5
Methyl Ethyl n-Propyl n-Hexyl n-Octyl
15 16 18 19 24
0 4 8 2 1
1 2 3 4 5
Methyl Ethyl n-Propyl n-Hexyl n-Octyl
10 12 14 15 17
6 4 7 0 9
14 1
15.7
19 4
1 2 3 4 5
Methyl Ethyl n-Propyl n-Hexyl n-Octyl
780 105 9 70 11 4 11 7 13 7
13.9
18 4
1 2 3 4 5
Methyl Ethyl n-Propyl %-Hexyl n-Octyl
2 4 4 5 6
56 30 97 85 54
29 3
4 31
32.9
6 31
(C) Flux Measurements. A two-compartment Lucite cell, previously described,g was used to measure the rates of ion transfer. At zero time each compartmerit, separated from the other by the ion-exchange inembrane, contained 10-nil. solutions of equal normalThe Journal of I’hysical Chemistry
41 9
8 52
Interdiff. Over-all ion-interchange coefficient, cm./sec. coeff., -------X lo’-------cm.Q/sec. 0 1 N 0 5 N 1 0 N 20,V 3 0 N x 106
27 56 66 74 98
2 6 9 2 5
19 40 48 49 69
1 7 2 0 8
24 5
13 28 33 33 45
2 0 7 9 9
4 05
2 42
1 43
25 2
9 22 25 25 35
62 2 81 2 5 8 8
1 62
10 2
3 43 1 04 8 83 10 5 11 6 14 9
0 62
45 3
7 82
4 65
2 84
2 13
1 32
3 4 4 5
41 38 93 10
0 2 3 3 3
97 56 29 57 82
1 08
0 1 2 2 2
67 87 34 50 62
0 96
0 72
0 45 1 35 1 67 1 74 1 83
0 36
0 26
0 0 0 0 0
17 55 66 71 77
ity. The cell agitator was set a t 300 oscillations/niin. and the two ionic species were allowed to interchange across the membrane for several 5-min. periods until a constant flux was obtained. The interchange was then allowed to proceed for various time intervals.
CATIOXISTERCHASGE ACROSS ION-EXCHAXGE MEMBRANES
At the end of each interval the contents of the compartiiients were analyzed by titration.
Results and Discussion Exaniples of the results of cation-interchange fluxes, over-all ion-interchange coefficients, and membrane interdiffusion co&icients, which have been obtained across five typical polystyrenesulfonic acid ion-exchange nieiiibranes formed from the various esters of p-styrenesulfonic acid, are given in Table 11. llenibraties 1. 2, 3, 4, and 5 had the same nominal exchange capacity and cross linking but were formed from the methyl, ethyl, n-propyl, n-hexyl, and noctyl esters of p-styrenesulfonic acid, respectively. The results mere calculated froiii the experimental data using the relationship described previously.' The over-all ion-interchange coefficient ( K , ) is given by expression 1. This quantity is determined entirely by changes in the external solutions.
K , is the over-all ion-interchange mass-transfer coefficient, cni./sec.; V is the volume in the cell conipartinent (10 nil.); A is the membrane surface area exposed to the solutions (3.14 c i x 2 ) ; ACo is the difference in concentration of the interchanging species between half-cells at zero time, equiv./nil. ; and ACr is the difference in concentration of the interchanging species between half-cells at time t , equiv./nil. The interdiffusion coefficient (D,) is given by expression 2 and is quite independent of solution concentration. D,
=
KiL-co Ci
Where D, is the membrane interdiffusion coefficient, cni.2/sec.; L is the membrane thickness, cm.; Co is the initial concentration of external solutions, equiv./ nil.; and C, is the membrane internal ion concentration, equiv./ml. I t is to be expected that the ester of p-styrenesulfonic acid with the larger alcohol group would produce membranes of a larger pore size. Indeed, the membrane nioisture contents in various ionic forms presented in Table I and the rates of ion interchange given in Table I1 indicate this effect. The data in Table I1 show that for a given ion pair the diffusivities of the ions through the membranes increase with increasing alcohol size of the ester mononier in the order membrane 1, 2, 3, 4, and 5 . I n all cases meinbrane porosity increased markedly with increasing alcohol size. The removal of successively larger alcohol groups froin the nienibranes during hy-
885
drolysis produced membranes of a successively larger pore size. I t may be seen from Table I1 that the fluxes, over-all ion-interchange coefficients, and interdiffusion coefficients for the exchange between hydrogen and the various univalent cations decrease in the order potassium, sodium, lithium, tetramethylammonium, and tetraethylanmoniuni; whereas the effective radii of these ions in their hydrated forms decrease in the sequence potassium, sodium, tetramethylammonium, lithium, and tetraethylaninioriiuni.'O This indicates that the ion-membrane interaction experienced by organic cations in the membranes is greater than that for inorganic cations of the same valence and size. For the membranes prepared from the methyl ester of p-styrenesulfonic acid, the observed dependence of the over-all ion-interchange coefficient on solution concentration for the univalent inorganic and organic cations is similar to that reported previously7 for other univalent inorganic cations interchanging with hydrogen across membranes formed from the n-propyl ester. It niight be expected that as the pore size of a iiienibrane becomes smaller, the diffusion of the larger counterions would be relatively more hampered than that of the smaller ions. I n Table I11 are given the values of the ratio of the observed meinbrane interdiffusion coefficient of one ion-pair exchange system to the membrane interdiffusion coefficient of a reference ion-pair exchange system (K+-H+) for eight different membranes. It can be seen that the ratios of nienibrane interdiffusion coefficients for any two exchange systems are quite constant regardless of differences in membrane porosity. There is very little sieve effect resulting from membrane network interference. The pore widths of these polystyrenesulfonic acid ion-exchange membranes appear to be much larger than the diameter of even a hydrated tetraethylammonium ion, reportedlo to be 8 A. I n order to determine the extent to which the interchanging ions were hindered in the nienibrane pores, the ratios of interdiffusion coefficients listed in Table I11 were divided by similar ratios of interdiffusion coefficients calculated using relationship 311 and limiting
(3) ionic mobilities in water.I2 The results, given in Table IV, show that the interdiffusion coefficients for univalent (10) R . A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworths, London, 1955. ( 1 1 ) K . S. Spiegler and C. D. Coryell, J . P h y s . Chem. 5 7 , 687 (1953).
Volume 69, Xumber 9
March 1965
M. WORSELY,A. S. TOXBALAKIAS, .4ND W. F. GRAYDOS
886
1.2
Table I11 : Ratio of Membrane Interdiffusion Coefficients Membrane
~~t~~
no
form
N a +-H K+-H+
Li +-H
+
+
~~
Methyl Ethyl n-Propyl %-Hexyl n-Octyl Methyl Ethyl n-Propyl
1 ‘2
3 4 5 6 7 8
0 0 0 0 0 0 0 0
K+-H+
0 0 0 0 0 0 0 0
74 75 75 73 75 75 79 76
(CHa),N +-H K +-H
+
+
0 0 0 0 0 0 0 0
51 55 53 52 51 52 58 54
(C2Hs)rN +-H K +-H
0 0 0 0 0 0 0 0
I
13 16 15 14 15 14 18 16
u
Table IV : Ratio of Interdiffusion Coefficient in Membrane to Water
1
2 3 4 5 6
7 8
,
...
~
.
,
Ua-H
1 1 1 1 1 1 1 1
03 04 04 02 04 04 10 05
...
.
,
. TEA-H
...
TMA-H
0.90 0.96 0.93 0.91 0.90 0.91 1.01 0.94
TLIA = tetramethylammonium ion. ammonium ion.
0 0 0 0 0 0 0 0
52 60 58 54 55 54 62 60
* TEA
,
--
0.27 0.33 0.31 0.29 0.31 0.29 0.37 0.33 =
tetraethyl-
and opposite concentration gradients and the resulting electrical cation diffusion potential. Application of
The Joiirnal of’Physical Chemistry
I
1
I
I
I
‘
inorganic cation-exchange systenis in the membrane are nearly in the same ratio as in aqueous solution, whereas the interdiffusion of univalent organic cations with hydrogen is considerably slower in the nienibrane solution than in water relative to the K+-H+ interchange. Although the inorganic and organic cations exhibit an increase in ion-membrane interactions with increasing ionic size, this effect is much greater for organic than inorganic cations (Figure 1). This interaction is quite independent of the pore size. The large counterion exerts the major control over the rate of ion interchange. Since solutions of equal volunie and concentration were used in these counterdiffusiori experiments, the two cation species interchanged across the membrane in equivalent quantities under the influence of equal
-~
I
I
0-2 6.0
Membrane no.
I
+
+
34 39 38 35 36 35 41 39
I
I
6.5
I
7.0
I
7.5
1
8.0
1 8.5
HYDRATED COUNTER ION DIAMETER, A o Figure 1. Dependence of ratio of interdiffusion coefficient, in membrane to water on inorganic and organic counterion ( X ) diameter. The plots are based on mean values of results (Table IY)for eight different membranes.
univalent cations across an ion-exchange nienibrane leads to the relationship
J,
=
DiD2C,A Ci’(D1 - D2) In Di - Dz Ci”(D1 - 0 2 )
+ CoD2 + CoDz
(4)
where J , is the interchange flux, equiv./sec.; D I , D zare the single ion diffusion coefficients of ion species 1 and 2 in the membrane, c m 2 ’see.; and C1’, Cl” are the concentration of ion species 1 in the two halfcells, equiv./nil. The cation-interchange fluxes obtained in the counterdiffusion experiments were used in a graphical integration of eq. 4 together with the assumption that liniiting inorganic ionic mobility ratios in water apply in the nienibrane solution to estimate the single ion diffusion coefficients for hydrogen (DH +). Examples of D H obtained by this method for two nienibranes formed from the ethyl and methyl esters of polystrenesulfonic acid are given in Table V. These results are lower than the values of DH obtained previously6 by counterdiffusion and electrical resistance measurements across membranes of higher porosity fornied froni the npropyl ester of p-styrenesulfonic acid. I t may be seen from Table V that the diffusivity of hydrogen ion in nienibrane 9 of low Cross linking and relatively larger pore size is greater than that observed for a tighter membrane 1 of a higher cross linking and smaller pore size. +
(12) H. S. Harned and B. B. Owen, “ T h e Physical Chemistry of Electrolk tic Solutions,” Reinhold Publishing Corp., New Tork, x, y,,1958,
C A T I O S ISTERCH.4KGE ACROSS
ION-EXCHANGE RIEMBRAKES
Table V : Single Ion Diffusion Coefficients of Hydrogen at 25.0”
887
Table VI:
Membrane Interdiffusion Coefficients a t 25“ --Dn,
lleinbrane no
9
Eater form
Ethyl
D H + ,cm.P/
Syateio
Extr. aoln. concn., molea/i.
KCI-HC1 KaC1-HCl LiC1-HCl
0 1 0 1 0 1
1 09 1 06 0 94
Av. 1
Methyl
KC1-HC1 NaC1-HCl
0 1 0.1
see.
x
lo6
Membrane no. 10
System KCI-HCI
1 03
0 61 0 60
LiC1-HCI
Av. 0 . 6 1 (CHa)4NCI-HCI
I t is of interest to compare the values of membrane interdiffusion coefficients obtained for our experimental conditions by eq. 2 with interdiffusion coefficients which may be estimated froin single ion diffusion coefficients of the interchanging ions in the nienibrane using eq. 5 and 3, which are limiting evaluations of DU from eq. 4 for initial and final diffusion conditions, respectively. l 3 (5)
In order to test the validity of eq. 3 and 5 , “differential” interdiffusion coefficients were determined using 10-niin. periods. Solutions of varied composition (0.1 N total solution concentration) corresponding to various time intervals during a normal integral interchange process were used. I n Table VI are given the observed “differential” interdiffusion coefficients as defined by eq. 2 for various ion-pair exchange systems. l h e values of interdiffusion coefficients calculated by eq. 3 and 5 using single ion diffusion coefficients of hydrogen obtained by graphical integration of eq. 4 and limiting ionic mobility ratios in water are also given. I t can be seen from Table VI that the values of the experimental “differential” interdiffusion coefficients obtained for the initial boundary condition of the iiienibrarie decrease by about 50% as the iriterchaiige nears equilibriuin. The interdiffusion coefficients calculated by eq. 3 and 5 are in fair agreement with meni-
11
NeCI-HCI
Initial counterion concn., equiv./l. HalfHalfcell 1 cell 2 0.10 0.09 0.08
ferential” exptl. eq. 2
Integral exptl
Calcd.
eq. 2
0 0.01 0 02
0.575 0.521
0
0.10 0.09 0.08
0.01 0.02
0.10
0
0 08 0.07
0.02 0.03
0.10 0.095 0.090
0
0.082
cm.P/aec. X I O L -
“Dif-
0.005 0.011 0.019
0.238 0.219
0.085 0.073
1.24 1 16
1.08
brane interdiffusion coefficients obtained for our experimental conditions by eq. 2. The interdiffusion coefficients previously reported3, are integral values over ranges up to 60-S0~0of equilibrium. Saiiiples of such values are listed in Table VI. These coefficients are of course of interiiiediate value. As shown previously,6 eq. 3 may be used to obtain a self-consistent set of single ion diffusion coefficients which serve to correlate integral diffusion behavior for various ion pairs. Such single coefficients are to some degree fictitious. Xeither eq. 3 nor 5 may be used to calculate single diffusivities from such integral interdiffusion coefficients. Indeed, the experimental range of short chord, “differential” ion interdiffusion coefficients is iiiuch larger than the range predicted by the Xernst-Planck equation (4).
Acknowledgment. The authors are indebted to the National Research Council, Ottawa, Canada, the Ontario Research Foundation, and the President’s Advisory Coininittee on Scientific Research, University of Toronto, for financial support.
Volume 69, Number 3
M a r c h 1.965
