7 An Electrical Study of Ion Transport in Cellulose Acetate 1
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M. A. CHAUDRY and P. MEARES Chemistry Department, University of Aberdeen, Scotland
Although cellulose acetate is not inherently a polyelectrolyte there are reports which indicate that it contains a low concentration of weak acid, presumably carboxylic, groups (1). Water absorbed by cellulose acetate membranes might be preferentially located, to some extent, in the region of these ionogenic groups and so assist in their dissociation. When ions permeate through cellulose acetate their transport pathways will tend to follow the regions where water is most concentrated. Thus they will meet and interact with the dissociated, fixed carboxylate ions. The concentrations of ions absorbed from salt solutions by swollen cellulose acetate are small for reasons connected with the low dielectric constant of the latter (2). The electro-chemical potentials of ions undergoing transport may therefore be influenced significantly by the presence of the fixed charges. Such influences are familiar with normal ion-exchange membranes. Because such behaviour would affect the performance of cellulose acetate membranes in desalination, it was studied twelve years ago by one of the authors using methods similar to those described here. The results were not widely publicized at that time (3). The work has now been repeated in greater detail and the earlier findings confirmed. This new work is reported here. In the intervening period other workers have referred to the effect of ion-exchange capacity of cellulose acetate on its membrane properties but their studies have been carried out differently from ours (4). O u t l i n e of Experimental Procedures We seek to determine an e f f e c t i v e fixed-charge d e n s i t y which i n f l u e n c e s i o n uptake and t r a n s p o r t . This may be d i f f e r e n t from an a n a l y t i c a l determination of t o t a l carboxyl content because some groups may not be i n swollen regions of the polymer and so may not 1
Current address: Chasma Nuclear Power Project, Pakistan Atomic Energy Commission, P.O. Box No. 1133, Islamabad, Pakistan. 0097-6156/81/0153-0101$05.00/0 © 1981 American Chemical Society
SYNTHETIC
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102
MEMBRANES:
DESALINATION
be exposed to the i o n f l u x e s . Three types of e l e c t r o c h e m i c a l measurements are r e q u i r e d i n our procedure. They are: the time course of the decrease i n r e s i s t a n c e of a membrane, p r e v i o u s l y soaked i n water or a very d i l u t e s a l t s o l u t i o n at a c o n t r o l l e d pH, a f t e r immersion i n a more concentrated s a l t s o l u t i o n (5); the membrane conductance at e q u i l i b r i u m i n that s o l u t i o n ; membrane c o n c e n t r a t i o n p o t e n t i a l s measured with the membrane interposed between a s e r i e s of s o l u t i o n s of the same s a l t over a range of concentrations. A l l measurements have been made on homogeneous membranes of Eastman Kodak 398-3 c e l l u l o s e acetate (6). The membranes were cast on g l a s s p l a t e s and evaporated slowly to dryness from 2% w/v s o l u t i o n i n pure acetone i n a c o n t r o l l e d atmosphere. The membranes were c a r e f u l l y outgassed under vacuum at 40°C before annealing i n water f o r 30 minutes at 80°C during which they became detached from t h e i r c a s t i n g p l a t e s . The membranes, of thickness u s u a l l y about 40 urn, were mounted i n a Perspex c e l l i n which a l l measurements were c a r r i e d out. The membrane faces were not obstructed by supports as zero pressure d i f f e r e n c e was maintained i n the c e l l . A.C. conductances at 1400 Hz were measured with platinum d i s c e l e c t r o d e s p a r a l l e l to the membrane and of area 7 cm , equal to that of the membrane. P o t e n t i a l s were measured w i t h r e v e r s i b l e Ag/AgCl e l e c t r o d e s . Large volumes of s o l u t i o n s , c i r c u l a t i n g through e x t e r n a l thermostatted r e s e r v o i r s were used. The e n t i r e set up was housed i n an a i r thermostat and the h a l f - c e l l s were each s t i r r e d by small motor-driven Perspex h e l i c e s . 2
A n a l y s i s of Experimental Data Provided one may n e g l e c t the small osmotic shrinkage that occurs when a membrane p r e v i o u s l y swollen i n a very d i l u t e s o l u t i o n i s t r a n s f e r r e d to a somewhat more concentrated s o l u t i o n , and provided no exchange of counterion-type occurs (by prec o n d i t i o n i n g i n a 10~4 M s a l t s o l u t i o n r a t h e r than i n water, a hydrogen ion/metal c a t i o n exchange was prevented from i n t e r f e r i n g with the r e s u l t s ) the a b s o r p t i o n of s a l t by the membrane w i l l follow Fickian d i f f u s i o n k i n e t i c s . The molar c o n c e n t r a t i o n c of s a l t at a plane d i s t a n t x from one face and time t i s given by
~ c
=
1
"~ 71
^ (i n=0^
\ n
s i n [ ( 2 n + 1) T T X / £ ] exp {-[(2n + 1 ) T T / £ ] Dt} 2
n
(1)
U
oo
where c^ i s the c o n c e n t r a t i o n everywhere i n the membrane when t=°°. I i s the membrane thickness and D the d i f f u s i o n c o e f f i c i e n t of the s a l t i n the membrane. When t exceeds a few minutes only the f i r s t term i n the summation i s important and equation 1 may be reduced to c
t
=
- Q sin
(TT
x/Z)]
(2)
7.
CHAUDRY AND ME ARES
where Q i s defined
Ion
Transport
in
Cellulose
Acetate
by
Q = £exp ( - TT2 Dt/S ) 2
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103
(3)
While s a l t i s e n t e r i n g the membrane i t s e l e c t r i c a l r e s i s t a n c e f a l l s progressively. I f the equivalent conductance A of the s a l t i n the membrane may be regarded as constant, which i s c o n s i s t e n t with the e q u i l i b r i u m conductance data to be discussed l a t e r , i n t e g r a t i o n of the l o c a l r e s i s t a n c e across the thickness of the membrane leads to K
-K
00
o
1
L *
(4) \(1
-
Q ) J —> are the membrane conductances at times 0, t
where K , K and K o t . and respectively. To evaluate D from experimental data a t a b l e was prepared of the r i g h t s i d e of equation 4 at s e l e c t e d values of Q over the range 0.7 > Q > 0.0005. From the experimental p l o t of the l e f t s i d e of equation 4 versus t a set of values of t can be read o f f at the s e l e c t e d values of Q by u s i n g the t a b l e . Equation 3 shows that a p l o t of l o g Q versus t should be a s t r a i g h t l i n e of slope S and i n t e r c e p t 0.105 on the l o g Q a x i s . D then f o l l o w s from 00
00
D =
-2.303 S (£/TT)
2
(5)
Figure 1 shows a t y p i c a l p l o t . The curvature at e a r l y times e x i s t s because higher terms i n the summation of equation 1 cannot then be neglected. Assuming that the s a l t i s d i s s o c i a t e d w i t h i n the membrane, D i s r e l a t e d to the i n d i v i d u a l i o n i c conductances A and A__ by +
RTv „2 F v v_ +
x
V (A +A ) +
(6)
where v and v_ are the s t o c h i o m e t r i c numbers of moles of c a t i o n s and anions per mole of s a l t and v i s t h e i r sum. If the membrane has c a t i o n exchange p r o p e r t i e s the t r a n s p o r t numbers t and t_ w i l l be f u n c t i o n s of c o n c e n t r a t i o n . In f a c t t w i l l r i s e sharply at low c o n c e n t r a t i o n s . At high concentrations the i o n exchange p r o p e r t i e s become swamped and l i m i t i n g values of t r a n s p o r t numbers t (£) and t_(£) are approached such that +
+
+
R
D =
T
V
A t U)
2
F
+
t_(*)
(7)
v v_ +
The molar d i s t r i b u t i o n c o e f f i c i e n t X
of s a l t between the s . . membrane and a s o l u t i o n of molar c o n c e n t r a t i o n c i s defined as the value of the r a t i o c /c at high c o n c e n t r a t i o n when i o n exchange e f f e c t s are swampecL A s t r a i g h t f o r w a r d c o n s i d e r a t i o n of the e q u i l i b r i u m conductance of the membrane leads to the r e l a t i o n
104
SYNTHETIC MEMBRANES: DESALINATION
K
RTv F
°°
v v_
A
s
+
where
d i v i d e d by c i s to be evaluated a t high c o n c e n t r a t i o n . To make f u r t h e r progress t ( & ) and t_(&) must be determined. Membrane p o t e n t i a l s can be used f o r t h i s purpose. The p o t e n t i a l d i f f e r e n c e AE between a p a i r of a n i o n - r e v e r s i b l e e l e c t r o d e s immersed i n s o l u t i o n s of m o l a l i t i e s m^ and m^ bathing opposite sides of the membrane i s given by
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+
m
2
(9) m
l provided, as we have confirmed experimentally, the e l e c t r o - o s m o t i c t r a n s p o r t of water i s n e g l i g i b l e . y i s the mean molal a c t i v i t y c o e f f i c i e n t of the s a l t . Membrane p o t e n t i a l s were measured across a number of contiguous small c o n c e n t r a t i o n i n t e r v a l s i n order to b u i l d up a curve of AE versus &n(y m) r e l a t i v e to a s i n g l e reference c o n c e n t r a t i o n by using "the now w e l l - e s t a b l i s h e d a d d i t i v i t y r u l e (7,8). Some measurements were made over wider c o n c e n t r a t i o n i n t e r v a l s to check that a d d i t i v i t y held f o r each system s t u d i e d . The AE versus In ( y m) p l o t s were gentle smooth curves as shown i n Figure 2. They were d i f f e r e n t i a t e d at any c o n c e n t r a t i o n of i n t e r e s t by f i t t i n g a second order polynomial to the curve i n the r e g i o n of that c o n c e n t r a t i o n and d i f f e r e n t i a t i n g the polynomial. The d e r i v a t i v e dE/d £n ( y m) gives (- v R T / v _ F ) t . Hence p l o t s of t versus m were constructed. To estimate the l i m i t i n g value t ( & ) and to introduce the molal f i x e d charge c o n c e n t r a t i o n X, expressed i n e q u i v a l e n t s of u n i v a l e n t f i x e d anions per kg of water sorbed by the membrane, we have t r e a t e d the i o n concentrations i n the membrane as being governed by a Donnan d i s t r i b u t i o n . If m and m_ are the m o l a l i t i e s of c a t i o n s and anions r e s p e c t i v e l y i n the membrane, e l e c t r o n e u t r a l i t y r e q u i r e s that +
+
+
+
+
+
+
+
z
+
m
= X + z_ m _
+
(10)
where z and z_ are the charge numbers ( i . e . both are p o s i t i v e numbers). The Donnan d i s t r i b u t i o n leads to +
- / X + z_m_
\ +
v V
m
= X m
~ _\
z
+
)
m
V
v v ~)
(v +
(11)
~
where X i s Y / y and y i s the mean molal a c t i v i t y c o e f f i c i e n t of the s a l t i n the membrane. I t i s convenient to note here that a l l the s a l t s s t u d i e d had u n i v a l e n t anions; hence we may s e t z_ = v = 1 and v_ = z . Equation 11 then reduces to +
+
+
+
+
Ion Transport
in Cellulose
Acetate
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CHAUDRY AND M E ARES
In (r ± m)
Figure 2.
Membrane potential E vs. In (y±m) relative to 0.01M KCl at
25°C
SYNTHETIC MEMBRANES: DESALINATION
106
V
m
(X + in ) = (v_ A m ) (12) m The high c o n c e n t r a t i o n l i m i t of i n t e r e s t i s reached when X 1 the equation e q u i v a l e n t to equation 15 i s of order higher than q u a d r a t i c , a cubic when v_ = 2 and a q u a r t i c when v_ = 3. The s o l u t i o n of these equations, though p o s s i b l e , does not lead to a value of X of acceptable p r e c i s i o n . A l t e r n a t i v e schemes f o r a n a l y z i n g the data on 2:1 and 3:1 s a l t s have been devised and w i l l be discussed i n a l a t e r p u b l i c a t i o n . m
Results The r e s u l t s obtained with NaCl at 25°C and with KC1 at 25°, 35° and 45°C i n Eastman Kodak 398-3 c e l l u l o s e acetate are l i s t e d i n Table I. When examining the data i t should be remembered that the f i x e d charge c a p a c i t y measured here i s that e f f e c t i v e i n e l e c t r o - k i n e t i c p r o p e r t i e s of the membrane; i t i s not a q u a n t i t y of a n a l y t i c a l chemistry. Nevertheless, because NaCl and KC1 are very s i m i l a r i n t h e i r e l e c t r o c h e m i c a l p r o p e r t i e s , one would expect the apparent number of moles of f i x e d charges per u n i t mass of dry
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SYNTHETIC MEMBRANES: DESALINATION
CHAUDRY AND MEARES
7.
Ion
Transport
polymer, M, to be a constant. 0.1m equiv kg" 1 .
in Cellulose
Acetate
109
The v a l u e found here i s 0.74
±
Table I. E l e c t r o c h e m i c a l l y measured data on c e l l u l o s e acetate
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Property
S a l t and NaCl, 25°
X/m equiv (kg
H^)"
1
KC1,
25°
Temperature KC1,
35°
KC1,
45°
5.51
5.38
6.71
5.61
0.737
0.720
0.836
0.654
X (molal) m
0.264
0.207
0.236
0.207
X
0.0404
0.0318
0.0335
0.0276
M/m equiv (kg CA)
(molar)
g
D/10"
1 4
2
m s
_ 1
1
2.24
2.90
3.44
5.36
2 -1 m s
1.81
2.37
2.73
4.25
- l 4 2 -1 D_/10 m s
3.21
3.64
4.64
7.34
n
7 1
D /10 +
n
/ i n
-14
On account of the r e l a t i v e l y low water r e g a i n of c e l l u l o s e acetate, the molal c o n c e n t r a t i o n of i o n i c groups i n the swollen m a t e r i a l exceeds 5mmolal. This i s comparable to the c o n c e n t r a t i o n of 300 ppm sodium c h l o r i d e , a t y p i c a l reverse osmosis product s o l u t i o n . Our homogeneous membranes are b e l i e v e d to be very s i m i l a r to the a c t i v e l a y e r of an asymmetric membrane as developed by Loeb and S o u r i r a j a n . I t i s evident t h e r e f o r e that the c o n c e n t r a t i o n of f i x e d charges i n the membrane i s s u f f i c i e n t to e x e r c i s e a s i g n i f i c a n t Donnan e x c l u s i o n of co-ions on the downstream side of the membranes i n a reverse osmosis plant. Lonsdale (1) quoted 0.009% by weight of carboxyl groups from chemical a n a l y s i s . T h i s i s e q u i v a l e n t to a value of M of 2 m e q u i v k g ~ l , almost three times our v a l u e . This suggests that only about one t h i r d of the carboxyl groups d e t e c t a b l e by a n a l y s i s are e f f e c t i v e i n i n f l u e n c i n g the i o n t r a n s p o r t phenomena. The value of X found here appears to agree w e l l with the values 5.0 and 2.3 mequiv dm"3 absorbed water found by Demisch and Pusch (4) by a n a l y t i c a l and e l e c t r o - c h e m i c a l measurements r e s p e c t i v e l y i n c e l l u l o s e acetate from a d i f f e r e n t manufacturer. The agreement i s deceptive however because t h e i r value i s based on the t o t a l water held i n an asymmetric membrane. A value of M estimated from t h e i r data i s almost ten times our M. I t may be noted that t h e i r e l e c t r o c h e m i c a l method and t h e i r assumptions are q u i t e d i f f e r e n t from ours. The most dubious assumption i n our work l i e s i n the use of
SYNTHETIC MEMBRANES: DESALINATION
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110
the Donnan e q u i l i b r i u m and the i m p l i c i t choice of an i d e a l 1 molal s o l u t i o n as the standard s t a t e f o r s a l t i n the s o l u t i o n and i n the swollen membrane. The more h i g h l y c l u s t e r e d i n the neighbourhood of the ions i s the water sorbed by the polymer the b e t t e r founded i s t h i s assumption. There i s good evidence from water s o r p t i o n isotherms and water transport data i n favour of such c l u s t e r i n g i n c e l l u l o s e acetate ( 9 ) . The f a c t that X f o r both s a l t s l i e s i n the range 0.20-0.25 shows that water i n ?he membrane i s a l e s s e f f e c t i v e solvent f o r ions than i s bulk water i . e . the l o w - d i e l e c t r i c - c o n s t a n t matrix polymer l i e s w e l l w i t h i n the range of the e l e c t r o s t a t i c f i e l d s around the i o n s . Our value of X , the molar d i s t r i b u t i o n c o e f f i c i e n t of sodium c h l o r i d e between polymer and s o l u t i o n , i s i n good agreement with values obtained by d i r e c t measurement (1,5,10, 11,12). This i s f u r t h e r evidence i n favour of our t h e o r i e s and assumptions. The d i f f u s i o n c o e f f i c i e n t s of potassium and sodium c h l o r i d e s i n the membrane we have found to be independent of s o l u t i o n c o n c e n t r a t i o n w i t h i n experimental e r r o r . The value of sodium c h l o r i d e agrees w e l l with those found by others bearing i n mind the d i f f e r e n c e s i n the polymer and i n the membrane c a s t i n g procedures (5,13). J u s t as i n f r e e aqueous s o l u t i o n , K i s more mobile than N a but i n the membrane K i s l e s s mobile than C I " whereas i n water t h e i r m o b i l i t i e s are equal. Perhaps t h i s i n d i c a t e s that the degrees of h y d r a t i o n of K and C l ~ are modified i n the membrane to d i f f e r e n t extents. Our data a t three temperatures on KC1 do not permit a c t i v a t i o n energies to be evaluated w i t h p r e c i s i o n . C l e a r l y the a c t i v a t i o n energy f o r t r a n s p o r t i n the polymer i s c o n s i d e r a b l y l a r g e r than i t i s i n f r e e s o l u t i o n and seems l a r g e r f o r CI" than for K . In c o n c l u s i o n , i t can be claimed that a combination of k i n e t i c and e q u i l i b r i u m conductance and membrane p o t e n t i a l measurements provides a powerful method f o r i n v e s t i g a t i n g the permselective p r o p e r t i e s of membranes of low f i x e d charge d e n s i t y . Such methods should be a p p l i c a b l e a l s o to other polymers u s e f u l i n h y p e r f i l t r a t i o n i f they can be prepared i n the form of homogeneous membranes. g
+
+
+
+
+
Literature Cited
1. 2. 3. 4.
Lonsdale, H.K. in Merten, U. Ed. "Desalination by Reverse Osmosis"; M.I.T. Press: Cambridge, Mass., 1966; p.93-160. Glueckauf, E. Desalination, 1976, 18, 155. Craig, J.B.; Meares, P.; Webster, J . "Physico-chemical studies on semi-permeable membranes"; Final report on EMR 1799, United Kingdom Atomic Energy Authority: Harwell, 1968. Demisch, H.-U.; Pusch, W. J . Electrochem. Soc., 1976, 123, 370.
7.
5. 6.
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7. 8. 9. 10. 11. 12. 13.
CHAUDRY AND ME ARES
Ion Transport
in Cellulose
Acetate
111
Saltonstall, C.W.; King, W.M.; Hoernshemeyer, D.L. Desalination, 1968, 4, 309. Meares, P.; Craig, J.B.; Webster, J . in Sherwood, J.N.; Chadwick, A.V.; Muir, W.M.; Swinton, F . L . , Ed. "Diffusion Processes"; Gordon & Breach: London, 1971; Vol. 1, p.609. Krämer, H.; Meares, P. Biophys. J., 1969, 9, 1006. Foley, T.; Meares, P. J . Chem. Soc. Faraday Trans. I, 1976, 72, 1105. Williams, J . L . ; Hopfenberg, H.B.; Stannett, V. J . Macromol. Sci.-Phys. (B), 1969, 3, 711. Lonsdale, H.K.; Merten, U.; Riley, R.L. J. Appl. Polymer Sci., 1965, 9, 1341. Thomas, C.R.; Barker, R.E. J . Appl. Polymer Sci., 1963, 7, 1933. Heyde, M.E.; Peters, C.R.; Anderson, J . E . J . Colloid Interf. Sci., 1975, 50, 467. Kimura, S. Proc. Int. Symp. Fresh Water from Sea, 4th, 1973, 4, 204.
RECEIVED December 4, 1980.
