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Electroosmotic transport of alcohol-water mixtures through ion-exchange membranes
Journal of Membrane Science, 5 (1979) 51-61 o Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
51
ELECTROOSMOTIC TRANSPORT OF ALCOHOL-WATER MIXTURES THROUGH ION-EXCHANGE MEMBRANES II. STUDIES ON THE ZEOKARB 225/METHANOL-WATER SYSTEM
RAJ KUMAR*
Chemistry Department,
Gorakhpur University, Gorakhpur-273001
(India)
(Received July 18, 1978; accepted in revised form December 11, 1978)
Summary Electroosmotic and hydrodynamic transport of methanol and methanol-water mixtures through Zeokarb 226 membranes in Na+, Ba++, and Al+* forms have been investigated. Electrical conductance of the membrane equilibrated with the permeant has also been measured. The membranes used were compressed plugs of ion-exchange resins. The data have been analysed by means of phenomenological theory of irreversible thermodynamics. An attempt has been made to explain the composition dependence of the phenomenological coefficients in terms of the nature of the membrane and permeant. A simple unambiguous method for the estimation of the average pore radius of membranes has been suggested and used to ascertain the average pore radii of the membranes under investigation.
Introduction
The electroosmotic effects across ion-exchange membranes are of considerable interest from the standpoint of electrodialysis [l] and biological transport [ 2-4). Electroosmosis is a typical non-equilibrium phenomenon which has been extensively investigated [ 5-141 in the last few years from the viewpoint of the phenomenological theory of irreversible thermodynamics. Recently it has been reported [15,16] that the electroosmosis of methanolwater mixtures through a Zeokarb 226 (Hf form) membrane exhibits an unusual behaviour of sign reversal. In the present communication, measurements of electroosmotic transport of methanol and methanol-water mixtures across membranes composed of Zeokarb 225 particles in various ionic forms are reported. The data have been analysed with the phenomenological theory of non-equilibrium thermodynamics. A simple method for the estimation of the equivalent pore radius of the membranes based on hydrodynamic permeability and conductance measurements has been suggested. *present ad&e=:
Chemistry Division, Ahmedahad Textile Industry’s Research
Ahmedabad-380015,
India.
Aslsociation,
52
Experimental Zeokarb 225 (Na+ form) obtained from the Permutit Company, London, was used. It had an exchange capacity of 4.8 meq/g dry resin and a moisture content of 45.5% by weight. B.D.H. (A.R. Grade) methanol was used without further purification. Ordinary distilled water was double distilled with alkaline KMn04 before use. The specific conductivity of the water used was of the order of 10e6 ohm-’ cm-‘. The membrane was prepared from ion-exchanger particles with the help of mechanical compression. A certain quantity of the ion-exchanger was taken in a Pyrex glass tube 30 cm long with a constriction in the middle. The ion exchange membrane was prepared by compressing the ion exchanger mechanically at the site of constriction. The membrane was converted into Ba++ and Al +++ forms by equilibrating it with molar barium chloride and aluminium chloride solutions, respectively. It was then washed with conductivity water to remove excess electrolyte present. The membrane was equilibrated with the experimental liquid for over 24 h before use. The experimental solution was renewed to insure that its composition remained the same as that before equilibration. The experimental set up described earlier [ 171 was used for hydrodynamic and electroosmotic permeability measurements. A known pressure difference was imposed across the membrane by maintaining a constant difference in the level of the experimental liquid on the two sides of the membrane. Constancy of applied pressure difference was ensured by using a pressure head. The volumetric flux was estimated by following the movement of the liquid meniscus in a horizontal graduated capillary tube of known cross-sectional area (1.420 X 10e2 cm’). For electroosmotic flux measurements, potential differences of up to 500 volts were applied from an electronically operated power supply (Toshniwal Co., Pvt. Ltd., India) through coiled platinum electrodes placed in contact with the two faces of the membrane, and the water flux was measured as described above. Current flowing through the system never exceeded 3 mA. No detectable polarization at the electrodes was observed in the present investigation. The conductance of the equilibrated membrane and the specific conductivity of the experimental liquid were measured with a Toshniwal conductivity bridge (India) at 50 cycles/s. The relative viscosity of methanol and methanol-water mixtures was measured with a modified Tuon-Fuoss viscometer described elsewhere [18]. All the measurements were carried out in an air thermostat maintained at 30 ? 0.5”C Results and discussion The electroosmotic flux of methanol and methanol-water mixtures across Zeokarb 225 membranes occurs towards the cathode and varies non-linearly with the applied potential difference. The following second order phenom-
53
enological
relationship
fits the experimental
J”=L($)+L,, ($)
+%L122
data:
(“,“)’
(1)
where Jv is the volume flux, AP and A$ are the pressure difference and potential difference across the membrane, respectively, and the L’s are the phenomenological coefficients. When AP alone is applied,
Plots of (J,)A+=o against AP always yielded straight lines, A typical plot is shown in Fig. 1. The phenomenological coefficients L,, were estimated from the slopes of these straight lines. When AP = 0, eqn. (1) reduces to: (Jv)Af’=O
=
L12 (",")+%L**2($)2
The validity of eqn. (3) has been tested in Figs. 2-4 in which (J,)Ap=o /A# has been plotted against A$. All plots are straight lines as required by eqn. (3). The phenomenological coefficients L 12 and LIZ2 were estimated from the intercept and slope, respectively, of these straight lines.
dPx102 (dyn
cm-*)
Fig. 1. Dependence of volume flux on pressure difference for Zeokarb 225 (Na+ form)/ methanol-water system. 0, xw = 0.0; X, xw = 0.1; A,xw = 0.2; 0, xw = 0.3; a, xw = 0.4; n, xw = 0.5. xw = the mole fraction of water in the methanol-water mixture.
Fig. 2. Tests of the validity of eqn. (3) for Zeokarb 225 (Na + form)/methanol-water 0, xw = 0.0; x, xw = 0.1; A, xw = 0.2; 0, xw = 0.3; a, xw = 0.4; ., xw = 0.5.
system.
54
r___-e _---
7
_ -&--L--A-_---_* ___
-,1 mE
4.0-
.
_L_r_
” 8 x : >
213ID
3
P
3
Fig. 3. Tests of the validity of eqn. (3) for Zeokarb 225 (Ba++ form)/methanol-water system. 0, xw = 0.0; X, xw = 0.1; A, x w =0.2;.,xw =0.3;a,xw =0.4;m, xw =0.5. Fig, 4. Tests of the validity of eqn. (3) for Zeokarb 225 (Al+++ form)/methanol-water system. 0.x~ =O.O;X,xw =O.l;A, xw =0.2;~,xw=O.3; *, xw =0.4.
The current flowing through the system always varied linearly with the applied potential difference in accordance with Ohm’s law. The phenomenological equation
I=Lzl
($)
+L,,
(9)
holds, since from eqn. (4), =
L,, IT
(5)
Typical current-voltage plots for Zeokarb 225 (Na+ form)/methanol-water system are given in Fig. 5. The phenomenological coefficients Lz2 were estimated from the slope of these lines. The transport coefficients Lll /T, LIZ/T, and Lzz /T estimated in the above manner have been compared with the values obtained by Tombalakian [5] and Meares [6] in Table 1. It is clear from the table that the LIZ’s are of comparable magnitude, whereas the L 11 and Lz2 values are significantly different. The difference in the values of LI1 and Lz2 is due to the fact that the membranes in the present investigation were heteroporous and non-electrolyte solutions were used as the permeant. The occurrence of electroosmosis is ascribed either to (i) the existence of an electrical double layer at the membrane-permeant interface, or (ii) an uneven distribution of ions in the solution contained within the pores of the membrane.
55
The average pore radius of the membrane under consideration is of the order of 10e4 cm which is much greater than the double layer thickness. Hence, for the present case the double layer model is adequate. The charge distribution at the Zeokarb 225 membrane/methanol-water interface would be as shown in Fig. 6 since it is known that the hydroxyl TABLE 1 Comparison of permeability coefficients System
L,, IT
(cm” s-’
_ PSSA membrane [ 51, H+ 0.1 M solution NH; K+ Na+
4.5 2.5 2.4 1.6
dyn-’
x 1o-‘J X lo-” X lo-I3 x lo-l3
Na+ Baf+ NC++
L,,IT
(cm” s-’
V-' )
LIT
(ohm-’
)
2.1 x 10-3 0.82 x 1o-3 0.75 x 1o-9 0.63 x 1O-3
0.8 x lo+ 0.8 x 1o-6 0.8 x lo-” 0.85 x 1O-6 4.77 x 10-h
Zeokarb 315 membrane [6], 0.05 M NaCl Zeokarb 225 (This work)
)
1.25 x lo-+ 0.94 x 1o-6 0.69 x lo+
1.10 x 1o-6 2.00 x 1om6 2.70 x 1O-6
13.65 x 1O-6 5.20 x 10-e 6.60 x 1o-6
1.59-
--a ctl,oti;
<
1.00 -
(c>cki30-
+(IIl
? x
CH~OH;
0 II
@--
3 5.
0.50
&J I I
I -
0+
the solof the ion exchanger
Represent
countericm
Fig. 5. Current-voltage characteristics for Zeokarb 225 (Na+ forrn)/methanol-water CJ,xw = 0.0; X, xw = 0.1; A, xw = 0.2; b,xw = 0.3;A, Xw = 0.4;m, Xw = 0.5.
system.
Fig. 6. Structure of the electrical double layer at the Zeokarb 225 membranelmethanolwater interface during electroosmosis (schematic).
56
protons of water and alcohols the equations: c++-ij:
.....
..I
H
_
ij:
A H
-6:
+
CHy-0:
&Ha .
H-6:
Ii
+
L
undergo
exchange
according
to
wj--i-jr
tit+
A H-6:
intermolecular
H+ +
A
:a-
A
f
Zeokarb 225 is a styrene divinyl benzene copolymer containing -SOi Na’ dissociable groups. When equilibrated with methanol and methanol-water mixtures, the ions produced by the dissociation of the ion exchanger are solvated and separated from the membrane phase by oriented methanol and water dipoles. They constitute the fixed part (OHP) of the electrical double layer. The intervention of solvent dipoles reduces the attractive force between positively charged ions and the membrane matrix, as a result of which negative ions in the solution experience an attractive force towards the positively charged OHP. This leads to an accumulation of negative ions in the neighbourhood of OHP as shown in Fig. 6. The diffusively dispersed part of the electrical double layer carries an excess of cations as a result of which electroosmosis occurs toward the negative electrode in conformity with the actual observations. The ions in the diffuse part of the electrical double layer are the charge carriers for the transport of electric current. The chemical processes occurring at the inert platinum electrodes during current flow may be written as [ 19 1: Cathode H,O + e
+%H,+OH-
CH,OH,+ + OH-
--f CH,OH + Hz0
H30+ + OH-
+ 2H,O
Membrane ,
Anode %H,O
,
CH,OHf H30+
CH,OOH
+ H+
+ H+
+
H+ + ‘/SO*
+
CH,OH
+
H,O
In Fig. 7, L, 1 has been plotted against the mole fraction of water, xw , in methanol-water mixtures for various ionic forms of the ion-exchange membrane. It is evident that L1i decreases both with the water content in the mixture and with the increase in valence of the counterion of the ion exchanger. For laminar flow through a membrane containing n parallel capillary channels, it can be shown that [20]
(6) where F = the average pore radius of the membrane; 77= the coefficient viscosity of the permeant; and I= the thickness of the membrane. Comparison of eqn. (6) with eqn. (2) leads to
of
57 L11 ---=-
T
nn?
8771
(7)
From eqn. (7), it follows that the decreasing trend of L,, may be due to (i) the increase in r7 and (ii) the decrease in r when xw and the valence of the counterion of the ion exchanger are increased, The data on relative viscosity included in Table 2 clearly show that 71increases with xw . The increased molecular interaction in hydrogen-bonded systems decreases the freedom of molecular motion and therefore tends to increase viscosity [ 211. A decrease in the value of F would occur due to increase in swelling of the ion-exchange membrane in different environments. It is known that [22] polar solvents are better swelling agents than non-polar solvents because they interact more strongly with the ions and polar groups in the resin. Hence, swelling of the resin in water (E = 81, M = 1.84 Debye) would be stronger than in pure methanol (e = 32, P = 1.68 Debye). It should be noted that in weakly cross-linked resins, which contain large amounts of free solvent, the number of counterions in the resin is, as a rule, the most important factor [ 221. This number is cut in half when univalent counterions are replaced by divalent ones. Ionic size and solvation effects are relatively unimportant and, hence, resins swell less when the valence of the counterion is high. However, in moderately and highly cross-linked resins, in which most of the solvent is present in the form of solvation shells, the size and solvation tendency of the counterions are most important [ 221. The resin expands when one counter-ion is replaced by another one which, in its solvated state, occupies more volume.
Fig. 7. Dependence of L, 1 on the mole fraction of water, xw for Zeocarb 225. 0, Na’ form, A Ba++ form; l, ti+* form. Fig. 8. Dependence of L, on the mole fraction of water, XW, for Zeocarb 225. 0, Na+ form; A, Ba++ form; a, @++ form.
59
F= &3qk
(11)
L1 IL,, I
It should be noted that methods for the estimation of averagepore radius reported earlier [25-271 require an unambiguous determination of zeta potential. This is not, in fact, possible because of the complicating effects [ 281 of surface conductivity and polarization during electroosmosis and the variation of rl and e within the electrical double layer. The average pore radii of the membrane under investigation in various ionic forms have been included in Fig. 10. Experimentally determined values of 9 and k of the permeating
L 0
I
01
I 0.2
I 0.3
I OA
,
I
0.5
0
0.1
I 0.2
I
0.3
I OA
I a.5
XW
XVI
Fig. 9. Dependence of L,, on the mole fraction of water, xw , for Zeocarb 225. 0, Na+ form; A, Ba++ form; l, Al+++ form. Fig. 10. Dependence of ; on the mole fraction of water,xW , for Zeocarb 225. 0,
A7Ba++ form; l, Al+++ form. TABLE 2 Specific conductivity Mole fraction of water
xw 0.0 0.1 0.2 0.3 0.4 0.5
and relative viscosity of methanol-water
Relative viscosity
v/s, *
Specific conductivity kX 106 (ohm-’ cm-’ )
1.000 1.232 1.472 1.761 1.947 2.382
2.219 2.280 2.375 2.451 2.637 2.801
*Q, is the viscosity of pure methanol.
mixtures at 30°C ~~__
Na+ form,
60 liquids
used
decreases
are given in Table 2. The results indicate that F in mole fraction of water and valence of the counter-
in the c&-ulation
with increase
ion of the ion exchanger.The dependence isconsistent withtheswelling cfmcteristicsof the membranein different environments discussed in the preceeding
section.
Acknowledgements The author is grateful to Professor R.P. Rastogi, Head, Chemistry Department, University of Gorakhpur, Gorakhpur, for providing facilities. Thanks are also due to the University Grants Commission, India for financial assistance.
References 1 R.E. Kesting, Synthetic Polymeric Membranes, McGraw-Hill, New York, 1974. 2 H.N. Christensen, Biological Transport, W.A. Benjamin, New York, 1962. 3 R.M. Friedenberg, The Electrostatics of Biological Cell Membranes, North Holland Publishing Co., Amsterdam, 1967. 4 T. Teorell, Transport phenomena in membranes, Discuss. Faraday Sot., 21 (1956) 9. 5 A. S. Tombalakian, Phenomenological coefficients for volume flow across an ionexchange membrane, J. Phys. Chem., 72 (1968) 1566. 6 D. Mackay and P. Meares, The electrical conductivity and electro-osmotic permeability of a cation-exchange resin, Trans. Faraday Sot., 55 (1959) 1221. 7 0. Kedem and A. Katchalsky, Permeability of composite membranes, Parts I, II, and IIL Trans. Faraday Sot., 59 (1963) 1918; 59 (1963) 1931; 59 (1963) 1941. 8 A. J. Staverman, Non-equilibrium thermodynamics of membrane processes, Trans. Faraday Sot., 48 (1952) 176. 9 H.F. Holmes, C.S. Shoup and C.H. Secoy, Electrokinetic phenomena at the thorium oxide-aqueous solution interface, J. Phys. Chem., 69 (1965) 3148. 10 R.C. Srivastava and M.G. Abraham, Non-equilibrium thermodynamics of electroosmosis of liquid mixtures, J. Chem. Sot., Faraday Transactions I, 72 (1976) 2631; J. Colloid Interface Sci., 57 (1976) 58. 11 R.P. Rastogi, K. Singh, J. Singh and Raj Kumar, Electroosmosis of aqueous solutions of the chlorides of sodium, barium and aluminium across Pyrex and Zeokarb 226 membranes, Ind. J. Chem., 14A (1976) 729. 12 F.A. Morrison and J.F. Osterle, Electrokinetic energy conversion in ultrafine capillaries, J. Chem. Phys., 43 (1965) 2111. 13 J.W. Lorimer, E.I. Boterenbrood and J.J. Hermans, Transport processes in ion-selective membranes, conductivities, transport numbers and electromotive forces, Discuss. Faraday Sot., 21 (1956) 141. 14 Y. Kobatake and H. Fujita, Flows through charged membranes, I; Flip-flop current VS. voltage relation, J. Chem. Phys., 40 (1964) 2212. and J. Singh, Electrokinetic studies on ion-exchange membranes, I: 15 R.P. Transport of non-aqueous and mixed solvents, J. Phys. Chem., 79 (1975) 2574. 16 ~_p. Ratogi and Ram @l&d, Non-linear electroosmotic flux equation, J. PM. Chem.,
&&ogi, K.Singh
81 (1977) 1953. 17 R.P. Rastogi, K. Singh, Raj Kumar and Ram Shabd, Electrokinetic studies on ionexchange membranes, III: Electroosmosis and electrophoresis, J. Membrane Sci., 2 (1977) 317.
61 18 Vishnu and V.P. Misra, Studies on electrolyte-non-electrolyte interactions; viscosity behaviour of alkali halides in aqueous sucrose solutions, Carbohydrate Res., 39 (1977) 35. 19 F. Helfferich, Ion Exchange, McGraw-Hill, New York, 1962, p. 400. 20 H.R. Kruyt, Colloid Science, Elsevier, Amsterdam, 1952. 21 S.N. Vinogradov and R.H. Linnell, Hydrogen Bonding, Van Nostrand Reinhold, London, 1971, p. 277. 22 Ref. 19, pp. 510,103. 23 B.E. Conway, Electrochemical Data, Elsevier, Amsterdam, 1952, p. 132. 24 R.P. Rastogi, Irreversible thermodynamics of electroosmotic effects, J. Sci. Ind. Res., 28 (1969) 284. 25 R.P. Rastogi, K. Singh and S.N. Singh, Membrane characteristics from measurements of electroosmosis, Ind. J. Chem., 6 (1968) 466. 26 N. Lakshiminarayanaiah, On the determination of average pore size of membranes, J. Phys. Chem., 73 (1969) 4428. 27 M.L. Srivastava and Raj Kumar, On the pore size of membranes, Ind. J. Biochem. Biophys., 13 (1976) 182. 28 E. Matjevic, Surface and Colloid Science, Vol. 7, John Wiley and Sons, New York, 1974, pp. 33,181-183.
51
ELECTROOSMOTIC TRANSPORT OF ALCOHOL-WATER MIXTURES THROUGH ION-EXCHANGE MEMBRANES II. STUDIES ON THE ZEOKARB 225/METHANOL-WATER SYSTEM
RAJ KUMAR*
Chemistry Department,
Gorakhpur University, Gorakhpur-273001
(India)
(Received July 18, 1978; accepted in revised form December 11, 1978)
Summary Electroosmotic and hydrodynamic transport of methanol and methanol-water mixtures through Zeokarb 226 membranes in Na+, Ba++, and Al+* forms have been investigated. Electrical conductance of the membrane equilibrated with the permeant has also been measured. The membranes used were compressed plugs of ion-exchange resins. The data have been analysed by means of phenomenological theory of irreversible thermodynamics. An attempt has been made to explain the composition dependence of the phenomenological coefficients in terms of the nature of the membrane and permeant. A simple unambiguous method for the estimation of the average pore radius of membranes has been suggested and used to ascertain the average pore radii of the membranes under investigation.
Introduction
The electroosmotic effects across ion-exchange membranes are of considerable interest from the standpoint of electrodialysis [l] and biological transport [ 2-4). Electroosmosis is a typical non-equilibrium phenomenon which has been extensively investigated [ 5-141 in the last few years from the viewpoint of the phenomenological theory of irreversible thermodynamics. Recently it has been reported [15,16] that the electroosmosis of methanolwater mixtures through a Zeokarb 226 (Hf form) membrane exhibits an unusual behaviour of sign reversal. In the present communication, measurements of electroosmotic transport of methanol and methanol-water mixtures across membranes composed of Zeokarb 225 particles in various ionic forms are reported. The data have been analysed with the phenomenological theory of non-equilibrium thermodynamics. A simple method for the estimation of the equivalent pore radius of the membranes based on hydrodynamic permeability and conductance measurements has been suggested. *present ad&e=:
Chemistry Division, Ahmedahad Textile Industry’s Research
Ahmedabad-380015,
India.
Aslsociation,
52
Experimental Zeokarb 225 (Na+ form) obtained from the Permutit Company, London, was used. It had an exchange capacity of 4.8 meq/g dry resin and a moisture content of 45.5% by weight. B.D.H. (A.R. Grade) methanol was used without further purification. Ordinary distilled water was double distilled with alkaline KMn04 before use. The specific conductivity of the water used was of the order of 10e6 ohm-’ cm-‘. The membrane was prepared from ion-exchanger particles with the help of mechanical compression. A certain quantity of the ion-exchanger was taken in a Pyrex glass tube 30 cm long with a constriction in the middle. The ion exchange membrane was prepared by compressing the ion exchanger mechanically at the site of constriction. The membrane was converted into Ba++ and Al +++ forms by equilibrating it with molar barium chloride and aluminium chloride solutions, respectively. It was then washed with conductivity water to remove excess electrolyte present. The membrane was equilibrated with the experimental liquid for over 24 h before use. The experimental solution was renewed to insure that its composition remained the same as that before equilibration. The experimental set up described earlier [ 171 was used for hydrodynamic and electroosmotic permeability measurements. A known pressure difference was imposed across the membrane by maintaining a constant difference in the level of the experimental liquid on the two sides of the membrane. Constancy of applied pressure difference was ensured by using a pressure head. The volumetric flux was estimated by following the movement of the liquid meniscus in a horizontal graduated capillary tube of known cross-sectional area (1.420 X 10e2 cm’). For electroosmotic flux measurements, potential differences of up to 500 volts were applied from an electronically operated power supply (Toshniwal Co., Pvt. Ltd., India) through coiled platinum electrodes placed in contact with the two faces of the membrane, and the water flux was measured as described above. Current flowing through the system never exceeded 3 mA. No detectable polarization at the electrodes was observed in the present investigation. The conductance of the equilibrated membrane and the specific conductivity of the experimental liquid were measured with a Toshniwal conductivity bridge (India) at 50 cycles/s. The relative viscosity of methanol and methanol-water mixtures was measured with a modified Tuon-Fuoss viscometer described elsewhere [18]. All the measurements were carried out in an air thermostat maintained at 30 ? 0.5”C Results and discussion The electroosmotic flux of methanol and methanol-water mixtures across Zeokarb 225 membranes occurs towards the cathode and varies non-linearly with the applied potential difference. The following second order phenom-
53
enological
relationship
fits the experimental
J”=L($)+L,, ($)
+%L122
data:
(“,“)’
(1)
where Jv is the volume flux, AP and A$ are the pressure difference and potential difference across the membrane, respectively, and the L’s are the phenomenological coefficients. When AP alone is applied,
Plots of (J,)A+=o against AP always yielded straight lines, A typical plot is shown in Fig. 1. The phenomenological coefficients L,, were estimated from the slopes of these straight lines. When AP = 0, eqn. (1) reduces to: (Jv)Af’=O
=
L12 (",")+%L**2($)2
The validity of eqn. (3) has been tested in Figs. 2-4 in which (J,)Ap=o /A# has been plotted against A$. All plots are straight lines as required by eqn. (3). The phenomenological coefficients L 12 and LIZ2 were estimated from the intercept and slope, respectively, of these straight lines.
dPx102 (dyn
cm-*)
Fig. 1. Dependence of volume flux on pressure difference for Zeokarb 225 (Na+ form)/ methanol-water system. 0, xw = 0.0; X, xw = 0.1; A,xw = 0.2; 0, xw = 0.3; a, xw = 0.4; n, xw = 0.5. xw = the mole fraction of water in the methanol-water mixture.
Fig. 2. Tests of the validity of eqn. (3) for Zeokarb 225 (Na + form)/methanol-water 0, xw = 0.0; x, xw = 0.1; A, xw = 0.2; 0, xw = 0.3; a, xw = 0.4; ., xw = 0.5.
system.
54
r___-e _---
7
_ -&--L--A-_---_* ___
-,1 mE
4.0-
.
_L_r_
” 8 x : >
213ID
3
P
3
Fig. 3. Tests of the validity of eqn. (3) for Zeokarb 225 (Ba++ form)/methanol-water system. 0, xw = 0.0; X, xw = 0.1; A, x w =0.2;.,xw =0.3;a,xw =0.4;m, xw =0.5. Fig, 4. Tests of the validity of eqn. (3) for Zeokarb 225 (Al+++ form)/methanol-water system. 0.x~ =O.O;X,xw =O.l;A, xw =0.2;~,xw=O.3; *, xw =0.4.
The current flowing through the system always varied linearly with the applied potential difference in accordance with Ohm’s law. The phenomenological equation
I=Lzl
($)
+L,,
(9)
holds, since from eqn. (4), =
L,, IT
(5)
Typical current-voltage plots for Zeokarb 225 (Na+ form)/methanol-water system are given in Fig. 5. The phenomenological coefficients Lz2 were estimated from the slope of these lines. The transport coefficients Lll /T, LIZ/T, and Lzz /T estimated in the above manner have been compared with the values obtained by Tombalakian [5] and Meares [6] in Table 1. It is clear from the table that the LIZ’s are of comparable magnitude, whereas the L 11 and Lz2 values are significantly different. The difference in the values of LI1 and Lz2 is due to the fact that the membranes in the present investigation were heteroporous and non-electrolyte solutions were used as the permeant. The occurrence of electroosmosis is ascribed either to (i) the existence of an electrical double layer at the membrane-permeant interface, or (ii) an uneven distribution of ions in the solution contained within the pores of the membrane.
55
The average pore radius of the membrane under consideration is of the order of 10e4 cm which is much greater than the double layer thickness. Hence, for the present case the double layer model is adequate. The charge distribution at the Zeokarb 225 membrane/methanol-water interface would be as shown in Fig. 6 since it is known that the hydroxyl TABLE 1 Comparison of permeability coefficients System
L,, IT
(cm” s-’
_ PSSA membrane [ 51, H+ 0.1 M solution NH; K+ Na+
4.5 2.5 2.4 1.6
dyn-’
x 1o-‘J X lo-” X lo-I3 x lo-l3
Na+ Baf+ NC++
L,,IT
(cm” s-’
V-' )
LIT
(ohm-’
)
2.1 x 10-3 0.82 x 1o-3 0.75 x 1o-9 0.63 x 1O-3
0.8 x lo+ 0.8 x 1o-6 0.8 x lo-” 0.85 x 1O-6 4.77 x 10-h
Zeokarb 315 membrane [6], 0.05 M NaCl Zeokarb 225 (This work)
)
1.25 x lo-+ 0.94 x 1o-6 0.69 x lo+
1.10 x 1o-6 2.00 x 1om6 2.70 x 1O-6
13.65 x 1O-6 5.20 x 10-e 6.60 x 1o-6
1.59-
--a ctl,oti;
<
1.00 -
(c>cki30-
+(IIl
? x
CH~OH;
0 II
@--
3 5.
0.50
&J I I
I -
0+
the solof the ion exchanger
Represent
countericm
Fig. 5. Current-voltage characteristics for Zeokarb 225 (Na+ forrn)/methanol-water CJ,xw = 0.0; X, xw = 0.1; A, xw = 0.2; b,xw = 0.3;A, Xw = 0.4;m, Xw = 0.5.
system.
Fig. 6. Structure of the electrical double layer at the Zeokarb 225 membranelmethanolwater interface during electroosmosis (schematic).
56
protons of water and alcohols the equations: c++-ij:
.....
..I
H
_
ij:
A H
-6:
+
CHy-0:
&Ha .
H-6:
Ii
+
L
undergo
exchange
according
to
wj--i-jr
tit+
A H-6:
intermolecular
H+ +
A
:a-
A
f
Zeokarb 225 is a styrene divinyl benzene copolymer containing -SOi Na’ dissociable groups. When equilibrated with methanol and methanol-water mixtures, the ions produced by the dissociation of the ion exchanger are solvated and separated from the membrane phase by oriented methanol and water dipoles. They constitute the fixed part (OHP) of the electrical double layer. The intervention of solvent dipoles reduces the attractive force between positively charged ions and the membrane matrix, as a result of which negative ions in the solution experience an attractive force towards the positively charged OHP. This leads to an accumulation of negative ions in the neighbourhood of OHP as shown in Fig. 6. The diffusively dispersed part of the electrical double layer carries an excess of cations as a result of which electroosmosis occurs toward the negative electrode in conformity with the actual observations. The ions in the diffuse part of the electrical double layer are the charge carriers for the transport of electric current. The chemical processes occurring at the inert platinum electrodes during current flow may be written as [ 19 1: Cathode H,O + e
+%H,+OH-
CH,OH,+ + OH-
--f CH,OH + Hz0
H30+ + OH-
+ 2H,O
Membrane ,
Anode %H,O
,
CH,OHf H30+
CH,OOH
+ H+
+ H+
+
H+ + ‘/SO*
+
CH,OH
+
H,O
In Fig. 7, L, 1 has been plotted against the mole fraction of water, xw , in methanol-water mixtures for various ionic forms of the ion-exchange membrane. It is evident that L1i decreases both with the water content in the mixture and with the increase in valence of the counterion of the ion exchanger. For laminar flow through a membrane containing n parallel capillary channels, it can be shown that [20]
(6) where F = the average pore radius of the membrane; 77= the coefficient viscosity of the permeant; and I= the thickness of the membrane. Comparison of eqn. (6) with eqn. (2) leads to
of
57 L11 ---=-
T
nn?
8771
(7)
From eqn. (7), it follows that the decreasing trend of L,, may be due to (i) the increase in r7 and (ii) the decrease in r when xw and the valence of the counterion of the ion exchanger are increased, The data on relative viscosity included in Table 2 clearly show that 71increases with xw . The increased molecular interaction in hydrogen-bonded systems decreases the freedom of molecular motion and therefore tends to increase viscosity [ 211. A decrease in the value of F would occur due to increase in swelling of the ion-exchange membrane in different environments. It is known that [22] polar solvents are better swelling agents than non-polar solvents because they interact more strongly with the ions and polar groups in the resin. Hence, swelling of the resin in water (E = 81, M = 1.84 Debye) would be stronger than in pure methanol (e = 32, P = 1.68 Debye). It should be noted that in weakly cross-linked resins, which contain large amounts of free solvent, the number of counterions in the resin is, as a rule, the most important factor [ 221. This number is cut in half when univalent counterions are replaced by divalent ones. Ionic size and solvation effects are relatively unimportant and, hence, resins swell less when the valence of the counterion is high. However, in moderately and highly cross-linked resins, in which most of the solvent is present in the form of solvation shells, the size and solvation tendency of the counterions are most important [ 221. The resin expands when one counter-ion is replaced by another one which, in its solvated state, occupies more volume.
Fig. 7. Dependence of L, 1 on the mole fraction of water, xw for Zeocarb 225. 0, Na’ form, A Ba++ form; l, ti+* form. Fig. 8. Dependence of L, on the mole fraction of water, XW, for Zeocarb 225. 0, Na+ form; A, Ba++ form; a, @++ form.
59
F= &3qk
(11)
L1 IL,, I
It should be noted that methods for the estimation of averagepore radius reported earlier [25-271 require an unambiguous determination of zeta potential. This is not, in fact, possible because of the complicating effects [ 281 of surface conductivity and polarization during electroosmosis and the variation of rl and e within the electrical double layer. The average pore radii of the membrane under investigation in various ionic forms have been included in Fig. 10. Experimentally determined values of 9 and k of the permeating
L 0
I
01
I 0.2
I 0.3
I OA
,
I
0.5
0
0.1
I 0.2
I
0.3
I OA
I a.5
XW
XVI
Fig. 9. Dependence of L,, on the mole fraction of water, xw , for Zeocarb 225. 0, Na+ form; A, Ba++ form; l, Al+++ form. Fig. 10. Dependence of ; on the mole fraction of water,xW , for Zeocarb 225. 0,
A7Ba++ form; l, Al+++ form. TABLE 2 Specific conductivity Mole fraction of water
xw 0.0 0.1 0.2 0.3 0.4 0.5
and relative viscosity of methanol-water
Relative viscosity
v/s, *
Specific conductivity kX 106 (ohm-’ cm-’ )
1.000 1.232 1.472 1.761 1.947 2.382
2.219 2.280 2.375 2.451 2.637 2.801
*Q, is the viscosity of pure methanol.
mixtures at 30°C ~~__
Na+ form,
60 liquids
used
decreases
are given in Table 2. The results indicate that F in mole fraction of water and valence of the counter-
in the c&-ulation
with increase
ion of the ion exchanger.The dependence isconsistent withtheswelling cfmcteristicsof the membranein different environments discussed in the preceeding
section.
Acknowledgements The author is grateful to Professor R.P. Rastogi, Head, Chemistry Department, University of Gorakhpur, Gorakhpur, for providing facilities. Thanks are also due to the University Grants Commission, India for financial assistance.
References 1 R.E. Kesting, Synthetic Polymeric Membranes, McGraw-Hill, New York, 1974. 2 H.N. Christensen, Biological Transport, W.A. Benjamin, New York, 1962. 3 R.M. Friedenberg, The Electrostatics of Biological Cell Membranes, North Holland Publishing Co., Amsterdam, 1967. 4 T. Teorell, Transport phenomena in membranes, Discuss. Faraday Sot., 21 (1956) 9. 5 A. S. Tombalakian, Phenomenological coefficients for volume flow across an ionexchange membrane, J. Phys. Chem., 72 (1968) 1566. 6 D. Mackay and P. Meares, The electrical conductivity and electro-osmotic permeability of a cation-exchange resin, Trans. Faraday Sot., 55 (1959) 1221. 7 0. Kedem and A. Katchalsky, Permeability of composite membranes, Parts I, II, and IIL Trans. Faraday Sot., 59 (1963) 1918; 59 (1963) 1931; 59 (1963) 1941. 8 A. J. Staverman, Non-equilibrium thermodynamics of membrane processes, Trans. Faraday Sot., 48 (1952) 176. 9 H.F. Holmes, C.S. Shoup and C.H. Secoy, Electrokinetic phenomena at the thorium oxide-aqueous solution interface, J. Phys. Chem., 69 (1965) 3148. 10 R.C. Srivastava and M.G. Abraham, Non-equilibrium thermodynamics of electroosmosis of liquid mixtures, J. Chem. Sot., Faraday Transactions I, 72 (1976) 2631; J. Colloid Interface Sci., 57 (1976) 58. 11 R.P. Rastogi, K. Singh, J. Singh and Raj Kumar, Electroosmosis of aqueous solutions of the chlorides of sodium, barium and aluminium across Pyrex and Zeokarb 226 membranes, Ind. J. Chem., 14A (1976) 729. 12 F.A. Morrison and J.F. Osterle, Electrokinetic energy conversion in ultrafine capillaries, J. Chem. Phys., 43 (1965) 2111. 13 J.W. Lorimer, E.I. Boterenbrood and J.J. Hermans, Transport processes in ion-selective membranes, conductivities, transport numbers and electromotive forces, Discuss. Faraday Sot., 21 (1956) 141. 14 Y. Kobatake and H. Fujita, Flows through charged membranes, I; Flip-flop current VS. voltage relation, J. Chem. Phys., 40 (1964) 2212. and J. Singh, Electrokinetic studies on ion-exchange membranes, I: 15 R.P. Transport of non-aqueous and mixed solvents, J. Phys. Chem., 79 (1975) 2574. 16 ~_p. Ratogi and Ram @l&d, Non-linear electroosmotic flux equation, J. PM. Chem.,
&&ogi, K.Singh
81 (1977) 1953. 17 R.P. Rastogi, K. Singh, Raj Kumar and Ram Shabd, Electrokinetic studies on ionexchange membranes, III: Electroosmosis and electrophoresis, J. Membrane Sci., 2 (1977) 317.
61 18 Vishnu and V.P. Misra, Studies on electrolyte-non-electrolyte interactions; viscosity behaviour of alkali halides in aqueous sucrose solutions, Carbohydrate Res., 39 (1977) 35. 19 F. Helfferich, Ion Exchange, McGraw-Hill, New York, 1962, p. 400. 20 H.R. Kruyt, Colloid Science, Elsevier, Amsterdam, 1952. 21 S.N. Vinogradov and R.H. Linnell, Hydrogen Bonding, Van Nostrand Reinhold, London, 1971, p. 277. 22 Ref. 19, pp. 510,103. 23 B.E. Conway, Electrochemical Data, Elsevier, Amsterdam, 1952, p. 132. 24 R.P. Rastogi, Irreversible thermodynamics of electroosmotic effects, J. Sci. Ind. Res., 28 (1969) 284. 25 R.P. Rastogi, K. Singh and S.N. Singh, Membrane characteristics from measurements of electroosmosis, Ind. J. Chem., 6 (1968) 466. 26 N. Lakshiminarayanaiah, On the determination of average pore size of membranes, J. Phys. Chem., 73 (1969) 4428. 27 M.L. Srivastava and Raj Kumar, On the pore size of membranes, Ind. J. Biochem. Biophys., 13 (1976) 182. 28 E. Matjevic, Surface and Colloid Science, Vol. 7, John Wiley and Sons, New York, 1974, pp. 33,181-183.