STUDIES WITH INORGANIC ION EXCHANGE MEMBRANES
SUMMARY
THESIS SUBMITTED FOR THE I>EGREE OF
iBottar of ^Iitlosioptip IN
CHEMISTRY TO
THE ALIGARH MUSLIM UNIVERSITY, ALIGARH
BY
KHURSHEED AHMAO
^ 7 ^ - ^ ^ ^
DEPARTMENT OF CHEMISTRY ALIGARH MUSLIM UNIVERSITY
ALIGARH SEPTEMBER, 1981
2 i JiAi 1382
S U M M A R Y
Transport processes occurring across a r t i f i c i a l
membranes separat ing d i f fe ren t s a l t so lu t ions have been
one of the most studied e lect rochemical and b i o e l e c t r i c a l
phenomena. The i n v e s t i g a t o r s from var ious d i s c i p l i n e s ,
e . g . , chemists , chemical engineers , b i o l o g i s t s e t c . have
contr ibuted ex tens ive ly although the s t a r t i n g po in t s and
aims have been qu i t e d i f f e r e n t . The l i t e r a t u r e in t h i s
f i e ld i s enormous but f requent ly not very coherent. The
cooperative e f f o r t s of the workers have contr ibuted s i g n i
f i c a n t l y to the p rosper i ty and phys ica l well being of a l l
mankind.
In t h i s t h e s i s , / a n ef for t has been made t o charac te
r i z e newly developed ion-exchange membranes, prepared from
inorganic p r e c i p i t a t e s , when placed in contact with aqueous
e l e c t r o l y t e so lu t i ons . The parameters governing membrane
phenomena have been derived from membrane p o t e n t i a l , mem
brane conductance and impedance measurement s. The t h e s i s
has been presented under th ree heads although c e r t a i n
amount of overlap has occurred. This type of overlap i s
permit ted as i t helps in the e luc ida t ion of the t op i c xmder
d i scuss ion .
In Chapter I , ( t h e prepara t ion of parchment supported
11
thallium dichromate and thalli\;m permanganate membranes,
and measurements of membrane potential,when these are used
to separate various 1:1 electrolyte (KCl, NaCl and LiCl)
solutions are reported./ Membrane potential data have been
used to derive thennodynamically effective fixed charge
density of the membranes, using the fundamental theory of
Teorell, keyer and Sievers and the recently developed theo
ries of Kobatake et al. and Tasaka et al. based on the
principles of irreversible thermodynamics. The results
have also been utilized to examine the validity of the
recently developed theoretical equations. It has been con
cluded that the membranes carry low charge density and that
the methods developed recently can be utilized for the eva
luation of effective fixed charge density of the systems
\inder investigation and such other systems.
^ In order to -understand the mechanism of transport of
simple metal ions through inorganic ion exchange membranes,
in Chapter II, the membrane conductance bathed in different
concentrations of various 1:1 electrolytes (KCl, NaCl and
LiCl) and measured at several temperatures are reported.
The data have been used to derive various thermodynamic
parameters like energy of activation, E , enthalpy of acti
vation, AH^, free energy of activation,AF^ and entropy of
activation,AS^, by the application of absolute reaction
I l l
r a t e theory . The i n t e r i o n i c ;ji;uiip d i s t ance , d, has also iDeeii
eva lua t ed . / The a c t i v a t i o n energies -were found t o depend on
the s ize of penetrant species and tha t i t decreased with i n
crease in the concentra t ions of the bathing e l e c t r o l y t e
s o l u t i o n s . The values of Z!^* were found to be negat ive i n
d i ca t i ng thereby tha t p a r t i a l immobilization of ions t akes
place wi thin the membrane. The order of membrane s e l e c t i
v i ty was fo\ind t o be Z > Na > Li which on the bas i s of
Eisenman-Sherry model of membrane s e l e c t i v i t y point towards
the weak f i e ld s t rength of charge groups at tached to the
membrane matr ix . I t has been concluded tha t the membranes
used i n the i n v e s t i g a t i o n are weakly charged and tha t the
permeating species r e t a i n , at l e a s t p a r t i a l l y , t h e i r hydra
t i o n s h e l l while d i f fus ing through the membrane. The par
t i a l immobility of the ion ic species has been a t t r i b u t e d
to i t s i n t e r a c t i o n with the membrane matr ix of low fixed
dens i ty .
In order to v i s u a l i z e s t r u c t u r a l d e t a i l s of the mem
b r a n e - e l e c t r o l y t e system, i n Chapter 111,/^the measurements
of e l e c t r i c a l r e s i s t a n c e , Rx, and capaci tance , C^, of the
parchment supported thallixom dichromate and thal l ium per
manganate membranes in contact with d i f f e ren t concentra t ions
of aqueous sodimn chlor ide so lu t ion at var ious frequencies
have been ca r r i ed out and t h e impedance c h a r a c t e r i s t i c com-
IV
puted. The double layer theory has been utilized to inter
pret the changes produced in the membrane capacitance, C_,
membrane resistance, R , and impedance, Z, with electrolyte
concentrations. It has been concluded that the double
layers at the interfaces control the diffusion processes,^
STUDIES WITH INORGANIC ION EXCHANGE MEMBRANES
THESIS SUBMITTED FOR THE DEGREE OF
Bottov of ^|)iIosiop!)p IN
CHEMISTRY TO
THE ALIGARH MUSLIM UNIVERSITY, ALIGARH
BY
KHURSHEED AHMAD
DEPARTMENT OF CHEMISTRY ALIGARH MUSLIM UNIVERSITY
ALIGARH SEPTEMBER, 1981
T2383
, ^ ^ ^ ^ . . A Z A D t ^ X^\i^
Ret No. iChem.
DEPARTMENT OF CHEMISTRY A L I G A R H M U S L I M U N I V E R S I T Y
A L I G A R H, U. P., I N D I A
Vhone : Office : 3345
Dote. Se£t,..9^.. 1.981
C E R T I F I C A T E
This i s to c e r t i f y t h a t the t h e s i s e n t i t l e d
"Studies with Inorganic Ion-Exchange Membranes" sub
mitted to Aligarh Muslim Univers i ty , Aligarh, des
c r ibes the o r i g i n a l work car r ied out by Kr, Khursheed
Ahmad under my supervis ion and i s su i t ab le for the
award of Ph.D. degree in, Chemistry.
(M. NASIM BEG)
A C K N O W L E D G E M E N T
I wish t o express my deep sense of g r a t i t ude to my
supervisor Dr. Mohammad Nasim Beg, Department of Chemistry,
for h i s most valuable gxiidance to carry out t h i s p r o j e c t .
I am thankful to Dr. Pasih Ahmad Siddiqi and Dr. Hasan
Arif of t h i s Department for t h e i r he lpfu l suggest ions and
to a l l my col leagues working i n t h i s labora tory who were
a l l along with me in my endeavour.
Thanks are due to Prof. Wasiur Rahman, Head of the
Department of Chemistry, for providing research f a c i l i t i e s
and to U.G.C. ( India) for the f i nanc i a l a s s i s t a n c e .
(KHURSHBED AHMAD)
LIST OP PUBLICATIONS
1. Transport of alkali chlorides in parchment supported
cupric hydroxide membrane and application of absolute
reaction rate theory.
J. Electroanal. Chem., 122, 313-319 (1981).
2. Ionic transport of alkali chlorides in parchment
supported cupric orthophosphate membrane and applica
tion of absolute reaction rate theory.
J. Membrane Sci., (1981) - In press.
3. Transport of simple metal ions through thallium dichro-
mate membrane: Conductance data and absolute reaction
rate theory.
Indian J. Chem. (Communicated).
4. Studies with inorganic precipitate membranes: Capaci
tance, resistance and impedance.
J. Membrane Sci. (Communicated).
C O N T E N T S
Page No,
1.
2. CHAPTER
5. CHAPTER II
4. CHAPTER III
(i) GENERAL INTRODUCTION 1
(ii) References 34
MEMBRANE POTENTIAL, EVALUATION
OF CHARGE DENSITY AND EXAMINATION OF RECENTLY DEVELOPED THEORIES 46
(i) Introduction 47
(il) Experimental 48
(iii) Discussion 49
(iv) References 69
MEMBRANE CONDUCTANCE AND APPLICATION OF ABSOLUTE
REACTION RATE THEORY 75
(i) Introduction 74
(ii) Experimental 77
(iii) Discussion 78
(iv) References 93
CAPACITANCE, RESISTANCE AND
IMPEDANCE OP THE MEMBRAI\nSS 98
(i) Introduction 99
(ii) Experimental 101
(iii) Discussion loi
(iv) References II7
SUMMARY i - iv
GENERAL INTRODUCTION
lytic desalination of brackish water (2-4), as ion selec
tive electrodes (5), as solid electrolytes for solid state
electrochemistry (6), as models for theoretical studies
(7-21) and in several other technological processes. Work
in this field is contributing significantly to the econo
mic prosperity and physical well-being of all mankind.
The literature in book form describing membrane
technology and applications is far too extensive to men
tion. Tae principal volumes containing significant sections
on, or totally devoted to membrane electrochemistry are by
Clarks and Nachmansohn (22), Helfferich (23), Spiegler (24,
25), Merten (26), Harinsky (27), Stem (28), Cole (29),
lakshminarayanaiah (5,30,31), Hope (32), Amdt and Roper
(33), Plonsey (34), Kotyk and Janacek (35), Keller (36),
Parlin and Eyring (37), Caplan and Mikulecky (38), Sand-
blom and Orme (39), Harris (40), Schlogl (41), Bittar (42),
Kirkwood (43) and others. Continiiing series are edited by
Bisenman (44), Danielli, Rosenberg and Gadenhead (45).
Application of membrane electrochemistry to yield activity
sensing electrodes are amply described in books edited by
Eisenman (46) and Durst (47). Numerous recent volumes are
concerned, in part, with membrane electrochemistry (48-55).
However, this field has produced such a variety of new
measuring devices and has opened so many analytical possi-
When two electrolytic solutions having different
concentrations are separated by an artificial membrane,
mobile species penetrate the membrane and various trane-
pooTt phenomena are induced into the system (1). During
the last two decades the study of these phenomena has
received special attention and has been one of the most
studied electrochemical and bioelectrical phenomena.
Investigators from various disciplines, e.g., chemists,
chemical engineers, biologists, etc. have contributed sig
nificantly in this field although the starting points and
aims have been quite different. Chemists and chemical en
gineers, utilizing artificial membranes and their several
modified forms, tried to understand the mechanism of trans
port so that with the knowledge so gained they might be
able to fabricate membranes of any desired property or pro
perties. Biologists, however, wished to use them as simple
model for physiological membranes in order to understand the
behaviour of complex cell membranes and finally, if possible,
to replace decaying or dead biological membranes. The co
operative efforts of the workers in this field to produce
artificial kidney and cellulose membrane technology used
in desalination are a few such success. Recently, severaJ.
inorganic ion-exchange membranes have been developed and
are known for their potential employment in fuel cells,
in nuclear technology, in hyperfiltration and electrodia-
bilities in terms of new analysis and new detection sys
tems that it is verylikely that additional volumes will
soon appear. There are several excellent books dealing
with transport phenomena in natural membranes but there
are none dealing exclusively with artificial membranes -
a topic whose literature is enormous but frequently not
coherent.
A membrane is a phase or structure interposed bet
ween two phases or compartments which obstructs or comp
letely prevents gross mass movement between the latter,
but permits passage, with various degree of restrictions
of one or several species of particles from the one to the
other or between the two adjacent phases or compartments
and which thereby acting as a physicochemical machine
transforms with various degree of efficiency according to
its nature and the composition of the two adjacent phases
or compartments. In simple terms it is described as a
phase, usually heterogeneous, acting as a barrier to the
flow of molecular and ionic species present in the liquid
and/or vapours contacting the two surfaces (50). The term
heterogeneous has been used to indicate the internal phy
sical structure and external physico-chemical performance
(56-60). From this point of view, most membranes in gene
ral are to be considered heterogeneous, despite the fact
5
that conventionally, membrane prepared from coherent gels
have heen called homogeneous (23).
The terms homogeneous versus heterogeneous proves
to be an important distinction from the point of view of
mass transport. In the dilute solution limit, the friction
coefficients for mass transport by diffusion or migration
are interconvertable by Onsager reciprocal relation, and
both can be related to JTimp distances and frequencies
according to random walk models. As long as there are no
preferred regions of low friction in the membrane, it is
isotopic on a molecular level and is considered to be homo
geneous. Uniformity of mesh on a molecular scale is another
view of homogeneity, Channel free solid and liquid mem
branes are usually homogeneous and two phase membranes,
such as solid crystallites imbedded in a nonionic resin
are clearly heterogeneous. The distinction, however, is
not always essential (61).
Membranes may be solid, liquid, or gas (62) and the
outer phases are usually liquid or solid. Although it is
frequently the case that membranes are thin in one dimen
sion relative to the other two dimensions. This property
is only functional or operational. In order to achieve a
measurable chemical change or electrochemical effect and
to make chemical or electrochemical measurements on a mem-
6
brane system in a reasonable time, some transport related
property must be susceptible to temporal change. Thus, a
change in potential, flux, or concentration (among many
varying and measurable quantities) require sample thick-
nesses such that d /2D is comparable with the observation
time (D is a mean diffusion coefficient). Although irregu
larly shaped membranes are conceivable, most theories and
experiments are restricted to systems with one dimensional
or spherical symmetry such that transport occurs in one
dimension, the X direction in parallel face planer membrane
or along a radius in membranes with spherical shape.
Membranes are considered to be porous or non-porous
depending upon the extent of solvent penetration (30). At
the non-porous extreme are membranes which are non-ionic
and contain negligible transportable species at equilibrium.
Ceramics, quartz, anthracene crystal and teflon films bet
ween metal electrodes or electrolyte bathing solutions are
solid membrane examples. Organic liquid films such as hyd
rocarbons and fluorocarbons in contact with aqueous elec
trolytes are liquid membrane examples. At the other ex
treme are porous membranes, which can be solvated and will
contain components from the outer phases. Among tnese are
non-ionic films such as cellophane, inorganic gels and
loosely compressed powders in contact with aqueous solu-
tions. These materials absorb solvent from the surrounding
media and may also extract other neutral molecules and
ionic salts. Kore widely studied are these membranes of
polyelectrolytes ("Solid" ion exchangers), aqueous-
immiscible organic liquid electrolytes ("liquid" ion ex
changers) (23, 30, 31), various parchment supported inorga
nic precipitates (7-21), solid ion conducting electrolytes,
including silver halides, rare earth fluorides and alkali
silicate and alumino-silicate glasses (46, 47, 63, 64).
All of these materials contain ionic or ionizable groups
within the membranes which are capable of transpoart under
diffusive or electric field forces. In addition, these
materials possess the properties of porosity, Polyelectro
lytes tend to swell rapidly by osmotic pressure driven up
take of solvent. Liquid ion exchangers are surprisingly
slow to take up water, while the inorganic salts have no
tendency to hydrate. Glass membranes are complicated by
simultaneous hydrolysis of the polyelectrolyte during up
take of water (65-67).
The frequent use of charged and uncharged in the
membrane literature is usually unsoujid electrostatically,
but does provide an intuitive chemical description. For
example, charged membrane usually refer to electrolyte
membranes such as solid and liquid ion exchangers where
8
the fixed and mobile sites are the charges. Actually these
membranes are quasi-electroneutral in their bulk when the
thickness is large compared with the Debye thickness at
each interface. Quasi-electroneutrality means that in any
vol-ume element large compared with the distance between
ions, the sum of ionic charge H z c = 0. In the litera-i
ture, uncharged membranes are those, like cellophane, with
no fixed charges. This frequently used literature defini
tion provides no place for liquid bilayer membranes which
are electrostatically neutral only in the absence of charge
carriers and in the absence of bathing solutions whose salts
possess preferential solubility of anion over cation or vice
versa, but are usually electrostatically charged by an
amount of ions of one sign in normal operation. Thick
hydrocarbon membranes and membranes of diphenyl ether (or
derivatives), phthalate, and sebacate esters are generally
neutral in the presence of most bathing electrolytes, but
may be charged electrostatically, depending on thickness,
in the presence of neutral carrier species which preferen
tially solubilize ions of one sign. The use of the terms
charged and imcharged to describe electrolyte or non-elec
trolyte membrane has been discouraged unless the precise
electrostatic connotation is involved (61).
Membranes may be broadly classified into natural and
9
artificial. Natural membranes are considered to possess
a fundamental unit membrane structure which is a bimole-
cular leaflet of lipid with polar groups oriented towards
the two aqueous phases of the cell, and protein is supposed
to exist close to the polar heads of the leaflet. This
type of universal structure is absent in artificial mem
branes.
Lakshminarayanaiah (30) has given a classification
of membranes on the basis of its preparation under the
heads: (A) Operationally useful membranes: (i) Homogeneous,
and (ii) Heterogeneous membranes which are subdivided into
(a) non-reinforced membrane, (b) fabric backed or rein
forced membranes, (c) membranes formed by chemical treatment
of other films or membranes, (d) membranes formed by the
mechanical treatment of the membrane forming monomers or
polymers, and (e) membranes fonned by photochemical treat
ment, (B) Membranes to serve as models for natural membranes;
(C) Composite and other special membranes.
Membranes can also be categorized according to whether
it contains sites for ion exchange or it is site-free, and it
is an ion exchanger, according to whether its sites are
fixed or mobile and whether the sites and their counter
ions are associated or dissociated. This type of classifi-
10
cation has been presented by Eisenman, Sandblom and Walker
(68). These authors have, however, restricted their dis
cussion to membrane whose properties are considered to be
homogeneous in the plane of the membrane, and have avoided
explicitly with the complexities which result from either
mozaic membranes, in which local eddy current occur (69) or
series membranes, in which space-charge regions exist ana
logous to those at p-n semiconductor junction (70).
Unlike the classification based on membrane structure,
membranes are usually classified either on the basis of their
nature, i.e., coherent gel or otherwise, or on the nature
of chemical reaction involved in their formation, i.e.,
addition or condensation reaction. The efforts of various
workers have been directed towards (A) Preparing membranes
of good chemical and mechanical stability and favourable
electrical perfonnances suitable for fundamental transport
studies and for applications in some industrial operations
sucsh as the treatment of brackish water, saline water con
version, etc. (B) Building suitable models to mimic the pro
perties of natural membranes, and (C) Preparing composite
membranes containing cationic and anionic groups in suitable
arrangement to demonstrate and to study the physicochemical
phenomena associated with rectification of alternating
current and other special membranes for specific purposes.
11
It is worthwhile to mention that most of the work concern
ing category (A) seems to be directed towards finding suit
able membrane materials for fabricating a structure for
effective desalting of sea water by application of pressure.
The most commonly used material for casting a membrane for
desalination is cellulose acetate, although, poljrmethacry-
lic acid (PMA), phenolsulphonic acid (PSA), polystyrene
sulphonic acid (PSSA) and cellulose esters have proved very
useful (5,30,51). In gategory (B) bilayer membranes, first
generated by Mueller (71),' have most widely been used as
model for living cells and the studies have given somewhat
a better understadning of the structure and function of
natural membranes. The membranes of category (C) are quite
niunerous (5,61,72-74).
The common ion-exchange membranes having an organic
matrix are largely employed in several technological pro
cesses. The first inorganic ion exchange membranes,
possessing very high resistance towards acid, temperature
and ionizing radiations and having, at the same time, a
high concentration of fixed charges, were obtained two
decades ago, independently by Dravnieks, Eregman (75) and
Alberti (76) who used amorphous zirconium phosphate as an
active inorganic material. Inorganic ion-exchange mem
branes have acquired particular significance in these two
12
decades. These membranes have several advantages over orga
nic ion-exchangers, e.g., their ability to withstand ioniz
ing radiations and very high temperatures without undergoing
degradation and their remarkably high selectivity (77). Due
to the ability of membranes to remain stable at relatively
high temperatures, to resist degradation and fouling and to
remain stable under corrosive and oxidizing conditions, they
have great utility in electrical membrane separatory pro
cesses; particularly in electrodialysis and transport deple
tion process. Their high electrical conductivity and better
current efficiency have found their use in cells for the
electrolytic desalting of brackish water (3,78,79), fuel
cells and electrical storage batteries (80) where extremely
strong, ion selective, membranes are required to maintain
ion separation between the electrodes of the battery or
fuell cell and wherein operating temperatures may approach
and exceed 125 C. The inorganic ion-exchange membranes are
useful in a variety of selective separation process, such
as water purification, and to process other solvents having
soluble ionic contaminants. However, they have made little
headway as models for biological membranes inspite of the
fact tnat comparatively simpler inorganic systems made up
of amino, iraido and phosphate groups comparable, to say,
phospholipids can be envisaged and subsequently synthesised.
13
Two types of inorganic ion-exctiangers are general ly
known, v i a . , ( i ) c r y s t a l l i n e and ( i i ) amorplious. Hetero-
p o l y s a l t s such as phosphomolybdates, alumino s i l i c a t e s ( 8 1 ,
82) , e t c . belong to the former category, and the simple and
mixed hydrous oxides oT group IV, V and YI to the l a t t e r
category ( 8 3 ) . They also d i f f e r i n t h e i r permeabil i ty . In
order to obtain them as sheets of suf f ic ien t mechanical
s t rength they are amalgamated with polystyrene (84-87) and
for the purpose of bas ic s t u d i e s , parchment supported mem
branes are mostly employed (7 -21) .
According t o Lonsdale, "membranes of t r a d i t i o n a l type
are very i ne f f i c i en t separa t ion devices and for two very
good reasons - f i r s t they are too slow and second, they are
too non - se l ec t i ve . " They are too slow for most conventional
separa t ions because the d i f fus ion coeff ic ients of most p e r -
meants of i n t e r e s t in polymeric membranes are qu i t e low
of the order of 10"'^ cm^/sec for the permanent gases ; two
or th ree orders of magnitude lower for permeants of l
cu la r weight 100 to 500, and v i r tua l ly unmeasurable for
permeants with molecular weight 1OO0.
Secondly they are generally insuff ic ient! . , -, ^j-enxxy select ive
for i t i s required tha t frequently al l of +„r. . t ^ ^ ^^ ^yPe A molecules
to pass and none of type B or any other t ype , in most cases , membrane separators are no match i n V^i^ regard for
14
the multi-effect distillation colimn. Even silicone rubber
membranes, in spite of their very high permeability, have
made limited headway in the separations field because of
their very low permselectivity. (Actually ultrathin sili
cone rubber membranes are now finding application in the
enrichment of Op in air).
The question arises "¥hy, then, would any one want to
mess around with membranes for separations?" The answer, is,
of course, that beginning in around I96O some creative people
have been doing some unconventional things with membranes to
improve their performance as separation barriers. First on
the list, Loeb and Sourira3an (88) developed the exquisitely
thinskinned cellulose acetate membrane for water desalina
tion by reverse osmosis. Since then, others have found
alternate ways of making membranes that are effectively
exceedingly thin. Some of these go down to a few hundred
Angstrom \inits in thickness, without apparent imperfections,
thereby nearly rivaling the 80A cell membrane in thickness.
The synthetic membranes require support for strength but,
based on both electron microscopic examination and flux
measurements on both conventional thick films and ultrathin
films of the same material, the effective thickness of
these new membranes is as stat^. This, then, was one
solution to the problem of low flux. And it led to the
reverse osmosis industry, now estimated to be valued at
^ S 10 /year.
A second solution to the problem of slowness is even
newer, so new, in fact, that it has not yet reached commer
cial realization, although it appears destined to do so.
That approach is based on the use of liquid membranes, in
-5 -6 which diffusion coefficients are typically 10 to 10
2 -7 -10 2
cm /sec instead of 10 to 10 cm /sec as in polymeric
films. But the real breakthrough associated with liquid
membranes is not the high fluxes they permit, but the high
selectivities, for the liquid membranes under development
today all contain carriers of some sort. With these carriers
the membranes become extremely permselective, in some cases
transporting a favoured species to the exclusion of ion-
favoured species with separation factors of a thousand or
more. Still more interesting, these new membranes readily
permit "uphill" diffusion, so that desired species cannot
only be cleanly separated from undesired species but concen
trated many-fold - actually, many thousandfold - at the
same time. The transport process is variously known as
coupled or facilitated transport, and it is reminiscent of
the process known as active transport in the biological
membrane.
For these reasons, then, there is a quiet revolution
16
occurring in membrane separation teclinology. In the near
term, we can reasonably expect increasing application of
membranes to gas separations, Beyond that, one can readily
envision the practical realization of quite clean, highly
specific separations in aqueous solution. At some point,
membranes may rival both the speed and specificity of the
biological membrane, and the uses to which they may be put
could exceed our present ability to project.
A characteristic property of chemically inert mem
branes is their ability to affect the transport of material
from one side to another. Consequently the thrust of theore
tical description has been the interpretation or explanation
of transport processes and the measuired effects resulting
from pressure difference, temperature difference, activity
difference, potential differences developed across membranes
and currents through membranes. A number of theoretical
approaches have been given, an accoimt of which is summa
rized below:
A. Irreversible ThermodyTiamic Approach
At the most general and abstract level, without
regard to the structure or chemical features of a membrane,
the flux of matter and energy can be found in terms of the
"forces" due to a pressure, temperature, activity, or poten-
17
tial difference across thin (or differential) membranes.
The gross thermodynamic "forces" are written as:
Xk = -TA( jlk/T); X^ = -d/T) (1)
the material flux of each species i = 1 through k is
and the flux of energy is
•u = ^ ^ u A + ^u^u ^5)
The proportionality factors between each partial flux con
tribution and the forces are the set of Onsager coefficients,
which are equivalent to system response fixnctions and:
For a symmetric set of n equations with n forces, there are
only 1/2n(n+1) independent coefficients, rather than n .
These forces are not arbitrarily defined but are deduced
from the general expression for entropy production (rate
of change of the system entropy) as the system approaches
equilibrium.
A most comprehensive experimental and theoretical
treatment of transport across membranes using the irrever
sible thermodynamic analysis is that by Meares, Thain, and
Dawson (89). Their excellent quality of work is the syste
matic presentation of forms for the flux equations, choices
18
of forces and fluxes in regard to ease in relating measured
responses to Onsager coefficients, and relations of rela
tive friction and Onsager coefficients. They advocate the
procedure of reversion of the phenomenological equations
in the form
which is closely related to the usual experimentally
accessible friction coefficient models where
Xk = 5: fkiC k - i)
The relative friction coefficients f,. and f., are related
^y k' ki ~ i" ik* " ' ^^^ velocities in the centre of mass
reference frame and f.,/C, and f, ./C. are forces between
1 mol of i and 1 mol of k at unit velocity difference. The
second part of Equation 5h follows from the definition of
a flux of a single species as a product of a local concen
tration and velocity.
At constant temperature, experimental values of zero
current fluxes of salt and solvent are determined for un-
symmetric bathing solutions. Electroosmotic flux of solvent
is determined as are tracer diffusion coefficients. There
are possibly eight items of data: (1) electrical conductance,
in
(2) ionic transport n\jmber, (3) electroosmotic flux, (4)
sal t diffusion flux, (5) volume or solvent osmotic flux,
(6) counter ion t racer diffusion coefficient, (7) co-ion
t racer diffusion coefficient, and (8) volume flow under
hydrostatic pressure difference. From experimental fluxes
of species under a given single gross thermodynamic force,
velocity terms are computed. The resul t ing matrix of un
known f values are solved using reciprocal re lat ions and
assumptions such as zero f r ic t ion coefficient for t racer
motion among ions of i t s own kind, zero f r ic t ion coeffi
cient for permselective ions interact ing with matrix s i t e s ,
or Spiegler 's assumption that f r ic t ion between cations and
anions in a permselective ion exchanger memhrane i s zero.
R, . values are computed from f values using equation 513
and L, . values followed by matrix manipulations. Finally,
expressions for conductivity and other measurable quanti
t i e s can be eijfpressed in terms of R's and L ' s .
In terpreta t ion of L, . in terms of local molecular k i
processes i s not d i rec t . Even interpreta t ion of L,, i s
d i f f icu l t because a single gross thermodynamic force X,
producing a flux J, simultaneously affects a l l other J ' s .
Presiamably these indirect interact ions can be unravelled by
assizming that f r ic t ion coefficients represent only in t e r
actions between a pair of flows.
20
Even in model systems, the "basic considerations of
system transport can lead to complicated mathematical des
criptions. The diversity in the theoretical forms for
transport phenomena, which results from simplifications
made by various authors, is a particular hazard to workers
in this field.
It may be mentioned here that the discipline of
irreversible thermodynamics provides a precise mathemati
cal description of the processes of transport and diffusion
in membrane systems. Its application to membrane processes
is a natural development of the basic theory of Onsager (90)
which has been developed by Kedem (91), Katchalsky (92),
Caplan (93), Hears (94), Spiegler (24,25), Rastogi (95-98),
Paterson (99), Kirkwood and Others (45,100,101) in an ex
tensive and expanding literature.
B, Chemical Engineering Approach
Closely related methods used by theoretical chemical
engineers to describe membrane transport are based on turn
ing the Nernst-Planck equations of motion inside out.
These equations, known as Stefan-Maxwell equations, account
for the motion of the centre of mass of the membrane system
and remove a source of concentration dependence that mea
sured diffusion coefficients will otherwise show when
21
measured in a labora tory coordinate system. For eadi of
n mobile species in one dimensional flow,
d In a dlJ/ .^
n IZ CRT/Di3=.j)Cv, - Vj)
= Z I (RT/D^jO^)(xjJj - Xj Jj ) (6)
where x, i s mole f r a c t i o n , C. i s concent ra t ion , in mol/cm ,
Vj i s p a r t i a l molar voliime, Vj and Vj are observable spe
c i e s v e l o c i t i e s , J ' s are usual f luxes in l abora to ry coordi
n a t e s , and D's are Stefan-Maxwell d i f fus ion coe f f i c i en t s .
These equations apply to closed systems, i . e . , t o t a l mass
of a system including bathing so lu t ions and membrane r e
mains cons tant . Considering a fixed membrane with s i t e s
designated as species 4, a s impl i f i ca t ion i s found.
S i 4 = 1 i = 4; <Si4 = 0 i ? 4 .
-RT d In a . /dx - Z^F d^/dx + {^.JC. - v . )dp /dz
n = JZ (RT/D. .C . ) (x . J . - X . J . ) (7)
Recent examples of t h i s approach are reported in papers
22
by Lightfoot (102) and Cussler (105). A characteristic
feature of this method, as with the entirely consistent
irreversible thermodynamic approach, is the large n amher
of transport parameters which take into account inter
actions among moving and static components.
C. Activation Barrier Kinetic Approach
A third type of theory treats transport processes
as harrier controlled kinetic events occurring sequentially
in space within the membrane. For a series of barriers
across which a continuous flux occurs, relations can be
derived to express flux in terms of concentrations just
inside the membrane surfaces. For n barriers of equal
height and spacing one obtains the trivial result:
J = -§- (C^ - Cn) =P'(C^ - C^) (8)
where P ' i s the i n t e r n a l permeabi l i ty , C and C^ are the
concentra t ions in f i r s t and nth b a r r i e r . Considering the
surface processes to be determined by r a t e constants K and
K, which must be assumed to be non-zero with t h e i r r a t i o ,
Z / K = E y . , the ex t r ac t ion coe f f i c i en t , has been re l a t ed
to the apparent ove ra l l permeabi l i ty ,
°- ^ext dK
23
when K and K are small compared with D/d , then the per
meability P = K/2. The interesting feature of this analy
sis, which was later improved and generalized to include
fliix limitation by external concentration polarization
(30), is that the unloading rate constant, K, does not
affect permeability. A small K at constant K simply means
that the extraction equilibrii^m favours the membrane. The
advantage of the so called kinetic analysis of membraJie
transport is that it provides an overview without the intro
duction of specific models for forces and system functions.
On the other hand, new parameters are introduced and are
related to the other better known quantities.
Absolute Reaction Rate Theory
A membrane can be thought of a series of potential
barriers existing one behind the other, across which mater
ial must pass in order to cross the membrane (30). To do
so, the permeating species must have a minimum amoiint of
energy.
The theory of absolute reaction rate has been applied
to diffusion processes in membranes by several investigators,
Zwolinski, Eyring and Reese (104) considered the diffusion
process as one of the basic phenomena for sustaining the
growth and development of plants and organisms. They pre-
24
sented a detailed kinetic approach to diffusion which clari
fies much established concepts and provide impetus to a
fresh approach to the problems in the field of biological
diffusion. The absolute reaction rate treatment of diffu
sion and membrane permeability provides a general unified
point of view applicable to systems of varying degrees of
complexity. It is equally adoptable to the treatment of
the permeabilities of membranes to electrolytes, to non-
electrolytes under the driving forces of a concentration
gradient, activity gradient, and external and internal
potential gradients. Zwolinski, Byring and Reese (104)
treatise on membrane diffusion is based on the "activated
state" or the"transition state" theory.
Laidler and Schuller (105) have also treated the
kinetics of membrane transport under steady state condi
tions. They employ similar principles and express the rate
constant of the overall process of surface penetration in
terms of a n\imber of specific rate constants. Various
special cases are considered and discussed with reference
to the experimental data. They developed flux equations
for solvent and solute specially as a function of the osmo
tic and hydrostatic pressures across the membrane. Tien
and Ting (100) have applied the theory of absolute reaction
rates to water permeation process through bilayer lipid
2 r:
membranes (BIM). Clough et al. (106), Li and Gainer (107)
and Navari et al. (108) have applied absolute reaction rate
theory to diffusion of solute in polymer solutions. They
attached importance to the influence of polymer on the
activation energy for diffusion. Tsimboukis and Petropoulos
(109) determined the diffusion coefficients of alkali metal
ions through cellulose membranes and discussed the results
in terms of the pore structure model and lijima et al. (110)
used activation analysis for the investigation of mechanism
of the diffusion of ions of simple salts through polyamide
membranes. Recently, Beg et al. (21) have applied absolute
reaction rate theory and have derived various thermodynamic
quantities like energy of activation E„, enthalpy of acti-Si
vation AH^, free energy of activation A F ^ , and entropy of
activation A S' and also the interionic jump distance d, in
order to investigate the mechanism of transport of simple
metal ions through inorganic precipitate membranes.
D. Phenomenological Equation of Motion Approach
The fourth and widely applied theory of transport is
based on the Nernst-Planck fluz equation (30). In its most
general form, it is consistent with irreversible thermodyna
mic flux:
2G
(10)
where
w w ' jx Dx'
is the solvent transport velocity for a membrane containing
sites. In its most simplified form the Hemst-Planck equa
tion for a single ion is
This form is the usual starting place for calculation of
concentration, field and potential profile within a mem
brane. Current densities in the absence of interaction
between species viz., ion pairing etc. are given by
^ = ^ ^ ^ 5 , -(g^) (12)
Time dependence follows from continuity condition
dt h^ ^^^
The second term of eqn. 10 i s a form of Poisons equation
which for space charge bui ld up at the surface due to
cur ren t flow. Use of Nemst-Planck equat ions in steady
27
state uniform (constant composition) e lectrolytes leads to
a l l of the c lass ical transport re la t ions .
Several milestones in the application of the stand
ard form of the N-P equation and in the interpretat ion and
modification of the N-P equation must be mentioned. The
f i r s t i s an integration to give membrane potent ia ls in
terms of external ionic a c t i v i t i e s , the h is tor ic Teorell-
Meyer-Sievers equation (111-115) which describes the mem
brane potent ia l for an ion exchanger membrane bathed in
uni-univalent electrolyte of different a c t i v i t i e s . Their
r e su l t s include the s i t e concentration specifically and
allows for co-ion t ransport . I t covers the range from
high s i t e dens i t ies , permselective membrane to s i t e free
membranes. No account i s taken of possible solvent t rans
port . Subsequently, Scatchard (114) derived an expression
for the membrane potent ia l , again for uni-univalent electro
l y t e s , which included an integral involving transport of
solvent.
The most extensive study of techniques, based on
P l e i j e l s procedure for integrat ion of the standard ITernst-
Planck equation system applicable to liquid junctions and
ion exchange membranes i s by Schlogl (115). His integra
t ion procedure gives the diffusion potent ia l in terms of
28
the fluxes and interior surface concentrations, and it gives
fluxes in terms of interior diffusion potential and interior
surface concentration, without the consideration of solvent
transport. The method while complicated, is quite general
and applicable to system involving ions of various charge.
Simplification are possible when ions fall into monogroups,
all ions have the same absolute charges. His subsequent
papers are concerned with solutions for species flux, diffu
sion potentials, and current-voltage curves when solvent
transport is included in the modified Nemst-Planck equation
(116). A comprehensive account of Nemst-Planck flux equa
tion is available in the book by Lakshminarayanaiah (5,30)
and in recent review by Buck (117).
This grouping attempt to classify the various mathe
matical approaches, according to ideal model on which they
are based. It is in fact too schematic, as many theories
occupy intermediate position. No author is likely to take
the view that one of these treatments is right and the
others wrong. The various descriptions supplement each
other, and depending on the system under consideration, one
of these will prove the most suitable.
Apart from various theoretical treatments used in
the investigation of membrane systems, one of the most im
portant approach in membrane studies is the application of
29
electrochemical principles. Electrochemistry in membrane
studies is pertinent at three levels (117). One is the
development of techniques with application to experimental
phenomenology including current-voltage-time-concentration
behaviour. A second is mathematical modelling implied by
experiment and tested against experiment. The third level
is experimental varification of models in tenns of the
molecular processes and properties and includes determina
tion of theoretical parameters by electrical methods and
by complementry nonelectrochemical methods: physical, opti
cal, ear, nmr, Raman, fluorescence, T-jump technique etc,
From transient and steady state measurement of current or
membrane potential as a function of chemical composition,
chemical treatment, and temperature, the roles of kinetic
and equilibrium parameters can be deduced or inferred. A
possible approach to modelling begins with the assumption
of the membrane as a linear system to which laws of network
theory may be applied. Another begins by solution of basic
electrodiffusion laws of transport v ith equilibrium or
kinetic boundary conditions in order to deduce forms for
system functions which satisfy the data.
The most important contribution of electro chemists
to membrane electrochemistry is the transfer of perspective
and wisdom to the new area. There are many sine qua nons
30
in electrochemistry which have occurred through extensive
studies of electrolytes and electrolyte/membrane interfaces.
Electrochemists have learned to subdivide systems into
interiacial and bulk processes and to expect effects of
dielectric constant (complex formation, ion pairing),
effects of short range forces (adsorption of charged and
uncharged species with, possibly, changes in rates of
interfacial processes), effects of high field near surfaces
(Wien effect, and dielectric saturation, for example), and
the important effect of local potentials on rates of inter
facial processes (irreversible charge transfers, psi
effects, etc.). In as much as the presence of the space
charge at interfaces is a natural consequence of the conti
nuity of potential from one phase to another, the presence
of space charge and space charge mediated effects in mem
brane systems is anticipated.
The success attending any unit operation in which
membranes form an integral part, such as demineralization
by electrolysis, salt filteration by application of pres
sure, etc. depends on the availability of suitable membraiKs.
The suitability of membrane for any particular operation is
determined by a number of factors. A very important re
quirement is that the membrane should be chemically stable
when immersed in salt solutions of various T^-K ^ A . XWU.O pn and in salt
31
solutions containing organic solvents or oxidizing agents
and should never become fouled "by surface active agents
or detergents likely to be present in solution to be emp
loyed with membranes. Besides this chemical stability, it
should have some mechanical strength and low electrical
resistance. In addition, the membrane should have good
dimensional stability under different wetting conditions.
Sufficient membrane flexibility is another property which
enhances membrane suitability, as it facilitates easier
handling without breakage during any operation. Other
desirable properties which a membrane may have to become
of practical importance are: (a) high ionic selectivity
even in high salt environment, (b) low salt diffusion in
a membrane concentration cell, (c) low electroosmotic
water transport. To "tailor make" a membrane satisfying
the above characteristics cells for affecting compromise
between opposing req\iirements, considerable attention,
therefore, has been paid, in recent years, to the develop
ment of membranes with particular and specific properties.
A variety of compounds and processes have been used to pre
pare them. The basic material and the chemical processes
involved are summarized in a few books and review articles.
Wagner and Moore (118) have contributed a section on osmotic
membranes. There are two chapters, one on cellulose mem
branes and other one on synthetic resin membranes, in the
32
book by Tuwiner (119). Short in t roduc t ion on the prepara
t i o n of ion exchange membranes have been wr i t t en by Kitche
ner (120) , Kunin (121), Spiegler (122) , Lakshminarayanaiah
(5,30,51) and o thers ( 7 - 2 1 , 84-87) . S imi la r ly , the re are
a sec t ion and two chapters i n the books by Helffer ich (23)
and Vilson (123) , r e s p e c t i v e l y . In t he recent review a r t i
c l e s , Bergsma and Kruissink (124) , Hazenberg (125) and
KriBhnaswamy (126) have included the patent l i t e r a t u r e on
the prepara t ion of ion exchange membranes a few hundred
microns t h i c k , whereas Carnel l and Cassidy (127) provide
cor re la ted information about the prepara t ion of th ick and
t h i n ion-exchange and non-ion-exchange membranes from var
ious m a t e r i a l s . Recently, two other reviews (73,128) have
appeared. Kel le r (36) has given a complete l i s t of pa ten t s
upto 1978 of the membranes used in desa l ina t ion and indus
t r i a l separa t ion .
In t h i s t h e s i s , the prepara t ion of parchment sup
ported inorganic ion-exchange membranes, t h e i r behaviour
i n contact with var ious 1:1 e l e c t r o l y t e s , evaluat ion of
t r anspor t parameters and the poss ib le mechanism of ion ic
t r anspor t through them are descr ibed. The membrane-electro
l y t e system has been considered to contain four chemical
spec ies , (1) counterion, (2) colon, (3) water and (4) the
membrane matrix car r ied fixed ionogenic groups.
33
The discuss ion has m^i-inly been r e s t r i c t e d to comment
ing on only a few po in t s concerning the following ionic
process in the membrane systems, "Permeabil i ty Phenomena":
(1) Membrane P o t e n t i a l , (2) E l e c t r i c a l conduct iv i ty , (3)
Ion ic Transport , "Flux", (4) Ion ic D i s t r i b u t i o n E q u i l i b r i a ,
(5) Spo t i a l •Distr ibut ion of Ions and the Soterxtial m t h i t i
the Membrane.
The content of the t h e s i s has been a r t i f i c i a l l y
separated and presented under the three heads for c l a r i t y ,
although ce r t a in amo\int of overlap has occurred. This type
of overlap i s permitted as i t helps in the e luc ida t ion of
the t op i c under d i scuss ion .
(a) Membrane P o t e n t i a l , Evaluat ion of Charge Density and
Examination of Recently Developed Theories .
(b) Membrane Conductance and Application of Absolute Reac
t i o n Rate Theory.
(c) Capacitance, Resistance and Impedance of the Membranes.
34
R E F E R E N C E S
1. Y. Kobatake and N, Kamo, P rog . Polym. S c i . J p n . , ^ , 257
(1972 ) .
2 . K. S. Rajan, D. B, B o i e s , T. A. Casolo and J . I . Breg-
man, D e s a l i n a t i o n , ^ , 371 ( 1 9 6 8 ) .
5 . A p p l i c a t i o n of I n o r g a n i c Ion-Exchange Membranes t o
E l e c t r o d i a l y s i s " , Res . Develop . P r o g . Rept . N. 328,
OSW, U .S . Dept . of I n t e r i o r Washington, D.C. (1968) .
4 . K, S, Rajan, D. B. B o i e s , A. J . Casole and J . I , Breg -<
man, Desalination, 1, 231 (1966).
5. N. Lakshminarayanaiah, "Membrane Electrode", Acad. Press,
New York, (1976).
6. R. P. Buck, CRC, Critical Reviews in Analytical Chemis
try, (1976).
7. M. N. Beg, F. A. Siddiqi and R. Shyam, Can. J. Chem.,
55(10). 1680 (1977).
8. M. N. Beg, P. A. Siddiqi, R. Shyam and M. Arshad, J.
Membrane Sci,, 2, 365 (1977).
9. F. A. Siddiqi, M. N. Beg, S. P. Singh and A. Haq, Bull.
Chem. Soc. Jpn., 49(19). 2864 (1976).
10. F. A. Siddiqi, M. N. Beg, A, Haq and S. P. Singh, Elec
tro chimica Acta. , 22(6). 631 (1977).
11. F. A. Siddiqi, M. N. Beg and P. Prakash, J. Electroanal.
Chem., 80, 223 (1977).
'6b
12. F. A, Siddiq.i, M. N. Beg and S. P. Singh, J. Polym.
Sci., i^, 959 (1977).
15. P. A, Siddiqi, M. N. Beg, A. Haq, M. A. Ahsan and
M. I. R. Khan, J. De Chimie Physique, 2i, 932 (1977).
14. P. A. Siddiqi, M. N. Beg, A. Husain and B. Islam, J.
Lipid, 11, 7, 682 (1978).
15. M. N. Beg, F, A. Siddiqi, R. Shyam and I. Altaf, J.
Electroanal. Chem., 8^, 141 (1978).
16. K. N. Beg, F. A. Siddiqi, S. P. Singh, P. Prakash and
(Miss) V. Gupta, J. Electrochim. Acta, 2^, 85 (1979).
17. M, K. Beg, F. A. Siddiqi, S. P. Singh, P. Prakash and
(Miss) V. Gupta, Bull. Chem. Soc., , 1337 (1979).
18. M, N. Beg, F. A. Siddiqi, R. Shyam, M. Arshad and M. M.
Beg, Proc. INSA, 4^ (6), 543 (1979).
19. M. N, Beg, F. A. Siddiqi, H. Arif, H. I. Khan and A.
Haq, Ind. J. Tech., 12» 419 (1979).
20. M. N. Beg, R. Shyam and M. M. Beg, J. Polym. Sci.,
June (1981), (In Press).
21. M. N. Beg, F. A. Siddiqi, K. Ahmad and I. Altaf, J.
Electroanal. Chem., r22, 313-319 (1981).
22. H. T. Clarke and D. Nachmansohn, eds., in "Ion Trans
port Across Membrane", Acad. Press, New York, (1954).
23. F. Helfferich, Ion Exchange, McGraw-Hill, New York,
(1962).
36
24. K. S. Spiegler, ed., "Principles of Desalination",
Acad. Press, New York, (1966).
25. K. S. Spiegler, "Salt Water Purification, Wiley, New
York, (1962).
26. U. Merten, ed., Desalination by Reverse Osmosis, M.I.T.
Press, Cambridge, Massacliusetts, (1966),
27. J. A. Marinsljy, ed., in "Ion-Exchange", Dekker, New
York, (1966).
28. W. D. Stein, The Movement of Molecules Across Cell Mem
branes", Acad. Press, New York, (1967).
29. K. S. Cole, "Membranes, Ions and Impulses", University
of California Press, Berkeley, (1968).
30. N. Lakshminarayanaiah, "Transport Phenomena in Mem
branes", Acad. Press, New York, (I966).
31. N. Lakshminarayanaiah, Electrochemistry Specialist,
Periodical Reports, vol. 4, Chemical Society London,
167 (1974).
32. A. B. Hope, "Ion Transport and Membrane", University
Park Press, Baltimore, Md., (1971).
33. R. A. Arndt and L. D. Roper, "Simple Membrane Electro-
diffusion Theory", University Publications PBSM, Blacks-
burg, Va., (1972).
34. R. Plonsey, Bioelectric Phenomena, McGraw-Hill, New
York, (1969).
37
35. A. Kotyk and K. Janacek, "Cell Membrane Transport,
Principles and Techniques", Plenum Press, New York,
(1970).
36. R. K. Keller, in Membrane Technology and Industrial
Separation Techniques", Noyes Building Park Ridge,
Hev Jersey-07656, London, England, (1976),
37. R, B, Parlin and H, Eyring, in "Ion Transport Across
Membranes", (H.T. Clarke and D, Nachmansohn, eds,),
Acad, Press, New York, (1954).
38. S, R, Caplan and D, C. Mikulecky in "Ion-Exchange",
(J.A. Marinsky, ed,), vol, 1, Dekker, New York, (1966),
39. J. Sandblom and E. Orme, in "Membrane", (G. Eisenman
ed.), vol. 1, Dekker, New York, (1972).
40. E, J, Harris, "Transport and Accumulation in Biological
Systems", Acad, Press, New York, (I96O),
41. R. Schlogl, "Stofftransport durch Membrane", Steinkopff,
Darmstadt, I964, Ber. (1967).
42. E, E, Bittar, ed, "Membrane and Ion Transport", vol, 1,
Interscience, New York, (I970),
43. J, G, Kirkwood, in "Ion Transport Across Membranes",
(H, T, Clarke and D, Nachmansohn, eds,), Acad. Press,
New York, (1954).
44. G, Eisenman, "Membranes", Dekker, New York, vol, 1,
(1972); vol. 2, (1973).
45. J. F. Danielli, M. D. Rosenberg and D. A. Cadenhead,
eds., "Progress in Surface and Membrane Science",
vol. 6, Acad. Press, New York, (1975).
46. G. Eisenman, ed., "Glass Electrodes for Hydrogen and
other Cations", Dekker, New York, (1967).
47. R. A. Durst, ed.,"Ion Selective Electrodes", National
Bureau of Standards, Special Pub. 314, U.S. G-ovemment
Printing Office, Washington, D.C., (1969).
48. D. C. Tosteson, ed., "Symposium on Molecular Basis of
Membrane Function", Prentice-Hall, Englewood Cliffs,
N.J., (1969).
49. M. Kotani, ed., "Advance in Biophysics", vol. 2,
University of Tokyo Press, University Park Press,
Baltimore, Md., (1971).
50. F. Snell, J. Walker, G. Iverson and J, lam, eds,,
"Physical Principles of Biological Membranes", Gordon
and Breach, New York, (1970).
51. J. A. Marinsky and Y. Marcus, eds., "Ion-Exchange and
Solvent Extraction", vol. 1-6, Dekker, New York, (1969-
1974).
52. M. Gereijido and C. A. Rotionne, "Introduction to the
Study of Biological Membranes", Gordon and Breach,
New York, (1970).
53. K. Sollner, in "Diffusion Process", G. N. Sherwood,
39
A. Y. Chadwick, W. M. Muir and F. L. Swinton, eds.,
Gordon and Breach, New York, (1971).
54. W. J. Andelman, ed.," Biophysics and Physiology of
Excitable Memhranes", Van Nostrand Reinhold, New York,
(1971).
55. F. Kreuzer and J. C. F. Siegers, eds., "Biomembranes",
vol. 5, Plenum Press, New York, (1972).
56. K. Sollner, in "Electrochemistry in Biology and Medi
cine", (T. Shedlovsky, ed.), Wiley, New York, (1955).
57. K. Sollner, J. Phys. Chem., 4^, 47 (1945).
58. J, A. Ketchener, in "Modem Aspects of Electrochemistry",
(J. OM. Bockris, ed.), vol. 2, Butterworths, London,
(1959).
59. V. Subrahmanyan and N. Lakshminarayanaiah, Current Sci.
(India), 22, 307 (I960).
60. R. N. Rickles and H. Z. Friedlander, Chem. Eng., 21»
165 (1966).
61. R, P. Buck, CRC Critical Reviews in Analytical Chemis
try, 323 (1976).
62. J. B. B. Randies, Trans. Faraday Soc, , 1573 (1956).
63. R. P. Buck and B. C. Toren, Anal. Chem., 42, 284R (1970).
64. R. P. Buck, Anal. Chem., 4^, 270R (1972); 28R (1974).
65. J. R. Sandifer and R. P. Buck, J. Electroanal. Chem.,
Interfacial Electrochem., ^ , 385 (1974).
40
66. A, ¥ik"by and B. Karlberg, Electrochim Acta , , 1_2, 323
(1974).
67. A. Wikby, Electrochim. Acta., 1^, 329 (1974).
68. G-. Eisenman, J. P. Sandblom and J. L, Walker, Reprint
from Science, 1^, 3765, 965-974 (1967).
69. R. Neihof and K. Sollner, Trans. Faraday Discussion,
No. 21, 94 (1956).
70. A. Mauro, Biophys. J., 2, 179 (1962).
71. P. Muller, D. 0. Rudin, H. T. Tien and W. C. Wescott,
Circular, 26, 1167 (1962); Nature, l^i, 979 (1962); J.
Phys. Chem., 61, 34 (1963).
72. E. Piangor and E. Toth, Anal. Chim. Acta., £][, 291
(1969); Analyst (London), 21f 625 (1970).
73. J. Koryta, Anal. Chim. Acta, 6i, 329 (1972); 21 (1977).
74. R. P. Buck, Anal. Chem., 0, 5, 17R (1978).
75. A. Dravnieks and J. I. Bregman, J. Chem. Eng. New,
I2» 42 (1961).
76. G. Alberti, Atti. Acad, Naz, Lincei, Rend. Classe Sci.
Mat. Nat., , 327 (1961).
77. J. Van R. Smit, J. J. Jacobs and V. Robb, J. Inorg.
Nucl. Chem., 12, 95, 104 (1959).
78. M. Block, Chem. Ind., 1882 (1962).
79. K. S. Rajan, D. B. Boiles, A. J. Casolo and J. I.
Bregman, Desalination, 1, 231 (1966).
41
8 0 . S. R. Caplan, J . E l ec t ro chem. S o c , 108 , 577 (1961 ) .
8 1 . L. Broussard and D. P . Shoemaker, J . Am. Chem. S o c ,
Q2, 1041 (1942) .
8 2 . R. M. B a r r e r , P r o c . Chem. S o c , 99 ( 1 9 5 8 ) .
8 5 . K. A. Kraus , H. 0 . P h i l l i p s , T. A. Ca r l son and J . S.
Johnson , 2nd I n t . Conf. P e a c e f u l Uses of Atomic Energy,
Geneva, 28 , 5 ( 1 9 5 8 ) .
8 4 . M. R. J . Wyl l ie and H. V. P a t n o d e , J . Phys . Chem., ^ ,
204 ( 1 9 5 0 ) .
8 5 . W. U. Mal ik , S. K. S r i v a s t a v a , V. M. Bhanda r i , and
S. Eumar, J . C o l l o i d . I n t e r f a c e S c i . , £^ , 1 (1974) .
8 6 . F . A. S i d d i q i , M. N. Beg, M. A. Ahsan, M. I . R. Khan,
B. I s l a m , J . Membrane S c i . , ±, 275 ( 1 9 7 8 ) .
8 7 . F . A. S i d d i q i , M. N. Beg, A. Haq, M. A. Ahsan, M. I . R.
Khan and S. A. Khan, J . De Chemie P h y s i q u e , i 6 , 57
( 1 9 7 9 ) .
88. S. Loeb and S. Sourirajan, Sea Water Demineralization
by Means of an Osmotic Membrane, Advan. Chem. Ser.,
^ , 117 (1962).
89. P. Mears, J. F. Thain and D. G. Dawson, in "Membranes",
(G. Eisenman, ed.), vol. 1, p. 55, Dekker, New York,
(1972).
90. L. Onsager, Ann. H. Y. Acad. Sci., £6, 241 (1945).
91. 0. Kedem and A. Essing, J. Gen. Physiol., 4^, 1047(1965)
42
92. A Katchalsky and P. F. Curran, "Fonequilibrium Ther
modynamics", Harvard Univ. Press, Cambridge, Massa
chusetts, (1955).
95. S. R. Caplan and D. C. Mikulecky, in "Ion-Exchange"
(J.A. Marinsky, ed.), vol. 1, Dekker, New York, (I966).
94. P. Hears, J. F. Thain, and D. G, Dawson, in
"Membrane - A Series of Advance", (G. Eisenman, Ed.)
Dekker, New York, Chap. 2, (1972).
95. R. P. Rastogi, S. N. Singh, and M. L. Srivastava,
J. Phys. Chem., 14, 1969 (1970); R. P. Rastogi, K.
Singh and J. Singh, ibid., 22» 2574 (1975).
96. R. P. Rastogi, and Ram Shabd, ibid., 81, 1955 (1977).
97. R. P. Rastogi, and K. M. Jha, J. Phys. Chem., 20, 1017
(i960); Trans. Faraday Soc, 6 , 585 (1966).
98. R. P. Rastogi, Z. Singh, and B. M. Misra, Desalina
tion, 1, 52 (1967).
99. H. Ferguson, C. R. Gardner, and R, Paterson, J.C.S.
Faraday I., 68, 2021 (1972).
100. H. T. Tien, and H. P. Ting, J. Colloid and Interface
Sci., 27, 702 (1968).
101. C. R. Gardner, and R. Paterson, J. Chem. Soc, A,
2254 (1971).
102. E. N. Light foot, R. E, Stafford and D. R. Stone,
CRC Crit. Rev. Bioeng., i, 69 (1971).
43
103. E. L. Crussler, J, Am. Inst. Chem. Bng., IX, 1300
(1971).
104. B. J. Zwolinski, H. Eyring and C. B. Reese, J. Phys.
Chem., 51, 1426 (1949).
105. K. J. Laidler and K, E. Shuller, J. Chem. Physic,
11» 851 (1949).
106. S. B. Clough, A. E. Read, A. B. Metzner and V. C.
Behn, 8, 346 (1962).
107. S, U, Li and J, L. Gainer, Ind. Eng. Chem, Fund.,
1, 433 (1968).
108. R. M. Uavari, J. 1. Gainer and K. R. Hall, AIChE. J.,
12, 1028 (1971).
109. D. G. Tsimboukis and J. H. Petropoulos, J. Chem.,
Soc. Faraday Trans. I, 21» 717 (1979).
110. T. lijima, T. Obara, M. Isshiki, T. Seki and K.
Adachi, J. Colloid. Interface Sci., §2* 421 (1978).
111. T. Teorell, Proc. Soc. Exp. Biol. Med., H , 282 (1935);
Proc. Natl. Acad. Sci.' (USA), 2i, 152 (1935); Z. Elec-
trochem., , 460 (1951); Prog. Biophys. Chem., 2, 385
(1953); Trans. Faraday Soc, 1, 1050 (1937).
112. T. Teorell, Discuss. Faraday Soc, No, 21, 9 (1956).
113. K. H. Meyer and J. F. Sievers, Helv. Chim, Acta,, 1_2.,
649 (1936); 1^, 665 (1936); 12, 987 (1936); 20, 634
(1937).
114. G. Scotcharged, J. Am. Chem. Soc, Jl* 2883 (1953).
44
115. R. Schlogl, Discuss. Faraday Soc, No. 2^_, 46 (1956).
116. R. Schlogl, Stofftransport durch Membrane, Steinkopff,
Darmstedt, (1964); Fortschr. Physik. Chem., 9 (1964).
117. R. P. Buck, CRC Critical Review in Analytical Chemis
try, p. 323 (1976).
118. R. H. Wagner, and L. D. Moore Jr., in "Technique of
Organic Chemistry", (A. Weiseberger, ed.), 3rd ed.,
vol. 1, Pat. 1, Wiley (Interscience), New York, 850
(1959).
119. S. B. Tuwiner, "Diffusion and Membrane Technology",
ACS Monograph No. 156, Reinhold, New York, (1962).
120. J. A. Kitchener, in "Modem Aspect of Electrochemis
try", (J.O'M. Bockris, ed.), vol. 2, p. 154, Butter-
worths, London, (1959).
121. R. Kumin, "Ion Exchange Resins", 2nd ed., Wiley, New
York, 100 (1958).
122. K. S. Spiegler, in "Ion-Exchange Technology", (F.C.
Nachod and J. Schubert, eds.), Acad. Press, New York,
127 (1956).
123. J. R. Wilson, ed, "Demineralization by Electrodialysis"
Butterworths, London, (I960).
124. F. Bergsma, and C. A. Kruissink, Fortschr. Hoch Polymer
Forsch., 2, 307 (1961),
125. J. F. A. Hazenberg, Dechema Monograph, ££, 487 (1962).
126. N. Krishnaswamy, J. Sci. Ind. Res. (India), 17A, 328
45
(1958); 20A, 656 (1961); g^A, 244 (1965).
127. P . H. Camel l and H. G. Cassidy, J . Polym. S c i . ,
i i , 233 (1961).
128. N. Laksluninarayanaiah, Chem. Rev., 6^, 491 (1965).
C H A P T S R - I
MEMBRANE POTENTIAL, EVALUATION OF CHARGE DENSITY
AND EXAMINATION OF RECENTLY DEVELOPED THEORIES
47
The electric and electroosmotic phenomena exhibited
by synthetic and biological membrane systems have received
a great deal of interest. An extensive review of the early
developments in the field of electrokinetic phenomena in
synthetic membranes was given by Sollner (1). Teorell (2)
reviewed more recent contributions to the understanding of
electrokinetic phenomena such as the membrane potential of
synthetic membranes, which has been widely discussed by
several authors (3-7) on the basis of theory of Teorell
(8),.Meyer and Sievers (9). However, there have been very
few attempts to apply the comprehensive treatment given
by Schlogl (10) to calculate membrane potentials of complex
synthetic membrane system, Nagasawa and Kagawa (6) measured
membrane potentials in binary salt solutions with cation
exchange membrane and compared their results with the
Schlogl relation. In order to understand the mechanism of
transport through the living systems, composite membranes
(11) for quite some time and polymeric and millipore filter
paper supported membranes in recent years have been deve
loped as models. We have been engaged in a similar studies
and have developed various parchment supported inorganic
precipitate membranes (12-21),
In this chapter, we have described the preparation
of parchment supported thallium dichromate and thallium
48
permanganate membranes and membrane p o t e n t i a l measurements.
The thermodynamics parameters governing the membrane pheno
mena have been evaluated from the membrane p o t e n t i a l measure
ments using the theory of Teore l l (25 ,24) , Meyer and Sievers
( 9 ) , Kobatake et a l . (25-36) and the r ecen t ly developed
theory of Tasaka et a l . (57) based on the p r i n c i p l e s of
i r r e v e r s i b l e thermodynamics.
E X P E R I M E N T A L
Thallium dichromate and thallixim permanganate mem
branes were prepared by the method of i n t e r a c t i o n suggested
by Beg and coworkers (12-22) using parchment paper (supp
l i e d by M/S. Baird and Tatlock L t d . , London) and 0.1M
aqueous so lu t ions of tha l l ium su lpha te , potassium d ich ro
mate and 0.01M potassixm permanganate. F i r s t of a l l parch
ment paper was soaked in d i s t i l l e d water and then t i e d to
the f l a t mouth of a beaker. A 0.1M so lu t ion of thal l ium
sulphate was taken ins ide i t . I t was then suspended in a
so lu t ion of 0.1M potassium dichromate for about 72 hours .
The two so lu t ions were l a t e r interchanged and kept for an
other 72 hours . The membrane thus obtained was washed with
deionized water for the removal of free e l e c t r o l y t e s .
Similar procedure was adopted for the prepara t ion of t h a l l
ium permanganate membrane by taking 0.1M so lu t ion of t h a l l
ium sulphate and O.OIM potassium permanganate.
49
The e lect rochemical c e l l of the type
Saturated calomel
e lec t rode
Solut ion I Memhrane } Solution | Saturated /p X ; ' (n \ • calomel ^^2^ • I '^^V I e lectrode
i I I
Donnan Donnan p o t e n t i a l p o t e n t i a l
Diffusion p o t e n t i a l
was used t o measure the membrane p o t e n t i a l . A tenfold
d i f fe rence i n concent ra t ion , 02/0-1 = 10, of the chlorides
of potassium, sodium, l i th ium and ammonium across the mem
brane was maintained. Al l measurements were carr ied out
using a water thermostat kept at temperature 25 + 0.1 °0 .
The so lu t ions i n both the chambers were s t i r r e d by a pa i r
of magnetic s t i r r e r s . The e l e c t r o l y t e so lu t ions were p r e
pared from a n a l y t i c a l grade reagents and deionized water.
D I S O U S S I O H
The values of membrane p o t e n t i a l E measured across
parchment supported tha l l ium dichromate and tha l l ium pe r
manganate membranes in contact with d i f f e ren t concentrat ions
of var ious 1:1 e l e c t r o l y t e s are given in Tables 1.1 and 1,2
and are also p lo t t ed in F i g s . 1.1 and 1.2 agains t log
(Ci+C2)/2.
The va lues of membrane p o t e n t i a l observed across the
TABLE 1.1
THE VALUES OF OBSERVED MEMBRANE POTENTIAL E ^ (mV) FOR 1:1
ELECTROLYTES AT VARIOUS CONCENTRATIONS ACROSS PARCHMENT
SUPPORTED THALLIUM DICHROMATE MEMBRANE
Concentrat ion (Mol. 1~') C2/C1
10xlO~Vlx10- ' '
5xlO'V53!:lO"^
1x10~VlxlO~2
5x10*^/5x10"^
1x10"^/1xlO~^
5xlO"^/5x10"'^
I x l O ' ^ / l x l O - ^
KCl
-1.15
-0.80
2.88
11.67
31.81
36.40
42.50
Elect:
NaCl
-9.76
-7.60
-4.80
2.68
23.47
29.40
32.00
ro ly te
L iC l
-16.89
-14.75
-12.50
-6.50
20.53
25.48
33.25
NH.Cl 4
0.74
1.08
6.60
12.28
31.43
36.87
41.12
TABLE 1.2
THE VALUES OF OBSERVED MEMBRANE POTENTIAL Ej (mV) FOR 1:1
ELECTROLYTES AT VARIOUS CONCENTRATIONS ACROSS PARCHMENT
SUPPORTED THALLIUM PERJIANGANATE MEMBRANE
C o n c e n t r a t i o n C2/C1
lOxlO~VlxlO"^
5x10 'V5x10 ' ' ^
l x l O " V l x l O " ^
5x l0"^ /5x l0 ' "^
1 x l 0 " ^ / 1 x l 0 " ^
5x l0"^ /5x l0" '^
I x l o ' ^ / l x i o " " ^
(Mol. 1""') KCl
- 0 . 7 1
- 0 . 4 0
5.50
13.35
35.11
38.26
44 ,25
E l e c t r o l y t e
NaCl
- 9 . 1 8
-8 .11
- 1 . 1 7
3.67
27.31
33.21
39.69
LiCl
- 1 7 . 0 0
- 1 5 . 3 4
-10 .82
2.29
22.51
28.53
35 .53
NH4CI
1.14
1.60
10.85
16.93
34.84
38.85
43.02
> e
e UJ
z
o Q.
Z < ffi
t i j
40
20
- 2 0 -A
Fi •q 11 Plots of membrane potential Em ( m V ) vs loq
(C2 + C | ) / 2 usinq 11 electrolyte solution across
parchment supported Thallium dichromate membrane
> •
<
o 0. tij z < at 0> I lU X
AO -
20
- 2 0 -L - 3 - 2
LOGlC2*C , ) /2
- I
-—A
0
Fiq. 1.2 Plots of membrane potential Em (mV ) vs.loc; ( C 2 * C | ) / 2 unnq I I electrolyte solution! across parchment supported Thallium permanqanate membrane
52
solution. By the addition of lani-univalent electrolytes,
there will be a tendency for the cations to accumulate on
the solution side of the fixed double layer by increasing
the positive charge density, the interfacial potential
difference changes thereby changing the overall membrane
potential. If the electrolyte concentrations are made
larger the electrical potential changes in a successive
manner. This type of phenomena is not peculiar to these
systems.
The fixed charge groups present in collodion material
were estimated by titration procedure (59). lakshminaraya-
naiah (40) used isotopic and potentiometric methods to eva
luate the apparent fixed charge on the thin membranes of
parlodion. In the present studies the titration method
proved inconvenient and very inaccurate, while the isotopic
method was discarded in view of the strong ionic adsorption
phenomena exhibited by these systems. Consequently the
potentiometric method was used. This method is based on
the fixed charge theory of membrane potential proposed
simultaneously by Teorell (25,24) and Meyer and Sievers (9),
The important feature of the TMS theory have been nicely
described by Lakshminarayanaiah (41) and recently used by
various investigators including Beg and coworkers in a num
ber of studies with ion exchange membranes (12-21). Accord
ing to this theory membrane potential is considered to be
53
composed of two Donnan potentials at the two solution-
membrane interfaces and a diffusion potential arising
from the unequal concentration of the two memhrane phases.
These authors (8,9,23,24) derived following equation for
membrane potential applicable to a highly idealized system,
viz. ,
Co (vAc? + x^ + X) . JAOI + X + X 5 ) Bj = 59.2 log f- + U log
^ ( v4c| + x2 + X (AC2 + r + xu )
(1.1)
where U = (u - v)/(u + v), u and v are the mobilities of
cation and anion, respectively in the membrane phase; X is
the charge on the membrane expressed in equivalents/litre
of imbibed solution. Equation 1.1 has been frequently used
for the evaluation of the fixed charge density X of a mem
brane (42). In order to evaluate this parameter for the
simple case of 1:1 electrolyte and membrane carrying a net
negative charge of unity (X = 1), theoretical concentra
tion potentials E^ existing across the membrane are calcu
lated as function C2. the ratio 02/0^ being kept at cons
tant value for different mobility ratios, u/v. These are
plotted as shown in Figs. 1.3 and 1.4. The observed mem
brane potential values are then plotted in the same figure.
The experimental curve is shifted horizontally xintil it co
incides with one of the theoretical curves. The extent of
Fi<j. 1,3 Eva lua t ion of membrane f ixed charqe density (X^and
mobi l i ty ra t io (U/^y ^ ,n the membrane phase. The smooth curves on the l e f t are theoret ica l me mbrane potent lal ( X r l l a t d i f f e r e n t mob i l i t y r a t i o ( U / \ / ) a n d an the r i q h t areobserved membrane p o t e n t i a l across Thalhum dichromate membrane as a f unc t i on o f _ l o q C2 using I 1 e lec t ro ly te so lu t ions .
L 0 C, C 2 »
Fiq I 4 Evaluation of membrane f i x e d charge density ( X )ini^ mobil(ty ra t io ( U / V ) m the membrane phase The smooth c_urvesonthe l e f t are t h e o r e t i c a l membrane potent ia l
( X - 1 ) at d i f ferent mobility r atio ( U / V ) and on the r iqht are observed membrane p o t e n t i a l across 1 hallium permanganate membrane as a f u n c t i o n of - i o q C 2 u s i n ^
r 1 e l t c t f o l y t e so lu t ions
54
this shift gives log X and the coinciding theoretical
curve, the value of u/v (vide Figs. 1,3 and 1.4). The
values of X and u/v, derived in this way, for the mem
branes iinder investigation are given in Table 1.3.
Recently, Kobatake, Woriaki, Toyoshima and Fujita
(30) on the basis of the thermodynamics of irreversible
processes derived the following equation for the electri
cal potential E which arises when a negatively charged
membrane separates two solutions of a 1:1 electrolyte of
concentration C and Cp (C. < Cp)
E = SI m P
1 Co 1 Co +°C/3X
i m -2 - (1 + i . 2c^) in (- - ) '^ 1 '^ C^ +o /3X
(1.2)
where -C = U/(u + v) ; / = 1 + KFX/u;
F and K represent, respectively, the Faraday constant and
a constant dependent upon the viscosity of the solution
and structural details of the polymer network of which the
membrane is composed. To evaluate the membrane parameters,
oC , fi and X, two limiting forms of the above equation were
derived. When the external concentration C is sufficiently
small,
\W\ := 1 m ^ - ( r - 1) (1 -H 1 - 2 )(^) + ... (1.3)
where | B^ | = FEm/RT and X" = C2/C1
55
H O
H O • H
i n
CO
o
IT*
LA
CO
o
H O cd 12!
O
VD
cr> o
t<>
H o CM " *
^
9
0)
CO
O o
-P >»
H O
o <D
H W
0)
0)
a o
o
• H H H 0}
EH
3 (D
I I
EH
56
when the s a l t concentra t ion C i s high
*- •• -"^ 2(1 ^ ) ^ n 7 ' ^2 (1.4)
where t_ i s the apparent t ransference niimber of coions
(anions) i n a negat ive ly charged membrane defined by
[ S ; | = (1 - 2 t j l n r (1.5)
The value of t_ ca lcula ted from observed membrane poten
t i a l s using equation 1.5 for the membranes, are given i n
Tables 1.4 and 1.5. Equation 1.3 was used to give the
value of ft and a r e l a t i o n between oC and X by evaluat ing
the i n t e r cep t and the i n i t i a l slope of the p lo t of | E j
against Cp (Fig . 1.5), while equation 1,4 was used t o eva
lua t e cKI from the in t e r cep t of a p lo t of 1/t_ against l/Cp
(P ig . 1.6) . The values of X were then determined by i n
se r t i ng t h i s value of oC i n the r e l a t i o n between and X
obtained e a r l i e r . The values ofoC,/? , and X derived in t h i s
way for the membranes using 1:1 electrolsr t es are given in
Table 1.6.
Once the values of the parameters tyC , fi and X for a
given membrane-electrolyte system have been determined, one
can get the t h e o r e t i c a l Ej versus C2 curves using equation
for any given 7" (T"= 03/0^) and compare i t with the co r r e s
ponding experimental d a t a . For t h i s comparison equation
57
TABLE 1.4
TRANSFERENCE NUMBER tsr r 0^ COIONS DERIVED FROM OBSERVED
14EMBRANB POTENTIAL AT VARIOUS ELECTROLYTE CONCENTRATIONS
THROUGH PARCHMENT SUPPORTED THALLIUT-I BICHROMATE MEMBRANE
Electrolyte __ Concentration (Mol. l" ) C2/C1
lOxlO"VlxlO~"'
5xl0"V5x10"^
1x10"Vlx10""^
5xl0"^/5x10"^
Ixl0~ /1x10"'
5xlO"^/5x10~^
Ix10"^/1x10~^
KCl
0.509
0.506
0.476
0.401
0.231
0.192
0.140
NaCl
0.582
0.564
0.540
0.477
0.300
0.252
0.229
Li CI
0.642
0.624
0.605
0.562
0.326
0.285
0.219
NH4CI
0.494
0.490
0.444
0.396
0.236
0.188
0.152
TABLE 1.5
TRANSFERENCE NUI'ffiER t - ^ OF COIONS DERIVED FROM OBSERVED app
MEMBRANE POTENTIAL AT VARIOUS ELECTROLYTE CONCENTRATIONS
THROUGH PARCHMENT SUPPORTED THALLIU I PERl'IANGANATE MEMBRANE E l e c t r o l y t e . KCl NaCl LiCl NH^Cl C o n c e n t r a t i o n (Mol. 1~ ) ^ ^2/^1
lOx lO 'V lx lO""* 0.506 0.578 0.663
5xlO"V5x10"^ 0.503 0.568 0.629
0.490
0.486
1x10"V lx lO-2 0.454 0.509 0.591 0.408
5x10~^/5x10"5 0.387 0.468 0.480 0.357
1x10-2/1x10-5 0.203 0.269 0.309 0.206
5x10-5/5x10"'^ 0.177 0.181 0.259 0.171
1x10-5/1 xlO"'^ 0.126 0.165 0.199 0.137
o
e UJ l l . I I
0 6
0 4
0.3 ± ± J-0 0 . 2 5 0 , 5 0 .75 I
0 2 X 1 0 ^
FJq. 1.5 P lo ts of FEm / 2 . 3 0 3 RT vs C2XIO2 fo r l iar thment s upported (A) Thall ium dichrc and ( B ) Thal l ium permanganate membrane j s i n q 1:1 e lectrolyte solutions .
f i q . 1.6 Plots of 1/tapp vs. 1 / C2 for parchment supported(AUhallium dichromate and (B) Thallium permanganate membranes usinq V\ electrolyte solutions at constant r ( Y ' - l O )
58
H O
OO to to
o LfN
o
H O •H
to to to
• o
o
EH P
H O
is
"i
VO
o
VO t o
VO
cvi
o to
II
o M
PM EH
is; o M
EH
o o o
H O M
a>
o u o <D
H
(D
^1
PM
0)
a>
•p OS
a o
•H
H H a
4:1
CO
9
«>
en
59
was wr i t t en in the form
i i : ^ - ^ = z (1.6)
(e'l - 1)
with, q and Z defined hy
|i | + (1 + 2<<) m r q. = -i-SJ , and Z = Cg/ /? X
1//3 + (1 - 2oC)
Thus if equation 1.6 is valid, the value of (T"-e^)/(e^-1)
calculated from the predetermined values of oC, /3 and X
through measured membrane potential E^, for a particular
value of T must fall on a straight line which should have
a vmit slope and pass the co-ordinate origin when plotted
against Z. This behaviour should be observed irrespective
of the value of 7 and the kind of membrane-electrolyte sys
tem used. Fig. 1.7 demonstrate that the theoretical pre
diction of equation 1.6 or equation 1.2 is borne out quite
satisfactorily by our experimental results.
Kobatake and Kamo (33) derived another equation 1.7
for the membrane potential starting with the basic flow
equation provided by the thermodynamics of irreversible
processes and using a different sets of assumptions: namely,
(a) the contribution of mass movement is negligible (33),
and (b) small ions do not behave idealy in charged membrane
(33). Their result is:
I I
or
I
o
0 K C I
• N a C I
& L i C l
Fiq, 1.7 P l o t s o f l o q ( Y ' - e ^ ) / ( e ^ - 1 ) v s . l o q Z for parchment supported (A) Thall ium dichromate and (B l Thallium permanganate membranes usmq 11 electrolyte solutions.
60
m F ^ /cf+??+ (2<-i) iz(x Uo^+^h^+^x
(1.7)
where j is a characteristic factor of the membrane-electro
lyte pair, and represents the fraction of counterions not
tightly hound to the membrane skeleton. The product jrfX is
termed the thermodynamically effective fixed charge density
of a membrane; the other terms have their usual signifi
cance. Equation 1.7 reduced to the IMS membrane potential
equation (eq. 1.1) for j = 1. Since it was somewhat trouble
some to evaluate ^X at an arbitrary external electrolyte
concentration from the observed membrane potential using
eq. 1.7, Kobatake and Eamo (35) proposed a simple method
using the following approximate equation for the diffusive
contribution to the emf of a cell with transport:
^m = - ¥ (1 - 2t-pp) in (C2/C1) (1.8)
where ^app ^^ '^^^ apparent t rans fe rence number of colons
in the membrane phase. Comparison of equations 1.7 and 1.8
g ives ,
I n /4^^ + 1 + 2 - 1 JA^I + 1 + 1
v4$ + 1 + 2 - 1 A j f + 1 + 1 app 2 I n y 2 I n f ^ ^^^
where ^ = C/^X
Gi
On the other hand (32,33)» the mass fixed transfer
ence number of colons in a negatively charged membrane
immersed in an electrolyte solution of concentration G was
defined by
t_ = vc_/(uc+ + vc_) (1.10)
where c . and c_ are the concent ra t ions of ca t ions and an
i o n s , r e s p e c t i v e l y , i n the membrane phase. This equation
was transformed to
k^ + 1 + 1 t_ = 1 -^ (1.11)
h^ + 1 + (2^- 1)
using appropriate equations for activity coefficients,
mobilities of small ions in the membrane phase, and the
equilibrium condition for electrical neutrality (32,33).
The difference between the apparent transference number
t- calculated from eq. 1.9 and t from equation 1,11 for app
various reduced concentrations (^ = C/^X) was found to
be always less than 2^ over a wide range of external elec
trolyte concentrations. Therefore, t- and t were con-app
sidered practically the same. As a result the apparent transference number t- evaluated from the membrane poten-
app
tial data was used for the determination of the thermodyna-
mically effective fixed charge density ^X of the membrane
at a given average salt concentration C [c = (C.+Cp)/2l
using equation 1,11 as follows:
G2
Rearrangement of equation 1.11 provides a defini
tion of permselectivity Pg by the expression
^ 1 - t_ -oC
U ^ T T ) ^ ^- (2cC - 1)(1 - tj ^ P« (1.12)
This equation can be used to find the value of the perm-
selectivity, Pg , from membrane potential measurements and
the values of t- using equation 1.8. The values of Pg
obtained using the right hand side of equation 1.12
(Tables 1.7 and 1.8) were plotted against log C. The con
centration at which Pg (where = C/^X = 1) becomes equal
to (1/5) gives the values of the thermodynamically effec
tive fixed charge density jX as required by the left side
of equation 1.12. Figs. 1,8 and 1.9 represent plots of
Pg versus log (0^+02)/2 for the parchment supported thall
ium dichromate and thallium permanganate membranes in con
tact with various 1:1 electrolytes. The values of jifX thus
derived for the membrane and 1:1 electrolyte combinations
2 -y2
are given in Table 1.9. The plots of Pg versus (1+4'E )
are drawn for both membranes with KCl, NaCl and LiCI and
shown in Fig. 1.10. It is evident that the line nearly
passes through the origin with \uiit slope, confirming the
applicability of Kobatake's equation to these membranes.
More recently, Tasaka et al. (37) derived an equa
tion for the membrane potential across a charged membrane.
G3
TABLE 1.7
VALUES OP PERMSELECTIVITY Pg OF PAHCHiyiENT SUPPORTED THALLIUM
BICHROMATE MEICBRANE USIN& VARIOUS 1:1 ELECTROLYTES AT DIF
FERENT CONCENTRATIONS
E l e c t r o l y t e _^ C o n c e n t r a t i o n (Mol. 1~ ) C2/G1
lOxlo"Vlx10~^
5z lO"V5x10"^
1 x l 0 " V l x 1 0 " ^
SxlO'^/SxIO"^
I x l O ' ^ / l x l o " ^
5x10"^/5x10~^
1x10*^/1x10"^
KCl
0.042
0 .048
0.119
0.255
0.579
0.652
0.748
TABLE 1.8
NaCl
0 .016
0 .053
0.102
0 .224
0.541
0.621
0 .658
LiCl
0.017
0.056
0.096
0.183
0.586
0.647
0.738
NH^Cl
0.031
0.039
0.143
0.227
0.546
0.636
0.706
VALUES OF PERMSELECTIVITY Pg OF PARCHMENT SUPPORTED THALLIUM
PERMANGANATE MEMBRANE USING VARIOUS 1:1 ELECTROLYTES AT DIF
FERENT CONCENTRATIONS
Electrolyte . Concentration (Mol. 1" ) c^/c^
KCl NaCl LiCl NH.Cl
lOxlo'VlxlO""*
5xlO"V5x10"^
1xlO"Vlx10"^
5xlO~^/5x10~^
Ixlo'^/lxlO"^
5xlO"^/5x10"^
IxlO'^/lxlO""^
0.028
0.034
0.132
0.265
0.619
0.669
0.765
0.004
0 .025
0.142 .
0.222
0.579
0.724
0.749
0.016
0.089
0.168
0.375
0.639
0.706
0.782
0.020
0.028
0.184
0.286
0.586
0.658
0.726
0.8
0.6 -
>-I -
I-o Ui
(A
z
0<A -
0 2
- 4 - 3 - 2 - I
LOG t C 2 * C | ) / 2
F'lq. 1.8 Ploti of Ps V8. loq (C2*C| ) /2 for parchment tupporttd Thallium permanqanate membrant in contact with M electrolyte solutions
0 8
>
Z flC Ui a.
0 6
O.A\-
0 2
- 3 - 2 - I 0
LOG « C2+ C i ) / 2
Fjq. 1,9 Plots of Ps vs log (C2*-C|')/2 for parchment supported ThaUtum dichromale membrane mcontacl With \'\ electrolyte solutions.
64
EH
pq
o 8 °
+1 in cvi
EH
en
H o
H o •H
tn
oo
<T\
M
EH PP O
EH 03
H O cd
O
o
EH o VO eg
«
if\ CM
•
s H P4
> M EH O
o CO w t3
0)
o -p o
H
<D
U
e s
• • p i o u ^ o •H
•O Q
3 •H H H
a a Bi
H " V . cf ®
• k
C\J O
"N I'M
^ k . - i '
o> •p at 9 tiO
s g 0) p< d
3 •H H H ed ^
e
H
o* a>
• k
CM O T *
M ^-^
IX v_x
0.8
o:
•o »
0.8 1 0
0.8
0.2
o K C l
* NaC(
a 0 6 I- • " - iCI
0.4 -
o
T
0 2 1.0 0 . 4 0 .6 0.8
iq. 1.10 Plots of P$ vs 1/^4^2+1 for parchment 5upported(A) Thallium d.chromate and (B) Thallium permanqanate membranes usinq 1 :1 electrolyte solutions.
Go
The total membrane potential E was considered as sum of
a diffusion potential, B^, inside the membrane and the
electrolytic potential difference, E , between the membrane
surfaces and the electrolyte solutions on both sides of the
membrane. The diffusion potential, E,, was obtained by
integrating the basic flow equation for diffusion (37),
while the electrostatic potential difference, B , was cal-
culated from the Donnan's theory, stated mathematically,
B„ = E, + E^ (1.13a) m a e
where
-E, = - / - ^ ^ :r- dx + 1 FCQ (C_ + X)u + C_v
,2 (L + X)u iiT J __ d In €L ^ 1 ( C_ + X) u + C.v
- ^ J -:: = = — d In a_ (1.13b) * 1 (C + X)u + C«v
and
-E = - ^ l n 3 ^ (1.13c) a— a« 1 2
where a- and a- are the activities of the electrolyte on 1 2
the two sides of the membrane, the overbars refer to the
phenomena in the membrane phase. J is the flow of elec
trolyte in the absence of an external electric field; C_
is the effective concentration of colon, and (C_ - X) is
GG
the effective concentration of counterion. Other symbols
have the i r usual significance. On integrating equation
1.13 in the limit of high electrolyte concentrations across
the membrane, one obtains the following equation for the
membrane potent ia l : -
m
1 -R T C Q ( U - V ) K
1 -XJ,
2RTCQVK
imr + RTX ( - ^ )
1 _ ^'^o^^-^^^ 4RTCQUVK
2Fuv RTC K o 1 -XJ.
2RTCQVK
( f - l )C^ (1.14)
At suff icient ly high e lect rolyte concentrations, equation
1.14 can be approximated to
RT /iT-K , A JL + (1.15)
Equation 1,15 predicts a linear relationship between E and
I/C2. Plots of EjQ versus I/C2 for the membranes are repre
sented in Pig. 1.11. A set of straight lines are in agree
ment with equation 1.15. This justifies the reduction of
equation 1.14 into equation 1.15. The values of X derived
from the slope of the lines are given in Table 1.10.
It is noted from Tables 1.3, 1.9 and 1.10 that the
20 o KCl • N a d
(A )
1/ca Fi'q. I l l Plots of Em/C( r~ l ) / y 3 vs. 1/C2for
parchment supported ( A ) Thallium dichronfate and ( 6 ) Thallrum permanganate membranes, using 11 electrolyte solutions
G7
0)
o
+1
CM
• *-
^
9 & I
X * « l
EH M
a
EH < CO
EH CO
fe
<«J O !> PM
H O
H O
H O
H o
a>
o u -p o 0) H
0)
•**•
"«*•
• Csl
t^ •«-
• t<
CM
GO
CM
Q o u Xi o
H H 05
EH
<D
CM
o
CM
cn <«i-• CM
ITV t -
• CM
u\
9
S (90
9 g < Pi <D
•H H
EH
CM
G8
values of the effective fixed charge densities evaluated
from the different methods are almost the same. The slight
deviations may be accounted to the different procedure
adopted for the evaluation. It may, therefore, be conclu
ded that the methods developed recently for the evaluation
of effective fixed charge density based on thermodynamics
of irreversible processes are valid for the membrane-
electrolyte systems under investigation.
59
R E F E R E N C E S
1. Z. Sollner, in "Charged Gels and Membranes" (E. Sele-
gny, Bd.)» vol. I, p. 3, Reidel, Dordrecht, Holland,
(1976).
2. T. Teorell, in "Charged Gels and Membranes", (E.
Selegny, Ed.), vol. I, p. 57, Reidel, Dordrecht,
Holland, (1976).
3. K. S. Spiegler, J. Electrochem. Soc., iQO, 303C (1953).
4. R. Schlogl, Z. Electrochem., , 644 (1952).
5. G. Schmid, Z. Electrochem., , 424 (1950); , 229
(1951).
6. M. Nagasawa and I. Kagawa, Discuss. Faraday Soc, 21 .
52 (1956).
7. W. Pusch, in "Charged Gels and Membranes", (E. Selegny,
Ed.), vol. I, p. 267, Reidel, Dordrecht, Holland, (1976)
8. T. Teorell, Proc. Soc. Exp. Biol. Med., 21, 282 (1935);
Trans. Faraday Soc, 2^, 1053, 1086 (1937).
9. K. H, Meyer and J. F. Sievers, Helv. Chim. Acta., j_2,
649 (1936).
10. R. Schlogl, Z. Phys. Chem., N.F. 1, 305 (1954).
11. N. laksliminarayanaiah and F. A. Siddiqi, in "Membrane
Processes in Industry and Biomedicine", M. Bier., Ed.,
Plenum Press, New York, p. 301 (1971).
12. M. N. Beg, F. A. Siddiqi and R. Shyam, Can. J. Chem.,
70
5 3 ( 1 0 ^ 1680 (1977 ) .
1 3 . M. N. Beg, F . A. S i d d i q i , R. Shyam and M. Arshad,
J . MemTDrane S c i . , 2 , 365 (1977 ) .
14. M. N. Beg, F . A. S i d d i q i , R. Shyam and I . A l t a f , J .
E l e c t r o a n a l . Chem., S^, 141 ( 1 9 7 8 ) .
15 . F . A. S i d d i q i , M. N, Beg, A. Husain ani B, I s l a m , J .
L i p i d s , l i , 7 , 682 ( 1 9 7 8 ) .
16 . F . A. S i d d i q i , M. N. Beg, S. P . Singh and A. Haq, B u l l .
Chem. Soc. J p n . , 4 9 ( 1 9 ) . 2864 (1976 ) .
17 . F . A. S i d d i q i , M. N. Beg, A. Haq and S. P . Singh,
E l e c t r o c h i m i c a A c t a . , 2 2 ( 6 ) . 631 ( 1 9 7 7 ) .
18 . F . A. S i d d i q i , M. N. Beg and P . P r a k a s h , J . E l e c t r o a n a l .
Chem., 8 0 , 223 ( 1 9 7 7 ) .
19 . F . A. S i d d i q i , M. N. Beg and S. P . S ingh , J . Polym.
S c i . , 1 1 , 959 ( 1 9 7 7 ) .
20 . F . A. S i d d i q i , M. N. Beg, A. Haq, M. A. Ahsan and M. I . R,
Khan, J . De Chimie P h y s i q u e , 2±, 932 ( 1 9 7 7 ) .
2 1 . M. N. Beg, R. Shyam and M. M. Beg, J . Polym. S c i . ,
June ( 1 9 8 1 ) , ( i n p r e s s ) .
22 . M. N. Beg, F . A. S i d d i q i , K. Ahmad and I . A l t a f , J .
E l e c t r o a n a l . Chem., 1 2 2 , 313-319 ( 1 9 8 1 ) .
2 3 . T. T e o r e l l , J . Gen, P h y s i o l . , 1 ^ , 917 (1936) ; P r o c ,
N a t l . Acad. S c i . , (USA), 2±, 152 (1936 ) ; Z. E l e c t r o c h e m . ,
i ^ , 460 (1951) ; N a t u r e , 162, 961 (1948) ; A r c h - S c i .
71
P h y s i o l . , 2 , 205 ( 1 9 4 9 ) ; JProg. Biophys . Chem., 1 ,
385 ( 1 9 5 3 ) .
24 . T. T e o r e l l , D i s c u s s . Faraday S o c , 2^,, 9 ( 1956 ) .
2 5 . T. Ueda, N. Kamo, N. I s h i d a and Y. Kobatake, J . Phys .
Chem., 1 6 , 2447 ( 1 9 7 2 ) .
26 . M. Nagasawa and Y. Kobatake , J . P h y s . Chem., ^ , 1017
( 1 9 5 2 ) .
2 7 . Y. Kobatake, J . Chem. P h y s . , 28 , 146 (1958 ) .
28 . Y. Kobatake , T. Njoriaki, Y. Toyoshima and H. F u j i t a ,
J . P h y s . Chem., 6£, 3981 (1965 ) .
29 . N. Kamo, Y. Toyoshima, H. Nozaki and Y. Kobatake,
K o l l o i d - Z , Z - P o l y m . , 2^8, (1971) ; 2 ^ , 1061 (1971 ) .
30 . Y. Toyoshima, M. Yuasa, Y. Kobatake and H. F u j i t a ,
T r a n s . Faraday S o c , 6^, 2803, 2814 ( 1 9 6 7 ) .
3 1 . M. Yuasa, Y. Kobatake and H. F u j i t a , J . Phys . Chem., 1 2 ,
2871 ( 1 9 6 8 ) .
32 . N. Kamo, M. Oikawa and Y. Kobatake , J , Phys . Chem.,
ZL. 92 ( 1 9 7 3 ) .
3 3 . Y. Kobatake and N. Kamo, P r o g . P o l y , S c i , J p n . , ^ ,
257 ( 1 9 7 2 ) .
34 . T. Ueda and Y. Kobatake, J . Phys . Chem., XL* 2995 (1973) ;
N. Kamo, Chem. Pharm. D u l l . J p n . , 2 ^ , 3146 (1976) .
3 5 . N. Kamo, N. Nazemota and Y. Kobatake, T a l e n t a , _24_, 111
( 1 9 7 7 ) .
72
36. H. Pujita and Y. KobataKe, J. Colloid. Interface Sci.,
22, 609 (1968).
37. M. Tasaka, N. Aoki, Y. Konda and M. Kagasawa, J. Phys.
Chem., 21f 1507 (1975).
58, N. Lakshminarayanaiah, "Transport Phenomena in Mem
branes", Academic Press, New York, p. 243 (1969).
39. K. S. Sollner, J. Phys. Chem., ^ , 171 (1945).
40. N. Lakshminarayanaiah and F, A. Siddiqi, Biophys.
J., il, 600, 617 (1971); ibid., 12, 540 (1972).
41. N. lakshminarayanaiah, "Transport Phenomena in Mem
branes", Academic Press, New York, N.Y., p. 196 (1969).
42. N. Lakshminarayanaiah, "Transport Phenomena in Mem
branes", Academic Press, New York, p. 202-203 (1969).
C H A P T E R - II
MEMBRANE CONDUCTANCE AND APPLICATION
OF ABSOLUTE REACTION RATE THEORY
74
When an e l e c t r i c f i e l d i s applied to a membrane
system
Anode I Solut ion (C) | Membrane | Solution (C) | Cathode
the current i s car r ied through the membrane by the ions
whose movement w i l l be f a c i l i t a t e d i f the membrane i s
highly conducting (high fixed charge d e n s i t y ) . The move
ment may not take place i f the membrane i s non-conducting
( d i e l e c t r i c ) . But, in genera l non-se lec t ive membranes
which are mostly porous are not completely non-conducting.
Both ca t ions and anions are t r ans fe r r ed across i t ; whereas
s e l e c t i v e membranes t r a n s f e r only counterions provided the
ex te rna l so lu t ions are d i l u t e ( 1 ) .
Ion penaeation in membranes i s usua l ly character ized
by such measurable parameters as conductance, current ( i ) -
vol tage (V) r e l a t i o n s h i p ( 2 ) , i on ic f luxes , and membrane
p o t e n t i a l s . The measurement of the conduct ivi ty of mem
brane systems with conventional ac or dc methods, although
s t r a i g h t forward, r equ i r e s spec ia l a t t e n t i o n due to some
p a r t i c u l a r f ea tu res not met wi thin bulk e l e c t r o l y t e so lu
t i o n s . A number of techniques reviewed by Steymans (3)
and othfer ( 4 ) , a l l based on Ohm's law, ex i s t to measure the
membrane ( ion exchange) conductance which depends on the
i n t r i n s i c p r o p e r t i e s such as the fixed charge concentrat ion,
75
temperature, and composition of the external solution (5).
The dependent of specific conductance upon the concentra
tion of the external solution can be qualitatively pre
dicted from the fixed charge theory (6).
According to Helfferich (7,8) ion-exchange kinetics
in organic resins are controlled by diffusion of counter-
ions rather than by the actual chemical reaction rate at
the exchange site. Brown et al (9,10) have explained the
observed kinetics in zeolites in terms of coupled diffu-
sional and exchange processes. Duffy and Rees (11,12) have
shown from isotopic tracer diffusion studies in charbazites
that the self diffusion coefficients of individual ion
depends on the cationic composition and energy heterogen
eity of the exchange sites. Similar observations on the
non-uniformity of the diffusion process have been ascribed
to cation location (13-15) and to the barriers to migrate
through windows of different dimensions (16). Barrer et al
(17) have shown by thermodynamic treatment that exchangers
provide a number of distinct intercrystalline environments
for cations and cosequently these cations have different
exchange properties. Brook et al have found that the ionic
diffusion rate depends on activity factors (18) for nonideal
exchangers and on the state of hydration (19-21) of the
exchangers whereas Barrer and Rees (22,23) have correlated
7G
activation energy of self diffusion with the polarizability
of cations and with the periodic variation of Coulombic
energy of cations diffusing along the channels.
The theory of absolute reaction rate has been applied
to the diffusion process in membrane by several investiga
tors. Zwolinski, Eyring, and Reese(24) examined the permea
bility data available in the literature for various plant
and animal cells by applying the theory of rate processes.
Similarly Schuler, Dames and Laidler (25) considered the
kinetics of membrane permeation of nonelectrolytes through
collodion membranes. Tien and Ting (26) studied water per
meation through lipid membranes and considered the permea
tion process from the stand of theory of rate process.
Clough et al (27), Li and Gainer (28) and Navari et al (29)
have applied absolute reaction rate theory to the diffusion
of solute in polymer solutions. They attached importance
to the influence of the polymer on the activation energy
for diffusion. Tsimboukis and Petropoulos (50) determined
the diffusion coefficients of alkali metal ions through
cellulose membrane and discussed the results in terms of
the pore structure model, and lijima et al (31) used acti
vation analysis for the investigation of mechanism of the
diffusion of ions of simple salts through polyamide mem
branes. Recently, Beg et al (32) have applied absolute
77
r eac t ion r a t e theory to i n v e s t i g a t e the mechanisms of
t r anspo r t of simple metal ions through inorganic p r e c i p i
t a t e membranes.
E X P E R I M E N T A L
Cupric hydroxide and cupric ortho-phosphate membranes
•were prepared by the method of i n t e r a c t i o n suggested by Beg
and coworkers (32,55) using parchment paper (supplied by
M/S Baird and Tatlock L td . , London) and 0.1M aqueous solu
t i o n of cupric ch lo r ide , potassium hydroxide and sodium
or tho-phsphate . F i r s t parchment paper was soaked i n d i s
t i l l e d water and then t i e d to the f l a t mouth of a beaker.
A 0.1M so lu t ion of potassium hydroxide was taken ins ide i t .
I t was then suspended i n a so lu t ion of 0.1M cupric chloride
for about 72 hours . The two so lu t ions were l a t e r i n t e r
changed and kept for another 72 hours . The membrane thus
obtained was washed with deionized water for the removal
of free e l e c t r o l y t e s . Similar procedure was adopted for
the p repara t ion of cupric ortho-phosphate membrane by taking
0.1M so lu t ions of cupric chlor ide and sodium ortho-phosphate.
Thallium dichromate membranes were prepared following the
procedure described in Chapter l.^^'Sh.e membranes thus ob
ta ined were sealed between two half c e l l s of an e l e c t r o
chemical c e l l (using adhesive) as shown in F ig . 2 . 1 . The
half c e l l s were f i r s t f i l l e d with el^^^EWijt^e s o l u t i ^ s
C O N D U C T I V I T Y
BRIDGE
^^STSTT^ HfXyG"
Pt .ELECTRODE
MEMBRANE
Fiq 2.1 Cfll for meaiurinq tlectncal conductanct
79
CM
S ^
a
o
I—I
P^
W
g 3
o |o
o +1
(D
0)
a
en
o
in
o
O
in CvJ
o (D .H
•P -P !>> «J'
H Js O +3
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H O
I H
H O H
o o <.- 00
""t CO
in
o
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m
en
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in en
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00
o o
in
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T- O
o tn C\J
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CM
in
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o vo T -
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->*-c -
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CVJ
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o in
in o
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in
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o o o • o
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81
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0. I 0.3 0 2
Fiq 2 2 Plots of specific conductance (m .v^'' Cm"') vs. square root of concentration for KC / at differt temperatures across {A ) Cupr ic hydru xide and (B^ Cupric ortho-phosphate membranes
C ' / ^ M ' / ' ^
0 3
^ 9 . 2 3 Plots of specific conductance ( m - r v - ' C m - ' ) vs square root of c o n c e n t r a t i o n for L i C | a td . f fe ren t temperatures across ( A ) Cupr ic hydrox ide and {^) Cupr ic ortho - phosphate membranes
C ' ^ ^ M ' / 2 )
Fiq. 2 . 4 Plots of specif ic conductance (m-rv - 'Cm'^
aqainst square root of concentrations for
(A^ KCI (B ) NaCi and IC ) L »C I at d i f ferent
temperatures across Thalhum dichrornate membrane
82
limiting value. This behaviour was seen with all the three
electrolytes used and at every temperature (Figs. 2.2-2.4).
The flow of ion and water are generally larger in
the more open structure of the membrane and decrease as
the membrane shrinks in more concentrated solution in part
at least due to increased obstruction of the polymer matrix
as diffusional pathways become more tortuous and that frac
tional pore volume decreases. On the other hand, the elec
trical conductivity should increase with the increased salt
uptake. These two opposing effects operate simultaneously
and at higher concentration as shown in Fig. 2.2-2,4, the
effect of salt uptake by the membrane overcomes the effect
of increased tortuosity and thus membrane conductance be
comes almost constant. This is in accordance with the
findings of Paterson in the case of C60N and C60E membranes
with NaCl used as invading electrolyte as well as lijima
et al. (51) for Nylon membranes with various alkali chlo
rides. The sequence of membrane conductance for the alkali
metal ions under the same conditions is
^ >Na+ >Li+
which follow the order of their ionic radii. Similar be
haviour was observed by (Jeorge and Courant (34), Manecke
and Lavpennuhlen (35), Gregor et al. (36,37), and lakshmi-
83
narayanaiah and Sutrahmanyan (4) for certain orgajiic mem
branes. This sequence refers to the fact that the size of
the ions would be the major factor in the diffusion process.
Their hydration would not only restrict permeation through
the pores but would also adversely affect the exchange
adsorption. There would, however, be an important opposing
factor, viz., smaller ion association due to hydration
which would facilitate the diffusion of ions. The combined
effect of the former two factors would outweigh the latter
with the result that the hydrated ions would penetrate
slower than the less hydrated ions (38).
According to Bisenman (39)» the selectivity depends
upon the energies of hydration and ion-site interaction.
For ion exchangers with fixed charged groupings having
weak field strength, the selectivity sequence is governed
by differences in the hydration energies of counterions.
In such cases a normal sequence, e.g., Li < Na <1 K •< Rb
<C Cs is followed. On the other hand, for ion-exchangers
with charged groupings having high field strength, the
selectivity sequence is governed by the crystallographic
radii of counter ions. In such cases a reverse selectivity
sequence, e.g., Li" >Na"*'>K"^ >• Rb' > Cs" should result.
For ion-exchangers having charged groups of intermediate
field strength, Eisenman (39) and Sherry (40) have predicted
a number of intermediate selectivity sequences. In the
84
light of these the membranes under investigation may be
referred to as weakly charged. This is in full agreement
with our results of charged density determination of parch
ment supported thallium dichromate described in Chapter I
and other inorganic precipitate membranes (41-44).
Membrane porosity in relation to the size of the
species (hydrated) flowing through the membrane seems to
determine the above sequence. Although the sizes of the
hydrated electrolytes are not known with certainty, there
are few tabulations (45,46) of the number of moles of water
associated with some electrolyte. However, in Fig. 2.5 a
plot of specific conductance of different electrolytes
(chlorides) against free energy of hydration of cation (47)
is given for the membrane. It is seen that specific con
ductance decreases with increasing hydration energy, that
is, greater size due to increase in hydration. This points
to the fact that the electrolyte is diffusing along pores
or channels of dimensions adequate to allow the substance
to penetrate the membrane. The state of hydration of the
penetrating electrolyte may be considered to exist in a
dynamic condition so that at higher temperatures consider
ably higher fraction of the total n\Amber of a given kind
would possess excess energy A E per mole according to the
Boltzmann distribution f = e^^'^^ (R is the gas constant).
Under these circ\imstances, those ionic species which have
& f ( K e a l w » l - ' )
Ft(j .2 .5 Specific c o n d u c t a n c e (mj-v-1 Cm-^) of various 1:1 e lec tro ly tes a t 2 5 ' C plotted aqainst the free enerqy of hydration ( A F ' ) o f cat ions for (A) Thallium dichromate (B) Cupric hydroxide (C ) Cupric orthophosphate membranes
85
lost sufficient water of hydration to be smaller than the
size of the pore would enter the membrane. This way the
specific conductance would increase with increase in tem
perature, subject, however, to the proviso that the mem
brane has undergone no irreversible change in its structure.
That no such structural change is involved is evident from
the linear plots of log A versus 1/T shown in Fig. 2.6. The
slope of which gives the energy of activation as required
by Arrhenius equation. Tables 2.4 to 2,6 refer that the
activation energy decreases with increase in concentration
of the bathing electrolyte solution and that for different
electrolytes at a particular concentration it follows
^QK^ > EaNa+ > EaLi+
The activation energies for electrolytic conduction follow
the sequence of crystaliographic radii of the alkali metal
cations. When the penetrant moves in a poljnner substance
containing relatively small amoiint of water, its motion
may be governed by the segmental mobility of the polymer
and its diffusivity may depend on the probability that the
segment will make a hole large enough to accommodate a
penetrant species (48). In such a system the activation
energy will depend on the size of the penetrant species,
that is, the activation energy will increase with the pene
trant size. If this is the case in our system, the depen-
3.IB 3.3 5
* . s .
o—'
0.55.
3.15 3.25 3 35 3.35 3.0 5
l / T X ) 0 ^
Fiq. 2 . 6 Arrhenius plot of specific condLctanceftrfA) Thallium dichromate; (^iCupric hydroxide and (C )Cupric ortho-phosphate membranes
86
dence of the a c t i v a t i o n energy on the kind of a l k a l i metal
ion may be in t e rp re t ed i n terms of the i o n ' s c r y s t a l l o -
graphic r a d i u s , which i s cons is tent with the r e su l t ob
tained' i n the d i f f u s i v i t y measurement in the same system
( 4 9 ) .
The theory of absolute r eac t ion r a t e s has been
applied to d i f fus ion process in membrane by several inves
t i g a t o r s (24-26,50 ,51) . Following Eyring (24 ,52) , we have
/y = RT e-^^/RT e ^ V (2.1) Nh
where-A i s the membrane conductance, h the Planck constant ,
R the gas cons tan t , IT the Avagadro niimber and T the abso
l u t e temperature . A F ^ i s the free energy of a c t i va t i on for
the d i f fus ion of ions and i s r e l a t ed by Gibbs-Helmoltz
equat ion:
A F ' ^ = AH'^ - TAS'^ (2.2)
is related to Arrhenius energy of activation Eg by
E^ = A H ^ + RT (2.3)
A plo t of logJMJh/RT versus 1/T from experimental
da ta gives s t r a i g h t l i n e , the slope and the in te rcep t of 4 4-
which gives the value forAH'^ andAS^as demanded by equa
t i o n 2 . 1 . This j u s t i f i e s the a p p l i c a b i l i t y of eqn. 2.1 to
87
the system \mder investigation. The derived values of AH
andAS^ were then used to get the value ofAF^ and E^ using
equations 2.2 and 2.3. The values of various thermodynamic
activation parameters ^^, AW , ^T andAS derived in this
way for the diffusion of various electrolytes in the mem
brane are given in Tables 2.4 to 2.6. These results indi
cate that the electrolyte permeation gives rise to a nega
tive value of As'^. According to Eyring and coworkers (24,
52) the values of As^ indicate the mechanism of flow, the
large positiveAS^ is interpreted to reflect breakage of
bonds, while low values indicate that permeation has taken
place without breaking bonds. The negative values are
considered to indicate either formation of covalent bond
between the penneating species and the membrane material
or that the permeation through the membrane may not be the
rate determining step. On the contrary, Barrer (50,53,54)
has developed the concept of "zone activation" and applied
it to the permeation of gases through poljnner membranes.
According to this zone hypothesis, a highAS^, which has
been correlated with high energy of activation for diffu
sion, means either the existance of a large zone of activa
tion or the reversible loosening of more chain segments of
the membrane. A lowAS'^, then means either a small zone
of activation or no loosening of the membrane structure on
the permeation. In view of these differences in the inter-
88
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89
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91
pretation of AS'^, Schuler et al. (25) who found negative
values of A S ^ for siigar permeation through collodion mem
brane have stated that "it would probably be correct to
interpret the small negative values of AS^ mechanically
as interstitial permeation of the membrane (minimum chain
loosening) with partial immobilization in the membrane
(small zone of disorder)". On the other hand, Tien and
Ting (26) who found negative S^ values for the permeation
of water through very thin (50 A thickness) bilayer mem
brane, stressed the possibility that the membrane may not
be the rate determining step but the solution-membrane
interface was the rate limiting step for permeation. Nega
tive AS'^ values for the systems under investigation may be
ascribed to the partial immobilization of ions within the
membrane and their interaction with the fixed charge group
of the membranes.
On the other hand we have (55)
J \ = A ^ e - V R T (2.4)
and J\ = 2.72(ZTd^/h)/^ /^ (2.5)
where K is the Boltzman constant and d is the interionic
jump distance, i.e., the distance between equilibrium posi
tions of diffusing species in the membrane. Equation 2.4
predicts a linear plot between log7\ versus 1/T, the slope
92
of which should give the value for Eg . Fig. 2,6 confirms
the validity of the equation 2.4 to the systems under inves
tigation. The values of Eg derived in this way are given in
Tables 2.4 to 2.6. Now substituting the values of E ^ and
AS^, determined earlier, into equations 2.4 and 2,5, the
values of the interionic jump distance, d, were ceuLculated.
A value of 1.5 A (approximately) for cupric hydro-0
oxide and orthophosphate membranes and 1.7 A for thallium
dichromate membrane were obtained. These values of 'd'
are not unusual to these systems. It may be pointed out
here that in such systems several investigators have used
empirical value of 'd' ranging from 1-5 A in their studies
(24-26,46, 47,49,50,56,57).
The results of all these investigations are that the
membrane conductance can be determined at different tempera
tures with reasonable accuracy. The membrane is weakly
charged and ionic species retain their hydration shell at-
least partially while diffusing through the membrane pores.
Negative AS'^ values suggest that the partial immobilization
of ions takes place most probably due to interstitial per
meation and ionic interaction with the fixed charge groups
of the membrane skeleton. The interionic jump distance for
cupric hydroxide, orthophosphate membranes was 1.5 i and
thallium dichromate membranes 1.7 A
93
R E F E R E N C E S
1. N. Lakehminarayanaial i , T ranspor t Phenomena i n Membranes,
Academic P r e s s , New York, p . 224, ( 1 9 6 9 ) .
2 . P . H i r sch -Aya lon , B l e c t r o c h i m . A c t a . , ^ 0 , 775 (1965) .
3 . C. Steymans, Ber . Bimsenges. Phys ik . Chem., 7 1 , 818
( 1 9 6 7 ) .
4. V. Subrahmanyan and N. Lakshminarayanaiali, J. Phys.
Chem., 12, 4314 (1968).
5. R. Arnold and D. F. A. Eoch, Australian, J. Chem.,
ia, 1299 (1966).
6. T. Teorell, Progr. Biophys. Biophys. Chem., 2, 305
(1953).
7 . F . H e l f f e r i c h and M. S. P l e s s e t , J . Chem. P h y s . , 28 ,
418 ( 1 9 5 8 ) .
8 . F . H e l f f e r i c h , " Ion Exchange", McGraw-Hill , (a)
Chapter 6, (b) p . 164, (c) p . 300 ( 1 9 6 2 ) .
9 . L. M. Brown, H. S. Sherry and F , J . Krambeck, J . Phys .
Chem., 1^ , 3846 (1971 ) .
10. L. M. Brown and H, S. She r ry , J . P h y s . Chem., 2 1 ,
3855 ( 1 9 7 1 ) .
11. S. C, Duffy and L. V. C. Rees, J. Chem. Soc,, Faraday
Trans. I, 20, 777 (1974).
12. S. C. Duffy and L. V. C. Rees, J. Chem. Soc, Faraday
Trans. I, 21, 602 (1975).
94
1 3 . H. Gaus and £• H o i n k i s , Z. N a t u r f o r s c h . A, 2£, 1511
( 1 9 6 9 ) .
14. E, Hoinkis and H. ¥. Lewi, Z. Naturforsch. A, 2 ,
1784 (1969).
1 5 . F . Wolf, C. &olz and K. P i l c h o w s k i , Z. Phys . Chem.
( L e i p z i g ) , 2 ^ , 1148 ( 1 9 7 6 ) .
16 . M. G u i l l o u x , P . P o u i l l o u x and P . B u s s i e r e , J . I n o r g .
Nucl . Chem., 2 1 , 2211-2217 ( 1 9 7 5 ) .
17 . R. M. B a r r e r , J . Klinowski and H. S. She r ry , J . Chem.
S o c , Faraday T r a n s . I I , 6^, 1669 ( 1 9 7 5 ) .
1 8 . F . M. Brooke and L, 7 . C. Rees , T r a n s . Faraday S o c ,
e±, 5383 (1968) ; 6^, 2728 ( 1 9 6 9 ) .
19 . A. Dyer and R. P . Townsend, J . I n o r g . Nucl . Chem.,
2 ^ , 3001 (1973) .
20. M. L. Costenohle, W. J. Mortier and J. B. Uytterhoven,
J. Chem. Soc, Faraday Trans. I, X2, 1877 (1976).
21. G. T. Kokotailo, S. L. Lawton and S. Sawruk, ACS Symp.
Ser., 40, 439 (1977).
22. R. M. Barrer and L. Y. C. Rees, Nature (London), 187.
768 (I960).
23. R. M. Barrer and L. V. C. Rees, Trans. Faraday Soc,
^ , 709 (I960).
24. B. J. Zwolinski, H. Eyring and C. E. Reese, J. Phys.
Chem., 53, 1426 (1949).
95
25 . K. B. S c h u l e r , C. A. Dames and K. J, L a i d l e r , J .
Chem. P h y s . , H , 860 ( 1 9 4 9 ) .
26 . H. T. Tien and H. P . Ting , J . C o l l o i d I n t e r f a c e
S c i . , 27 , 702 ( 1 9 6 8 ) .
27 . S. B. Clough, A. E. Read, A. B. Metzner and Y. C.
Behn, 8 , 346 ( 1 9 6 2 ) .
28 . S. U. Li and J . L. Ga ine r , I n d . Eng. Chem. Fund . , X,
433 ( 1 9 6 8 ) .
29 . R. M. N a v a r i , J . L. Gainer and K. R. H a l l , AIChE. J . ,
1 2 , 1028 (1971 ) .
3 0 . D. G. Tsimboukis and J . H. P e t r o p o u l o s , J . Chem.,
S o c , Faraday T r a n s . I , 7^ , 717 ( 1 9 7 9 ) .
3 1 . T. l i j i m a , T. Obara, M. I s s h i k i , T. Seki and K. Adachi ,
J . Co l lo id I n t e r f a c e S c i . , ^ , 421 ( 1 9 7 8 ) .
32 . M. N. Beg, F . A. S i d d i q i , K. Ahmad and I . A l t a f , J .
E l e c t r o a n a l . Chem., 122 , 313-319 ( 1 9 8 1 ) .
3 3 . M. N. Beg, R. Shyam and M. M. Beg, J . Polym. S c i . ,
J\ine ( 1 9 8 1 ) , ( I n p r e s s ) .
3 4 . J . H. B. Gregre and R. A. Couran t , J . Phys . Chem,,
l i , 246 ( 1 9 6 7 ) .
3 5 . G. Hanecke and E. 0 . Lavpennuhlen, Z. Phys . (Frank
f u r t ) , 2 , 336 (1954 ) .
3 6 . H. P . Gregor , H, Jacobson , R. C. S h a l l and D. M.
Westone, J . Phys . Chem., 6^, 141 ( 1 9 5 7 ) .
96
57. H. P. Gregor, K. Kawabe, H. Jacobson and I. F. Miller,
J. Colloid. Interface Sci., 21, 79 (1966).
38. W. U. Malik, S. K. Srivastava, Y. M. Bhandari, S,
Kumar, J. Electroanal. Chem,, HO, 181 (1980).
59. &. Eisenman, Biophys. J. Suppl., , 259 (1962).
40. H, Sherry, in J. A. Marinsky (eds.), Ion Exchange,
Dekker, New York, 2 (1968).
41. M. W. Beg, F. A. Siddiqi and R. Shyam, Canadian J.
Chem., 53(10). 1680 (1977).
42. M. N. Beg, F. A. Siddiqi, R. Shyam and M. Arshad, J.
Membrane Sci., 2, 565 (1977).
43. M. N. Beg, F. A. Siddiqi, R. Shyam, I. Altaf, J.
Electroanal. Chem., 98(2) . 231 (1979).
44. M. N. Beg, F. A. Siddiqi, S. P. Singh, P. Prakash and
V. Gupta, Indian J. Chem., VTA, 434 (1979).
45. H. S. Earned and B, B. Owen, The Physical Chemistry
of Electrolyte Solutions, 3rd Ed., Reinhold, New York,
5225 (1958).
46.. R. A. Robinson and R. H. Stokes, Electrolyte Solutions,
2nd Ed., Butterworths (London), 62 (1959).
47. Y, Marcus and A. S. Kerters, Ion Exchange and Solvent
Extraction of Metal Complexes, Interscience, New York,
13 (1969).
48. C. A. Kumins and T, K. Kwei, Diffusion in Polymers
97
( J . Crank and G. S. P a r k , Bds . ) , Chapter 4 , Academic
P r e s s (London), ( 1 9 6 8 ) .
49 . F . A. S i d d i q i , M. N. Beg, M. I . R. Khan, A. Haq,
S. K, Saksena and B. I s l a m , Canadian J . Chem,, _ ^ ,
2205 ( 1 9 7 8 ) .
50. R. M. B a r r e r and G. Sk i r row, J . Polym. S c i . , 2> 549
( 1 9 4 8 ) .
5 1 . ¥ . D, S t e i n , The Movement of Molecules Across C e l l
Membranes, Academic P r e s s , New York, 70-89 (1967 ) .
52 . S. .G-lasstone, K. J , L a i d l e r and H. E y r i n g , The Theory
of Rate P r o c e s s e s , McGraw-Hill , New York, 525-544
( 1 9 4 1 ) .
5 3 . R. M. B a r r e r , T r a n s . Faraday S o c , ^ , 322 (1942 ) .
54. R. M. B a r r e r and H. T. Ohio, i n Transpor t Phenomena
i n Polymer ic F i lms ( J . Polym. S c i . , C10), C. A. Kumins
• E d . ) , I n t e r s c i e n c e , New York, 111 ( 1 9 6 5 ) .
5 5 . R. M. B a r r e r , E. F . Bartholomew and L. V. C. Rees , J ,
P h y s . Chem. S o l i d s , 2 1 , 12 ( I 9 6 I ) .
56 . F , A. S i d d i q i , N. Lakshminarayanaiah and M. N. Beg,
J . Polym. S c i . , % 2853 ( 1 9 7 1 ) .
57 . A. Dyer and J . M. F a w c e t t , J . I n o r g . Nuc l . Chem.,
2 8 , 615 (1966 ) .
C H A P T E R - I I I
CAPACITMCE, RESISTANCE, AND IKPEDANCE OF THE MEMBRANES
99
Impedance measurements provide a powerful diagnos
tic tool for the analysis of many electrochemical systems,
including cells with solid and liquid electrolytes, semi
conductors, as well as the artificial and biological mem
branes. The theoretical and experimental study of mem
branes and cell impedance has been in progress for many
years. In 1899 VJarburg (1) developed the theory of the
diffusional impedances and derived the expression for it.
The recent work of Macdonald (2) provides the most complete
and systematic treatment of the small signal a.c. response
of conducting cell and membranes. From the impedance
measurements Brynza et al. (3) showed that passive layer
formed on titanium has varying nature dependent on the
potential. Lakshminarayanaiah has prepared composite mem
branes of polystyrene sulphonic acid (PSSA) and determined
the impedance characteristics of these membranes and dis
cussed in terms of the resistance and capacitance charac
teristics of simple membranes from which the composite
structures have been formed.
In order to understand the behaviour of the complex
living membranes, simple polymeric membranes for sometime
(4), lipid bilayer membranes (5a,b), parchment (6-14) and
millipore filter paper (15-18) supported membranes in re
cent years have been used as model by a number of investi-
100
gators. In a series of theoretical papers, Kedem and
Zatchalsky (19) have discussed the behaviour of complex
membranes. Such complex membranes have been prepared by
Liquori and Botre (20,21), Liquori, Constantino and S,
Segre (22), Hays (23) and De Korosy (24), and used in few
studies as models by Botre et al. (25) and Hays (23) to
understand the behaviour of living membranes. We have in
a series of papers reported various inorganic precipitate
membranes which have been utilized as a model for under
standing the mechanism of transport through membranes.
In this chapter the electrical resistance and capa
citance of parchment supported thallium dichromate and
thallium permanganate membranes in contact with aqueous
sodium chloride solutions measured at different concentra
tions and various frequencies have been described. The
impedance characteristics, which is an important electri
cal property governing the membrane phenomena, have been
computed. These parameters have been determined in order
to substantiate our findings regarding the mechanism of
transport through the membranes under investigation with
particular reference to its function in different environ
ment.
101
E X P E R I M E N T A L
The parchment supported thall i i im dichromate and
tha l l ium permanganate membranes were prepared by the pro
cedure described i n the chapters I and I I . The e l e c t r i c a l
r e s i s t ance R and capacitance O- were determined by s e t t -
ing up a c e l l of the type shown in Figure 3 . 1 . The two
ha l f c e l l s were f i r s t f i l l e d with e l e c t r o l y t e so lu t ions
(sodiiim chloride) t o e q u i l i b r a t e the membranes. The solu
t i o n s were then replaced by pur i f ied mercury without remov
ing the adhering surface l iqu id (26) . Air bubbles, i f any,
on the surface of the membranes were removed by t i l t i n g
the c e l l assembly. Platinum e lec t rodes dipped i n mercury
were used to e s t a b l i s h e l e c t r i c a l con tac t s . The capaci
tance and r e s i s t ance were measured by a un ive r sa l LCR
Bridge 921 at d i f f e ren t frequencies ( 1 , 2 .5 , 4 .0 , 5 .5 , 7,
8.5 and 10 KH ) using RC O s c i l l a t o r 1005. Al l the measure-
ments were car r ied out using a water thermostat maintained
at 25 +0.1°C. The sodium chlor ide so lu t ions were prepared
from a n a l y t i c a l grade reagent and deionized water.
D I S C U S S I O N
The values of membrane r e s i s t a n c e , R , and membrane
capac i tance , C , of parchment supported tha l l ium dichromate
and thallixim permanganate membranes bathed in d i f fe ren t
J" n . ^ - _
^ i _ ^ H j - _ -
1
M E M
_ - _ H ? - _ -
3RANE
]
I
LCR BRIDGE
Pt
-o
0-
F1F r TRnnF
RC OSCILLATOP O O
Fiq. 3.1 Cell for measurinq the mfmb'rinc r t i i i t i n c f and capacitance
102
concentrations of aqueous solutions of sodium chloride and
measured at frequencies 1-10 KH , are given in OJables 3.1
to 5.4. For comparison these are also depicted in Figures
3.2 to 3.6 as a fxinction of concentrations and applied
frequency. Figure 3.2 demonstrate that membrane resistance
decreases with increase in electrolyte concentration. This
behaviour was seen at every frequency and with both the
membranes under investigation. The decrease in membrane
resistance with increase in electrolyte concentration may
be ascribed due to the progressive accumulation of ionic
species within the membrane and thus making the membrane
more conducting.
On the other hand, membrane capacitance, C_, in-
creases with the increase in the electrolyte concentra
tions. This behaviour was seen at each frequency at which
measurements were made. The capacitance of a system usually
depends upon two factors, viz., directly proportional to
dielectric properties and inversely to effective thickness
of the capacitor. According to the equation for parallel
plate capacitor:
°m " ^ /^^ ^ lO^^Ad) (3.1)
i.e., membrane capacitance C ^ is numerically related to the
dielectric constant,C » and effective thickness, d, of the
103
TABLE 3.1
OBSERVED VALUES OF MEMBRAEB RESISTANCE, R x lO" ( ^ ) AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL
IUM DICHROMATE MEMBRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 . 5 4 . 0
5.5 7 . 0
8 .5 10.0
1.0
0.75 0.70 0.61
0.57 0.53 0.51 0.48
Concentration (Mol
0.1
1.00
0.93 0.85 0.78 0.76
0.73 0.71
0.01
7.50 6.30 5.30 4.40 3.50 2.80 2.00
. 1-')
0.001
9.30 8.30 7.20 6.10 5.20 4.40 3.60
0.0001
13.00
11.20 9.60 8,40 7.30 6.90 6.00
TABLE 3.2
OBSERVED VALUES OF MEMBRANE RESISTANCE, R^ x 10~^ ( L) AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL
IUM PERMANGANATE MBI4BRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5
4 .0
5.5 7 .0
8 .5 10.0
1.0
0.45 0.33 0.29 0.23 0.20 0.19 0.18
Concentration (Mol
0.1
0.80 0.78
0.70 0.65 0.58 0.50 0.42
0.01
3.50 3.30 2.90 2.50 2.25 1.90 1.20
. 1-n 0.001
7.00 6.80 6.00 5.60 4.90 4.40 4.00
0.0001
9.50 8.80 7.90 7.30 6.80 6.30 5.80
104
TABLE 3.5
OBSERVED VALUES OF MEMBRAKB CAPACITANCE C^ x 10^ ( )iP) AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL
IUM DICHROMATE MBl'IBRAira EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5 4 . 0
5 .5 7 .0
8 .5 10.0
1.0
750 .0
510.0
280.0
210.0 165.0
120.0
80 .0
C o n c e n t r a t i o n (Mol,
0 .1
265.0
180.0
155.0
114.0
99 .0
96 .0
7 0 . 0
0.01
7 9 . 0
68.5 58.0
48 .6
44 .6
41 .7
57 .0
. 1 - ^
0.001
16.0
12 .5
7 . 5
4 . 5 5 .0
1.5 1.0
0.0001
7 .80
6.50 4 .50
3.50
2.80
0 .65 0 .56
TABLE 5.4
OBSERVED VALUES OF MEMBRANE CAPACITANCE C^ x 10^ ( >JF) AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL-
ITOI PERMANGANATE MEMBRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5 4 .0
5.5 7 .0
8 .5 10.0
1.0
1150.0
900.0
450.0
500.0 260.0
200.0 140.0
Concentration (Mol,
0.1
460.0
280.0
160.0
75.0 50.0
55.0
20.0
0.01
340.0
220.0
140.0
68.0 45.0
50.0
18.0
. i-b 0.001
85.0
6.6
5.2
4 .1
2 .7 1.8
0.93
0.0001
5.20
5.10
2.00
1.50 1.10
0.97 0.90
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Fiq 3 3 Plots of capacitance , C X { >i F ) aqamst
square root of conct ntrations f NaCl at different
frequencies,f ( K H 2 ) t h r o u q h Thallium dichron^att
membrane
109
Negative values of C^ may be referred to the opposite pola
rity of the double layer capacitors connected in series
with geometric capacitors, G , O
The resistance R^ and the reactance X^ of simple
membranes are, in general, considered equivalent to the
electrical circuit as shown in Fig. 3.7. Lakshminarayanaiah
and Shanes (27) have evaluated the membrane resistance R j
and capacitance Cjj. by the usual analysis from the equations
(3.3)
or
^
^CA
Cm
Xx
= Rz
Xx ~ R
X
Xx
1
-XY 2
1 + ( -2)2
) - i -
(3.4)
and ^y:=^ (5.5) ^x
where ^ = 2j\f and f is the frequency (KH ,) used to measure
C^ and Rjj. and for the calculation of Cm, R^ and X^ which
are given in Tables 3.7 to 3.12 as a function of both exter
nal electrolyte concentration and frequencies. The impe
dance Z of a membrane is given by
2 = J^l + X^ (3.6)
Rm
C m
F i q . 3 . 7 The equiva lent e l ec t r i ca l c i r cu i t for the membrane, Rm and Cm are membrane
res is tance and capac i tance respec t i ve ly
> o 3 I I
u
I r r V / R
P'q 3 8 For loss angle 6 ano phase anqle 0
110
TABLE 5.7
VALUES OF MEMBRANE REACTANCE X^ x 10 ^ i-O- ) AT DIFFERENT
FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALLIUM D I -
CHROMATE MEMBRANE EQUILIBRATED WITH DIFFERENT CONCENTRA
TIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 . 5 4 .0
5 .5 7 . 0
8 .5 10.0
1.0
0.212
0.142
0.141
0.137 0.136
0 .156
0.199
C o n c e n t r a t i o n (Mol. 1" )
0.1
0 .60
0 .35 0 .29
0 .25 0 .22
0 .19 0.17
0.01
2.02
0 .9
0.69
0 .59
0.51
0.44
0 .43
0.001
9.95
9.4
8.5
7.6
6.3
5.9
5.5
0.0001
20.41
10.11
8.85
8.77 8.12
7.07 6.22
TABLE 3 .8
VALUES OF MEMBRANE REACTANCE X x lo"^ ( . T L ) AT DIFFERENT
FREQUENCIES (KHz) FOR PARCHl IENT SUPPORTED THALLICQi PER
MANGANATE MEMBRANE EQUILIBRATED WITH DIFFERENT CONCENTRA
TIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5 4 . 0
5 .5
7 .0 8 .5
10 .0
1.0
0 .14
0.07 0 .08
0 .09
0.087
0 .093
0.113
Concent ra t ion (
0.1
0.35
0.22 0 .25 0 .38
0 .46
0 .53
0 .79
O.01
4.00
2.90 2.80
2.40
1.00 0.88 0.62
!MO1. 1""')
0.001
18.7
9.6 7.6
6.0 2.8
2.3
1.7
o.ooot
30.6 21.0
20.5 20.0 19.0 18.0 17.0
I l l
TAB3LE 5.9 2 2
CALCULATED VALUES OF MEMBRANE RESISTANCE R^ x 10" ( -^cm )
AT DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED
THALLIUM DICHROMATE MEMBRANE EQUILIBRATED WITH DIFFERENT
CONCENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5 4 .0
5.5
7 .0
8 .5 10 .0
1.0
0.81
0 .73 0 .62
0 .60
0 .56
0 .56 0 .56
C o n c e n t r a t i o n (Mol.
0.1
1.36
1.06
0 .95 0 .86
0 .83
0 .78
0 .75
0.01
7 .50
6.30
5.38
4 .49
3.57
3 .87
2.09
. 1 - ^
0.001
19.9
11 .4
11.09 12.8
14.3 24 .6
7 .3
0.0001
-
20 .3
17.7
17.5
16.3
14.1
12.4
TABLE 3.10
CALCULATED VALUES OF MEMBRANE RESISTANCE R^ x 1 0 " ^ ( - ^ cm^)
AT DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED
THALLIUM PERMANGANATE MEMBRANE EQUILIBRATED WITH DIFFERENT
CONCENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5
4 . 0
5.5 7 .0
8 .5 10.0
1.0
0 .49 0 .35 0 .38
0 .26
0 .24 0 .23
0 .25
Concen t r a t i on (Mol,
0.1
0 .95 0 .84 0 .78
0 .76
0 .94
1.07 1.92
0.01
3.56
3.33 2.92
2.57
2.37
2.09
1.85
^ r . 0.001
,
20.5 15.7 16.6 18.1 26.8 82.1
0.0001
10.8 56.8 57.8
_
69.6 65.3 56.3
112
TABLE 3.11
CALCULATED VALUES OF MEMBRANE CAPACITANCE C^^xlO^ [)iF(cm^)'*^
AT DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED
THALLIUM DICHROMATE MEMBRANE EQUILIBRATED WITH DIFFERENT
CONCENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 . 5
4 . 0
5.5 7.0 8.5
10.0
1.0
0.55
0.27
0.25
0.15
0.11
0.10
0.11
Concentration
0.1
0.45
0.25
0.14
0.09
0.07
0.09
0.08
0.01
0.24
0.14
0.09 0.08
0.05 0.06
0.062
(Mol. 1'^)
0.001
0.08
0.06
0.04 0.028
0.019 0.009
0.031 -—
0.0001
0.06
0.028
0.02
0.017
0.015 0.01
0 .013
TABLE 3.12
CALCULATED VALUES OP MEMBRANE CAPACITANaS C r l . ^ f r 2 ll
AT DIFFERENT FREQUENCIES (KHz) FOR PARGHM™^ o l ' ^ ^ ' " ^ ^ ^ ^
THALLIUM PERMANGANATE MEMBRANE miLlBmZ^^^'''''^''
CONCENTRATIONS OF SODIUM CHLORIDE SOlu r ioT ' ^ ^ ^ ™ ^ T
Frequency (KHz)
1.0
2.5
4 .0
5.5
7.0
8 .5
10.0
Concent rat I O ^ T M O I , ^ ^
0.001
1.00
0.30
0.28
0.42
0.38
0.39
0.39
0.70
0.21
0.18
0.32
0.1?
0.18
0.16
0.5O
0.17
0.097
0.14
0.048
0.04
0.044
0.39
0.043
0.032
0.018
0.007
0.034
0.013
0.32
0.026
0.018
O.blo 0.009
0.008
0.0072
6
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U
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u z < »-
u <
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•
A
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X
1.0
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5 5
7 0
8 . 5
KHz
»»
)»
>;
I >
);
(> 10 0 >'
A - 2 r
0.5 -
C ' ' ^ M " 2 )
Fiq. 3 3 Plots of capac i tance ,Cx { > i F ) aqamst
square root of concentrations f NaCl at different frequencies,f ( K H z ) through Thallium dichromate membrane
12
O
o z <
< a. <
6 f -
c-
•
A
A
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H
f?
1.0 KH2
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4.0 " 5.5 "
7.0 "'
8.5 "
10.0 "
0 5
Fcq. 3 4 Plots of capacilarict, Cx ( AJ F ) aqainst square root of concentrations for NaC| at different frequencies, f ( KHz ) throuqh Thallium dichromate membrane.
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c e 0* =» (- J^ 4, —
«<- fQ **- C
f« CO
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4. o 3 • -c r "O
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4-< ro c fl> cr c rt
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105
membrane. The increase in the value of C with electrolyte
solution can arise from decrease in the thickness of the
membrane or an increase in the dielectric constant of the
membrane material or both. Since the species present in
the membrane causing this change in C are polar in nature
(i.e., ion and water), increase in Cj with increase in
electrolyte content of the membrane can be attributed to
an increase in the values of . A similar effect of elec
trolyte concentration on C was noted with thin parlodion
membranes by Lakshminarayanaiah and Shanes (27). Accord
ingly the increase in membrane capacitance with electrolyte
concentration may be attributed to the accumulation of
polar substances (ions) within the membrane consequently
increase dielectric constant and decrease in the effective
thickness of the membrane, most probably due to the de-
swelling of the membrane because of the squeezing of water
molecules from the membrane framework by the incoming ions.
It may be mentioned here that the effective membrane thick
ness consists of the membrane matrix and two interfacial
surfaces on the two sides of the membrane and that the
interfacial thickness controls the membrane phenomena which
is electrolyte concentration dependent.
The double layer theory (28) has been utilized in
several studies to interpret the changes in the membrane
106
capacitance, C , with electrolyte concentrations (29,30).
C is determined primarily by the dielectric constant and
the membrane thickness (31,52), i.e., by the so called
specific geometric capacitance C . The polarization change
on the geometric capacitor, in the form of double layer
that depends upon electrolyte concentration, plays an impor
tant role and affects the overall membrane capacitance C .
Thus C_ in series with two double layers is given by the S
expression (33)
(5.2) J_ _ Cx "
1
Cg +
2 M M M M
Cd
Here C^ is the capacitance of the interfacial double layer
and other symbols have their usual significance. Parchment
paper, except for the presence of some stray and end car-
boxy lie acid group, contains very few fixed groups. Depo
sition of inorganic precipitates gives rise to a net nega
tive charge on the membrane surface in the case of dilute
solution of uni--univalent electrolytes leading to the type
of ionic distribution associated with the electrical double
layer. The membranes in contact with water or dilute elec
trolyte solutions may be assumed to have a constant capaci
tance, C_, which may be assumed to depend upon the struc-
tural details of the network of which the membranes are
composed. The stepwise increase in the membrane capacitance
107
C^, with the changes made in the electrolyte concentrations
may be ascribed to the changes produced in the electrical
double layer at the interfaces in the form of interfacial
capacitance/capacitor, 0^, In order to analyse the mem
brane capacitance in terms of geometric capacitance, Cg,
and interfacial capacitance, C j, the observed membrane
capacitance in contact with dilute electrolyte solutions
was taken equal to the geometric capacitance C_, This
approximation was made due to the fact that membrane capa
citance was almost constant particularly in the region of
dilute bathing electrolyte solution. Now taking this value
of C as C„, the values of C^ at all other electrolyte con
centrations were calculated using equation 3.2. The values
of C^ thus calculated are given in Tables 5.5 and 5.6. The
values of C^ decrease;3 (numerically) with increasing the
electrolyte concentrations. This confirms our view point
that effective thickness decreases with increasing electro
lyte concentration.
It may also be concluded that the overall membrane
capacitance is more dependent upon C^ values which is in
agreement with our earlier findings of membrane potential
measiu-ement s; as well as in agreement with Tien and Ting
for bilayer lipid membranes (BM) that the double layers
at the interfaces control the diffusion processes (54).
108
TABLE 3.5
CALCULATED VALUES OF CAPACITANCE OF DOUBLE LAYER, C^ , AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL
IUM DICHROMATE MEMBRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5
4 .0
5 .5 7 .0
8 .5 10 .0
1.0
- 1 4 . 5 4
-11 .97 - 8 . 3 2
- 5 . 9 6
- 4 . 8 3 - 0 . 5 0
- 0 . 3 2
C o n c e n t r a t i o n (Mol.
0.1
- 1 4 . 8 0
- 1 2 . 3 4
- 8 . 4 5
- 6 . 0 4
- 4 . 8 7 -0 .501
-0 .3207
TABLE
0.01
- 1 5 . 8 4
- 1 2 . 9 5 - 8 . 8 2
- 6 . 2 7
- 5 . 0 3
- 0 . 5 0 3 -0 .321
3 .6
1 - ^
0.001
- 2 6 . 1 8
-22 .47
-18 .07 - 1 6 . 9 8
-
-0 .599 - 0 . 3 8
0.0001
-187 .00
-
-91 .84
-54 .09 -31 .82
- 0 . 8 1 :
-0 .44!
CALCULATED VALUES OF CAPACITANCE OF DOUBLE LAYER, C^, AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL
IUM PERl'iANaANATE MEMBRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2.5
4 .0
5.5
7.0
8 .5
10.0
1.0
- 9 . 6 6
- 5 . 8 2
- 3 . 2 1
- 1 . 5 5
- 1 . 4 0
- 1 .146
- 1 . 0 0
Concen t ra t i on (Mo l .
0.1
- 9 . 7 2
- 5 . 8 6
- 3 . 2 3
- 1 . 8 2
- 1 . 4 2
- 1 . 1 6 2
-
0.01
- 9 . 7 5
- 5 . 8 7
- 3 . 2 4
- 1 . 8 3 - 1 . 4 2 2
-1 .165
-1 .03
1 - ^
0.001
-10 .19
-10 .33 - 4 . 6 2
-2 .31
- 1 . 8 9
-1 .67
-
0.0001
-127.45 -89 .21
-16 .13
- 5 . 8 9
-3 .84
-2 .78
-2 .25
113
and the values derived for the membranes in equilibrioam
with different concentration of sodium chloride solution
are given in Tables 3.13 and 3.14.
Membranes imder investigation possess negatively
charge and the counterions fona the double layer at the
membrane surfaces. By the increase of electrolyte concen
tration the counterions in the form of double layer are
pushed inside the membrane resulting thereby a decrease in
the effective thickness of the membrane and increase in the
ionic charge within the membrane. These conclusions support
our data on membrane resistance and our earlier findings
that the double layer at the interface controls the trans
port phenomena. Impedance of the system increases with
decrease in the electrolyte concentration whereas it dec
reases insignificantly with the increase in the frequency
at which the measurements were made . Thus membranes may
be considered to be more effective as barrier when it is
separating dilute electrolyte.concentration and that at
higher concentration the effect of the membrane tend to
vanish. These data again support our findings of membrane
potential measurements described in Chapter I of this thesis,
A capacitor (35) fails to present a perfect and cons-2
tant capacitance due to I R losses in the plates, connecting
wires, interfacial polarization and power loss in dielectric
11
TABLE 5.13
CALCULATED VALUES OP MEMBRANE IMPEDANCE Z x 10"^ ( P L ) AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHI'IENT SUPPORTED THAL
LIUM DICHROMATE MEMBRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODim^ CHLORIDE SOLUTION
Frequency (KHz)
1.0
2 .5 4 .0
5.5 7 .0
8 .5 10.0
1.0
0 .78
0.71
0 .65
0 .59
0.55 0 .53
0.52
C o n c e n t r a t i o n
0.1
1.17
0 .99
0 .89 0 .82
0 .79 0 .76
0 .73
TABLE
0.01
7 .77 6.36
4 .34
3.44
3 .53
3 .83
2 .05
3 .14
(Mol. I" ' ' )
0.001
9.31 9.74
8 .94
8 .84
8 .64 9.46
16.32
0.0001
24.20 20.32
13.06
12.14
10.92 9.88
8.64
CALCULATED VALUES OF MEMBRANE IMPEDANCE Z x 10"^ ( - T L ) AT
DIFFERENT FREQUENCIES (KHz) FOR PARCHMENT SUPPORTED THALL
IUM PERMANGANATE MEMBRANE EQUILIBRATED WITH DIFFERENT CON
CENTRATIONS OF SODIUM CHLORIDE SOLUTION
Frequency (KHz)
1.0
2.5
4 .0
5.5
7 .0
8 .5
10.0
1.0
0.47 0.34 0.30
0.25 0.21 0.21 0.21
Concentrat ion
0.1
0.87 0.81
0.74 0.70
0.74 0.79 0.73
0.01
3.53 3.31 2.91 2.54 2.31 1.19 1.99
(Mol . 1"'')
0.001
19.99 11.81 9.72
9.10
9.74 10.87 18.14
0.0001
32.06
22.37 21.41 23.44 21.78
20.31 18.07
115
TABLE 3.15
VALUES OF LOSS ANGLE S OF THALLIOTl DICHROMTE MEMBRAEE
USING AQUEOUS SODIUM CHLORIDE SOLUTION AT DIFFERENT
CONCENTRATIONS AND FREQUENCIES
C o n c e n t r a t i o n (Mol. l " ) Frequency
(KHz) 1.0 0.1 0.01 0.001 0.0001
1.0 19'>48' 15'*12' 8°36' 5*'42' 2054'
2.5
4.0
5.5
7.0
8.5
10.0 14°36' 13°30' 10<*18' 5* 36' 4** 6'
TABLE 3.16
VALUES OF LOSS ANGLE g OF THALLIUM PERMANGANATE MEMBRANE USING AQUEOUS SODIUM CHLORIDE SOLUTION AT DIFFERENT CONCENTRATIONS km FREQUENCIES
170421
16012 '
14'^36'
2 0 ° 1 8 '
18018 '
14035 '
1 3 ° 3 0 '
12054 '
19048 '
1 5 M 2 '
5012 '
5018 '
4'^36'
7 0 2 4 '
4"* 4 8 '
40 6 '
50 6 '
4 0 3 6 '
4<*48'
4«>36'
1048 '
30241
40 6 ' 40 3 .
1048 '
F r e q u e n c y (KHz)
1.0
2 . 5
4 . 0
5.5 7 . 0
8 . 5
1 0 . 0
1.0
1 7 0 4 8 '
3 1 " 0 '
200 2 4 '
1 5 ° 1 2 '
I 303O '
1 0 0 4 8 '
90 6 '
C o n c e n t r a t i o n (Mol
0 .1
I303O'
1 9 * 4 8 '
2 4 0 1 8 '
5 0 3 0 '
1 0 0 4 8 ' 3 0 5 4 .
2 0 5 4 '
0 . 01
5°42' 6 0 1 8 '
80 0 '
4 0 3 6 '
9 0 4 2 '
I03O '
20 1 2 '
. 1 - ' )
0 . 001
4 0 3 6 '
40 6 ' 40 gt
-
7 0 3 0 '
1012 '
1 0 1 2 '
0 .0001
30541
2 0 1 8 '
2 0 1 2 '
2 0 1 8 '
20 6 '
-
10 6 '
IIG
etc. which, is usually described in terms of loss angle'^.
In a perfect capacitor, the phase angle i "between current
I and voltage V is 90° whereas the decrease in the phase
angle represents the imperfectness in the capacitor as
shown in Fig. 3.8. For a perfect capacitor jz( = 90 and
S = 0. Loss angle is defined mathematically by the expre
ssion
where the symbols have their used significance. The loss
angle calculated at various electrolyte concentrations
using equation for the parchment supported thallium dichro-
mate and thallium permanganate membranes are given in Tables
3.15 and 3.16. The value of loss angle increases with the
increase of electrolyte concentration resulting thereby that
capacitors in the form of membrane tend towards imperfect
ness. This is again in accordance with our conclusions of
the impedance determinations. It is quite probable that
in these cases the polarization produced at the interfaces
in the form of electrical double layer play a dominant role
in the diffusion processes.
117
R E F E R E N C E S
1. E. Warburg, Ann. P h y s . , 67 , 493 (1899 ) ; 6 , 125 (1901 ) .
2 . D. R. F a n c e s c h e t t i and J , R. Macdonald, J . E l e c t r o a n a l .
Chem., i O i , 307-316 ( 1 9 7 9 ) .
3 . A, P , Brynza , L. I . Gevasjrutina and E, A. Z h i v o t s k i i ,
Z a s h c h i t a M e t a l . , 2 , 38 (1966 ) .
4 . N. Laksi iminarayanaiah, Chem. R e v . , 6^, 491 ( 1 9 6 5 ) .
5 . P . M u e l l e r , D. 0 . Ruding, H. T. Tien and W. C. Wescot t ,
(a) N a t u r e , \ ^ , 979 (1962) ; (b) C i r c u l a t i o n , 2^ , 1167
( 1 9 6 2 ) .
6 . F . A. S i d d i q i , N. l ak shmina rayana i ah and M. N. Beg,
J . Polymer S c i . , 2» 2853 ( 1 9 7 1 ) .
7 . M. N, Beg, P . A. S i d d i q i and R, Shyam, Can. J , Chem.,
^ , 1680 (1977 ) .
8 . M. N. Beg, F . A. S i d d i q i , R, Shyam and I . A l t a f , J .
E l e c t r o a n a l . Chem., 8^ , 141 (1978 ) .
9 . M. N. Beg, F . A. S i d d i q i , R. Shyam and M. Arshad, J .
Memb. S c i . , 2 , 365 ( 1 9 7 8 ) .
10 . P . A. S i d d i q i , M. N. Beg and P . P r a k a s h , J . E l e c t r o a n a l .
Chem., 8£ , 223 ( 1 9 7 7 ) .
1 1 . F . A. S i d d i q i , M. N. Beg, S. P . Singh and A. Haq,
E l e c t r o c h i m i c a Acta , 2^ , 631 ( 1 9 7 7 ) .
12 . P . A. S i d d i q i , M. N. Beg, S. P . Singh and A. Haq,
B u l l . Chem. Sco. J p n . , 49 , 2858 ( 1 9 7 6 ) ,
118
15. F . A. S idd iq i , M. N. Beg and S. P . Singh, J . Polymer.
S c i . , 11 , 959 (1977).
U . M. N, Beg, F. A. S idd iq i , K. Ahmad and I . Altaf, J .
E l ec t roana l . Chem., 122, 315-319 (1981).
15 . Y. Kobatake, A. I r i m a j i r i and Matsiimoto, Biophys. J . ,
10, 728 (1970).
16. M. Yoshida, N. Kamo and Y. Kobatake, J . Mem. B i o l . ,
8, 389 (1972). 17. M. Yoshida, Y. Kobatake, M. Hashimoto and S. Morita, J .
Mem. B i o l . , ^ , 185 (1971).
18. K. Kamo, T. Yoshiioda, M. Yoshida, T. Sujita, J. Mem.
Biol., 12, 193 (1973).
19. 0. Kedem, A. Katchalsky, Trans. Faraday Soc, , 1918,
1931, 1941 (1963).
20. A. M, Liquori and 0. Borte, Ric. Sci., 34(6) . 71 (1964)
21. A. M. Liquori and C. Borte, J. Phys. Chem., 2i» 3765
(1967).
22. A. M. Liquori, L. Constantino and G. Segre, Ric Sci
16, 591 (1966).
23. R. M. Hays, J. Qen. Physiol., , 385 (I968)
24. F. De Korosy, J . Phys. Chem., 72, 2591 (1963)
25. C. Borte , S. Borghi and M. Maichetti B^ , ^ ' Biochem. Biophys
Acta, 1 ^ , 162 (1967).
26. V. Subramanya^ and N. Lakehmiiarayanaiah, j . p^yg
119
Chem., 2 i . 4314 (1968).
27. W. Lakshminarayanaiah and A. M, Shanes, J . Appl. Polym.
S c i . , 2 , 689 (1965).
28. C. T. E v e r i t t and D. A. Haydon, J . Theorel. B i o l . , 18,
371-379 (1968).
29. A. W. Clowes, R. J . Cherry and D. Chapman, Biochim,
Biophys. Acta, 24^, 301, 317 (1971).
30. D. A. Haydon, Progr . Surface S c i . , 1_, 94, 158 (1964).
3 1 . S. H. White and T. E. Thompson, Biochim. Biophys. Acta,
323. 7 , 22 (1973).
32. C. P . Freeman and D. West, J , Lipid Res . , 1 , 324 (1966).
33 . S. H. White, Biochem. Biophys. Acta, 221» 344, 350
(1973).
34. H. T. Tien and H. P . Ting, J . Col loid . In te r face S c i . ,
21 , 702 (1968).
35 . A. K. Showhney, A course in E l e c t r i c a l and Elec t ron ics
measurements and Ins t rumenta t ion , 2nd e d . , p . 93 (1976).
S U M M A R Y
Transport processes occurring across artificial
memtranes separating different salt solutions have been
one of the most studied electrochemical and bioelectrical
phenomena. The investigators from various disciplines,
e.g., chemists, chemical engineers, biologists etc. have
contributed extensively although the starting points and
aims have been quite different. The literature in this
field is enormous but frequently not very coherent. The
cooperative efforts of the workers have contributed signi
ficantly to the prosperity and physical well being of all
mankind.
In this thesis, an effort has been made to characte
rize newly developed ion-exchange membranes, prepared from
inorganic precipitates, when placed in contact with aqueous
electrolyte solutions. The parameters governing membrane
phenomena have been derived from membrane potential, mem
brane conductance and impedance measurements. The thesis
has been presented under three heads although certain
amount of overlap has occurred. This type of overlap is
permitted as it helps in the elucidation of the topic under
discussion.
In Chapter I, the preparation of parchment supported
11
thalliiM dichromate and thallitim permanganate membranes,
and measurements of membrane potential,when these are used
to separate various 1:1 electrolyte (KCl, NaCl and LiCl)
solutions are reported. Membrane potential data have been
used to derive thermodynamically effective fixed charge
density of the membranes, using the fundamental theory of
Teorell, Meyer and Sievers and the recently developed theo
ries of Kobatake et al. and Tasaka et al. based on the
principles of irreversible thermodynamics. The results
have also been utilized to examine the validity of the
recently developed theoretical equations. It has been con
cluded that the membranes carry low charge density and that
the methods developed recently can be utilized for the eva
luation of effective fixed charge density of the systems
\inder investigation and such other systems.
In order to imderstand the mechanism of transport of
simple metal ions through inorganic ion exchange membranes,
in Chapter II, the membrane conductance bathed in different
concentrations of various 1:1 electrolytes (KCl, NaCl and
liCl) and measured at several temperatures are reported.
The data have been used to derive various thermodynamic
parameters like energy of activation, E^, enthalpy of acti-
vation.AH'^, free energy of activation,AP'' and entropy of
activation,AS^, by the application of absolute reaction
iii
rate theory. The interionic jiimp distance, d, has also been
evaluated. The activation energies were found to depend on
the size of penetrant species and that it decreased with in
crease in the concentrations of the bathing electrolyte
solutions. The values ofAS^ were found to be negative in
dicating thereby that partial immobilization of ions takes
place within the membrane. The order of membrane selecti-
+ + + vity was found to be K > Na > Li which on the basis of
Eisenman-Sherry model of membrane selectivity point towards
the weak field strength of charge groups attached to the
membrane matrix. It has been concluded that the membranes
used in the investigation are weakly charged and that the
permeating species retain, at least partially, their hydra
tion shell while diffusing through the membrane. The par
tial immobility of the ionic species has been attributed
to its interaction with the membrane matrix of low fixed
density.
In order to visualize structural details of the mem
brane-electrolyte system, in Chapter III, the measurements
of electrical resistance, R ., and capacitance, C , of the
parchment supported thallium dichromate and thalliiun per
manganate membranes in contact with different concentrations
of aqueous sodium chloride solution at various frequencies
have been carried out and the impedance characteristic com-
iv
puted. The double layer theory has "been utilized to inter
pret the changes produced in the membrane capacitance, C ,
membrane resistance, R^, and impedance, Z, with electrolyte
concentrations. It has been concluded that the double
layers at the interfaces control the diffusion processes.
J Electroanal Chem , 122 (1981) 313-319 313 Elsevier Sequoia S A , Lausanne — Printed in The Netherlands
TRANSPORT OF ALKALI CHLORIDES IN PARCHMENT SUPPORTED CUPRIC HYDROXIDE MEMBRANE AND APPLICATION OF ABSOLUTE REACTION RATE THEORY
MOHAMMAD N BEG, FASIH A SIDDIQI, K AHMAD and I ALTAF
Physical Chemistry Division, Department of Chemistry, Ahgarh Muslim University, Aligarh 202001 (India)
(Received 26th September 1980)
ABSTRACT
The preparation of a parchment supported cupric hydroxide membrane is described Membrane conductance in contact with various alkali—metal chlorides at different concentrations and temperatures have been measured in order to investigate the mechanism of transport of simple salts through the membrane Various thermodynamic parameters E^, AH , AG and AS and also the mterionic distance, d, were evaluated by the application of absolute reaction rate theory The activation energies for electrolytic conduction follow the sequence of crystallographic radii of alkali—metal cations, which shows that activation energy depends on the size of the penetrant species The activation energy decreases with increase in the bathing electrolyte concentrations It has been concluded that the membrane IS weakly charged and ionic species retain their hydration shell at least partially while diffusing through the membrane pores The values of AS"^ were found to be negative, suggesting that the partial immobilization of ions takes place, most probably, due to the interstitial permeation and ionic interaction with the fixed charge groups of the membrane skeleton.
INTRODUCTION
Diffusion of salts in polymers is closely related to the transport phenomena in various systems, namely, ion exchange, desalination, dyeing and biological systems. Many studies and various theories on diffusion of simple salts in membranes have been reported and are reviewed comprehensively by Helfferich [1,2] Lakshminarayanaiah [3], Buck [4] and others in an expanding literature.
The theory of absolute reaction rates has been applied to the diffusion process in membranes by several investigators. Zwolinski et al. [5] examined the permeability data available in the literature for various plant and animal cells by applying the theory of rate processes. Similarly Shuller, Dames and Laidler [6] considered the kinetics of membrane permeation of non-electrolytes through collodion membranes. Tien and Ting [7] studied water permeation through thin lipid membranes and considered the permeation process from the standpoint of the theory of rate process. Clough et al. [8], Li and Gainer [9], and Navan et al. [10] have applied absolute reaction rate theory to the diffusion of solute m polymer solutions. They attached importance to the influence of the polymer on the activation energy for diffusion. Recently, Tsimboukis and
0022 0728/81/0000—0000/$ 02 50, © 1981, Elsevier Sequoia S.A.
314
Petropoulos [11] determined the diffusion coefficient of alkali metal ions through cellulose acetate membranes and discussed the results in terms of the pore structure model, and lijima et al. [12] used activation analysis for the investigation of the mechanism of the diffusion of ions of simple salts through polyamide membranes.
In a series of communications we have [13—17], on the basis of the Eisen-man [18—20] and Sherry [21] model of membranes selectivity, and from membrane potential measurements and utilizing various recently developed theories based on the principles of irreversible thermodynamics, demonstrated that the inorganic precipitate membranes, both parchment supported and polystyrene based, possess a small density of fixed charge. In this paper we describe a series of membrane conductance measurements in contact with alkali—metal chlorides at different concentrations and temperatures in order to investigate the transport mechanism of simple salts in inorganic precipitate membranes by the application of absolute reaction rate theory.
EXPERIMENTAL
Cupric hydroxide membranes were prepared by the method of interaction suggested by Beg and co-workers [13—17]. Parchment paper (supplied by Baird and Tatlock Ltd., London) was first soaked in distilled water and then tied to the flat bottom of a glass tube. A 0.1 M solution of potassium hydroxide was taken inside it. It was then suspended in a solution of 0.1 M CUCI2 for about 72 h. The two solutions were later interchanged and kept for another 72 h. The membrane thus obtained was washed with deionized water for the removal of free electrolytes. It was then cut into a circular disc form and sealed between two half-cells of an electrochemical cell (using adhesive) of the type shown in Fig. 1 of ref. 17. The half-cells were first filled with electrolyte solutions to equilibrate the membrane. The solutions were then replaced by purified mercury without removing the adhering surface liquid [22]. Platinum electrodes dipping in mercury were used to establish electrical contact. The membrane conductance was monitored on a direct reading conductivity meter 303 (Sys-tronics) at a frequency of 10^ Hz. All measurements were carried out using a water thermostat maintained at temperatures of 25, 30, 35, 40, 45 and 50° C (±0.1° C). The electrolyte solutions were prepared from analytical grade reagents and deionized water.
Extensive use of the method has indicated that, to obtain reproducible results, there should be no trapped air particularly at the membrane—mercury interfaces and the mercury used should be purified as it easily becomes oxidized.
RESULTS AND DISCUSSION
The specific conductance of parchment supported Cu(0H)2 membranes in contact with various 1 : 1 electrolyte solutions at a temperature range of 25— 50° C (+0.1° C) have been measured and the results are shown in Fig. 1.
The specific conductance of the membrane increases almost linearly with the square root of the concentration of the bathing electrolyte solutions and
315
Fig 1 Arrhenius plot of specific conductance.
Fig. 2. Plots of specific conductance (mi l" ' cm" ' ) against square root of concentrations for KCl at different temperatures through cupric hydroxide membranes.
attains a maximum limiting vaJue. This behaviour was seen with all the electrolytes used and at every temperature.
The flow of ion and water is generally larger in the more open structure of the membrane and decreases as the membrane shrinks in more concentrated solution, due, in part at least to increased obstruction of the polymer matrix as diffusional pathways become more tortuous and that fractional pore volume decreases. On the other hand, the electrical conductivity should increase with the increased salt uptake. These two opposing effects operate simultaneously and at higher concentration, as shovm in Fig. 2; the effect of salt uptake by the membrane overcomes the effect of increased tortuosity and thus membrane conductance becomes almost constant. This is in accordance with the findings of Paterson in the case of C60N and C60E membranes with NaCl used as invading electrolyte, as well as those of lijima et al. [12] for nylon membranes with various alkali chlorides. The sequence of membranes conductance for the alkali—metal ions under the same condition (0.01 M, 25° C) was
K* > Na* > Li'
which is parallel to mobility of alkali metal ions in aqueous solution. This sequence refers to the fact that the membrane is weakly charged [18—21] and the ionic species retain their hydration shells, at least partially [13]. This is in full agreement with our results of charge density determinations (charge ^10"^ mM). The selectivity of alkali metal ions in ion-exchange resin has been discussed in detail by Reichenberg [23].
Membrane porosity in relation to the size of the species (hydrated) flowing through the membrane seems to determine the above sequence. Although the sizes of the hydrated electrolytes are not known with certainty, there are a few
316
!•
80
AG°/
Na*
/ k j mof'
9 0
t LI
Fig 3. Specific conductance (m^ ' cm ' ) of various 1 : 1 electrolytes at 25°C through cupric hydroxide membranes plotted against the free energy of hydration (AG") of cations.
tabulations [24,25] of the number of moles of water associated with some electrolytes. However, in Fig. 3 a plot of specific conductance of different electrolytes (chlorides) against the free energy of hydration of cation [26] is given for the membrane. It is seen that specific conductance decreases with increasing hydration energy, i.e., greater size due to increase in hydration. This points to the fact that the electrolyte is diffusing along pores or channels of dimensions adequate to allow the substance to penetrate the membrane. The state of hydration of the penetrating electrolyte may be considered to exist in a dynamic condition, so that at higher temperatures a considerably higher fraction of the total number of a given kind would possess excess energy AE per mole according to the Boltzmann distribution f=e = ^-AE/RT {R is the gas constant). Under theses circumstances, those ionic species which have lost sufficient water of hydration to become smaller than the size of the pore would enter the membrane. In this way the specific conductance would increase with increase in temperature, subject, however, to the proviso that the membrane has undergone no irreversible change in its structure. That no such structural change is involved is evident from the linear plots of log n vs. 1/T shown in Fig. 1. The slope of these gives the energy of activation as required by the Arrhenius equation.
Table 1 shows that the activation energy decreases with the increase in concentration of the bathing electrolyte solution, and that for different electrolytes at a particular concentration it follows that:
*>E, Li"
The activation energies for electrolytic conduction follow the sequence of crys-tallographic radii of the alkali metal cations. When the penetrant moves in a polymer substance containing a relatively small amount of water, its motion
317
TABLE 1
Values of thermodynamic parameters, energy of activation E^, free energy of activation AG^ and entropy of activation AS*, for parchment supported cupric hydroxide membrane in contact with different concentrations of various 1 : 1 electrolyte solutions
Electrolyte
concentration c/mol r '
KCl 0.1 0.01 0.001 0.0001 NaCl 0.01 LiCl 0.1 0.01 0.001
Parameters
Ba/kJ
18.4 25.0 25.4 25.4
24.3
18.3 22.0 24.5
mol"' AC^/kJmor '
73.4 71,1 75.5 78.0
74.2
72.1 75.7 78.5
AS^/J K"
241 163 176 185
177
190 190 189
' m o P '
may be governed by the segmental mobility of the polymer, and its diffusivity may depend on the probability that the segment will make a hole large enough to accommodate a penetrant species [27]. In such a system the activation energy w ill depend on the size of the penetrant species, i.e., the activation energy will increase with the penetrant size. If this is the case in our system, the dependence of the activation energy on the kind of alkali metal ion may be interpreted in terms of the crystallographic radius of the ion, which is consistent with the result obtained in the diffusivity measurement in the same system [12].
The theory of absolute reaction rates has been applied to diffusion processes in the membrane by several investigators [5—7,28,29]. Following Eyring [5,30] we have:
where n is the membrane conductance, h the Planck constant, R the gas constant, N the Avogadro constant and T the absolute temperature. Here, AG* is the free energy of activation for the diffusion of ions and is related by the Gibbs—Helmholtz equation:
AG* = AH* - TAS* (2)
AH* is related to the Arrhenius energy of activation E^ by
E^ = AH* + RT (3)
A plot of log nNh/RTvs. 1/T from experimental data gives a straight line, the slope and the intercept of which gives the value for AH* and A.S' as demanded by eqn. (1). This justifies the applicability of eqn. (1) to the system under investigation. The derived values of AH* and AS* were then used to obtain the value of AG* and E^, using eqns. (2) and (3). The values of various
318
thermodynamic activation parameters E^, AH*, AG* and AS* derived in this way for the diffusion of various electrolytes in the membrane are given in Table 1. The results indicate that the electrolyte permeation is associated with negative values of AS*. According to Eyring and co-workers [5,30], the values of AS^ indicate the mechanism of flow, the large positive AS* being interpreted to reflect breakage of bonds, while low values indicate that permeation has taken place without breaking bonds. The negative AiS^ values are considered to indicate either formation of covalent bonds between the permeating species and the membrane material, or that the permeation through the membrane may not be the rate-determining step.
Conversely, Barrer [28,31,32] has developed the concept of "zone activation" and applied it to the permeation of gases through polymer membranes. According to this zone hypothesis, a high AS*, which has been correlated with high energy of activation for diffusion, means either the existence of a large zone of activation or the reversible loosening of more chain segments of the membrane. A low AS*, then, means either a small zone of activation or no loosening of the membrane structure on the permeation. In view of these differences in the interpretation of AS" , Shuller et al. [6], who found negative values of AS* for sugar permeation through the collodion membrane, have stated that "it would probably be correct to interpret the small negative values of AS* mechanically as interstitial permeation of the membrane (minimum chain loosening) with partial immobilization in the membrane (small zone of disorder)". On the other hand, Tien and Ting [7], who found negative AiS^ values for the permeation of water through very thin (5 nm thickness) bilayer membrane, stressed the possibility that the membrane may not be the rate-determining step, but the solution—membrane interface was the rate-limiting step for permeation. Negative A.S' values may be ascribed to the partial immobilization of ions and its interaction with the membrane fixed-charge groups.
On the other hand we have [33]:
and
TTo=2.12{kTdyh)e^^*l^ (5)
where k is the Boltzmann constant and d is the interionic jump distance, i.e. the distance between equilibrium positions of diffusing species in the membrane. Equation (4) predicts that a plot of log IT vs. 1/T gives a straight line and Ea may be obtained. Substituting the value of parameter AS* and E^ in eqns. (4) and (5) we obtain the value of interionic distance ^0.15 nm. This value of d is not unusual in these systems. Various investigators [5—7,13,25,34,35] have used values of d ranging from 0.1 to 0.5 nm.
The results of all these investigations are that the membrane conductance can be determined at different temperatures with reasonable accuracy. The membrane is weakly charged and ionic species retain their hydration shell at least partially while diffusing through the membrane pores. Negative AS'' values suggest that the partial immobilization of ions takes place most probably due to interstitial permeation and ionic interaction with the fixed-charge groups of the membrane skeleton. The interionic jump distance for the system was 0.15 nm.
319
ACKNOWLEDGEMENTS
The authors are grateful to Prof. Wasiur Rahman, Head of the Department of Chemistry, for providing research facilities, and to U.G.C. (India) for the award of fellowship to one of us (K.A.)
REFERENCES
1 F. Helftench, Ion Exchange, McGraw-Hill, New York, 1962. 2 F Helffench in J.A. Mannski (Ed.), Ion Exchange: A Series of Advances, Marcel Dekker, New York,
1966, Ch. 2. 3 N. Lakshminarayanaiah, Chem. Rev., 53 (1949) 392, Transport Phenomena in Membranes, Academic
Press, New York, 1969. 4 R.P. Buck, CRC Cnt. Rev. Anal. Chem., (1976) 323. 5 B.J. Zwohnski, H. Eynng and C.E. Reese. J Phys. Chem., 53 (1949) 1426. 6 K.E. Shuller. C.A. Dames and K.J. Laidler, J. Chem. Phys., 17 (1949) 860. 7 H.T Tien and H.P. Ting, J CoUoid Interface Sci., 27 (1968) 702. 8 S.B. Clough, A.E. Read, A.B. Metzner and V.C. Behn, A.I.Ch. J., 8 (1962) 346. 9 S.U. Li and J.L. Gainer, Ind. Eng Chem. Fund., 7 (1968) 433.
10 R.M. Navan, J.L. Gainer and K.R. Hall, A.I Ch.J , 17 (1971) 1028. 11 D. Tsimboukis and J.H. Petropoulos, 17th Discussion Meeting on Dyeing Chemistry, Sen-i-Gakkal
(The Society of Fibre Science and Technology, Japan), 1975, preprint. 12 T hjima, T. Obara, M. Isshiki, T. Seki and K. Adochi, J. CoUoid Interface Sci., 63 (1978) 421. 13 F.A. Siddiqi, N. Lakshmmarayanaiah and M.N. Beg, J. Polym. Sci., 9 (1971) 2853. 14 F.A. Siddiqi, M.N. Beg and S.P. Singh, J. Polym. Sci., 15 (1977) 959. 15 M.N Beg, F.A. Siddiqi and R Shyam, Can. J. Chem., 55 (1977) 1680. 16 M.N. Beg, F.A. Siddiqi, R. Shyam and M. Arshad, J. Membrane Sci., 2 (1977) 365. 17 M.N Beg, F A. Siddiqi, R. Shyam and I. Altaf, J. Electroanal Chem., 98 (1979) 231. 18 G. Eisenman, The Glass Electrode, Interscience, New York, 1965, p. 215. 19 G. Eisenman, Biophys. J. Suppl., 2 (1962) 259. 20 G. Eisenman in A. Kleinzellers and A. Kotyk (Eds.), Membrane Transport and Metabohsm, Academic
Press, New York, 1961, p. 163. 21 H. Sherry in J.A. Mannsky (Ed ), Ion Exchange, Vol. 2, Marcel Dekker, New York, 1969, p. 89. 22 V. Subramanyan and N. Lakshminarayanaiah, J. Phys. Chem., 72 (1968) 4314. 23 D. Reichenberg in J.A. Mannsky (Ed.), Ion Exchange: A Senes of Advances, Marcel Dekker, New
York, 1966, Ch. 7. 24 H S Hamed and B.B. Owen, The Physical Chemistry of Electrolyte Solutions, Reinhold, New York,
3rd edn., 1958, p. 525 25 R.A. Robinson and R.H. Stokes, Electrolyte Solutions, Butterworths, London, 2nd edn., 1959, p. 62. 26 Y. Marcus and A.S. Kertes, Ion Exchange and Solvent Extraction of Metal Complexes, Interscience,
New York, 1969, p 13. 27 C.A Kumins and T.K. Kwei in J. Crank and G.S. Park (Eds.), Diffusion in Polymers, Academic Press,
London, 1968, Ch. 4 28 R.M. Barrer and G. Skirrow, J. Polym. Sci., 3 (1948) 549. 29 W.D. Stein, The Movement of Molecules Across Cell Membranes, Academic Press, New York, 1967,
pp. 70—89. 30 S. Glasstone, K.J. Laidler and H. Eynng, The Theory of Rate Processes, McGraw-Hill, New York,
1941, pp 525—544. 31 R M. Barrer, Trans. Faraday Soc , 38 (1942) 322. 32 R.M Barrer and H T. Chio in C.A. Kumins (Ed.), Transport Phenomena in Polymenc Films (J. Polym.
Sci. C, 10), Interscience, New York, 1965, p. 111. 33 R.M. Barrer, R.F. Bartholomew and L.V.C. Rees, J. Phys. Chem. Solids, 21 (1961) 12. 34 F.A. Siddiqi. S.K. Saksena and I.R. Khan, J. Polym. Sci., 15 (1977) 1935, 1956. 35 A. Dyer and J.M. Fawcett, J. Inorg. Nucl. Chem., 28 (1966) 615.
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