Macromolecular Chemistry–11. Plenary and Sectional Lectures Presented at the International Symposium on Macromolecules (the Third Aharon Katzir–Katchalsky Conference)

158 Pages·1977·8.353 MB·English

by  H. Eisenberg (Eds.)

Organizing Committee
President: E. Katzir
Chairman: A. Silberberg
Vice-Chairman: D. Vofsi
Secretary: LR. Miller
Associate Secretary: R. Corett
Symposium Editor: H. Eisenberg
Chairman, Scientific Programme: I. Michaeli
Members: D. Katz
O. Kedem
M. Lewin
A. Ram
A. Zilkha
Z. Zurr
Z. Alexandrowicz
C. Forgacs
A. Patchornik
S. Reich
International Union of Pure and Applied Chemistry
(Macromolecular Division)
in conjunction with
Israel National Academy of Sciences and Humanities
Israel Chemical Society
and
Weizmann Institute of Science
Macromolecular
Chemistry - 11
Plenary and Sectional lectures presented at
the International Symposium
on Macromolecules(The Third Aharon Katzir-
Katchalsky Conference)
Jerusalem, Israel, 13-18 July 1975
Symposium Editor:
H. Eisenberg
The Weizmann Institute of Science
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Pure & Appl. Chem., Vol. 46, pp. 91-101. Pergamon Press, 1976. Printed in Great Britain.
POLYELECTROLYTES, PAST, PRESENT AND FUTURE
J. TH. G. OVERBEEK
Van't Hoff Laboratory, University of Utrecht ,The Netherlands
Abstract—In the introduction the close relation between polyelectrolytes and hydrophilic colloids is stressed. A
survey is given of present day polyelectrolyte knowledg eas accumulated since about 1940. In this respect mention is
made of osmotic pressure, Donnan pressure, light scattering, titration, activity of small ions in polyelectrolyte
solutions, swelling and viscosity, protective action and sensitization, electrophoresis and electrical conductance, and
dielectric polarization. A preference is indicated for a cylinder model with the possibility of counterion condensation
above a porous sphere model and a list o fgaps in our knowledge with a few suggestions for further applications are
given.
INTRODUCTION of the spheres, r their radius, κ the specific conductance
Some natural polyelectrolytes, such as glue and gums, of the solution, e its dielectric constant and ζ the surface
have been used from time immemorial as thickeners and potential (zeta-potential) of the particles. In Von
the use of gum as a protective colloid is as old as the use Smoluchowski's theory the increase of the viscosity
of India ink, which is finely ground soot, suspended in above the Einstein value is due to the distortion of the
water and stabilized with gum arabic. The term colloid spherical electrical double layer into a quadrupole in the
was coined by Graham1 who derived it from the Greek field of flow.
word for glue (κόλλα). After the discovery that small particles, such as quartz,
In early colloid research most systems investigated had carbon, or oil droplets adsorb hydrophilic colloids and
water as the dispersion medium and it was soon recog- assume an electrophoretic mobility similar to that of the
nized that a rather sharp division into two main groups, free hydrophilic colloid, microscopic electrophoresis be-
the hydrophobic and the hydrophilic colloids, was indi- came a favourite tool for studying charge and zeta-
cated. Later, with the introduction of solvents other than potential of these substances. Figure 2 shows7 how lead
water, the two groups were extended to lyophobic and nitrate affects the electrophoretic mobility of a variety of
lyophilic colloids. carriers, but that after addition of only 0.09% of Na-
The hydrophilic (lyophilic) colloids are truly soluble in arabinate all curves come together and obviously this
water (the solvent) and derive their colloidal nature from curve represents the mobility of adsorbed arabinate.
the huge size of their molecules or from reversible Figure 3 shows7 how the concentration of charge reversal
association of many small molecules to micelles. In either (zero electrophoretic mobility) by hexamine-cobalt
case the solubility in water requires the presence of polar chloride changes from its low value for quartz to a much
groups in the molecules, and since these polar groups are higher one characteristic for arabinate on increasing the
often ionizable, especially in natural hydrophilic colloids,
it is self evident that a great part of the early research on
lyophilic systems dealt with polyelectrolytes in aqueous
solution.
It had been shown that the presence of an electric
charge on the particles of hydrophobic colloids was
essential for their existence (Freundlich2 called them
electrocratic). So it was only natural for Kruyt and
Bungenberg de Jong,3 when they started their research on
agar-agar in 1919, to look for effects of the electric charge
of the particles. In that time electrophoresis was a difficult
and very time consuming technique, but they found that
the viscosity of agar-agar solutions decreased in a pro-
nounced way on the addition of electrolytes and that the
valence of the cation was the determining factor in this
decrease (see Fig. 1). They recognized the rule of Schulze
and Hardy,4 (effect much more than proportional to the
valence of the cation) well known from the research on the
stability of hydrophobic colloids and explained their
findings on the basis of an eqn (1) derived in 1916 by Von
Smoluchowski5 as an extension of Einstein's eqn6 for the
viscosity of a suspension of spherical particles.
m.equiv/l.
(1)
ηο L τ/οΚΓ \2π/ J Fig. 1. Relative increase of the viscosity of a 0.14% solution of
agar-agar at 50°C over the viscosity of the solvent as a function of
In this equation η5 and r/0 are the viscosity of the the concentration (in m-equiv/1 of added electrolyte). Pt(en3)
suspension and the solvent resp. φ is the volume fraction stands for the four valen tplatinum (ethylenediamine) ion.
3
91
92 J. TH. G. OVERBEEK
50
TiCL Paraffin oil
-90
-100 J_
-4 -3 -2
logC Pb (N03)2
Fig. 2. Electrophoretic mobility, U, in arbitrary units, of a number of different carrier particles and of these particles in
a 0.09% Na arabinate solution as affected by the concentration of lead nitrate in equiv/1.
are pure chemical entities with a well defined molecular
weight allowed proteins to become for a time the main
objects of polyelectrolyte research, although the research
was aimed more at structure and function of proteins than
at their properties as electrolytes.
In the Dutch school the further study of viscosity,
electrophoretic mobility, turbidity and precipitation of
polyelectrolytes as affected by low molecular weight salt
led to the appreciation of the charge density (as character-
ized by the equivalent weight) and the nature of the
charged groups ("phosphate-, carboxyl-, and sulphate
colloids") as determining factors. It was found that re-
versal of charge caused by "adsorption" of cations
often was accompanied by precipitation and the higher
the charge density the lower the valence of the cation that
would suffice for precipitation12 (see Fig. 4). In addition to
the influence of the valence, specific influences of the
nature of the cations on the concentration needed to
obtain charge reversal were found.13 For example, for
carboxyl- and sulphate colloids the concentration of
charge reversal increases in the order Ba, Sr, Ca, Mg, K,
Fig. 3. Logarithm of the concentration of hexamine-cobalt Na, Li but for phosphate-colloids the order in the alkaline
chloride in equiv/1 needed for charge reversal (zero electrophoretic earth ions is irregular and for the alkali ions it is Li, Na, K.
mobility) of quartz particles in solutions of Na-arabinate .Csoi These polyelectrolytes are not only precipitated by
expressed in %. multivalent small ions, but also by polyions of opposite
sign. The precipitates are liquid, although sometimes quite
arabinate concentration from 10"5 to 0.1%. Kruyt and viscous. They are called coacervates, or complex coacer-
especially Bungenberg de Jong and his school8 continued vates in the case of mutual precipitation of oppositely
their work with hydrophilic colloids using agar-agar, charged polyions. Here again the charge density proved to
gums, gelatine and other long-chain poly electrolytes, al- be a very important factor as exemplified by Fig. 5, in
though in the first years of this research they still consi- which the complex-coacervation between gum arabic
dered these colloids as aggregates rather than as mac- (negative) and gelatin (positive below pH = 5) is shown as
ro molecules. a decrease in viscosity below the additive value.14 Going
The physical chemical approach to proteins, in particu- from pH = 5 where gelatin has no charge, but gum arabic
lar to soluble corpuscular proteins profited from the is strongly negative, via pH = 3.5 (gelatin strongly posi-
development of refined new instrumentation. I mention tive, gum arabic still rather strongly negative) to pH = 1.2
here Svedberg's ultracentrifuge9 (1926), Tiselius' elec- where gelatin is positive, but gum arabic practically
trophoresis10 method (1930) and light scattering, as first uncharged, the complexcoacervation starts at zero, goes
applied by Putzeys and Brosteaux11 (1935) to proteins. through a maximum and returns to zero. Addition of low
These new techniques, the better methods of separation molecular weight salts, which screen the charges of the
and purification and, above all, the fact that many proteins polyions suppresses complex-coacervation.
Polyelectrolytes, past, present and future 93
3-6 phosphate colloids
8-11 Carboxyl colloids
12-14 Sulfate colloids
J I L
I05 O 10 20 30 40 50 60 70 80 90
equivalent weight of the colloidanion (b)
Fig. 4. Relation between tendency to precipitation and equivalent
weight of the polyanion (colloidanion). The points on the graph
correspond to the salt of the highest valence type that will not
precipitate the polyion. 3 = soya bean phosphatide I (alcohol
soluble); 4 = soya bean phosphatide II (alcohol insoluble);
5 = NaDNA (thymus); 6 = NaRNA (yeast); 8 = Na arabinate;
9 = Na pectinate; 10 = Na semenlini mucilage; 11 =Na pectate;
12 = Na agar; 13 = K chondroitin sulphate; 14 = Na carragene; 3
and 4 are association colloids, not polyelectrolytes, but they fit in
the whole picture.
With two polyelectrolytes of high charge density very
dense coacervates are formed, which can be cast in stable
membranes.15 Another application of the coacervates is
based on the very low interfacial tension (0.001-0.01 dyn
cm-1). It allows the coacervate to envelop substances of
low polarity and is the basis of the so-called micro- 0 10 20 30 40 50 60 70 80 90 100
encapsulation.16 (a)
Fig. 5. Effect of pH on the viscosity of mixtures of 0.67% solutions
of gelatin (G) and gum arabic (A) as an indication of complex-
DEVELOPMENTS SINCE 1945 coacervation. Ordinates: measured value of (η* - τ/0)/ι?ο as a
percentage of the calculated value of (17, - η)Ιη o assuming
During the development of polymer science in the 0
thirties and early forties (Staudinger,17 Carothers,18 additivity. Abscissae: mixing proportion of G and A, expressed in
% A. The lower the value of the ordinate, the stronger the tendency
Kuhn19) little attention was given to the behavior of linear
to coacervation, i.e. the higher the polyion concentration in the
polyelectrolytes, with the notable exception of a few coacervate.
papers by Kern20 on the osmotic pressure, activity of
counterions, electrical conductance and viscosity of behavior are:
synthetic polyacids.
But at a symposium, held in Liege (Belgium) in 1948 at (a) as a consequence of the concentration of electric
the occasion of H. Mark's presence there as a visiting charges along the polyelectrolyte chain, there is strong
professor, it became clear that polyelectrolytes had electrical interaction amongst these charges and the sur-
caught the attention of several groups of scientists, who rounding small ions,
worked at achieving a synthesis between the theory of (b) therefore, the solutions show large non-idealities in
electrolytes and the electrical double layer and the statisti- their osmotic pressure, ion activities and electrical trans-
cal and thermodynamic treatment of coiled polymer port,
chains. (c) moreover, the coils will swell under the influence of
In papers by Kuhn, Künzle and Katchalsky21 and by the repulsion amongst the charges on the chain, as mod-
Hermans and the present author22 a treatment was given ified, of course, by the surrounding ionic atmospheres,
of the swelling and shrinking of polyelectrolyte coils (d) this swelling will increase the viscosity of the
under the influence of their charge (or degree of dissocia- solutions and express itself in the swelling of polyelectro-
tion) and the presence of salts, leading to an explanation lyte gels.
of the electroviscous effect, and of the influence of charge In the quantitative theory the following problems must
and salts on the titration curve. At the presentation of be solved.
these papers H. Mark remarked that R. Fuoss was work- (e) How does one describe the electrical free energy of
ing on the same subjects at Yale University. a coil in a given conformation with its ionic atmosphere?
From that time on polyelectrolyte research developed (f) Which model for the coil is applicable?
rapidly, a good part of it by the able hands of Katchalsky (g) Is it sufficient to assume complete dissociation
and his well chosen coworkers. between polyion and counterions, with only electrostatic
The central concepts in understanding polyelectrolyte binding or should some site binding be introduced?
94 J. TH. G. OVERBEEK
(h) Even if no site binding has to be introduced, should The Donnan pressure can then be written:
the finite size of the small ions be introduced or is a
description as point charges adequate?
^Donnan = CmRT\-p + «J + (2CS ~ U [)RT (7)
Before trying to answer these questions, we shall first
present briefly some of the experimental observations. where we have neglected the difference of the salt activity
coefficients and unity. Using eqn (6) we have
Osmotic pressure
The ideal osmotic pressure, π , of a very dilute, saltfree
ίά ^ = cJ?r(^+a(2jß-l)) (8)
solution of c mol/unit volume of a polyelectrolyte of onnan
p
degree of polymerization, P, with P ionizable groups per
molecule (the extension to different numbers for the which for high c, (β = 0.5), approaches to
s
degree of polymerization and number of ionizable groups
is trivial) of which the fraction a is actually ionized would
cJlT-p (9)
be ''Donnan
v = c RT(\ + aP). (2) and shows that by using high concentrations of supporting
id p
electrolyte we may determine the degree of polymeriza-
The actual osmotic pressure, π, is considerably lower tion (and thus the molecular weight, M) by osmotic
and this can be described by assigning an osmotic coeffi- measurements.
cient, y, to the counterions, leading to
p
Light scattering
7Γ = c RT(\ + yaP)« cRT · yaP (3) Light scattering may be considered to be due to the
p p p p
fluctuations in refractive index. In solutions these fluctua-
where the second form is a very good approximation since tions are mostly due to fluctuations in concentration. In
P>\. Introducing the concentration c = cP in polyelectrolyte solutions the fluctuating entity is not the
m p
monomoles per unit volume, we have: polyion, but an electroneutral region containing the poly-
ion plus its surrounding ionic atmosphere, that is the
77 = c RTya. (4) polyion, the counterions, and a negative contribution from
m p
the expelled salt.24 Vrij pointed out, that this salt expul-
It is found that y is nearly independent of the degree of sion has also to be taken into account in the value of an lac,
p
polymerization, it decreases with increasing charge den- the refractive index gradient. This can be done by
sity (increasing a) and except for the lowest values of a, determining the salt expulsion per unit charge of the
ya is nearly constant. See Katchalsky, Alexandrowicz polyion separately, or by measuring an lac in a Donnan
p
and Kedem.23 equilibrium, in which the salt expulsion occurs spontane-
The quantity, yc a, may be interpreted as the counter- ously. This agrees with the fact that in the value of d7r/dc,
p m
ion concentration midway between two polyions, i.e. at a occurring in the light scattering equation, π is the Donnan
location where the electric field strength is zero. pressure, because the fluctuations in polyion concentration
When salt (for simplicity we consider only mono- take place in a salt containing medium, and not in pure
monovalent salts), is added to the polyelectrolyte solution solvent.
it is found that the osmotic pressures are additive. So The strong repulsion between polyions leads to a high
second virial coefficient and a relative decrease of the
light scattering at higher concentrations. But with ex-
TTtot = TTp + 1TS (5)
trapolation to zero polyion concentration in the presence
where n is the observed osmotic pressure in a mixture of a constant salt concentration (c = constant) or salt
tot s
where polyelectrolyte and salt, if present alone, would activity (c' = constant) and with the above mentioned
s
exert osmotic pressures of π and TT respectively. precaution with respect to an lac, light scattering leads to
ρ S
correct values of the molecular weight of polyelectro-
Donnan pressure lytes.
When the osmotic pressure is determined with a mem-
brane, permeable to the solvent and all small ions, but Titration of polyacids
impermeable to the polyions, we obtain the Donnan In a titration of a polycarboxylic acid, such as poly ac-
pressure or oncotic pressure. The solution outside the rylic acid or gum arabic, the dissociation constant, as
membrane then contains a salt concentration c' in equilib- conventionally defined, appears to decrease with increas-
s
rium with c and c inside the membrane. It is useful to ing degree of neutralization, a. This is easily explained,
p s
describe this equilibrium as an expulsion of some salt since with increasing negative charge of the polyion it
from the neighbourhood of the polyions, so that their becomes more and more difficult to dissociate a further
charge, aP, is compensated for a fraction, (1-jß), by a hydrogen ion. The equilibrium equation therefore has to
deficit of co-ions and a fraction, ß, by an excess of contain an extra term, LG, which represents the increase
d
counterions above the concentration c', present outside in electrical free energy of the polyion and its atmosphere
s
the range of the electric field of the poly ion. Thus: on increasing the polyion charge by one unit.
c' = c+ aPc (\ -ß) = c+ ac (\ - ß). (6)
s s p s m pH = pKo + log γ^ + 0.43 ^ (10)
ß approaches to 0.5 when c is high (say IM) but is larger,
s
up to about 0.9 for small c (and, of course, equal to 1 where pK is the intrinsic dissociation constant (at zero
s 0
when no salt is present). charge). Since AG, is expected to increase with a, it is not
C
Poly electrolytes, past, present and future 95
astonishing that Katchalsky and Spitnik25 found that the liquid junction potential between the KC1 bridge and the
titration data would often fit the empirical equation polyelectrolyte solution.
The product of the activities of the small ions, in which
this uncertainty cancels, and which must be equal to the
pH = pK + m logy^ (11)
0 activity product for the ions in the Donnan outside
solution, agrees well with the following data about the
where m is a constant, larger than unity. single ion activities.
The theoretical calculation of AG, depends strongly on Single co-ion activity coefficients are rather indepen-
e
the model chosen for the polyion and is not easy.26 dent of the polymer concentration (Nagasawa, Izumi and
Moreover, the matter is not quite as simple as it looks Kagawa31) in agreement with the fact that they are pushed
here, since it is questionable whether the pH calculated away from the polyions.
from the e.m.f. between a glass electrode and a calomel Counterion activity coefficients are low in saltfree
electrode with a saturated KC1 salt bridge inserted in the polyelectrolytes and the activities are often found to be
polyelectrolyte solution is the correct value to be inserted additive when salt is added, as shown particularly nicely
in eqn (10). AG/ is calculated assuming that the H+-ions by Mock and Marshall32 for HC1 added to poly-
e
participating in the equilirium come from a region with an styrenesulphonic acid.
electrical potential zero, but the salt bridge comes at some Nevertheless, consider the role of the saltbridge in
kind of an average potential in the solution and this is these measurements and the fact that the liquid junction
certainly more negative than a point far away from all the potential, E is given by
ih
polyions. A good way to see whether this is a quantita-
tively important effect is to consider the titration cell as i C solution U djit,
part of a Donnan system.27 E,,- -p\ Σ (14)
F Jsat.KCI i
calomel satur. polyelectrolyte equilibrium satur. calomel
electrode KC1 solution solution KC1 electrode
glass glass
(12)
electr. electr.
-E , polyel. -E=0 -£ ,equil.
H H
~ *-* Donnan "
In the equilibrium solution the H+-ions are indeed far where t μ, and Z, are the transference numbers, the
h
away from the polyions and may be considered to be at chemical potential and the valence with sign included
electrical potential zero. Therefore the pH in eqn (10) is resp. of the ions i. Then it is obvious that the liquid
the pH of the equilibrium solution, not that of the junction potential not only depends on ion activities, but
polyelectrolyte solution. Since the two glass electrodes also on ion mobilities. As the mobilities are strongly
are at the same potential (otherwise work could be affected by the presence of polyions (Overbeek27) it is
extracted from a system in equilibrium) the two pH's amazing that such simple additivity laws should hold. We
differ by E J59 mV, or come back to this point later.
Donn
FE
pHequil. - pHp( -0.43 ROT (13)
where üOonnan has the same sign as the charge on the
polyions.
The effect described in eqn (13) has been known since
1930 in soil science as the Pallmann and Wiegner effect2.8
It can be eliminated in polyacid titrations by extrapolating
to polyion concentration zero, but keeping at least some
low molecular weight salt present.
An old measurement29 on the titration of gum arabic
shows the influence of the concentration quite clearly
(see Fig. 6).
Activities of polyions, counterions and co-ions
The mean activity coefficient, γ , for the polyion-
±
counterion combination can be determined either from
osmotic pressure data, using the Gibbs-Duhem relation,
or directly (Dolar and Leskovsek30) using a galvanic cell
with transference. In agreement with the fact that the
osmotic coefficient is low, but fairly independent of the
polyelectrolyte concentration, log y decreases strongly
±
and linearly with the logarithm of this concentration.
Determinations of the single ion activities of the coun- IOO%- -NaOH
terions and co-ions suffer from the same uncertainty as
discussed above for the pH, viz. the uncertainty about the Fig. 6. Titration curves of gum arabic and of pectic acid.
96 J. TH. G. OVERBEEK
Swelling of poly electrolyte coils and electroviscous effect tions of protective agents may act as sensitizers by the
As mentioned in the introduction, the spectacular fact that under such circumstances one polyion may get
changes in viscosity caused by changes in charge density adsorbed on two particles and thus bind them together.
and salt concentration formed perhaps the most typical Sensitization has obtained a new importance in the pro-
entry to polyelectrolyte research, and already at the Liege tection of the environment because it may be used as a
symposium in 1948, quantitative, although rather primi- method for precipitating otherwise persistent suspen-
tive theories of the electroviscous effect were given. sions. One example is the cleaning of effluents of coal
Nevertheless, notwithstanding a great deal of effort from washeries.38
many sides the quantitative situation is still not satisfac- The mechanism of protection as such is fairly well
tory. understood. Loosely protruding chains behave nearly as
In the first place there are really three electroviscous free molecules and when the protruding ends of the chains
effects, the classical, Smoluchowski5 one, depending on adsorbed on two different particles come close together,
distortion of the ionic atmosphere, the one caused by the both the local increase in concentration and the loss of
swelling of individual coils, and one caused by the mutual conformational freedom represent an increase in the free
repulsion between two polyions. The last one can be energy of the system and thus lead to repulsion. See
eliminated by dilution of the polyelectrolyte, but this has Hesselink and others.39
to be done at constant activity of the small ions, in order The quantitative description of the adsorption and
to keep the average conformation of the polyion indepen- especially the influence of small ions on it still leaves
dent of its concentration. Isoionic dilution (keeping the something to be desired. Moreover the mutal repulsion of
total number of small ions constant) has been introduced33 polyelectrolytes is more complex than that of uncharged
to achieve this aim at least approximately. Dilution in a polymers, treated in the above mentioned theories.
Donnan equilibrium with the outside solution kept con-
stant would be still better. Transport phenomena, in particular electrophoresis
Furthermore the relation between (intrinsic) viscosity Having discussed viscosity earlier, the main remaining
and shape of the coil is not at all simple. Semi-empirical transport phenomena are sedimentation, diffusion and
equations are used here, derived from work on non ionic electrical conductance and electrophoresis. We shall con-
polymers and one of the stumbling-blocks is the uncer- centrate our attention to the transport in an electric field.
tainty about the friction constant of individual chain ele- Experimentally it is found that electric transport is
ments or of a given length of the chain. We shall later nearly independent of molecular weight; the co-ions have
encounter the same difficulty in the interpretation of about the same mobility that they have in the absence of
electrophoresis. polyelectrolyte; the mobility of the counterions is quite
Finally the problem of minimizing the total free energy low and in some cases even negative. The mobility of the
of the coil, consisting of the electrical free energy of its polyions increases less than proportionally with charge
charges and their ionic atmospheres and of the configura- density, and generally decreases with increasing ionic
tional free energy has not yet received a completely strength. An exception has been reported by Nagasawa et
satisfactory answer. ai40 at very low ionic strength.
There are other ways of obtaining information on the Theoretically one expects the electrical transport to be
coil expansion. The best one probably is to use the angular determined by the ideal mobilities of polyion and small
dependence of the light scattering with a Zimm-plot as ions, as modified by the electrophoretic retardation (hyd-
worked out by Orofino and Flory.34 Another is studying rodynamic interaction between polyion and small ions),
the swelling of lightly cross linked gels (Katchalsky, the relaxation effect (distortion of the ionic atmosphere)
Lifson and Eisenberg35). and possibly by binding between polyion and small ions.
Kuhn and Katchalsky and coworkers36 drew attention There are several more or less complete theories for the
to the possibility of deriving mechanical work from the electrophoretic retardation, in which the polyion is either
changes in volume of polyelectrolyte gels and coined the treated as a porous sphere, or as a randomly kinked
term "mechanochemistry". Since living organisms can cylinder, but the theories for the relaxation effect (Long-
convert chemical into mechanical energy, it is tempting to worth and Hermans,41 Imai and Iwasa42) are still in
look for a possible relation with the changes in size of development and not easily applicable. With the aid,
polyions. however, of the semiempirical method introduced by
Finally we should mention that in heavily crosslinked Möller, van Os and Overbeek43 the effect of the distortion
poly electrolytes, used as ion exchangers, on the one hand of the ionic atmosphere can be eliminated and then
swelling and shrinking is a nuisance, but on the other hand theories, which only take the electrophoretic retardation
the high concentration of charges and therefore of coun- into account, can be used. The method of Möller et al. is
terions may give possibilities for specific differences based upon the idea, that the ionic atmosphere, either
between ions of the same valence, say K vs Na.37 resting or distorted depends little on the kind of counter-
ions (only on their valence), and further that the relaxa-
Protective action and sensitization tion effect is due to an electrical interaction between the
Amongst one of the oldest applications of polyelectro- polyion and its atmosphere and thus can be represented
lytes is their use as protective agents. When the surfaces by an average electric field acting on polyion and on its
of hydrophobic particles or emulsion droplets are fully counterions and slowing them all down in the same
covered by an adsorbed layer of polyelectrolyte, these proportion.
particles become very resistant against flocculation, be- This being the case the electrophoretic mobility of the
cause now their surface layers are compatible with water. polyion can be written as
As a matter of fact important natural emulsions, such as
milk and latex, are protected in this way by adsorbed U =(U °-U , )(l-bXlX) (15)
p p per
proteins.
Only later it was discovered that very small concentra- and the mobility of the counterions as
Polyelectrolytes, past, present and future 97
U=(U0-U, )(l-kXlX) (16) Table 1. Values of {\-AX\X) at different de-
c c cer
grees of neutralization, a, and at different
where U ° and U° represent the ideal mobilities of bromide concentrations, c
p c
polyion and counterion resp., £/ and [/, the respective
p>er cer
electrophoretic retardations, X the applied field strength c(mol/l)
0.001 0.003 0.01 0.03 0.1
and AX the average relaxation field. Since the distribution
a
of counterions is assumed to be independent of their
nature (at constant valence), Uc<eT is also independent of it, 0.3 0.54 0.56 0.54
Therefore for two different counterions, say 1 and 2, we 0.5 0.52 0.52 0.54 0.57 0.63
obtain two eqns (16) from which [/c,er can be eliminated 0.7 0.42 0.45 0.62
leading to
By using Hittorf transference measurements, Van der
1 AXlX- o_ \ (17)
u u Drift44 determined electrophoretic mobilities of the poly-
ions and mobilities of co- and counter-ions. The mobilities
or, introducing equivalent conductancies, λ = FU, we of the co-ions decreased slightly with increasing
have polyelectrolyte concentration, the cation mobilities were
low and sometimes negative, due to the combination of
electrophoretic retardation and relaxation effect, the poly-
1-ΔΧ/Χ = - ^ -^ (18)
ion mobilities decreased strongly with increasing ionic
strength, were independent of the polymer concentration
The mobility and the equivalent conductance of the and increased only slowly with the degree of dissociation,
polyion are also independent of the kind of counterion as shown in Figs. 8-10 and in Tables 2 and 3.
and so λ,-λ = A - A where A represents the equi- Electrophoretic mobilities, corrected for relaxation by
2 pl p2 p/
valent conductance of the polyelectrolyte with its coun- dividing them by (1 - AXIX), can now be compared with
terions of type /. Consequently the different theories. However, whatever model is cho-
sen, the friction constant per unit length of the molecule
remains an adaptable parameter in any model. We come
\-AXIX = (19)
A,°-A°· back to this interpretation in a later section.
2
The fact that the r.h.s. of eqn (19) is independent of the
This equation can not only be applied to salt free choice of the counterions has been signalled by Eisen-
polyelectrolytes but also to the increase of the conduc- berg46 and has been interpreted on the simple basis that a
tance of a salt solution, caused by the addition of fraction, (1 - /), of the counterions is bound to the polyion
polyelectrolyte. Equation (19) has been tested recently by and moves along with it (cf. Huizinga, Grieger and Wall47).
Van der Drift44 by determining the conductance of Manning48 indicates still another interpretation of the
LiPMA, NaPMA and KPMA (salts of polymethacrylic same quantity, /, viz. as the ratio of the self-diffusion
acid) at different degrees of neutralization, a, and in the coefficient of the counterions in the (salt-free) polyelec-
presence of different concentrations of the corresponding trolyte solution to that of the free ions, but in these
bromide. If eqn (19) is rewritten as interpretations the total conductance of the polyelectro-
lyte salt is given as A = f(Xi° + λ), whereas in the one
p! ρ
AP, = Ap2 - A2°(l - AXIX) + A,°(l - AXIX) (20) given above it is Αρ1 = (1-ΔΛ:/ΛΓχΑ10-Α1,βΓ) + Αρ.
it is clear that straight lines with a slope (1 - AXIX) are
expected when Ai is plotted against λΛ Figure 7 shows
p
that this is indeed the case. The values of (1 - AXIX) are
collected in Table 1 and are seen to be on the order of 0.5.
0.7
O.OOI M XBr Δ
0.003 M XBr A
Ο.ΟΙ M XBr D
Fig. 8. Influence of the PMA concentration on the equivalent
conductance of the bromide ions at a = 0.3, a = 0.5 and a = 0.7
with Li, Na or K as counterions. Symbols are marked 0.3,0.5, Li or
Fig. 7. Equivalent conductance of XPMA at a = 0.5 (polymethac- K for experiments at a = 0.3, a = 0.5, Li or K as counterions.
rylic acid, half neutralized with XOH, X being Li, Na or K) against Symbols are not marked for a = 0.5 and for Na as counterions.
the corresponding equivalent conductance at infinite dilution of X a CPMA = concentration of ionized COCT-groups in equiv/1.
in solutions of X Br. Equivalent conductances in ΓΓ1 cm2 eq_1. CBr = concentration of bromide ions in equiv/1. ABr-in Ω-1 cm2 eq~ \