1. Polymer concentration dependence of kilohertz electric polarizability of alumina colloid
particles with adsorbed carboxymethyl cellulose
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2. IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 22 (2010) 494112 (7pp) doi:10.1088/0953-8984/22/49/494112
Polymer concentration dependence of
kilohertz electric polarizability of alumina
colloid particles with adsorbed
carboxymethyl cellulose
Alexandar M Zhivkov and Rosen P Hristov
Institute of Physical Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonchev Str.,
bl. 11, Sofia 1113, Bulgaria
E-mail: zhivkov ipc@doctor.bg
Received 23 April 2010, in final form 9 June 2010
Published 23 November 2010
Online at stacks.iop.org/JPhysCM/22/494112
Abstract
Polyelectrolytes are soluble polymers composed of units having charged groups. Because of the
high charge density, some of the counterions are adsorbed electrostatically (ion condensation)
on the polyelectrolyte chain. It was shown that in direct electric field the condensed counterions
and the chain move together as one whole but it is assumed that they are mobile in alternating
field and participate in the polarization. Experimental evidence is obtained by electro-optical
investigations of polyelectrolytes adsorbed on colloid particles—the observed low-frequency
shift of the polarizability relaxation has been interpreted as condensed counterions’ mobility.
The present investigation aims to verify the reports for the condensed counterions’ mobility
in sinusoidal electric field. By means of electric light scattering we investigated a water
suspension of γ -alumina particles with adsorbed carboxymethyl cellulose. Instead of the
previously used frequency approach (dispersion dependence at saturated adsorption of the
polyelectrolyte) we applied an amplitude approach—determination of the polarizability at
frequency 1 kHz and increasing polyelectrolyte concentration (from zero to full adsorption
saturation). The results indicate the absence of polarization owing to the condensed
counterions. The main evidence was obtained by comparison of the concentration dependences
of the polarizability (depending on all mobile counterions) and the electrophoretic mobility
(determined only by the diffuse counterions). We concluded that the condensed counterions are
immobile in sinusoidal field with intensity up to 0.5 kV cm−1
and frequency of 1 kHz and
higher.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Polyelectrolytes are colloid particles or macromolecules with
high charge density determined by the dense package of
uniform charged units [1]. In particular, this term is used to
indicate linear polymers whose charge is usually determined
by the dissociation or association of a hydrogen ion from
pH-dependent groups [2]. The high electric field intensity
around the polyelectrolyte chain causes electrostatic adsorption
of counterions. It is called ion condensation and appears
when the linear charge density exceeds a certain critical value
independently of the ionic strength of the solution [3].
For the description of counterion condensation several
models have been suggested; the best investigated is the
cylindrical model. It describes the polyelectrolyte chain as
an infinite cylinder with determined diameter and delocalized
surface charge. This model allows the solution of the two-
dimensional equation of Poisson–Boltzmann calculated by
Oosawa [4]. Manning has shown that the condensation
of ions is determined by a boundary condition, expressed
0953-8984/10/494112+07$30.00 © 2010 IOP Publishing Ltd Printed in the UK & the USA1

3. J. Phys.: Condens. Matter 22 (2010) 494112 A M Zhivkov and R P Hristov
by the dimensionless parameter ξ = lB/b, where lB =
e2
/4πε0εkT is the Bjerrum length and b is the average charge
distance [5]. The ξ parameter determines the presence of
condensed counterions at ξ > 1 or their absence at ξ < 1.
The condensation process continues until the total charge
density decreases to ξ = 1. As a result, the polyelectrolyte
chain bears excessive charge due to uncompensated charges of
polyelectrolyte groups [6].
There is no unanimous opinion on the condensed ions’
mobility. In older publications such a possibility is assumed [7]
and even their mobility is estimated as one third from that
of the diffused counterions [8]. Most of these theoretical
elaborations are based on the cylindrical model which does not
reject the possibility of charge transfer along the cylinder. The
Monte Carlo simulations, however, indicate that the condensed
counterions are practically fixed and do not participate in the
electric polarizability of the polyelectrolyte chain [9, 10].
Results of nearly all the experimental investigations also
indicate that the condensed counterions are immobile because
they do not give any contribution to the electric properties
of the polyelectrolyte chain. The presence of condensed
counterions is assumed indirectly when a certain electrical
property reaches a plateau at ξ = 1 while the linear
charge density still increases [6]. In external d.c. electric
field the condensed counterions and the polyelectrolyte chain
behave as one whole [2]. For example, negative values
of Na+
transference number (always positive in solution
of simple electrolyte) appear in polyelectrolyte solution.
This phenomenon is due to the transference of condensed
counterions against the electric field gradient, i.e. in a direction
opposite to that of the free counterions [11].
Electro-optical results are exceptions among the exper-
imental investigations. In the last 20 years Radeva et al
published a series of articles in which they claimed that
the condensed counterions are mobile in external sinusoidal
electric field [12, 13]. This has been concluded because of the
observed low-frequency shift of the relaxation frequency of the
electro-optical effect (EOE) of polyelectrolyte-coated colloid
particles. This conclusion is expected because the condensed
counterions, strongly bound to the chain, have to become less
mobile. The discrepancy between electro-optics and the other
methods may be explained with the mobility of the condensed
counterions along the polyelectrolyte chain but their inability
to depart from it. In that case their behavior is revealed in an
alternate electric field but they remain hidden for the methods
based on direct electric field such as electrophoresis. If that
hypothesis is true the electro-optical method appears to be
a unique technique for condensed counterion investigations
because it experimentally detects their mobility in electric field
orienting polyelectrolyte-coated colloid particles.
We assume that the changes in the dispersion of the
EOE are not convincing enough evidence of the condensed
counterions’ mobility because such changes are observed
in other cases as well. For instance, addition of ethanol
in water suspensions of bacteria leads to low-frequency
shift of the relaxation frequency despite the absence of
polyelectrolyte [14]. For condensed counterion investigations
we apply an amplitude–frequency approach, based on the
change in the value of the electrical polarizability at a certain
electric field frequency. It is based on the assumption that if
the condensed counterions are mobile they must contribute to
the electric polarizability, proportionally to their quantity in
the adsorbed polyelectrolyte layer on the particles’ interface.
This contribution is summed up to the polarization caused
by the diffuse counterions in the electric double layer (EDL)
surrounding the polyelectrolyte-coated particle [15]. Thus, the
torque has to be a result of the appearance of two induced
dipole moments—one caused by the dense part of the EDL and
another one caused by the diffuse part of the EDL, represented
by the condensed and the diffuse counterions, respectively.
The present work aims to find out if the counterions
condensed on the polyelectrolyte chain of carboxymethyl
cellulose (CMC) adsorbed on alumina colloid particles (γ -
Al2O3) are mobile. We follow the changes in the electric
polarizability of the particles with the increase of the adsorbed
amount of CMC. Their polarizability was investigated at 1 kHz
which is two orders lower than the relaxation frequency of the
condensed counterions according to the results of Radeva et al
[12, 13]. Adsorption of CMC on alumina particles allows us
to avoid polymer chain deformation under the action of the
electric field and to use low electric field intensities to find
EOE.
To decrease the differences in the experimental condi-
tions we use the same polymer (CMC with molar mass
250 kg mol−1
) and the same experimental technique (electric
light scattering) as in the works of Radeva et al [16, 17]. The
difference is only in the dispersed particles. We use aluminum
oxide particles, achromic in the optical spectrum, while in
the quoted publications the authors have used β-ferrioxide
particles, colored in the visible range. Due to the latter, in
ferrioxide suspension two electro-optical phenomena appear—
scattering and dichroism, having different orientation-optical
functions. This circumstance is not taken into account by
Radeva et al and is a prerequisite for an incorrect interpretation.
2. Materials and methods
2.1. Materials
A sodium salt of carboxymethyl cellulose (NaCMC) with
degree of substitution 1.2 and molar mass 250 kg mol−1
(103
monomers per chain) was investigated. Thus, on average
80% of the glucose monomeric units have one carboxymethyl
residue attached, 20% have two such residues and almost all
carboxyl residues are ionized at pH 6 [18]. Gamma-aluminum
oxide (γ -Al2O3) particles with mean size 300 nm and point of
zero charge at pH 8.5 were used as adsorbent. The suspension
was prepared by mixing a water suspension of alumina
particles and water solution of NaCMC and continuous stirring
at 20 ◦
C for 30 min. The pH of the suspension was controlled
before and after the electro-optical measurements; its value
was about pH 6. At these conditions the linear charge density
of CMC is higher than the Manning’s parameter requires (ξ ≈
1.66 at full ionization) and condensation of Na+
counterions
on COO−
groups of the polymer chain appears (but the
CMC-polyion keeps a residual negative charge). Thus, the
2

4. J. Phys.: Condens. Matter 22 (2010) 494112 A M Zhivkov and R P Hristov
adsorption of CMC chains on the positive particle surface is
electrostatically conditioned because of their opposite electric
charge [19].
2.2. Electrophoresis
The electrophoretic mobility Uel of particles was measured
by Mark II apparatus (Rank Brothers, UK) with a flat
quartz cell at 20 ◦
C. The mobility is determined by the
electrokinetic potential ζ (the electric potential in the so-called
slipping plain), bulk viscosity η and dielectric permittivity εε0
according to Smoluchowski’s equation: ζ = (η/εε0)Uel.
2.3. Electric light scattering
In the Rayleigh–Debye–Gans approximation [20] the light
scattering intensity I0 at random orientation of the particles
of a disperse system is determined by the function of internal
interference P(θ) at scattering angle θ [21]:
I0 = kcH M P(θ), (1)
where k is the apparatus constant determined by the scattering
volume and the solid angle of the photoreceiver; c is the weight
concentration of the dispersed substance; H is the optical
constant of the suspension, defined by the wavelength λ0 in
vacuum and the refractive indexes of the particles n1 and the
medium n0 at λ0; M is the particle mass.
When an electric field is applied to the suspension, the
light scattering intensity IE is changed due to the orientation of
the particles [22]. The EOE I = IE − I0 can be determined
by the functions of internal interference at a certain degree of
orientation P(θ, E) and at random orientation P(θ) [23]:
I = kcH M[P(θ, E) − P(θ)]. (2)
At an orientation degree F (varying from 0 at random
orientation to 1 at full orientation):
P(θ, E) = P(θ) + A(K L) × F(γ, E, T ), (3)
where the function A(K L) is determined by the form and
the relative size L/λ (where the wavelength in the medium
λ = λ0/n0) of the particles with length L; K L =
2π(L/λ) sin(θ/2). The orientation degree F at steady-state
EOE is a function of the electric polarizability γ , the electric
field strength E and the temperature T.
The relative EOE I/I0 does not depend on c, H, M and
it is defined at a moment t only by P(θ, E) and P(θ), which
are functions of the form, the size and the optical anisotropy of
the particles:
It /I0 = [P(θ, E)/P(θ)] − 1 = [A(K L)/P(θ)]
× F(γ, E, T, t). (4)
The average degree of orientation of the particles is
proportional to the torque M = d × E, averaged on all
the orientations, which is determined by the induced dipole
moment d and the effective strength E of the electric field.
The value of d = γ E is a linear function of E and the electric
polarizability γ at not too high values of E.
Figure 1. Dependence of electrophoretic mobility Uel of γ -Al2O3
particles on the concentration CCMC of the sodium salt of
carboxymethyl cellulose (NaCMC) in water suspension.
In the steady-state F(γ, E, T ) depends only on the ratio
between the orientation energy γ E2
and the energy of random
motion kT . Then the relative EOE at low degrees of orientation
(γ E2
kT ) is:
I/I0 = [A(K L)/P(θ)] × (γ E2
/15kT). (5)
The EOE were measured at θ = 90◦
by computerized
home-made apparatus whose optical scheme is described
in [24]. The electro-optical cell is made of glass and platinum
electrodes with surface areas 1 cm2
, interelectrode distance of
2.6 mm and volume of 10 ml. The light scattering intensity I0
(in the absence of electric field) was measured after reaching
steady-state polymer adsorption for a minimum of three times:
before, during and at the end of the electro-optical experiment.
3. Results and discussion
3.1. Electrophoretic mobility
The electrophoretic mobility is determined by the slipping
plain potential (ζ-potential) which is proportional to the
surface electric charge of the particles [25, 26]. This fact allows
investigation of polyelectrolyte adsorption on colloid particles.
Figure 1 indicates how the electrophoretic mobility of the
alumina particles depends on the CMC concentration in the
suspension. The beginning of the measurements was about
30 min after the alumina suspension and the CMC solution
were mixed. Investigations indicate that this is enough time
to reach steady-state polyelectrolyte adsorption. Alumina
particles are positively charged at pH 6.0, and the CMC is
negatively charged. Therefore, at low CMC concentrations the
total charge of the alumina–CMC complexes is positive and
at high CMC concentration it is negative, i.e. the particles are
overcharged. At 3 × 10−3
g dm−3
an isoelectric point (zero
total charge) is observed.
The dependence of the electrophoretic mobility on CMC
concentration is not an analog of the adsorption isotherm
3

5. J. Phys.: Condens. Matter 22 (2010) 494112 A M Zhivkov and R P Hristov
Figure 2. Light scattering intensity at θ = 90◦
of the γ -Al2O3 water
suspension at a concentration CCMC of NaCMC.
because the mobility is determined both by the ζ-potential
and the translational friction coefficient. Since CMC is a
charged polymer with decreased flexibility (small fragments
behave as rodlike particles [27]) and the used specimen is
high molecular (the chain contour length is about 1 μm), the
polyelectrolyte chain in the solution has a conformation of
random coil with increased dimensions [18, 28]. When such
linear macromolecules are adsorbed on the colloid particles
a small part of the polymer segments lies on their surface
and the others protrude into the solution [29] as was shown
by atomic-force microscopy for α-helix of poly-L-lysine [30].
This is a reason for an increase in the viscous coefficient. Due
to the latter, the electrophoretic mobility dependence on the
polymer concentration Uel(CNaCMC) (figure 1) represents only
semiquantitatively the CMC adsorption.
3.2. Light scattering intensity at random orientation
The particles’ interface polarizability depends not only on
the particles’ charge but on their form and size as well [31].
Therefore, the particles’ unchanged geometry is a necessary
condition for a correct interpretation. The decrease in the total
charge around the point of zero charge (PZC) is a prerequisite
for an increase in the particles’ size because of aggregation.
The electro-optic researchers usually choose the rotational
diffusion coefficient Dr as a criterion for particles’ dimensions
due to its cubic dependence on their size. However, it
is not suitable in the case of adsorption of high molecular
polyelectrolytes with rigid chain as CMC because Dr
is determined by the interface friction which increases
proportionally to the adsorbed polyelectrolyte amount. Due
to the latter, we chose light scattering intensity at random
orientation, I0, as a particle’s geometry criterion. According
to equation (1), I0 is proportional to the mass of the particles,
M, whose growth is accompanied by P(θ) diminishing (at
scattering angles θ > 0 due to increase in the inner
interference). However, the effect of P(θ) on I0 is weaker
than that of M [32], so the I0 constancy is a reliable enough
Figure 3. Dependence of EOE in a water suspension of γ -Al2O3
particles on the square of the field intensity at 1 kHz at polymer
concentration 4 × 10−4
(1), 5 × 10−4
(2) and 6 × 10−4
(3) g dm−3
NaCMC (under the recharging point).
indication of the absence of aggregation. Despite being more
insensitive to the particles’ dimensions than Dr, in our case
I0 is a better criterion due to its weaker dependence on the
adsorbed polyelectrolyte amount: the total polymer mass of
one particle is much smaller (by three orders in the PZC) than
the alumina particle’s mass.
Figure 2 indicates the way the light scattering intensity I0
depends on the CMC concentration in the solution. Values of
I0 have been measured during the measurements of the EOE’s
dependence on the electric field strength I(E2
), used for the
electric polarizability determination, γ ∼ ( I/I0)/E2
. We
assumed that there is no aggregation if the values of I0 at the
beginning and at the end of the electro-optic experiment are
equal. According to the results shown in figure 2, aggregation
is lacking at CMC concentrations below 5 × 10−4
g dm−3
and
above 7×10−3
g dm−3
. Suspensions flocculate quickly around
the PZC (3 × 10−3
g dm−3
CMC). This is an indication that
the electrostatic repulsion between the particles is weak and
the van der Waals attraction forces dominate according to the
theory of Derjaguin–Landau–Verwey–Overbeek [33].
The absence of flocculation above the PZC shows
that the polyelectrolyte adsorption process is quicker than
the aggregation process. There are two reasons for this
observation. The first one is the opposite electric charge
of the alumina particles and the CMC macromolecules at
pH 6, responsible for fast electrostatic adsorption. The
second one is the low alumina particles’ concentration—a
reason for low interparticle interactions probability in the
time before polyelectrolyte adsorption reaches equilibrium and
the particles become strongly (negatively) charged. The low
particle concentration is possible due to higher sensitivity
of electric light scattering in comparison to the electric
birefringence in the case of particles’ size being commensurate
with the wavelength in the medium.
4

6. J. Phys.: Condens. Matter 22 (2010) 494112 A M Zhivkov and R P Hristov
Figure 4. Dependence of EOE in a water suspension of γ -Al2O3
particles on the square of the field intensity at 1 kHz at polymer
concentration: 5 × 10−3
(1), 7 × 10−3
(2), 1 × 10−2
(3), 3 × 10−2
(4)
and 5 × 10−2
(5) g dm−3
NaCMC (above the recharging point).
3.3. Field strength dependence of EOE
Figures 3 and 4 represent the dependence of the relative EOE
( I/I0) on the electric field strength squared (E2
) at several
CMC concentrations. The linearity of the graphics means that
the orientation energy owing to the induced dipole moment
is lower than the energy of the thermal motion, γ E2
kT .
Therefore, the electric polarizability γ is proportional (with
accuracy to a constant) to the slope of the lines [( I/I0)/E2
]
according to equation (5).
When the CMC concentration in the suspension is
low, nearly all the polyelectrolyte chains are adsorbed at
the particles’ surface. Increasing the amount of adsorbed
polyelectrolyte (below the PZC) decreases the amount of the
diffuse counterions (due to a decrease in the total surface
charge) and, respectively, decreases their contribution to the
interfacial electric polarizability. Above the PZC we observe
the opposite tendency—an increase in the quantity and the
contribution of the diffuse counterions. Simultaneously, the
quantity of the condensed counterions increases as well as
their hypothetical contribution in the polarizability. Thus,
the dependence of the field function I(E2
) on the CMC
concentration can provide information about the relation
between the two components of the polarizability.
Figure 3 indicates that the slope of the lines is smaller
at higher concentration of the polymer. This means that at
CMC concentrations below the PZC the diffuse counterions’
contribution dominates.
Figure 4 represents the opposite case—the slope of
the lines is bigger at higher CMC concentrations. This
change in the slopes’ alteration tendency is caused by the
particles’ overcharging—the total charge becomes negative
and the diffuse counterions become positive. In this
concentration range the polyelectrolyte adsorption layer
growth is accompanied by electric polarizability growth. Since
the quantity of both the diffuse and condensed counterions
Figure 5. Slope of the field strength dependence ( I/I0)/E2
of the
EOE in a water suspension of γ -Al2O3 particles on NaCMC
concentration under (curve 1) and above (curve 2) the recharging
point.
increases, their contributions to the electric polarizability
cannot be distinguished.
3.4. Polymer concentration dependence of the polarizability
Comparing the slopes of the field strength dependences
(section 3.3) we find out that the polarization is caused predom-
inantly by the diffuse counterions but this comparison cannot
provide information about any condensed ion contribution to
the polarization. We can judge their supposed participation
by taking into account the polarizability’s polyelectrolyte
concentration dependence, γ (c), below and above the PZC.
These changes are with opposite sign, so the participation of
the condensed ions would diminish the slope of the γ (c) curve
before the PZC and would increase it after the PZC. If the
condensed ions do not take part in the polarization the slopes
in these two concentration ranges need to be equal (in the case
where the adsorption is a linear function of the concentration).
Figure 5 shows the dependence [( I/I0)/E2
] = const ×
γ as a function of the CMC concentration in the suspension.
In the concentration range 0–7 × 10−4
g dm−3
the electric
polarizability decreases with the increase in the polymer
concentration and above 5 × 10−3
g dm−3
, it increases; that
illustrates the conclusions made in section 3.3. The new
feature in figure 5 is the different slope of the concentration
dependence of the polarizability: contrary to expectation, the
γ (c) slope above the PZC (5 × 10−3
–1 × 10−2
g dm−3
) is
smaller in comparison with the slope below this point (0–
7 × 10−4
g dm−3
).
This experimental result is an indication that the
condensed counterions do not take part in the polarization
responsible for the orientation of the particles in sinusoidal
electric field. The limitation of this approach, however, is
the fact that the polyelectrolyte concentration growth reduces
the adsorption probability because the polyelectrolyte chains,
coating and overcharging the surface of the particles, repulse
electrostatically the chains which are still free in the bulk of
the solution. Therefore, the adsorbed amount of CMC is no
5

7. J. Phys.: Condens. Matter 22 (2010) 494112 A M Zhivkov and R P Hristov
longer proportional to its bulk concentration c. This deviation
increases with c and leads to a decrease of the slope of the
γ (c) curve above the PZC, observed in figure 5. Therefore, the
lower slope of this curve does not reject entirely the probability
for condensed counterions participating in the polarization.
Another possible reason for the lower slope of the curve
γ (c) above the PZC is the increase in the ionic strength due to
the increase of Na+
ions whose quantity is equal to that of the
carboxyl groups on the polymer chains of the used sodium salt
of the CMC. Ionic strength growth diminishes the component
of the electric polarizability owing to the polarization of
the diffuse part of the EDL. At 5 × 10−2
g dm−3
NaCMC
(the maximal polymer concentration in our experiment) with
degree of substitution 1.2 the concentration of the Na+
ions is 1 × 10−5
M, which corresponds to 3 × 10−5
M
NaCl. Measurements indicated that at such ionic strength the
polarizability of the alumina particles in NaCl solution does
not differ significantly from the ionic strength in triple distilled
water. The latter shows that when the ionic strength increases
due to NaCMC concentration increase in the investigated
concentration range the electric polarizability is influenced
insignificantly, so the slope of the curve γ (c) cannot be
changed by Na+
.
3.5. Correlation between the polarizability and the
electrophoretic mobility
The limitations of the approach applied in the previous section
can be escaped by additional information about the quantity of
the adsorbed polyelectrolyte because it is proportional to the
number of condensed counterions. As a first approximation,
if we ignore the friction caused by the adsorbed chains, the
adsorbed polyelectrolyte amount is proportional to the change
in the electrophoretic mobility, Uel, caused by the adsorption
of the negatively charged CMC chains on the positively
charged alumina interface. The total charge of the particles
and Uel are strongly sensitive to the adsorption because of the
big charge density and the high molecular mass of the CMC
specimen that we use (about 1200 carboxyl groups per chain
and 0.43 nm distance between them) compared to the low
density of the particles’ surface charge.
The information for the participation of the condensed
counterions in the polarization can be extracted by a com-
parison of the concentration dependences of the polarizability
γ (c) and the electrophoretic mobility Uel(c). This approach
is based on the fact that the condensed counterions are not
manifested in electrophoretic measurements [2] while the
electro-orientational effect is determined by all the mobile
counterions present. The form of the Uel(c) curve is
determined by the total charge of the coated particles (not
taking into account the increased friction force) and represents
the influence of the diffuse counterions. Consequently, if
the condensed counterions contribute to the polarization, the
two curves have to diverge with the growth of the polymer
concentration, i.e. the γ (c) curve has to grow faster above the
PZC. If the two curves are parallel, the condensed counterions
are immobile and do not contribute.
The concentration dependences of the polarizability and
the absolute value of the mobility are shown in figure 6. As
Figure 6. Dependences of the electrophoretic mobility module |Uel|
(curve 1, left ordinate) and the field strength dependence slope
( I/I0)/E2
of the EOE (curve 2, right ordinate) of the γ -Al2O3
particles in water–polymer medium on the concentration of NaCMC.
we see, above the PZC the curve of the polarizability does
not increase faster than the curve of the mobility. This result
rejects the hypothesis for the contribution of the condensed
counterions to the electric polarizability. It means that the
condensed counterions are immobile in sinusoidal electric field
with intensity 0.5 kV cm−1
and frequency 1 kHz.
4. Summary
The dependence of the electrophoretic mobility of the alumina
particles on the concentration of the CMC in the suspension
indicates a reversal of the particles’ charge due to the opposite
charge of the bare particles and the adsorbed polyelectrolyte
chains—the total charge turns from positive to negative. Light
scattering intensity at random orientation indicates that in
the concentration range in which the charge reverses the
suspension is unstable but there is no aggregation out of this
range. The slope of the field strength dependences of the
EOE shows that below the PZC the electric polarizability
decreases with the polyelectrolyte concentration growth (but
above this point it increases); this indicates a dominating
contribution of the diffuse counterions to the polarizability.
At CMC concentrations above the PZC the slope of the
polarizability–concentration curve, γ (c), is lower than that
below the PZC, which is an indication of a lack of participation
of the condensed counterions in the polarization. This
conclusion is confirmed by the comparison of the concentration
dependences Uel(c) and γ (c) because the mobility Uel
reflects the diffuse counterions only, while the polarizability
γ is determined by the two types of counterions (if the
condensed ones have any mobility). Thus, by application
of two methods (electric light scattering and electrophoresis)
it has been shown that the counterions condensed on the
CMC chains are immobile in sinusoidal electric field with
intensity up to 0.5 kV cm−1
and frequency 1 kHz and higher.
Consequently, the electro-orientational effect is caused by an
interfacial electric polarizability having only one component—
polarization of the diffuse part of the electric double layer. This
6

8. J. Phys.: Condens. Matter 22 (2010) 494112 A M Zhivkov and R P Hristov
result disproves the conclusions of Radeva et al (obtained for
the same polyelectrolyte with the same method) that the EOE
is due to polarization of the condensed counterions.
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