1. 1959
Research Article
Received: 3 July 2013 Revised: 5 March 2014 Accepted article published: 21 March 2014 Published online in Wiley Online Library: 14 April 2014
(wileyonlinelibrary.com) DOI 10.1002/pi.4738
Coiling/uncoiling behaviour of sodium
polystyrenesulfonate in
2-ethoxyethanol–water mixed solvent media
as probed using viscometry
Ranjit De†
and Bijan Das*
Abstract
Precise measurements of the viscosities of solutions of sodium polystyrenesulfonate in water and in 2-ethoxyethanol–water
mixtures containing varying amounts of 2-ethoxyethanol have been performed at 308.15, 313.15, 318.15 and 323.15 K.
The intramolecular contributions to the reduced viscosities of the polyelectrolyte solutions were obtained through isoionic
dilution maintaining the total ionic strengths of the solutions at polyelectrolyte concentrations of 0.0033, 0.0054 and 0.0080
eq L−1
with sodium chloride. The Huggins constants were also obtained from the experimental data. The influences of the
medium and the temperature on the intramolecular contributions to the reduced viscosities as well as on the Huggins
constants have been interpreted from the points of view of the conformational characteristics and polyelectrolyte–solvent
and polyelectrolyte–polyelectrolyte interactions prevailing in the polyelectrolyte solutions under investigation. Polyion chains
were found to coil upon addition of 2-ethoxyethanol to water or upon an increase of temperature. Thermodynamic affinities for
polyelectrolyte–solvent and polyelectrolyte–polyelectrolyte interactions were found to depend greatly on the medium.
© 2014 Society of Chemical Industry
Keywords: sodium polystyrenesulfonate; 2-ethoxyethanol–water mixed solvent; intramolecular contribution to reduced viscosity;
isoionic dilution; Huggins constant; coiling/uncoiling of polyion chain; thermodynamic affinity of interactions
INTRODUCTION
The solution behaviour of polyelectrolytes is entirely different from
that of uncharged polymers because of the presence of charged
sites along the polymer chains in polyelectrolytes. This is due to
the existence of long-range intermolecular electrostatic interac-
tions and their coupling with the conformation of the polyions in
polyelectrolytesolutions.Hencepolyelectrolytesolutionsarechar-
acterized by complex interactions, conformations, structures and
dynamics.1–4
Viscometry of polyelectrolyte solutions has been widely used
to obtain information as to the conformational behaviour of
polyelectrolytes in solution.5–18
The reduced viscosity of poly-
electrolyte solutions (𝜂sp/cp, where 𝜂sp = specific viscosity and
cp = polyelectrolyte concentration) can be considered as orig-
inating from conformational and intermolecular electrostatic
contributions. Nishida et al.8
successfully separated the confor-
mational contribution to the polyelectrolyte reduced viscosity
from the intermolecular electrostatic contribution purely from
theoretical considerations. Later, Wolf and co-workers11
applied a
phenomenological approach to viscosity data of polyelectrolyte
solutions to provide information about the dependence of the
polyion conformation on the polyion charge density as well as on
solvent composition.
Recently, a convenient method has been developed by us
to decompose the reduced viscosity of a polyelectrolyte solu-
tion into its intramolecular (conformational) and intermolecular
components from experimental considerations.15
We applied this
method to sodium carboxymethylcellulose dissolved in ethylene
glycol–water mixed solvent media to examine the variation in
polyion conformation with solvent composition which governs
the electrostatic interaction at a selected temperature. In that
study, unfortunately, we had to confine our measurements within
a narrow relative permittivity range owing to the limited solubility
of sodium carboxymethylcellulose in ethylene glycol–water mix-
tures. Moreover, the effect of temperature on the coiling behaviour
of polyions needs to be studied.
It is thus intended in this experimental work to show that
accurate viscosity data, which considers a number of parameters
including polyelectrolyte concentration, temperature and the rel-
ative permittivity of the medium over a wide range, lead to gen-
eral dependencies and interrelations. The excellent solubility of
sodium polystyrenesulfonate (NaPSS) in 2-ethoxyethanol–water
media over a wide range of relative permittivity (ca 41 to 75;
Table 1) prompted us to select this system for investigation. The
∗ Correspondence to: Bijan Das, Department of Chemistry, Presidency University,
86/1 College Street, Kolkata 700 073, India. E-mail: bijan.chem@presiuniv.ac.in
† Present address: Department of Nanobiomaterials and Electronics, Gwangju
Institute of Science and Technology, 123 Oryng-dong, Buk-gu, Gwangju
500-712, Republic of Korea
Department of Chemistry, Presidency University, 86/1 College Street, Kolkata
700 073, India
Polym Int 2014; 63: 1959–1964 www.soci.org © 2014 Society of Chemical Industry

2. 1960
www.soci.org R De, B Das
Table 1. The relative permittivities (𝜖) of water and
2-ethoxyethanol–water mixtures containing 10, 25, 40 and 50
mass% of 2-ethoxyethanol (w) at various temperatures
𝜖 values in 2-ethoxyethanol–water mixtures
T (K) w = 0 w = 10 w = 25 w = 40 w = 50
308.15 74.82 69.87 60.13 50.54 44.30
313.15 73.15 68.13 58.70 49.28 43.03
318.15 71.51 66.55 57.37 48.14 41.95
323.15 69.91 65.08 56.11 47.10 40.96
coiling/uncoiling behaviour of this widely investigated polyelec-
trolyte in aqueous solution is well understood. The influence of
electrostatic interactions on the coiling/uncoiling behaviour of
NaPSS is, however, yet to be investigated. Mixed solvent media
with varying relative permittivities provide an opportunity to
study the influence of these interactions.
METHOD OF DETERMINATION
OF INTRAMOLECULAR CONTRIBUTION
TO REDUCED VISCOSITY
We have employed15
the method of isoionic dilution19,20
for the
determination of the intramolecular contribution to the reduced
viscosity of a polyelectrolyte in solution. In accordance with this
method, a polyelectrolyte solution in pure solvent (in the absence
of any low-molar-mass electrolyte) is diluted with solutions of
increasing concentration of an electrolyte solution. The dilution of
the solution is performed in such a manner that, after each addi-
tion of salt solution, the total ionic strength of the solution remains
the same and equal to its original value due to the polyelectrolyte
alone. The importance of the method of isoionic dilution is that
under the circumstances pointed out above the reduced viscosity
decreases linearly as one lowers the polyelectrolyte concentration
and thus extrapolation to a limiting value becomes possible for
each value of the total ionic strength, i.e. at each of the polyelec-
trolyte concentrations where isoionic dilutions were carried out.
Furthermore, since the ionic environment in the neighbourhood
of the polyion chains remains unchanged as a result of isoionic
dilution, the original conformation of the polyion in the salt-free
situation can be considered to be preserved. In other words, this
means that the limiting reduced viscosity as polyelectrolyte con-
centration approaches zero obtained for a given ionic strength
(and hence for a given concentration) of a salt-free polyelectrolyte
solution by the method of isoionic dilution corresponds to its
actual conformational state in salt-free situation and, thus, can be
considered as the intramolecular contribution to the reduced vis-
cosity, (𝜂sp/cp)conformation, and can be obtained from the Huggins
equation:21
𝜂sp
cp
=
(
𝜂sp
cp
)
conformation
+ kH
(
𝜂sp
cp
)2
conformation
cp (1)
where kH is the Huggins constant which is a characteristic for a
given polyelectrolyte–solvent system.
It is worth mentioning that the method of isoionic dilution was
proposed by Pal and Hermans19,20
to determine the intrinsic vis-
cosity of salt-free polyelectrolyte solutions. Eich and Wolf22
exam-
ined the intrinsic viscosity values obtained by the isoionic dilution
method against those obtained using the Wolf phenomenological
approach:9,11–13
ln 𝜂rel =
cp [𝜂] + Bc2
p
[𝜂] [𝜂]∗
1 + Bcp [𝜂]
(2)
where 𝜂rel is the relative viscosity, [𝜂] is the intrinsic viscosity and
B and [𝜂]*
are two system-specific constants. The values of the
parameters [𝜂], B and [𝜂]*
can be easily determined using a per-
sonal computer from a sufficiently large number of viscosity mea-
surements at various polymer concentrations with any nonlinear
least-squares fitting program.
It was concluded by Eich and Wolf22
that, due to the simulta-
neous changes of polymer concentration and salt concentration,
the former procedure merely yields the apparent intrinsic viscosity,
which is actually the intramolecular (conformational) contribution
to the reduced viscosity under salt-free situation as pointed out
by us15
as described above. It may be noted that intrinsic viscosity
values [𝜂] in Eqn (2) should be replaced by (𝜂sp/cp)conformation values
when this equation is applied to the present ln 𝜂rel versus cp values
obtained by the method of isoionic dilution.
EXPERIMENTAL
NaPSS was purchased from Aldrich Chemical Company, Inc. The
average molecular weight (M) of the sample was ca 70 000 g mol−1
with a degree of sulfonation of 1 and a polydispersity index
Mw/Mn < 1.2. This molecular weight value agreed well with that
determined in this study obtained in the presence of 0.05 mol L−1
sodium chloride (NaCl) at 298.15 K using the Mark–Houwink
relationship:23
[𝜂] = 1.39 × 10− 4
M0.72
, where [𝜂] is the intrinsic vis-
cosity and M is the average molecular weight. The molar absorp-
tion coefficient of the NaPSS solutions used at 261 nm, which
is considered to be a characteristic indicator of sample purity,24
was found to be 400 dm3
cm−1
mol−1
. Spectrophotometric exam-
ination of the polyelectrolyte sample using this criterion was
employed periodically to substantiate the purity of the sample
used.
2-Ethoxyethanol (GRE Merck) was distilled with phosphorus pen-
toxide and then redistilled over calcium hydride. The purified
solvent had a density of 0.92497 g cm−3
and a coefficient of
viscosity of 1.8277 mPa s at 298.15 K; these values agree very
well with those reported in the literature.25
While preparing the
mixed solvents, triply distilled water with a specific conductance
of less than 10−6
S cm−1
at 308.15 K was used. The relative per-
mittivities of 2-ethoxyethanol–water mixtures at the experimen-
tal temperatures, obtained with the equations as described in the
literature26
using the density and relative permittivity data of the
pure solvents27,28
and the densities of the mixed solvents29
from
theliterature,aregiveninTable 1.Alsoincludedinthistablearethe
relative permittivities of water at the experimental temperatures.
Viscosity measurements were carried out at the experimental
temperatures using a Schultz–Immergut-type viscometer30
with
a sintered disc fitted to the widest arm to exclude dust particles,
if any, from the solution/solvent. The measurements were made
in a thermostatically controlled water bath maintained to within
±0.01 K of the desired temperature by means of a mercury-in-glass
thermoregulator, and the absolute temperature was determined
using a calibrated platinum resistance thermometer and Muller
bridge.31,32
Different sets of independent solutions were prepared,
and runs were performed to ensure the reproducibility of the
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3. 1961
Coiling/uncoiling behaviour of sodium polystyrenesulfonate www.soci.org
results. To check whether the reduced viscosities depend on the
shear rate in the concentration range investigated, measurements
with viscometers having capillaries of different sizes were per-
formed. The reduced viscosity values were found to be invariant
in these cases.
The reduced viscosity is obtained from
𝜂sp
cp
=
t − t0
t0
1
cp
(3)
where t and t0 are the measured flow times of the polyelectrolyte
solution and of the pure solvent, respectively.
To avoid moisture pickup, all of the solutions were prepared
in a dehumidified room with utmost care. In order to check the
reproducibility of the results, in all cases the experiments were
performed with at least three replicates.
RESULTS AND DISCUSSION
Dependence of reduced viscosity on polyelectrolyte
concentration
The variations of the reduced viscosity with NaPSS concentration
in the absence of an added electrolyte in aqueous solution at
308.15 K and in a 2-ethoxyethanol–water mixed solvent medium
having 10 mass% of 2-ethoxyethanol at 318.15 K are depicted,
respectively, in Figs 1 and 2. In the absence of an added electrolyte,
the reduced viscosity increases monotonically with a decrease in
NaPSS concentration, for all the systems investigated here, bend-
ing up at low concentrations. This is a manifestation of typical
polyelectrolyte behaviour. No maximum is detected, however, in
the 𝜂sp/cp versuscp profiles within the concentration range studied
here(2 × 10−4
–2 × 10−3
g mL−1
).Maximainthe 𝜂sp/cp versuscp pro-
files have, however, been reported for very dilute polyelectrolyte
solutions below 10−5
g mL−1
, the actual concentration being a
characteristic of the polyelectrolyte under consideration.6,7,33
Analysis of viscosity data: intramolecular contributions to the
reduced viscosity
Isoionic dilution was performed on NaPSS solutions at three dif-
ferent polyelectrolyte concentrations (0.0033, 0.0054 and 0.0080
eq L−1
) using NaCl in water and in four 2-ethoxyethanol–water
mixtures containing 10, 25, 40 and 50 mass% of 2-ethoxyethanol
at 308.15, 313.15, 318.15 and 323.15 K. Figures 1 and 2 also include
the experimental data for isoionic dilution for the three different
polyelectrolyte concentrations.
The reduced viscosity values as functions of polyelectrolyte
concentration resulting from the isoionic dilution are found to
decrease linearly as the polyelectrolyte concentration is lowered,
and hence extrapolation to reasonable values for the intramolec-
ular contributions to the reduced viscosity, (𝜂sp/cp)conformation,
becomes possible for each value of the total ionic strength inves-
tigated using the well-known Huggins equation (Eqn (1)).21
The
values of (𝜂sp/cp)conformation and kH obtained using the Huggins
equation along with their errors and the correlation coefficients
of the fits are recorded in Table 2. We have also analysed the
present viscosity data in terms of the Wolf equation (Eqn (2))
to obtain the intramolecular contributions to the reduced vis-
cosity. A representative plot (Fig. 3) shows the fits to the Wolf
equation of the experimental relative viscosity values (as ln 𝜂rel)
versus polyelectrolyte concentration data for a selected system.
The (𝜂sp/cp)conformation values obtained following the Wolf phe-
nomenological approach9,11–13
are included within parentheses
0
50
100
150
0 0.004 0.008 0.012
cp (Eqv L-1
)
ηspcp
-1
(LEqv-1
)
Figure 1. Variation of reduced viscosity for NaPSS with polyelectrolyte
concentration in water at 308.15 K ( ). Also included are the straight lines
obtained in accordance with the isoionic dilution technique with constant
total ionic strengths at polyelectrolyte concentrations (eq L−1) 0.0033 ( ),
0.0054 ( ) and 0.0080 ( ).
0
50
100
150
0 0.004 0.008 0.012
cp (Eqv L-1
)
ηspcp
-1(LEqv-1)
Figure 2. Variation of reduced viscosity for NaPSS with polyelectrolyte
concentration in 2-ethoxyethanol–water mixture containing 25 mass%
2-ethoxyethanol at 313.15 K ( ). Also included are the straight lines
obtained in accordance with the isoionic dilution technique with total ionic
strengths (eq L−1) 0.0033 ( ), 0.0054 ( ) and 0.0080 ( ).
in the fourth column of Table 2. It is important to note that
the (𝜂sp/cp)conformation values obtained by both procedures agree
excellently well.
Conformational and thermodynamic behaviour
Table 2 and Figs 4–7 demonstrate clearly that the values of the
intramolecular contributions to the reduced viscosities and the
Huggins constants of NaPSS in 2-ethoxyethanol–water media
vary appreciably with the total ionic strength of the solution, the
medium and the temperature of the experiment. In what fol-
lows we will interpret these observations in terms of the coil-
ing/uncoiling behaviour of the polyion chains and the thermody-
namic affinity of the solvent media for the polyelectrolyte.34,35
Variation of intramolecular contributions to reduced viscosity
with polyelectrolyte concentration at a given temperature in a given
solvent medium
At a particular temperature and in a given solvent medium,
the intramolecular contributions to the reduced viscosity,
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4. 1962
www.soci.org R De, B Das
Table 2. Intramolecular contributions to the reduced viscosity
((𝜂sp)conformation) and Huggins constant (kH), and the correlation coef-
ficients of fits (as r2) of NaPSS in water and in 2-ethoxyethanol–water
mixtures containing 10, 25, 40 and 50 mass% of 2-ethoxyethanol (w)
at the polyelectrolyte concentrations where isoionic dilution was per-
formed at various temperaturesa
T (K) w
cp
(eq L−1)
(𝜂sp)conformation
(L eq−1) kH r2
308.15 0 0.0033 43.7 ± 0.3 (43.7) 4.52 ± 0.09 0.997
0.0054 40.0 ± 0.2 (40.1) 1.68 ± 0.04 0.995
0.0080 35.6 ± 0.3 (35.6) 1.02 ± 0.05 0.980
10 0.0033 37.9 ± 0.1 (37.9) 6.08 ± 0.06 0.999
0.0054 35.9 ± 0.2 (36.0) 2.28 ± 0.05 0.996
0.0080 30.8 ± 0.1 (31.0) 1.45 ± 0.04 0.995
25 0.0033 34.4 ± 0.3 (34.4) 7.52 ± 0.13 0.997
0.0054 31.8 ± 0.1 (31.8) 2.83 ± 0.07 0.995
0.0080 28.8 ± 0.2 (28.9) 1.46 ± 0.07 0.979
40 0.0033 32.7 ± 0.2 (32.7) 7.61 ± 0.12 0.998
0.0054 29.8 ± 0.2 (29.7) 3.05 ± 0.06 0.996
0.0080 26.6 ± 0.3 (26.5) 1.59 ± 0.11 0.963
50 0.0033 31.7 ± 0.2 (31.7) 7.65 ± 0.18 0.996
0.0054 26.8 ± 0.4 (26.8) 3.69 ± 0.21 0.974
0.0080 24.4 ± 0.2 (24.4) 1.81 ± 0.07 0.988
313.15 0 0.0033 41.2 ± 0.2 (41.2) 5.15 ± 0.07 0.999
0.0054 38.9 ± 0.2 (38.8) 1.78 ± 0.04 0.996
0.0080 34.1 ± 0.2 (34.0) 1.13 ± 0.04 0.990
10 0.0033 36.8 ± 0.2 (36.8) 6.51 ± 0.09 0.998
0.0054 34.5 ± 0.2 (34.7) 2.38 ± 0.06 0.995
0.0080 30.0 ± 0.2 (30.0) 1.52 ± 0.05 0.990
25 0.0033 33.7 ± 0.3 (33.7) 7.89 ± 0.17 0.996
0.0054 31.2 ± 0.2 (31.2) 3.00 ± 0.06 0.997
0.0080 28.2 ± 0.3 (28.2) 1.57 ± 0.06 0.986
40 0.0033 31.5 ± 0.3 (31.7) 7.94 ± 0.19 0.996
0.0054 28.7 ± 0.2 (28.7) 3.11 ± 0.08 0.994
0.0080 25.6 ± 0.2 (25.5) 1.62 ± 0.09 0.986
50 0.0033 30.2 ± 0.3 (30.1) 7.99 ± 0.19 0.995
0.0054 25.9 ± 0.2 (26.0) 3.73 ± 0.09 0.996
0.0080 23.4 ± 0.1 (23.3) 1.90 ± 0.05 0.994
318.15 0 0.0033 39.3 ± 0.1 (39.3) 5.83 ± 0.06 0.999
0.0054 37.4 ± 0.2 (37.5) 2.01 ± 0.06 0.993
0.0080 32.8 ± 0.2 (32.8) 1.25 ± 0.05 0.985
10 0.0033 35.7 ± 0.2 (35.7) 6.87 ± 0.10 0.998
0.0054 33.4 ± 0.2 (33.4) 2.57 ± 0.06 0.996
0.0080 29.2 ± 0.3 (29.4) 1.64 ± 0.08 0.980
25 0.0033 32.4 ± 0.3 (32.4) 7.93 ± 0.30 0.989
0.0054 30.7 ± 0.2 (30.7) 3.08 ± 0.06 0.995
0.0080 27.0 ± 0.1 (27.2) 1.66 ± 0.07 0.985
40 0.0033 31.0 ± 0.3 (30.9) 7.97 ± 0.15 0.997
0.0054 28.0 ± 0.3 (28.2) 3.22 ± 0.10 0.992
0.0080 25.1 ± 0.2 (25.1) 1.68 ± 0.08 0.982
50 0.0033 28.9 ± 0.3 (28.9) 8.07 ± 0.22 0.994
0.0054 24.8 ± 0.3 (24.8) 3.88 ± 0.15 0.989
0.0080 21.9 ± 0.1 (21.8) 2.15 ± 0.06 0.994
323.15 0 0.0033 38.1 ± 0.3 (38.3) 5.93 ± 0.12 0.997
0.0054 35.9 ± 0.2 (35.8) 2.08 ± 0.06 0.993
0.0080 31.3 ± 0.2 (31.3) 1.32 ± 0.05 0.987
10 0.0033 34.1 ± 0.2 (34.0) 6.89 ± 0.14 0.997
0.0054 32.1 ± 0.2 (32.1) 2.60 ± 0.08 0.992
0.0080 28.0 ± 0.2 (28.0) 1.66 ± 0.04 0.994
Table 2. Continued
T (K) w
cp
(eq L−1)
(𝜂sp)conformation
(L eq−1) kH r2
25 0.0033 31.1 ± 0.3 (31.1) 7.98 ± 0.16 0.997
0.0054 30.3 ± 0.1 (30.3) 3.18 ± 0.05 0.997
0.0080 26.7 ± 0.2 (26.7) 1.70 ± 0.08 0.984
40 0.0033 30.2 ± 0.3 (30.3) 8.05 ± 0.15 0.997
0.0054 27.3 ± 0.2 (27.3) 3.33 ± 0.09 0.994
0.0080 24.2 ± 0.2 (24.0) 1.91 ± 0.08 0.986
50 0.0033 27.6 ± 0.3 (27.7) 8.13 ± 0.24 0.995
0.0054 23.6 ± 0.2 (23.6) 3.91 ± 0.15 0.992
0.0080 20.7 ± 0.1 (20.7) 2.64 ± 0.06 0.996
a The relevant values obtained using the Wolf phenomenological
approach (Eqn (2)) are given within parentheses in the fourth column.
0
0.1
0.2
0.3
0.4
0.5
0 0.002 0.004 0.006 0.008 0.010 0.012
cp (Eqv L-1
)
lnηrel
Figure 3. Variation of ln 𝜂rel for NaPSS with polyelectrolyte concentration
in 2-ethoxyethanol–water mixture containing 40 mass% 2-ethoxyethanol
at 323.15 K with total ionic strengths (eq L−1) 0.0033 ( ), 0.0054 ( ) and
0.0080 ( ), along with fitted profiles according to the Wolf approach
(Eqn (2)).
(𝜂sp/cp)conformation, are found to decrease as the polyelectrolyte
concentration increases (Table 2 and Figs 4 and 6). More coun-
terion condensation onto the polyion chains commences with
increasing polyelectrolyte concentration. This results in a lower
level of intramolecular electrostatic repulsion and contraction
of the polyion chains with an increase of the polyelectrolyte
concentration.
Variation of intramolecular contributions to reduced viscosity
with solvent medium at a given temperature and a given
polyelectrolyte concentration
At a particular temperature and at a given polyelectrolyte concen-
tration, the intramolecular contributions to the reduced viscosity,
(𝜂sp/cp)conformation, are found to decrease as the 2-ethoxyethanol
content of the medium increases (Table 2 and Fig. 4). With the
addition of 2-ethoxyethanol to water, there is a gradual lower-
ing of the relative permittivity of the medium (Table 1) which
causes an enhanced electrostatic attraction between the polyion
and the counterions thus resulting in more counterion conden-
sation onto the polyion chains. Greater counterion condensation
reduces the effective charge on the polyion; this causes a contrac-
tion of the polyion chains facilitated by the relief of intramolecular
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20
30
40
50
0 10 20 30 40 50
Mass% of 2-Ethoxyethanol
(ηsp/cp)conformation(LEqv-1
)
Figure 4. Effect of medium on intramolecular contribution to reduced
viscosity of NaPSS in 2-ethoxyethanol–water mixed solvent at 308.15 K
obtained by the method of isoionic dilution at polyelectrolyte concentra-
tions (eq L−1) 0.0033 ( ), 0.0054 ( ) and 0.0080 ( ).
0
2
4
6
8
10
0 10 20 30 40 50
Mass% 2-Ethoxyethanol
kH
Figure 5. Effect of medium on Huggins constant of NaPSS in
2-ethoxyethanol–water mixed solvent at 308.15 K obtained by the
method of isoionic dilution at polyelectrolyte concentrations (eq L−1)
0.0033 ( ), 0.0054 ( ) and 0.0080 ( ).
coulombic interactions. This is amply manifested by the decreas-
ing (𝜂sp/cp)conformation values of the polyelectrolyte as the solvent
medium gets richer in 2-ethoxyethanol.
Variation of intramolecular contributions to reduced viscosity
with temperature in a given solvent medium and at a given
polyelectrolyte concentration
Table 2 and Fig. 6 show that in a given solvent medium and at a
given polyelectrolyte concentration, (𝜂sp/cp)conformation is found to
decrease with increasing temperature. This may be attributed to
the gradual contraction of the polyion chains at higher tempera-
tures. It is instructive to examine the factors involved in this pro-
cess. With an increase of temperature, the polyion chains would
tend to expand by uncoiling. However, an increase in tempera-
ture causes a reduction in the relative permittivity of the medium
thereby leading to a coiling of the polyion chains due to more
counterion condensation. The balance of these two opposing
effects would be responsible for the present observation. Clearly,
the later effect (i.e. coiling) predominates over the former in
20
30
40
50
305 310 315 320 325
T (K)
(ηsp/cp)conformation(LEqv-1
)
Figure 6. Effect of temperature on intramolecular contribution to reduced
viscosity of NaPSS in 2-ethoxyethanol–water mixed solvent containing 40
mass% 2-ethoxyethanol obtained by the method of isoionic dilution at
polyelectrolyte concentrations (eq L−1) 0.0033 ( ), 0.0054 ( ) and 0.0080
( ).
0
0.5
1.0
1.5
2.0
2.5
305 310 315 320 325
lnkH
T (K)
Figure 7. Effect of temperature on Huggins constant of NaPSS
in 2-ethoxyethanol–water mixed solvent containing 10 mass%
2-ethoxyethanol obtained by the method of isoionic dilution at poly-
electrolyte concentrations (eq L−1) 0.0033 ( ), 0.0054 ( ) and 0.0080
( ).
controlling the value of (𝜂sp/cp)conformation of the polyelectrolyte as
a function of temperature in a given solvent medium.
Variation of Huggins constant with solvent medium at a given
temperature and a given polyelectrolyte concentration
At a given temperature and for a given polyelectrolyte concen-
tration, the Huggins constant is found to increase as the solvent
medium becomes richer in 2-ethoxyethanol (Table 2 and Fig. 5).
This clearly demonstrates that the solvent interacts with the
polyelectrolyte with less thermodynamic affinity (i.e. weaker
polyelectrolyte–solvent interactions) as the medium gets richer
in 2-ethoxyethanol. Hence the polyelectrolyte–polyelectrolyte
contacts become more probable than the polyelectrolyte–solvent
contacts, and therefore the coil dimension of the polyion chains
will be gradually reduced. This accounts for both the lower
values of (𝜂sp/cp)conformation (mentioned above) and the higher
values of the Huggins constant in a solvent medium richer
in 2-ethoxyethanol. This is in complete agreement with the
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6. 1964
www.soci.org R De, B Das
view that poor solvents are generally characterized by high kH
values.36
Variation of Huggins constant with temperature in a given solvent
medium and at a given polyelectrolyte concentration
In a given solvent medium and at a given polyelectrolyte con-
centration, the values of the Huggins constant are found to
increase with an increase of temperature (Table 2 and Fig. 7). This
is directly connected to the temperature coefficient of the sec-
ond virial coefficient (A2). The present observation points to the
fact that the thermodynamic affinity of the solvent for the poly-
electrolyte (i.e. the polyelectrolyte–solvent interaction) worsens
as the temperature rises (i.e. A2 increases) in a given solvent,
and hence chain contraction occurs resulting in a decrease in
the (𝜂sp/cp)conformation values with an increase of temperature. This
decrease in the polyelectrolyte–solvent interaction results in an
increase in the polyelectrolyte–polyelectrolyte interaction36
man-
ifested by increasing Huggins constant values as a function of tem-
perature.
Variation of Huggins constant with polyelectrolyte concentration
at a given temperature in a given solvent medium
In a given solvent medium and at a given temperature, the values
of the Huggins constant are found to decrease with polyelectrolyte
concentration (Table 2). As the concentration of the ions in the
solution increases, there is a considerable enhancement of coun-
terion population within the polyion chains. This causes greater
screening of the affixed charges on the chains with increasing ionic
strengthofthesolution,decreasingtheintrapolyionicelectrostatic
repulsions (and hence decreasing kH; Table 2) and resulting in a
contraction of the polyion chains and, hence, in a decrease in the
intramolecular contribution to the reduced viscosity of the solu-
tion.
CONCLUSIONS
Precise measurements have been reported of the viscosities of
solutions of a sample of NaPSS in water and its mixtures with
2-ethoxyethanol at different temperatures. The intramolecular
contributions to the reduced viscosity of the polyelectrolyte solu-
tions were obtained through isoionic dilution maintaining the
total ionic strengths of the solutions at constant levels using
sodium chloride. The intramolecular contributions to the reduced
viscosity of the polyelectrolyte solutions were also obtained using
the phenomenological approach to the viscosity of polyelectrolyte
solutions as proposed by Wolf. The agreement between the val-
ues as determined using these two methods is excellent. The Hug-
gins constant was also obtained from the experimental results. The
influences of the medium and the temperature on the intramolec-
ular contributions to the reduced viscosity as well as on the
Huggins constant have been interpreted in order to elucidate the
polyion conformational behaviour and polyelectrolyte–solvent
and polyelectrolyte–polyelectrolyte interactions in these solu-
tions.
ACKNOWLEDGEMENTS
This work was supported by the Department of Science and Tech-
nology, New Delhi, Government of India (SR/S1/PC-67/2010). The
Department of Chemistry, North Bengal University is also grate-
fully acknowledged for its support while part of the experimental
work was carried out there.
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