Shichen Dou and Ralph H. Colby
Materials Science and Engineering
The Pennsylvania State University
University Park, Pennsylvania 16802
Introduction
Owing to the practical importance for industrial coatings, the viscosity
of polyelectolyte solutions in both water and organic solvents has received
considerable attention.1,2,3,4.5 The maximum value of reduced viscosity in
dilution is caused by the residual salt in the aqueous solution rather than the
dilution itself.6 Carbon dioxide dissolves in water and forms carbonic acid,7
which dissociates to make pH ≈ 5.4 and salt concentration of 4x10-6 M.4,5,6
Furthermore, charge density effects on the rheology of salt-free
polyelectrolyte solutions have not been reported over a wide range of
concentration. In this paper, we study how charge density impacts the
rheology of polyelectrolyte solutions over a wide concentration range
compared to the rheology of the parent neutral polymer solutions in the same
solvent (ethylene glycol) by a study of random copolymers of 2-vinyl pyridine
and N-methyl-2-vinyl pyridinium chloride (PMVP-Cl) with various charge
density and uncharged neutral parent poly (2-vinyl pyridine) (P2VP). This
partially charged copolymer/solvent system was chosen because it has
previously been studied by SANS.8
Experimental
Materials. P2VP (Mw = 364,000 g/mol and Mw/Mn = 1.06) purchased
from Polymer Source Inc. was used without further purification. Anhydrous
reagent dimethyl sulfate (DMS, 99+ %, DuPont) and sodium chloride (J.T.
Baker, 99.9%) were used as received. N, N-dimethyl formamide (DMF:
Aldrich, anhydrous, 99.8%) was redistilled under vacuum in the presence of
sodium. Ethylene glycol (EG: J. T. Baker, 99.8%, anhydrous; water < 0.02%,
ε=37.3) was used as the solvent for all samples in this study after it has been
redistilled under low pressure and protection of argon.
Preparation of the random copolymers of 2-vinyl pyridine and Nmethyl-2-vinyl pyridinium chloride. First, the parent dry P2VP was
dissolved in DMF (10 wt/wt %) and then DMS was added into a 100 ml
reactor with three openings under the protection of argon. The reaction was
kept at room temperature for 24 hrs. Second, the resultant with charge density
above 30 mole % was precipitated into acetone, filtered and then redissolved
in 2M NaCl solution in water with at least 50 fold excess of chloride to methyl
pyridinium ion. The resultant with lower charge density was dissolved in 2M
NaCl water-methanol (50/50 volume) directly. Third, the quaternized polymer
in 2 M NaCl solution was dialyzed against deionized water until a constant
conductivity (lower than 2µS/cm) of the dialyzate was attained. Finally, the
salt-free polyelectrolyte solution was lyophilized at low pressure, and the solid
quaternized polymer was dried in a vacuum oven at 40°C to a constant mass.
Quaternized polymers with various charge density were obtained by varying
the molar ratio of DMS and pyridine.
Degree of quaternization. The degree of quaternization of the partially
quaternized polymers was determined by using sodium chloride (Aldrich,
99.999%) and silver nitrate (Aldrich, 99.9+%) based on the standard
counterion titration technique. Aside from the counterion titration, 1H-NMR
was used to confirm the degree of quaternization.
Preparation of polymer solutions. Dry polymers were dissolved in
ethylene glycol to prepare the highest concentration and lower concentrations
were prepared by serial dilution. Polymer concentration is reported in moles
of monomers (vinyl pyridine or vinyl pyridinium chloride) per liter of
solution.
Rheology. The viscosity was measured using four rheometers: A
Rheometric Scientific Ares (controlled strain), a Rheometric Scientific SR2000 (controlled stress), a computerized Contraves Low Shear 30 viscometer
(controlled strain rate), and a capillary viscometer (Cannon Ubbelohde No. 2
with a diameter of 1.03mm and a capillary length of 90mm).
Results and Discussion
The preparation of partially quaternized polymers is shown in Figure 1
and α = y/(x+y) is the degree of quaternization. Our sample nomenclature
involves α, as we define the polymer samples with degree of quaternization of
0, 2.6, 10, 17, 42, 55 mole % as P2VP, 2.6PMVP-Cl, 10PMVP-Cl, 17PMVPCl, 42PMVP-Cl, and 55PMVP-Cl, respectively.
Figure 1. Preparation of random copolymers of 2-vinyl pyridine and Nmethyl-2-vinyl pyridinium chloride (PMVP-Cl)
Viscosity as a function of shear rate was measured and the zero shear rte
viscosity ŋ0 was determined for each polymer over a wide range of
concentration in EG, spanning more than four decades. Figure 2 shows how
specific viscosity ŋsp = (ŋ0-ŋs)/ŋs , where ŋs is the solvent viscosity, depends on
the charge density and concentration of the polyelectrolyte solutions. It is
interesting to see that the viscosity of 10PMVP-Cl and 17PMVP-Cl in
ethylene glycol are similar to the highly charged polymers 42PMVP-Cl and
55PMVP-Cl, while the weakly charged 2.6PMVP-Cl has lower viscosity. The
specific viscosity of both neutral polymer and polyelectrolyte solutions is
proportional to concentration in dilute solution. The overlap concentration c*
depends strongly on charge density until counterion condensation occurs. The
specific viscosity of all charged polymers increases with concentration
roughly as ŋsp ~ c1/2 in the semidilute unentangled concentration regime (c*
< c < ce, where ce ≈ 0.15M is the entanglement concentration). The
entanglement concentration is independent of charge density, whereas theory3
expects it to be proportional to c*.
Specific viscosity
CHARGE DENSITY EFFECTS IN SALT -FREE
POLYELECTROLYTE SOLUTION RHEOLOGY
10
4
10
3
10
2
10
1
10
0
10
-1
10
-2
10
P2VP
2.6PM VP-C l
10PM VP-C l
17PM VP-C l
42PM VP-C l
55PM VP-C l
-4
10
-3
10
-2
10
-1
10
0
C oncentration, c (M )
Figure 2. The specific viscosity at 25 °C in EG as a function of
concentration, for copolymers of different charge density and the neutral
parent polymer.
The reduced viscosity (ηsp/c) as a function of concentration is shown in
Figure 3. Our experimental results show the reduced viscosity of neutral or
charged polymer solutions without added salt is independent of concentration
below c*. The reduced viscosity of polyelectrolyte solutions agrees with the
Fuoss law1 only in the semidilute unentangled regime.
Aqueous
polyelectrolyte solutions have a maximum in reduced viscosity due to residual
Polymer Preprints 2004, 45(2), 261
10
4
10
3
P 2V P
2.6P M V P -C l
10P M V P -C l
17P M V P -C l
42P M V P -C l
55P M V P -C l
10
10
10
2
1
10
-4
10
-3
10
-2
10
-1
10
0
C oncentration, c (M )
Figure 3. The reduced viscosity at 25 °C in EG as a function of
concentration, for copolymers of different charge density and the neutral
parent polymer.
Shear thinning phenomena of charged polymer solutions above c* were
observed at high shear rates, while the shear thinning of neutral P2VP
solutions was observed only at concentrations above ce. The relaxation time
of the polymers in solution was estimated from the reciprocal of the shear rate
at which shear thinning starts.4,5 The concentration dependence of this
relaxation time is presented in Figure 4. For semidilute unentangled solutions
(c* < c < ce) the relaxation time of charged polymers decreases with increasing
concentration (τ ~ c-1/2) and the relaxation time increases with increasing
charge density. In the semidilute entangled region, the relaxation time does
not vary a lot with increasing concentration, in agreement with Dobrynin’s
prediction.3 At concentrations above cD ≈ 0.6 M, the relaxation time of the
strongly charged polymer solutions increases rapidly with increasing
concentration (τ ~ c2), while the relaxation time of neutral and weakly charged
polymers increases even faster (τ ~ c2.8).
10
Relaxation Time (s)
Scaling theory9 predicts that the ratio of zero-shear rate viscosity and
relaxation time determines the terminal modulus of polymer solutions G = ŋ/τ.
The terminal modulus is predicted by Dobrynin, et al.3 to be kT per chain
(G = ckT/N, where N is the degree of polymerization). Our experimental
results qualitatively obey Dobrynin et al.’s prediction as shown in Figure 5. It
is not clear whether the scatter represents real differences between samples or
uncertainty in determination of the relaxation time. The observation that the
terminal modulus of P2VP becomes independent of concentration at the
higher concentrations is surprising and warrants further study.
0
10
-1
10
-2
10
-3
10
P2VP
2 .6 P M V P -C l
1 0 P M V P -C l
1 7 P M V P -C l
4 2 P M V P -C l
5 5 P M V P -C l
-3
10
-2
10
-1
10
0
C o n c e n tr a tio n , c ( M )
Figure 4. The relaxation time at 25 °C in EG as a function of concentration,
for copolymers of different charge density and the neutral parent polymer.
Terminal Modulus, G (Pa)
Reduced viscosity (1/M)
salt.4,6 However, ethylene glycol neither dissociates nor reacts with any
molecules in air to form ionic impurities, as evidenced by a conductivity < 0.1
µS/cm. Hence, solutions in EG can be truly salt-free.
10
4
P2VP
2.6PMVP-Cl
10PMVP-Cl
17PMVP-Cl
42PMVP-Cl
55PMVP-Cl
3
10
2
10
1
10
0
10
-1
10
-3
10
-2
10
-1
10
0
Concentration, c (M)
Figure 5. The terminal modulus of polymer solutions at 25 °C in EG as a
function of concentration, for copolymers of different charge density and the
neutral parent polymer.
Conclusions
Polyelectrolyte solutions in EG can be truly salt-free with no ionic
impurity and as such have no local maximum in the concentration dependence
of their reduced viscosity. The specific viscosity is simply proportional to
concentration below c*. Counterion condensation makes the viscosity and
relaxation time of samples with 0.1 < α < 0.55 in EG nearly identical.
Dobrynin’s theory3 qualitatively describes all viscosity, relaxation time, and
modulus data for c < cD. For c > cD ≈ 0.6 M, the scaling model expects
polyelectrolyte solutions to be rheologically indistinguishable from neutral
solutions. Instead at these high concentrations, the neutral polymer has the
lowest viscosity and shortest relaxation time, the weakly charged
polyelectrolyte (2.6PMVP-Cl) has the highest viscosity and longest relaxation
time, and the more strongly charged polyelectrolytes are between these limits.
Acknowledgement is made to the donors of the Petroleum Research
Fund, administered by the American Chemical Society, for support of this
research.
References
(1) Fuoss , R. M. and Strauss, U. P., J. Polym. Sci., 1948, 3, 246.
(2) Oosawa, F., Polyelectrolytes, 1971, Marcel Dekker.
(3) Dobrynin, A. V., Colby, R. H., and Rubinstein, M., Macromolecules,
1995, 28, 1859.
(4) Boris, D. C. and Colby, R. H., Macromolecules, 1998, 31, 5746.
(5) Krause, W. E., Tan , J. S. and Colby, R. H., J. Polym. Sci. Part B:
Polym. Phys., 1999, 37, 3429.
(6) Cohen, J. and Priel, Z., J. Chem. Phys., 1988, 88, 7111
(7) Shedlovsky, T. and Mac Innes, D. A., J. Amer. Chem. Soc. 1935, 57,
1765.
(8) Ermi, B. D. and Amis, E. J., Macromolecules, 1997, 30, 6937.
(9) de Gennes, P.-G., Scaling Concepts in Polymer Physics, 1979, Cornell
University Press: Ithaca, NY.
Polymer Preprints 2004, 45(2), 262