Viscosity of Semidilute and Concentrated Nonentangled Flexible Polyelectrolytes in Salt-Free Solution

Abstract

We report viscosity data of nonentangled sodium polystyrene sulfonate (NaPSS) in salt-free aqueous solution as a function of polymer concentration (c) and degree of polymerization (N). Different empirical equations are examined and found not to describe the semidilute solution viscosity over a wide concentration range and/or to yield values of [η] that do not match dilute solution measurements. Deviations from the scaling prediction of ηsp ∝ c 1/2 (Fuoss’ law) are observed at high concentrations. Specifically, we find ηsp ≈ N 1.26 c 1/2 e1.4c in the semidilute regime, which agrees with the scaling prediction only for c ≲ 0.02 M. The viscosity data presented in this study and in earlier reports show a high degree of consistency. A comparison with diffusion measurements for NaPSS in salt-free solution by Oostwal and co-workers suggests that the disagreement between the scaling theory and experiments does not arise solely from the concentration dependence of the monomeric friction coefficient.

Diffusion and viscosity of non-entangled polyelectrolytes

“…The viscosity of polyelectrolyte solutions was first studied by Fuoss and co-workers 79,80 , who observed a linear dependence of the reduced viscosity (η red ) and the on the square root of the polymer concentration for poly-4vinylpyridine derivatives in water-ethanol mixtures. Similar behaviour was observed for many other systems and eventually became known as the Fuoss law 25,81 . A theoretical explanation for this unusual dependence was first put forward by de Gennes' and co-workers 16 , and later incorporated into the theories of Yamaguchi et al 82 and Dobrynin et al 19 among others.…”

“…22 The scaling treatment of polyelectrolyte dynamics on the other hand displays poorer agreement with experimental results. [22][23][24][25][26][27] In salt-free or low ionic strength media, polyelectrolytes adopt highly extended conformations 22,[26][27][28][29][30][31][32][33][34][35] , meaning that their solutions are above the overlap concentration (c * ) for most practical applications. While the overlap concentration of polyelectrolytes is much lower than that of non-ionic polymers, especially for high degrees of polymerisation (N ), the entanglement concentration (c e ) is only weakly dependent on charge fraction 26,36 .…”

“…Studies on solvent, counter-ion and co-solute diffusion in polyelectrolyte and ionomer solutions and gels have also been reported. [51][52][53][54][55][56][57][58][59] Rheological data, particularly the zero shear-rate viscosity of solutions, provide a complementary test to the macroscopic dynamics of polyelectrolytes 18,[22][23][24][25]36,60 . Due to the relative ease with which such measurements can be carried out, a vast literature on the viscosity of polyelectrolytes exists, covering a wide range of polyelectrolyte types [61][62][63] , molar masses 23,[63][64][65] , charge densities [66][67][68] , solvent quality 69 , dielectric constant 60,[70][71][72] and added salts 27,[73][74][75][76][77][78] .…”

“…Recently, an extensive analysis of literature data for the viscosity of non-entangled NaPSS 25 in salt-free water showed that the power-law exponent of the specific viscosity with concentration increases with increasing polymer concentration, and agrees with the Fuoss law only for c 0.05 M. The origin of the concentration dependence of the viscosity-concentration exponent could however not be established as viscosity and diffusion data were in apparent conflict. 22,25,49,50 While it is common to treat solvent dynamics as independent of polymer concentration, it is known that the addition of polymers, salts, co-solvents or nanoparticles alters the cohesive energy between solvent molecules 59,[86][87][88][89][90][91] . The structuring of water by solutes with ionic groups in particular has received renewed attention over the last few years, as recent results indicate that nuclear quantum effects [92][93][94] .…”

Effect of metal salts on high‐voltage atmospheric cold plasma‐induced polymerization of acrylamide

“…In other cases, it was a power law, as also found in previous studies. 53 Measurements were conducted in triplicate and the average viscosity values were used to determine the intrinsic viscosity.…”