Does Electrical Conductivity of Linear Polyelectrolytes in Aqueous Solutions Follow the Dynamic Scaling Laws? A Critical Review and a Summary of the Key Relations

Abstract

Abstract:In this review, we focus on the electrical conductivity of aqueous polyelectrolyte solutions in the light of the dynamic scaling laws, recently proposed by Dobrynin and Rubinstein, to take into account the polymer conformations in different concentration regimes, both in good and poor solvent conditions. This approach allows us to separate contributions due to polymer conformation from those due to the ionic character of the chain, and offers the possibility to extend the validity of the Manning conductivity model to dilute and semidilute regimes. The electrical conductivity in the light of the scaling approach compares reasonably well with the observed values for different polyelectrolytes in aqueous solutions, over an extended concentration range, from the dilute to the semidilute regime.

Importance of Varying Permittivity on the Conductivity of Polyelectrolyte Solutions

“…We performed two sets of simulations with a constant background permittivity, one with ε r = 78.5 and one where the ion concentration in the simulation box was substituted into equation 1 to determine the background permittivity. Both sets of simulations with a constant dielectric background show a monotonic decrease in the equivalent conductivity, in good agreement with scaling theories which ignore the effect of dielectric contrast [24,25,27,29,30,68]. More importantly, our simulations that adapt the permittivity to the local ion concentration quantitatively reproduce the unexpected rise in conductivity at high salt concentrations.…”

Universal conductivity dependence of pure water polyelectrolyte solutions

“…9 But even with this upgrade experimental results cannot be explained with such state-of-the-art conductivity theories. 8,9 Beyond this effect numerous more effects are incorporated into conductivity equation, which now has more than 15 different symbols, like eqn 83 from Ref. 8, but still experimental data can not be explained.…”

“…where c i is molar concentration of the charge specie of type i, valency |z i | and molar conductivity λ i . 8,9 For simple pure water polyelectrolyte consisting of charged polyions (p) and counterions (c) Eqn. 1 can be reduced to…”

“…Next effect for which was thought that would fix this mismatch was the conductivity contribution of polyion conformation. 8,9 Cametti used Dobrynin's description of polyion conformation 10 to include its contribution to total conductivity. 9 But even with this upgrade experimental results cannot be explained with such state-of-the-art conductivity theories.…”

“…8,9 Cametti used Dobrynin's description of polyion conformation 10 to include its contribution to total conductivity. 9 But even with this upgrade experimental results cannot be explained with such state-of-the-art conductivity theories. 8,9 Beyond this effect numerous more effects are incorporated into conductivity equation, which now has more than 15 different symbols, like eqn 83 from Ref.…”