Some New Contributions to the Theory of Polyelectrolyte Solutions: Prediction of Polyion Conformation and Interpretation of Some Deviations from Kohlrausch’s Law According to the Superposition Principle and the Dielectric Friction Effect

Abstract

Conductivity measurements in water and at 25 °C show that the variation of the equivalent conductivity Λ_PX with the counter ion concentration C_X of some PDDPX polyelectrolytes, poly(1,1-dimethyl-3,5-dimethylene piperidinium, X), for X ≡ Br⁻, Cl⁻, ${\text{NO}}_{3}^{ - }$ and F⁻, is characterized by an inversion in Kohlraush’s law (i.e., $\forall$C, Λ_PX < Λ_PX′ if $\lambda_{\text{X}}^{ \circ }$ > $\lambda_{{\text{X}}^{\prime}}^{ \circ }$), where $\lambda_{\text{X}}^{ \circ }$ is the conductivity of the counter ion X at infinite dilution. This anomaly cannot be explained in the case of stretched polyions, by the dependence of Λ_PX with the degree of dissociation α_X, since α_X remains quasi-constant at about 0.7 for C_X < 2 × 10⁻² mol·L⁻¹. On the other hand, such a reversal implies that in the case of a coiled conformation, there is an increase in the ionic condensation, which is incompatible with hydrophobic folding. Similarly, hydrodynamic, electrophoretic and ionic frictions on these PDDPX polyelectrolytes cannot explain this inversion given their weak dependence with the nature of the counter ion X. In fact, for X ≡ Br⁻, Cl⁻, ${\text{NO}}_{3}^{ - }$, and for X ≡ F⁻ with C_X > 10⁻³ mol·L⁻¹, this anomaly occurs for PDDP^ZS+ polyions having a completely stretched chain conformation for which the translational dielectric friction effect on their charged groups becomes important to a variable degree depending on the nature of X. For PDDPF polyelectrolytes, this anomaly is amplified at high dilution because of possible synergy between the ionic dissociation and the hydrophobic character of the polyion, giving rise to a “pearl-necklace conformation” of effective length, L, decreasing with the dilution. In this work, we represent the conformation of polyions by an ellipsoid with a variable eccentricity γ_p, or by a chain of charged spheres with a variable group radius Rg, or by a pearl necklace model with a variable length L and a variable bead radius. The stability of the general configuration was formally studied according to a new approach based on the principle of superposition of ionic screening effects on the different charged groups.