Conductivity measurements in water and at 25 °C show that the variation of the equivalent conductivity ΛPX with the counter ion concentration CX of some PDDPX polyelectrolytes, poly(1,1-dimethyl-3,5-dimethylene piperidinium, X), for X ≡ Br−, Cl−, NO3-\documentclass[12pt]{minimal}
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\begin{document}$${\text{NO}}_{3}^{ - }$$\end{document} and F−, is characterized by an inversion in Kohlraush’s law (i.e., ∀\documentclass[12pt]{minimal}
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\begin{document}$$\forall$$\end{document}C, ΛPX < ΛPX′ if λX∘\documentclass[12pt]{minimal}
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\begin{document}$$\lambda_{\text{X}}^{ \circ }$$\end{document} > λX′∘\documentclass[12pt]{minimal}
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\begin{document}$$\lambda_{{\text{X}}^{\prime}}^{ \circ }$$\end{document}), where λX∘\documentclass[12pt]{minimal}
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\begin{document}$$\lambda_{\text{X}}^{ \circ }$$\end{document} 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 ΛPX with the degree of dissociation αX, since αX remains quasi-constant at about 0.7 for CX < 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−, NO3-\documentclass[12pt]{minimal}
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\begin{document}$${\text{NO}}_{3}^{ - }$$\end{document}, and for X ≡ F− with CX > 10−3 mol·L−1, this anomaly occurs for PDDPZS+ 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 γp, 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.
