About the correlation between the mobility of a polyion and that of its counterions

Abstract

In this paper, we propose a new approach in order to interpret the variation of the conductibility of the PSS polyion with the nature and the concentration of the alkaline counter-ions Li+, Na+ and K+, and the hydrophobic cations Et4N+ and Bu4N+. This approach is based on a recent model in which the stretched polyion is represented by a chain of successive charged spheres, partially condensed by the counter-ions. We have found that the moderate variation of the hydrodynamic friction on the polyion with the size RM of condensed counter-ions, cannot completely explain the important decrease (of about 35% from K+ to Bu4N+) of the conductibility (lPSS,M ) of the PSS polyion with the nature of the counter-ions. Consequently, we have proposed a supplementary explanation by taking into account of the translational dielectric friction on the moving polyion. Formal analysis of this friction shows that it is very sensitive to the local structure of water surrounding the polyions. As this local structure depends in its turn, on the nature of the condensed counter-ions; we suggested that this specific sensitivity could explain the high dependence of the mobility of the polyion with the nature of its counter-ions.

New interpretation of the dependence of the conductibility of PSS and PAA polyions with the nature of the counterions

“…λ P°H yd is the purely hydrodynamic contribution due to the viscosity η of the solvent [28]; Δλ P el is the so-called electrophoretic contribution which expresses the hydrodynamic friction of the solvent on the ionic atmosphere of the polyion; β ir P is the ionic friction coefficient expressing the reaction undergone by the polyion following the perturbation of its ionic atmosphere by the external field E (ionic relaxation effect [1][2][3]); and β P,M dfi is the dielectric friction coefficient expressing the reaction undergone by the polyion resulting from the local polarization of its surrounding solvent molecules by its own "apparent charge" α M (Z S e) (dielectric relaxation effect [5,14,15]). …”

“…In some recent works [1][2][3][4][5][13][14][15], we have proposed a new approach in order to obtain an adequate semi-analytical expression, describing correctly the variation of the polyelectrolyte conductibility Λ MP with the concentration of the counterions, for different polyion configurations. This approach is based on a general model in which the coiled polyion is represented by an ellipsoidal macroion, and the stretched polyion is represented by a chain of successive charged spheres.…”

“…Indeed, according to this "chain of charged spheres" model [5,14,15], the dielectric friction coefficient, 3 , where ε ∞ is the highfrequency dielectric constant, and ε′ is the local permittivity of the solvent in the vicinity of the charged groups of the polyion, which are represented by spheres of radius R′ g,M . In fact, the term (ε′−ε ∞ )ε′ −1 can be interpreted as follows: In general, the local structure of the solvent, near the polyion, is partially broken by the condensed counterions, so the local permittivity ε′ is smaller than the dielectric constant ε o of the bulk solvent.…”