Electrolyte friction on charged spherical macroparticles: Beyond the Debye–Hückel limit

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Abstract
The contribution to the friction coefficient of a charged spherical polyion diffusing in an ionic solution due to its interactions with the electrolyte ions is calculated, in the absence of hydrodynamic interactions, starting from a formal expression for ζel previously derived by Medina-Noyola and Vizcarra-Rendón. It is shown that such a formal expression can be given a particularly simple form in terms of the equilibrium distribution neqi(r) of the small ions around the tracer, which allows us to study effects ignored in Debye–Hückel level theories. We consider, for example, the effect of a finite size of the small ions and nonlinear contributions to ζel on the polyion charge. We show that the correct Debye–Hückel limit differs from Schurr’s result for ζel, and the source of the disagreement is clearly exposed. The results derived here for ζel are not restricted in the number of species of electrolyte ions or in their charges or mobilities.