Analytical Theories of Transport in Concentrated Electrolyte Solutions from the MSA

Ion transport coefficients in electrolyte solutions (e.g., diffusion coefficients or electric conductivity) have
been a subject of extensive studies for a long time. Whereas in the pioneering works of Debye, Hückel, and
Onsager the ions were entirely characterized by their charge, recent theories allow specific effects of the ions
(such as the ion size dependence or the pair association) to be obtained, both from simulation and from
analytical theories. Such an approach, based on a combination of dynamic theories (Smoluchowski equation
and mode-coupling theory) and of the mean spherical approximation (MSA) for the equilibrium pair correlation,
is presented here. The various predicted equilibrium (osmotic pressure and activity coefficients) and transport
coefficients (mutual diffusion, electric conductivity, self-diffusion, and transport numbers) are in good agreement
with the experimental values up to high concentrations (1−2 mol L-1). Simple analytical expressions are
obtained, and for practical use, the formula are given explicitly. We discuss the validity of such an approach
which is nothing but a coarse-graining procedure.