Capillary electrophoresis of small solutes in linear polymer solutions: relation between ionic mobility, diffusion coefficient and viscosity

Electrophoretic mobilities, mu, and diffusion coefficients, D, of a small ion (molecular weight 579) were determined in dependence on the viscosity, eta, of aqueous buffer solutions containing ethylene glycol, or polyethylene glycol (PEG) with average molecular weights of 400, 20000, 100000 or 2000000, respectively, as additives. The values for mu and D are inversely proportional to the viscosity for the solutions with small-sized additives (ethylene glycol and PEG400), in accordance to Walden's rule. In contrast, for the longest polymers the mobilities and the diffusion coefficients approximate the values observed for pure water, and are nearly independent of the viscosity. This result agrees with the model of fractional free volume and the obstruction theory. For solutions with equal viscosity, three ranges can be differentiated for mu and D in relation to the size of the additive: for small additives, on the one hand, and the long-chained polymers, on the other hand, the values for mu and D are nearly independent of the size of the additive. In contrast, a pronounced increase of mu and D is found with increasing polymer size in the molecular weight range between 20000 and 100000. The ratio mu/D, occurring in a number of expressions for the plate height contributions, exhibits a remarkably small change over the entire polymer size and viscosity range (between 1 and 7 cP) under consideration. Consequently, the separation efficiency, expressed by the plate number, is found to be nearly constant, and is independent of viscosity.