The relaxation effect as observed on lipid suspensions of low polydispersity

The Dukhin-Deryaguin equation for the electrophoretic mobility in monovalent electrolytes with arbitrary ion mobilities

The Dukhin-Deryaguin equation, used in the modern theory of electrophoresis for the calculation of electrophoretic mobility (EPM) in the region of double layer polarization, is known from literature [4-6] in its form (DD1) valid for the equal mobilities of the cation and anion in solutions of symmetrical electrolytes. Here we describe the other version of this equation (DD2), for arbitrary ion mobilities in 1:1 electrolytes. The EPMs calculated from this latter version are in good agreement with an exact computer solution [12]. The use of DD2 is illustrated in a series of EMP vs. IgC curves, calculated for selected examples of negatively charged lipid membranes. In addition, we describe two simplified versions of DD2, which are valid, respectively, for the high zeta potentials and when the electroosmotic component of ions' fluxes at the charged surface is neglected. Comparing DD2 with DD1 shows that the latter equation results in an error which may exceed the experimental dispersion of EPM values in the absence of specific ion binding. This error is reduced if the counter-ion binding is not small; hence, DD1 may also be used in some cases for solutions with arbitrary ion mobilities.

The validity of the Smoluchowski equation in electrophoretic studies of lipid membranes

The Helmholtz-Smoluchowski theory, widely used for the calculation of zeta potential from the measured electrophoretic mobility (EPM), is known to be invalid in the region where the mobility is affected by the surface conductivity and polarization of the electrical double layer. In this region, the zeta potential found according to the Smoluchowski equation (zeta sm) is not identical to the true electrostatic potential at the hydrodynamic plane of shear (zeta), which is considered in the Gouy-Chapman-Stern theory of the electrical double layer. As a result, zeta sm cannot be used for the subsequent calculation of surface potential and surface charge density of a membrane studied. here we suggest a simple way, allowing one to decide between the validity and nonvalidity of the Smoluchowski equation in various sets of experimental conditions used in electrophoretic measurements on lipid membranes. We calculated the dimensionless criterion Rel, accepted in the Dukhin theory of electrophoresis as a measure of the extent of the influence of surface conductivity and double layer polarization on EPM. The Rel changes, with membrane charge density, ionic strength and vesicle radius, were found to be helpful in finding the combinations of these three parameters, corresponding to the validity of the Smoluchowski equation.