From small charged molecules to oligomers: a semiempirical approach to the modeling of actual mobility in free solution.

According to Stokes' treatment, the ionic mobility of particles, which are small with respect to Debye length, is usually considered to be proportional to the nominal charge and inversely proportional to the hydrodynamic radius. Experimentally, it is well known, however, that the ionic mobility of a small multicharged molecule does not depend linearly on its nominal charge in a wide range. This behavior can be accounted for by a condensation of the charge or a modification of the friction coefficient with the charge. This paper presents a semiempirical modeling of the actual mobility based on the assumption of additivity of frictional contributions pertaining to the uncharged molecular backbone and to each charged or uncharged moiety. Condensation of the charge was not considered. The model first appeared to be suitable for multicharged analytes having a characteristic dimension smaller than the Debye length, such as benzene polycarboxylic acids and polysulfated disaccharides. This approach was then adapted to account for the actual mobilities of singly and evenly charged oligomers (N-mers) having a dimension smaller than or similar to the Debye length. Rather good experimental agreement was obtained for polyalanines and polyglycines (N < or = 6), fatty acid homologs, fully sulfonated polystyrene oligomers (N < or = 13), and polycytidines (N < or = 10). Especially the influence of the polymerization degree on the mobility of oligomers having identical charge densities was clarified. It is also shown that the electrophoretic contribution to the overall friction coefficient increases linearly with the nominal charge but hardly depends on the chemical nature of the charged moieties. This model should be of interest to evaluate the role of various physicochemical phenomena (hydrodynamic and electrophoretic frictions, hydrodynamic coupling, charge condensation) involved in the migration of charged oligomers.