A semi-empirical approach to the modeling of the electrophoretic mobility in free solution: application to polystyrenesulfonates of various sulfonation rates

This work focuses on the understanding of the electrophoretic behavior of flexible chains of polystyrenesulfonates (PSSs) in free solution. It deals mainly with the variation of the electrophoretic mobility with (i) the polymerization degree (N) of fully sulfonated PSSs and (ii) the sulfonation rate of randomly sulfonated PSSs. In both cases, the electrophoretic mobility was modeled following a semi-empirical approach which involves parameters retaining a physical meaning. Fully sulfonated PSS oligomers, having a length smaller than or similar to the Debye length, exhibit a particular electrophoretic behavior, in-between that observed for multicharged small molecules and that for polyelectrolytes. The electrophoretic mobility of these oligomers increases strongly with N, which is attributed to a hydrodynamic coupling between monomers. Then the mobility is maximum for an N of about 10, for which the PSS oligomers are still in a rod-like conformation. Afterwards, as N increases and the PSSs are larger than the Debye length, the electrophoretic mobility decreases slowly until it reaches a constant value corresponding to the free-draining behavior. Next, the electrophoretic behavior of long PSS (N about 1,200) differing in their sulfonation rates was investigated. The effective charge rates were determined independently by conductimetric measurements and the mobilities were modeled as a function of the sulfonation rate. The PSS behavior observed was compared to the one previously reported for classical polyelectrolytes having hydrophilic backbones, such as copolymers of poly(acryamide-coacrylic acid). A specific behavior has been pointed out for these partially sulfonated PSSs, which is attributed to the hydrophobicity of their backbone. Finally, it is shown that separations of PSSs of different sulfonation rates can be obtained with electrolytes containing an anionic surfactant or methanol.