Theory of electrophoretic mobility of a polyelectrolyte in semidilute solutions of neutral polymers

An explicit formula is derived for the electrophoretic mobility of a polyelectrolyte molecule in a semidilute solution of neutral polymers in terms of the molecular weight N of a polyelectrolyte, concentration c of neutral polymers, Debye length and solvent quality. The nature of the crossover between different regimes, as c, N, and the salt concentration are varied, is presented. The calculations show that one progressively enters into regimes of no-separation, separation, and no-separation in the electrophoresis of polyelectrolytes as c is increased. If c is very high, one returns to the mechanism of separation in gel electrophoresis.