Chain-length dependence of the electrophoretic mobility in random gels

The electrophoretic mobility μ of a flexible N-segment probe polymer has been measured in cross-linked gels of concentration c. Assuming μ∼${\mathit{N}}^{\mathrm{-}\mathrm{\alpha }}$ ${\mathit{c}}^{\mathrm{-}\gamma }$, α initially increases with N, reaches a maximum of ∼2 in a crossover regime, and finally decreases to 1, the exponent of reptation. In accord with a semidilute-solution scaling argument, an analogous maximum in γ is observed. Behavior at intermediate N and c is consistent with ‘‘entropic-barrier’’-mediated transport, while larger N or c leads to reptation.