Monte Carlo simulations of probe-host chain entanglement: Influence of host mobility and size on probe electrophoretic motion

A Monte Carlo method simulates chain trajectories during the pairwise configurational interactions of a single field-driven polyelectrolyte "probe" chain and a single neutral "host" chain. The goal is to understand how the mobility and chain length of dilute, neutral polymers affect the separation of dilute polyelectrolytes during capillary electrophoresis in a neutral polymer solution. The simulations fix probe charge density, Debye-Huckel screening length, and probe-host starting displacement, but vary chain length from 50 to 200 and 70 to 200 Kuhn steps, respectively, for flexible probe and hosts. Many trajectories lead to probe-host chain entanglement, an event believed responsible for the polyelectrolyte size discrimination observed in actual experiments. Chain distortions in response to such entanglement frequently produce double hairpin configurations that persist until the shortest hairpin arm slides past the locus of entanglement. Average probe velocity exhibits a minimum when probe and host chain lengths are nearly equal. The minimum reflects an interplay of two effects: the average duration of entanglement, which by increasing with probe length reduces mobility, and the average displacement of an entanglement, which by increasing with probe length raises mobility.