  The electrophoretic behaviour of flexible polyelectrolyte chains ranging from
single monomers up to long fragments of hundred repeat units is studied by a
mesoscopic simulation approach. Abstracting from the atomistic details of the
polyelectrolyte and the fluid, a coarse-grained molecular dynamics model
connected to a mesoscopic fluid described by the Lattice Boltzmann approach is
used to investigate free-solution electrophoresis. Our study demonstrates the
importance of hydrodynamic interactions for the electrophoretic motion of
polyelectrolytes and quantifies the influence of surrounding ions. The
length-dependence of the electrophoretic mobility can be understood by
evaluating the scaling behavior of the effective charge and the effective
friction. The perfect agreement of our results with experimental measurements
shows that all chemical details and fluid structure can be safely neglected,
and a suitable coarse-grained approach can yield an accurate description of the
physics of the problem, provided that electrostatic and hydrodynamic
interactions between all entities in the system, i.e., the polyelectrolyte,
dissociated counterions, additional salt and the solvent, are properly
accounted for. Our model is able to bridge the single molecule regime of a few
nm up to macromolecules with contour lengths of more than 100 nm, a length
scale that is currently not accessible to atomistic simulations.
