Polyelectrolytes in electric fields: measuring the dynamical effective charge and effective friction

Abstract

We use a coarse-grained molecular dynamics model to study the electrophoretic behaviour of flexible polyelectrolyte chains. We first characterize the static properties of the model with respect to the chain length, the polyelectrolyte concentration, additional salt and the influence of an applied external field. Next we investigate the dynamic behaviour in the oligomer range and find excellent correspondence of simulations to experimental observations when hydrodynamic interactions are accounted for in the simulations. We then present novel estimators for the dynamical effective charge during free-solution electrophoresis and compare them to static estimators. We find complete agreement between the static and the dynamic estimators. We further evaluate the scaling behaviour of the effective friction of the polyelectrolyte-counterion complex with the surrounding fluid. We identify a hydrodynamic screening length beyond which the friction during electrophoresis is linear depending on the chain length resulting in a constant mobility for long polyelectrolyte chains. Our results show a convincing agreement with experimental data and demonstrate that it is possible to model dynamic behaviour of polyelectrolytes using coarse-grained models, provided they include the effects of hydrodynamical interactions.