Electrophoretic mobilities of counterions and a polymer in cylindrical pores

We have simulated the transport properties of a uniformly charged flexible polymer chain and its counterions confined inside cylindrical nanopores under an external electric field. The hydrodynamic interaction is treated by describing the solvent molecules explicitly with the multiparticle collision dynamics method. The chain consisting of charged monomers and the counterions interact electrostatically with themselves and with the external electric field. We find rich behavior of the counterions around the polymer under confinement in the presence of the external electric field. The mobility of the counterions is heterogeneous depending on their location relative to the polymer. The adsorption isotherm of the counterions on the polymer depends nonlinearly on the electric field. As a result, the effective charge of the polymer exhibits a sigmoidal dependence on the electric field. This in turn leads to a nascent nonlinearity in the chain stretching and electrophoretic mobility of the polymer in terms of their dependence on the electric field. The product of the electric field and the effective polymer charge is found to be the key variable to unify our simulation data for various polymer lengths. Chain extension and the electrophoretic mobility show sigmoidal dependence on the electric field, with crossovers from the linear response regime to the nonlinear regime and then to the saturation regime. The mobility of adsorbed counterions is nonmonotonic with the electric field. For weaker and moderate fields, the adsorbed counterions move with the polymer and at higher fields they move opposite to the polymer's direction. We find that the effective charge and the mobility of the polymer decrease with a decrease in the pore radius.