Conformational behavior of a single polymer chain confined by a two-dimensional harmonic potential in good solvents

Monte Carlo simulations have been conducted to investigate the conformational behavior of a flexible chain polymer confined to a two-dimensional harmonic potential. The polymer molecule is modeled as a tangent hard sphere chain, and the two-dimensional harmonic potential is chosen to mimic nonrigid cylindrical pores. The simulations show that as field strength is increased, the mean chain dimension decreases first and then increases again after passing a minimum due to anisotropic deformation. A modified Flory-type theory is utilized to derive the power laws for the chain deformation against the strength of the applied field in different directions. These power laws agree with the simulations at strong fields when the confined polymer molecule exhibits a rodlike conformation. Meanwhile, a simple model, consisting of a dimer in a two-dimensional harmonic potential, is solved to elucidate the alignment of chain segments in very strong applied potentials. From this model, the crossover regime of a tangent hard sphere chain from the rodlike chain to a totally stretched chain at limiting strong fields is identified. Furthermore, a first-order perturbation theory is employed to interpolate the mean chain size for different field strengths. The field strength corresponding to the minimum mean chain size decreases as chain length is increased, consistent with the prediction of the modified Flory-type theory. These studies provide physical insights into the conformational behavior of a flexible polymer chain in nonspherical two-dimensional harmonic potentials.