Confinement free energy for a polymer chain: Corrections to scaling

Abstract

Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior Δ F/ N ∼ D− γ with γ ≈ 1.70, where Δ F is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving Δ F/ N ∼ D− γ(1 − h( N, D)), where the correction-to-scaling term has the form h ∼ D y/ NΔ with exponents y = 3 − γ ≈ 1.30 and Δ = 3/ γ − 1 ≈ 0.76. To test these scaling predictions, we carry out Wang–Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/ σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).