Escape Transition of a Grafted Polymer Chain

Abstract

The escape transition of a flexible polymer chain of chain length N, end-grafted at a hard wall and compressed by a piston of radius R in good solvent conditions, is studied by Monte Carlo simulation and by phenomenological arguments. In contrast to previous theories which have predicted a jump in the force f at a critical value H _t of the height H of the piston above the wall, we find that the transition (which is sharp only for N → ∞) is characterized by a flat region of f in the f — H isotherm, i. e. a jump in the height occurs at the transition from H _esc , _t to H _imptt , with (H _imp , _t — H _esc , _t )/H _esc , _t ≈ 0.26. At the transition the constant force f _t is predicted and observed to scale with R and N as f _t ∝ ${R^{\frac{{1 + v}}{{1 - v}}}}/{N^{\frac{{2v}}{{1 - v}}}}$ where the Flory exponent v ≈ 0.589.