Escape transition of a polymer chain: Phenomenological theory and Monte Carlo simulations

Abstract

The escape transition of a polymer mushroom (i.e., a flexible polymer chain of length N end-grafted onto a flat repulsive surface), occurring when a piston of radius R which is much larger than the size of the mushroom (R₀≈aN^ν, here a is the segment length and ν≈3/5) but much smaller than the linearly stretched chain (R_max=aN), compresses the polymer to height H, is investigated for good solvent conditions. We argue that in the limit of N→∞ a sharp first-order type transition emerges, characterized in the isotherm force fvs. height H by a flat region from H_esc,t=Ĥ₁[N/(R/a)]^ν/(1-ν) to H_imp,t=Ĥ₂[N/(R/a)]^ν/(1-ν), with (Ĥ₂-Ĥ₁)/Ĥ₁≈0.26.

Monte Carlo methods are developed (combining configurational bias methods with pivot- and random-hopping moves) which allow the study of this transition for chain lengths up to N=1024. It is found that even for such long chains the transition is still slightly rounded. The expected scaling of the transition heights with N and R is nevertheless verified. We show that the transition shows up via a double-peak structure of the radial distribution function of the monomers underneath the piston.