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

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 p iston of radius R which is much larger than the size of the mushroom (R-0 a pproximate to aN(v), here a is the segment length and v approximate to 3/5) but much smaller than the linearly stretched chain (R-max = aN), compresse s the polymer to height H, is investigated for good solvent conditions. We argue that in the limit of N --> infinity a sharp first-order type transiti on emerges, characterized in the isotherm force f vs. height H by a flat re gion from H-esc,H- t = (H) over cap(1)[N/(R/a)](v/(1 - v)) to H-imp,H- t = (H) over cap(2)[N/(R/a)](v/(1 - v)), with ((H) over cap(2) - (H) over cap(1 ))/(H) over cap 1 approximate to 0.26. Monte Carlo methods are developed (combining configurational bias methods w ith pivot- and random-hopping moves) which allow the study of this transiti on for chain lengths up to N = 1024. It is found that even for such long ch ains 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.