Delayed collapse transitions in a pinned polymer system.

Abstract

Employing Langevin dynamics simulations, we investigated the kinetics of the collapse transition for a polymer of length N when a particular monomer at a position 1≤X≤N is pinned. The results are compared with the kinetics of a free polymer. The equilibrium θ-point separating the coil from the globule phase is located by a crossover in 〈R_{g}^{2}〉/N plots of different chain lengths. Our simulation supports a three-stage mechanism for free and pinned polymer collapse: the formation of pearls, the coarsening of pearls, and the formation of a compact globule. Pinning the central monomer has negligible effects on the kinetics as it does not break the symmetry. However, pinning a monomer elsewhere causes the process to be delayed by a constant factor ϕ_{X} depending linearly upon X. The total collapse time scales with N as τ_{c}∼ϕ_{X}N^{1.60±0.03}, which implies τ_{c} is maximum when an end monomer is pinned (X=1 or N), while when pinning the central monomer (X=N/2) it is minimum and identical to that of a free polymer. The average cluster size N_{c}(t) grows in time as t^{z}, where z=1.00±0.04 for a free particle, whereas we identify two time regimes separated by a plateau for pinned polymers. At longer times, z=1.00±0.04, while it deviates in early time regimes significantly, depending on the value of X.