Delayed collapse transitions in a pinned polymer system

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 ??-point separating the coil from the globule phase is located by a crossover in (R2g)/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 ??X depending linearly upon X. The total collapse time scales with N as ??c - ??XN1.60??0.03, which implies ??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 Nc(t) grows in time as tz, 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.

Automated summary

Using Langevin dynamics simulations, we investigated the kinetics of collapse transition in free and pinned polymers. Pinning the central monomer has negligible effects on the kinetics, while pinning other monomers causes a delay in the process. The total collapse time scales with the polymer length and is maximum when an end monomer is pinned. The average cluster size of pinned polymers shows two time regimes and deviates from that of free polymers.