Chauhan, KeertiSingh, Ankit2025-01-272025-01-27202224700045https://dl.bhu.ac.in/ir/handle/123456789/13638Employing 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 (Rg2)/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 fX depending linearly upon X. The total collapse time scales with N as tc~fXN1.60�0.03, which implies tc 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. � 2022 American Physical Society.Articlehttps://doi.org/10.1103/PhysRevE.105.064505