Effect of Cylindrical Confinement on the Collapse Dynamics of a Polymer

Structure and dynamics of a polymer under confinement gets significantly altered due to the imposed geometric restrictions. Using molecular dynamics simulations, here, we explore the effect of cylindrical confinement on the kinetics of collapse of a homopolymer, when the solvent condition is abruptly changed from good to poor. The observed phenomenology for a range of the cylinder radius $R$, reveals two distinct stages of the collapse. The first stage is highlighted by the formation and growth of local connected clusters resembling a pearl necklace, eventually ending with a single sausage-like cluster. In the second stage, the sausage-like intermediate approaches a spherical globule via surface-energy minimization. These two stages are disentangled using a shape parameter of the individual pearls or clusters, allowing us to also extract the respective relaxation times, and thereby their scaling behaviors with respect to the length of the polymer. We find that the pearl-necklace relaxation time $\tau_p$ is independent of $R$. On the other hand, the sausage-relaxation time $\tau_s$ varies inversely up to a certain $R$, beyond which it also saturates. From the Arrhenius plots of the temperature dependence of $\tau_p$ and $\tau_s$, we extract the activation energies $E_{\rm a}$ of the two stages. While the estimated $E_{\rm a}$ for the pearl-necklace stage is independent of $R$, for the sausage relaxation it is significantly higher in the strongly confined case than in the weakly one. Surprisingly, at a fixed temperature, the growth of the average cluster size obeys a universal power law irrespective of $R$. However, for a fixed $R$, the behavior is rather non-universal with respect to temperature. We propose viable scenarios for experimental realization of polymer collapse inside cylindrical nanochannels.