Effect of Cylindrical Confinement on the Collapse Dynamics of a Polymer

Abstract

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 $τ_p$ is independent of $R$. On the other hand, the sausage-relaxation time $τ_s$ varies inversely up to a certain $R$, beyond which it also saturates. From the Arrhenius plots of the temperature dependence of $τ_p$ and $τ_s$, 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.

Figures (9)

• Figure 1: Time-evolution snapshots of a polymer of length $N=1024$, undergoing collapse transition at temperature $T=1.0$, for three different cases -- a stretched bulk, and inside cylindrical confinement of radius $R=10$ and $4$. Here, and for all the subsequent plots concerning the stretched bulk case, $R$ refers to the radius of the cylinder where the equilibration at high $T$ is performed, before getting rid of the confinement for the quench to a low $T$. In the confined cases only the relevant portion of the infinitely long cylinders are shown. To obtain a clear view of the temporal changes of the polymer conformation, the appearances of the cylinder at different times are adjusted accordingly.
• Figure 2: Time dependence of the squared radius of gyration $R_g^2$ of a collapsing polymer at a temperature $T=1.0$, for different cases in (a)-(d), as mentioned. In each case, results for different chain lengths $N$ are presented.
• Figure 3: Time dependence of the average asphericity $A_c$ of individual clusters at a temperature $T=1.0$, for a collapsing polymer of length $N=1024$, under different conditions. Corresponding data (black dashed line) for the overall asphericity $A_3$ of a polymer under confinement of $R=10$ is also presented. The shades with different colors represent two stages of the collapse.
• Figure 4: (a) Dependence of the pearl-necklace relaxation time $\tau_p$ on the radius $R$ of the cylindrical confinement for polymers of different chain lengths $N$, at a fixed temperature $T=1.0$. (b) Scaling of $\tau_p$ with $N$, for both the confined and stretched-bulk polymer at two values of $R$. The dashed line represents the power-law scaling of the form in Eq. \ref{['equation:tau_p_scaling']} with $z_p=1.56$. The region shaded with lighter color marks the fitting range.
• Figure 5: (a) Dependence of the sausage relaxation time $\tau_s$ on the cylinder radius $R$ for confined polymers of different chain lengths $N$, at a fixed temperature $T=1.0$. (b) Scaling of $\tau_s$ with $N$, for both the confined and stretched bulk cases at two values of $R$. The dashed lines represent the power-law scaling of the form in Eq. \ref{['equation:tau_s_scaling']} with the quoted values of $z_s$. The region shaded with lighter color marks the fitting range.