Expansion Kinetics of Single Flexible Polymers upon Release from a Circular Cavity in Three- and Two-Dimensional Spaces

In this study, we investigate the behavior of single polymers when they are instantaneously released from a spherical confinement in a d-dimensional space. We develop a compelling theory to explain the intricate kinetics of the expansion process, which can be divided into two main stages. During the first stage, the chain undergoes a rapid expansion while maintaining its structure as a sphere. In the second stage, the expansion process slows down significantly, and the chain assumes a coil-like conformation. The kinetics of the expansion are derived by using Onsager's variational principle. Molecular dynamics simulations are then conducted to examine the theory in both quasi-2D and three-dimensional spaces. The average time evolution of the chain size displays a featured sigmoidal variation on a logarithmic scale, characterized by two times and associated exponents that represent the fast and slow dynamics, respectively. Through a direct analysis of the kinetic equations, we discover two important and unique universal behaviors for the two expansion stages. We also investigate the scaling properties of the characteristic times and exponents under different confinement conditions. The results confirm the validity of our theory, demonstrating its robustness in describing the kinetics of polymer expansion in both two- and three-dimensional spaces.