Kinetics of Single Chain Expansion upon Release from a Cavity in Theta-Solvent Conditions

The expansion of biopolymers, released from a confined state, is a significant process in microbiology and nanotechnology applications. In this study, we explore the kinetics of this process through computer simulations. We utilize a freely-jointed chain model to simulate theta-solvent conditions using Langevin dynamics. Initially, we confine a chain within a spherical cavity and allow it to reach equilibrium. The process begins when the confining wall is instantaneously removed, leading to free expansion of the chain. We observe that the expansion unfolds in two distinct stages. During the first stage, the chain expands rapidly while maintaining a globular conformation, which we refer to as "globule expansion." In the second stage, the expansion decelerates, and the chain shape gradually transforms into a coil-like structure, termed the "coil expansion" stage. By varying the chain length and the diameter of the confining cavity, we investigate the scaling behavior of chain size variations and compute the characteristic times and exponents associated with the two expansion stages. A robust theoretical framework is developed, and the kinetic equations for the both stages are derived using Onsager's variational principle. The predictions derived from the theory are validated through the simulations.