Expansion Kinetics of Single Polymers Released from 2D and 3D Cavities under Theta-Solvent Conditions

Pai-Yi Hsiao^1*

¹Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Pai-Yi Hsiao, email:pyhsiao@ess.nthu.edu.tw

The expansion of biopolymers released from a confined state is a crucial process in microbiology and nanotechnology applications. In this study, we investigate the kinetics of this process using computer simulations in d-dimensional spaces. We employ a freely-jointed chain model to simulate theta-solvent conditions through Langevin dynamics. Initially, we confine a chain within a cavity; the shape of the cavity is circular for d=2 and spherical for d=3. The process commences when the confining wall is instantaneously removed, resulting in a free expansion of the chain. We find that the expansion can be divided into two distinct stages. In the first stage, the chain expands rapidly while maintaining a globular conformation, referred to as “globule expansion.” In the second stage, the expansion slows down, and the chain gradually transforms into a coil-like structure, known as the “coil expansion” stage. By varying the chain length and the diameter of the confining cavity, we explore the scaling behavior of chain size and calculate the characteristic times and exponents related to the two expansion stages. We develop a robust theoretical framework, deriving the kinetic equations for both stages using Onsager’s variational principle. The predictions of our theory are carefully validated through simulations. (Funding: NSTC 112-2112-M-007-019 and NSTC 113-2112-M-007-010)

Keywords: expansion kinetics, scaling theory, polymer physics, Langevin dynamics simulations