Expansion Kinetics of Flexible Polymers upon Release from a Disk-Shaped Confinement

A general theory is developed to explain the expansion kinetics of a polymer released from a confining cavity in a d-dimensional space. At beginning, the decompressed chain undergoes an explosive expansion while keeping the structure resembling a sphere. As the process continues, the chain transitions to a coil conformation, and the expansion significantly slows down. The kinetics are derived by applying Onsager's variational principle. Computer simulations are then conducted in a quasi-two-dimensional space to verify the theory. The average expansion of the chain size exhibits a distinctive sigmoidal variation on a logarithmic scale, characterized by two times and associated exponents that represent the fast and the slow dynamics, respectively. Through an analysis of the kinetic state diagrams, two important universal behaviors are discovered in the two expansion stages. The intersection of the expansion speed curves allows us to define the crossover point between the stages and study its properties. The scaling relations of the characteristic times and exponents are thoroughly investigated under different confining conditions, with the results strongly supporting the theory. Additional calculations conducted in a three-dimensional (3D) space demonstrate the robustness of the proposed theory in describing the kinetics of polymer expansion in both 2D and 3D spaces.