Kinetics of Polymer Expansion Released from a Confined Cavity

Understanding releasing mechanism of genetic materials such as DNA or RNA chains from a viral capsid is important. It helps researchers to design efficient vectors for gene therapy and drug delivery. In this study, we develop a two-stage model to explain expansion phenomena of an enclosed chain freely released from a cavity. In the first stage, the chain is presumed to expand with a spherical structure while in the second stage, it expands like a coil. The kinetic equation for the evolution of the chain size is derived in the two stages via Onsager's variational principle. The theory is then verified by performing extensive Langevin dynamics simulations. We find that the expansion process is dominated by the second stage, and the variation of chain size follows the predicted curve which depends on the chain length. It allows us to define the principal expansion time for the process. Scaling analysis shows that the chain does undergo a coil expansion in the second stage but in the first stage, the presumed spherical structure is not truly held. Nonetheless, the variation of the chain size can be still approximated by the derived equation for the first stage. The characteristic time and the associated scaling exponents are analyzed in detail and compared with the theory. A universal route for the chain expansion is proposed at the end.