Polymer Ejecting from a Cavity through a Nanochannel into a Semi-Infinite Space*

The outstanding problem of a polymer ejecting spontaneously from a confining cavity into an outer semi-space through a nanochannel is investigated. A two-stage model, which divides the process into the confined and the non-confined stages, is developed. By using the Onsager's variational principle, ejection velocity is derived in the two stages. The decrease of the number of the monomers in the cavity can be calculated by solving the kinetics equations. The scaling properties of the ejection velocity and the ejection time are carefully studied. The theory is then verified by performing molecular dynamics simulations. We vary systematically the chain length and the cavity size, and explore the scaling behaviors over the entire parameter spaces. An astonishing stalling behavior is observed at the beginning of a process. We are able to identify the behavior as a pre-stage related to the transportation of the heading monomers through the channel. By varying the channel length, we show that the pre-stage is analogous to a nucleation process and can be treated as a Kramers escape problem. After the pre-stage, the ejection process goes smoothly and can be properly described by the two-stage model. Physical pictures behind different ejection conditions are stated. This study provides deep insight into the complicated phenomena of biopolymer ejection occurred in nature and in applications.