Dynamics of Polymer Ejection from a Nano-sphere

Polymer ejection from nano-confinement has been of interest due to its relation to various fundamental sciences and applications. However, the ejection dynamics of a polymer with different persistence lengths from confinement through a nanopore is still poorly understood. In this manuscript, a theory is developed for the ejection dynamics of a polymer with the total length $L_0$ and persistence length $l$ from a sphere of diameter $D$. These length-scales specify different regimes, which determine the polymer dynamics and its ejection rate. It is seen that the polymer undergoes between two to three confinement regimes, in some cases. The total ejection time $\tau$ depends on the polymer dynamics in various relevant regimes that the polymer experiences. Dependence of the ejection time on the system parameters is discussed according to the theory. The theory predicts that $\alpha$ in $\tau \sim L_0^{\alpha}$ changes between 1 and 1.7, $\beta$ in $\tau \sim D^{\beta}$ changes between 3 and 5, and $\gamma$ in $\tau \sim l^{\gamma}$ is often smaller than 1, in the studied range of the parameters.