An efficient Kinetic Monte Carlo to study analyte capture by a nanopore: Transients, boundary conditions and time-dependent fields

To better understand the capture process by a nanopore, we introduce an efficient Kinetic Monte Carlo (KMC) algorithm that can simulate long times and large system sizes by mapping the dynamic of a point-like particle in a 3D spherically symmetric system onto the 1D biased random walk. Our algorithm recovers the steady-state analytical solution and allows us to study time-dependent processes such as transients. Simulation results show that the steady-state depletion zone near pore is barely larger than the pore radius and narrows at higher field intensities; as a result, the time to reach steady-state is much smaller than the time required to empty a zone of the size of the capture radius $\lambda_e$. When the sample reservoir has a finite size, a second depletion region propagates inward from the outer wall, and the capture rate starts decreasing when it reaches the capture radius $\lambda_e$. We also note that the flatness of the electric field near the pore, which is often neglected, induces a traffic jam that can increase the transient time by several orders of magnitude. Finally, we propose a new proof-of-concept scheme to separate two analytes of the same mobility but different diffusion coefficients using time-varying fields.