Statistical properties of the electrophoretic collision of a long DNA molecule with a small obstacle

We present experimental results for the collision of a single λ-DNA molecule with isolated cylindrical nanoposts whose radii range from 350 nm to 1.37 μm. The experimental apparatus was fabricated in oxidized silicon using a plasma-thinning method. The probability density for the dimensionless holdup time is described by a gamma distribution, which accurately represents the behavior of the probability density for X collisions and U/J collisions for short-lived and long-lived collisions, respectively. The shape parameter of the gamma distribution reflects the nature of the short-lived collisions, whereas the scaling parameter captures the role of the finite size of the post on the U/J collisions. When rendered in an appropriate dimensionless form, the existing models for the role of electric field gradients extend to all post sizes, indicating that 350 nm is still well above the point-sized limit. Our experiments provide insights into a regime that is very challenging for numerical simulations but highly relevant for separation processes.