Pattern recognition by polyelectrolytes

Abstract

The statistical mechanical problem of recognition of different patterns imprinted on a surface by polyelectrolyte chains is studied. The necessary condition for the binding of a polyelectrolyte in a salt solution to an oppositely charged pattern is derived in terms of the charge densities of the polymer and the pattern, Debye length, characteristic size of the pattern, and the molecular weight of the polymer. The key features of the criterion for the binding are supported by Monte Carlo simulations. We find the kinetics of the recognition process to take place in two distinct stages: a fast complexation without registry and a very slow occurrence of registry. We show that the distance between different trajectories in the second stage diverges with time due to the untimely minimization of temporal free energy.