Polyelectrolyte dynamical self-consistent field theory

Recent experiments that examine the reconstitution of proteins into artificial triblock copolymer membranes have implicated a charge-driven reconstitution mechanism. As a first step to model the dynamics of this mechanism, we incorporate electrostatic interactions into dynamical self-consistent field theory. We begin with microscopic Langevin equations for interacting polyelectrolytes, solvent, and counterions. These equations are recast as a dynamical functional integral over collective field variables. We then make a saddle-point approximation, leading to a coupled set of dynamical mean field equations which includes the Poisson equation governing the electrostatic potential. Our approach reduces the interacting many-chain problem to a single polyelectrolyte chain in a dynamical mean force field. This simplification enables us to probe a broad range of length- and time-scales. We simulate the dynamics of insertion of a charged triblock copolymer (a model protein) into an oppositely-charged, self-assembled, triblock copolymer membrane.