Conformational Averaging as a Route To Understanding Out-of-Equilibrium Polymer Solutions in Flow

Solution-processing methods typically involve polymer concentrations in the semidilute range, where polymer coils impinge on each other and ‘overlap’. This is particularly true when polymers are driven out-of-equilibrium by strong processing flows, and polymer dimensions are extended in the flow direction. Despite the practical importance of such systems, they are difficult to simulate due to the computational expense required to include hydrodynamic interactions (HI); yet, HI is necessary to capture the correct polymer dynamics. We have developed a new “Conformational Averaging” (CA) method for incorporating HI into semidilute polymer dynamics, in a way inspired by classical theoretical efforts in single-molecule kinetic theory. CA is an iterative procedure that uses an averaged hydrodynamic tensor in Brownian Dynamics simulation, which is used to get a new hydrodynamic tensor averaged over the simulation trajectory. We are able to simulate semidilute solutions rapidly, and explore molecular diffusion and relaxation, as well as hydrodynamic screening. We show standard scaling laws in equilibrium, including how HI screening length behaves as polymer concentration increases. We also demonstrate how polymers stretch in semi dilute solutions under steady-state flow conditions, and how this affects the behavior of hydrodynamic screening.