Fraenkel Springs as an Efficient Approximation to Rods for Brownian Dynamics Simulations and Modeling of Polymer Chains

Abstract

AbstractRecent studies indicate the importance of using bead‐rod models for polymer chains, resolving to a single Kuhn step, especially in strong flows. Earlier, researchers suggested the Fene‐Fraenkel spring as a computationally efficient approximation to the rod for Brownian dynamics (BD) simulations. This analysis reveals that the Fraenkel spring is an even better alternative. The predictions from BD simulations with stiff Fraenkel springs are nearly identical to those using Fene‐Fraenkel springs and rigid rods. Significantly, such excellent agreement is obtained when the spring lengths at every time step are updated once, without any further iterations for refinement. The computational speeds for single‐step update of the spring lengths, using Fraenkel springs, is an order of magnitude faster than the usual procedure of iterating until convergence. Even when multiple iterations are allowed within each time step, the computational time remains about 20–25% lower for longer chains with Fraenkel springs than Fene‐Fraenkel springs. The merits of using highly resolved chains, using Fraenkel springs, in preaveraged models are also highlighted. The predictions of such preaveraged models agree reasonably well with BD simulations. This is particularly advantageous since the predictions for shear flows are poor, especially at higher shear rates, for well‐known models like FENE‐P.