Conformationally averaged iterative Brownian dynamics simulations of semidilute polymer solutions

Abstract

The dynamics of semidilute polymer solutions are important to many polymer solution processing techniques such as fiber spinning and solution printing. The out-of-equilibrium molecular conformations resulting from processing flows directly impact material properties. Brownian dynamics (BD) simulations are a standard technique for studying this connection between polymer conformations in solution and processing flows because they can capture molecular-level polymer dynamics. However, BD simulations of semidilute polymer solutions are computationally limited by the calculation of hydrodynamic interactions (HIs) via an Ewald summed diffusion tensor and stochastic Brownian displacements via the decomposition of the diffusion tensor. Techniques based on the Cholesky decomposition scale with the number of particles N as O(N3) and approximations in the literature have reduced this scaling to as low as O(N). These methods still require continuous updating of the diffusion tensor and Brownian displacements, resulting in a significant constant per-time step cost. Previously, we introduced a method that avoids this cost for dilute polymer solutions by iterative conformational averaging (CA) of intramolecular HIs. In this work, we extend the CA method to semidilute solutions by introducing a grid-space average of intermolecular HIs and a pairwise approximation to the Brownian displacements based on the truncated expansion ansatz of Geyer and Winter. We evaluate our method by first comparing the computational cost with that of other simulation techniques. We verify our approximations by comparison with expected results for static and dynamic properties at equilibrium and use our method to demonstrate the concentration dependence of HI screening.

Simulation of semidilute polymer solutions in planar extensional flow via conformationally averaged Brownian noise

“…The CA method approaches the full BD simulation upon another iteration w = 2, indicating the errors in the w = 1 iteration arise from conformationally averaging the Brownian noise over the While there is noise in the measurement, similar fluctuations are observed even in the dilute case and there is no observable trend in the error of the CA method. Solution stress is highly sensitive to preaveraging approximations, 14,19,75 so this is a promising result validating the accuracy of our CA approach.…”

“…While there are inherent approximations in the TEA, 67 we have previously shown that these lead to only small errors in the static polymer size and do not alter dynamic properties relative to simulations using the Krylov subspace. 75 We expect the method to match best in this case as shown by theory and our previous simulations, 74,75 which focus on steady state dynamics. We consider the ensemble average fractional extension projected along the axis of flow extension, ∆x f /L = (max({x i }) − min({x i }))/L, where L is the contour length.…”

“…74 We have also extended the method to semidilute equilibrium systems by utilizing a discrete approximation to the RPY tensor for intermolecular HI to account for fluctuations as chain center of masses diffusive relative to each other over time. 75 We have also constructed the Brownian noise to be consistent with these fluctuations using a modified version of the truncated expansion ansatz (TEA). 67 The semidilute CA method then quantitatively reproduces diffusion constant results of traditional BD simulations using the TEA, and also reproduces static properties and zero-shear viscosity from simulations using the Krylov subspace decomposition up to small quantitative differences.…”

“…75 In this method, the conformationdependent diffusion tensor is replaced by a single diffusion tensor, averaged over the non-equilibrium polymer conformations. 74,75 In this work, we extend the CA method to semidilute solutions in planar extensional flows. Notably, we no longer preaverage the intramolecular HI over the out-of-equilibrium polymer conformation, which is important for adequately sampling the broad conformational distributions in semidilute solutions.…”

“…Effectively, only the Brownian noise remains conformationally averaged in this approach, which retains the computational speedup of the equilibrium semidilute CA method. 75 In this paper, we use the semidilute, out-of-equilibrium CA method to perform detailed investigation of polymer dynamics in planar extensional flow. The remainder of the article is organized as follows: In Section II A we state the governing equations for BD simulations.…”