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

Abstract

The dynamics and rheology of semidilute polymer solutions in strong flows are of great practical relevance. Processing applications can in principle be designed utilizing the relationship between nonequilibrium polymer conformations and the material properties of the solution. However, the interplay between concentration, flow, hydrodynamic interactions (HI), and topological interactions which govern semidilute polymer dynamics are challenging to characterize. Brownian dynamics (BD) simulations are particularly valuable as a way to direct visualize how molecular interactions arise in these systems, and are quantitatively comparable to single-molecule experiments. However such simulations are often computationally intractable, and are limited by the need to calculate the correlated Brownian noise via decomposition of the diffusion tensor. Previously we have introduced an iterative conformational averaging (CA) method for BD simulations which bypasses these limitations by preaveraging the HI and Brownian noise in an iterative procedure. In this work, we generalize the CA method to flowing semidilute solutions by introducing a conformation dependent diffusion tensor and a strain dependent approximation to the conformationally averaged Brownian noise. We find that this approach nearly quantitatively reproduces both transient and steady state polymer dynamics and rheology while achieving an order of magnitude computational acceleration. We then utilize the CA method to investigate the concentration and flow rate dependence of polymer dynamics in planar extensional flows. Our results are consistent with previous experimental and simulation studies and provide a detailed view of broad conformational distributions in the semidilute regime. We observe interconversion between stretched and coiled states at steady state, which we conjecture occur due to the effect of concentration on the conformation dependent polymer drag. Additionally, we observe transient flow-induced intermolecular hooks in the startup of flow which lead to diverse and unique stretching pathways.

Recent progress in the science of complex coacervation

“…118 There have been very few examples of simulations of semidilute polymer dynamics, with most focusing on algorithmic advances to circumvent the otherwise-prohibitive computational cost of performing these calculations. [315][316][317][318][319] Thus, it remains unclear how feasible it is to perform molecular simulations of coacervates, with sufficient molecular resolution to see how e.g., small molecule ions may affect the dynamics observed in experiment. 320,321 The detailed motion of coacervate chains and ions represents a challenge, but also an opportunity to clarify the molecular interpretation of salt effects in coacervate dynamics.…”

Investigating the Transition between Polymer Melts and Solutions in Nonlinear Elongational Flow

“…As it has been discussed in refs. [52][53][54], a different concentration dependence of the steady viscosity could also be due to the emergence of local hydrodynamics when diluting the polymer chains, with the oligomers acting more and more like a good solvent. However, as it is shown in ref.…”

Dynamics and Rheology of Ring-Linear Blend Semidilute Solutions in Extensional Flow: Single Molecule Experiments

“…The Brownian noise ξi is approximated by the truncated expansion ansatz [65]. Evaluation of the diffusion tensor and Brownian noise is accelerated by the iterative conformational averaging method [66][67][68]. We simulate ring and linear polymers with an equal number of beads per chain N R = N L = 150.…”

“…Generally we consider N C = 128 chains per simulation, with the number of rings and linear chains chosen to match the blend ratios in experiments. Further details and verification of the method are available in previous work [67,68], and generalization to ring-linear polymer blends is described in a companion article [58].…”

“…SMFM can be used to identify and characterize molecular subpopulations of polymer chains that adopt different transient conformations or show molecular individualism in flow [43][44][45]. In recent years, SMFM has been used to study the dynamics of linear polymers in dilute solution large amplitude oscillatory extensional flow (LAOE) [46,47] and in semidilute unentangled solutions in extensional flow [48][49][50]. Single polymer dynamics was also used to study the relaxation of linear polymers in entangled solutions [51], revealing unexpectedly heterogeneous dynamics.…”