Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties

Abstract

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Scheme 1. Illustration of the Interdependence between Structural and Dynamical Properties in Poylmer Systems at Different Length and Time Scales, From a Microscopic Bottom-Up Perspective. Each Item in This Scheme Represent One of the Representative System Property on Corresponding Scale

Note that we are not trying to include all system properties in this scheme.

Scheme 2. Illustration of the 1:1 CG Mapping Scheme for PS, Where Each Monomer Is Represented by a CG bead

VMD package^, is used for visualization.

Scheme 3. Iterative Optimization Procedure of the Memory Kernel

Figure 1

Intermediate (a) memory kernels and (b) velocity ACFs during iteration using eq 13. After 90 iterations, we switch to use eq 16 for another 40 iterations. Changes of memory kernel are shown in (c), and the resulted velocity ACFs are compared in (d).

Figure 2

(a) MSD curves, (b) velocity ACFs, and (c) force ACFs calculated from AA simulation, GLE simulation with the final optimized kernel, LE simulation with ζ_eff^* and CG simulation without any friction, respectively.

Figure 3

(a) Self-VHF and (b) distinct VHF for AA reference (solid line) and the GLE model (dashed line).

Figure 4

Incoherent ISF F_s(q, t) calculated from different simulations, as a function of time. Different q values are used to represent multiple spatial scales: (a) q = 18q₀, (b) q = 14q₀, (c) q = 9q₀, and (d) q = 5q₀, with q₀ = 2π/L and L = 7.22 nm.

Figure 5

Comparison of the stress relaxation modulus G(t) calculated from GLE and AA simulations.

Figure 6

(a) RDF, (b) bond length distribution, and (c) angle distributions between CG beads calculated from AA simulation, GLE simulation with the final optimized kernel, and CG simulation without any friction, respectively.