Energy renormalization for coarse-graining polymers having different segmental structures

Abstract

Multiscale coarse-grained (CG) modeling of soft materials, such as polymers, is currently an art form because CG models normally have significantly altered dynamics and thermodynamic properties compared to their atomistic counterparts. We address this problem by exploiting concepts derived from the generalized entropy theory (GET), emphasizing the central role of configurational entropy sc in the dynamics of complex fluids. Our energy renormalization (ER) method involves varying the cohesive interaction strength in the CG models in such a way that dynamic properties related to sc are preserved. We test this ER method by applying it to coarse-graining polymer melts (i.e., polybutadiene, polystyrene, and polycarbonate), representing polymer materials having a relatively low, intermediate, and high degree of glass “fragility”. We find that the ER method allows the dynamics of the atomistic polymer models to be faithfully described to a good approximation by CG models over a wide temperature range.

Energy Renormalization for Coarse‐Graining Polymers with Different Fragilities: Predictions from the Generalized Entropy Theory

“…This direct comparison between the AA and CG models shows that the CG models without ER (or with fixed ε) cannot preserve the T ‐dependent AA τ α , which demonstrates the necessity of renormalizing ε under coarse‐graining to preserve the AA dynamics over a wide temperature range. This observation is also consistent with our recent CG studies based on MD simulations 22,27. The ER factor ε CG (i.e., the value of ε/ k B ) can thus be determined by demanding the τ α of the AA model to be consistent with that of the CG model with M = 6 at any given T .…”

“…ε CG is found to increase as the polymer is cooled toward T g . However, at higher T (i.e., above T A ), ε CG is expected to depend weakly on T , consistent with our previous CG‐MD simulations 22,27…”

“…We next turn to the issue of CG modeling of polymer melts within the framework of GET. The recent ER method provides an attractive approach for quantitatively describing the dynamics of the underlying AA polymer models under coarse‐graining over a wide temperature range 21,22,27. In the previous formulation of ER method, the CG models of polymers are developed by the exploiting the localization model of relaxation that relates the Debye–Waller factor (DWF; i.e., a fast‐dynamics property at a picosecond timescale) to τ α in MD simulations.…”

“…AA model thus has a value of λ = 1, considered to be a special case. In line with the common approach in the CG modeling of polymers,14,22 the total volume of a single chain is preserved to be a constant for varying λ. For instance, a value of λ = 4 indicates that four united‐atom groups in the AA model is clustered as one CG bead in the CG model (as illustrated in Figure 1), and accordingly, the cell volume parameter V cell for the CG model is four times that for the AA model to preserve the total volume or density.…”

“…To address this fundamental problem, we recently proposed a coarse‐graining strategy, called the energy‐renormalization (ER) approach, which aims to preserve essential dynamic properties of GF liquids to a good approximation 20–22. By borrowing ideas from the Adam–Gibbs (AG) theory16 and the more recent generalized entropy theory (GET) of glass formation,23 both of which emphasize the central role of configurational entropy in describing the dynamics of GF liquids, we introduce the ER factors to rescale the energy parameter ε in the cohesive interaction (based on the established “entropy–enthalpy compensation” effect)24–26 in a temperature dependent manner to recover the dynamics of polymers over a wide temperature range, that is, from the high‐temperature Arrhenius to low‐temperature supercooled and even glassy regimes 22,27. In the meantime, the rescaling of the length‐scale parameter σ in the cohesive interaction allows for preserving the atomistic density, a key thermodynamic property 27.…”