Temperature Transferable and Thermodynamically Consistent Coarse-Grained Model for Binary Polymer Systems

Abstract

For the simulations of polymer systems, coarse-grained (CG) models are often developed to tackle the length and time scale limitations that are not feasible by all-atom molecular dynamic simulations. However, due to the necessary simplification or reduction in atomistic degrees of freedom, CG models usually have poor transferability over various temperatures, compositions, or thermodynamic states. In this work, the structure-based iterative Boltzmann inversion (IBI) method is further developed to obtain temperature transferable and thermodynamically consistent CG potentials for binary polymer systems. In particular, the conventional IBI procedure is first utilized to optimize single-component CG potentials from homopolymer systems while cross-interaction potentials from a random block copolymer system. Afterward, a thermodynamic integration method is applied to refine the cross-interaction potential between two constituent components in binary systems until the Flory−Huggins parameter (χ) between two components is matched with experimental value. We apply the above optimization procedure for the polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) as an example, which is widely studied experimentally, and the χ value can be easily obtained in the literature. To validate the transferability of the obtained CG potential, systems of both PS and PMMA homopolymers, random block copolymers, diblock copolymers, and PS/PMMA blends with various compositions are simulated. Many properties, including the mass density, radius distribution function, and bonded distribution functions, between CG beads generated from CG simulations match very well with those from atomistic simulations in the simulated temperature range, i.e., from 453 to 500 K. More importantly, phase morphologies of diblock copolymers and phase diagram of PS/PMMA binary blends over wide temperature and compositional ranges generated from CG simulations using our model are in good agreement with experimental results and predictions from self-consistent field theory.

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

“…In this study, a previously developed CG PS model derived from the IBI method is adopted. More details about IBI method can be found elsewhere. ,, In brief, a 1:1 CG mapping scheme as illustrated in Scheme is used, i.e., one CG bead represents one styrene monomer. The CG bead is located at the center of mass of the monomer.…”

Manipulating the Void Nucleation and Propagation in Silica Nanoparticle/Polyisoprene Nanocomposites via Grafted Chains: A Multiscale Simulation

“…Thus, the total CG potential is divided into two independent contributions: U total CG = U nonbonded CG + U bonded CG . The initial CG potentials are derived via the Boltzmann inverse of the target structural distribution of the bond length P CG ( l ), bending angle P CG (θ), the dihedral angle P CG (ϕ), and the nonbonded distance g ref ( r ) from AA simulation, which are as follows: where k B is the Boltzmann constant; l , θ, ϕ, and r represent the bond length, bending angle, dihedral angle, and nonbonded distance, respectively; and l 2 and sin θ are metric factors for bond and angle terms, respectively. , A new structural distribution is obtained based on the initial potential function of the CG model, which generally deviates from the target distribution. Therefore, it is necessary to optimize the potential function via repeated iterations by using the following equation: where P i ( q ) and U i CG ( q ) denote the probability distribution and potential of mean force, respectively, along the coordinate q at the i th iteration.…”

“…where k B is the Boltzmann constant; l, θ, ϕ, and r represent the bond length, bending angle, dihedral angle, and nonbonded distance, respectively; and l 2 and sin θ are metric factors for bond and angle terms, respectively. 38,46 A new structural distribution is obtained based on the initial potential function of the CG model, which generally deviates from the target distribution. Therefore, it is necessary to optimize the potential function via repeated iterations by using the following equation:…”

“…Thus, the total CG potential is divided into two independent contributions: U total CG = U nonbonded CG + U bonded CG . The initial CG potentials are derived via the Boltzmann inverse of the target structural distribution of the bond length P CG ( l ), bending angle P CG (θ), the dihedral angle P CG (ϕ), and the nonbonded distance g ref ( r ) from AA simulation, which are as follows: U bond CG ( l ) prefix= prefix− k B T 0.25em ln ( P CG false( l false) / l 2 ) U angle CG ( θ ) prefix= prefix− k B T 0.25em ln ( P CG false( θ false) / sin ⁡ θ ) U dihedral CG ( ϕ ) prefix= prefix− k B T 0.25em ln nobreak0em0.25em⁡ P CG ( ϕ ) U nonbonded CG ( r ) prefix= prefix− k B T 0.25em ln nobreak0em0.25em⁡ g ref ( r ) where k B is the Boltzmann constant; l , θ, ϕ, and r represent the bond length, bending angle, dihedral angle, and nonbonded distance, respectively; and l 2 and sin θ are metric factors for bond and angle terms, respectively. , A new structural distributi...…”

Temperature-Transferable Coarse-Grained Models for Volumetric Properties of Poly(lactic Acid)

“…More than two decades ago, coarse graining was proposed to extend the space-time scales of MD simulations for investigating soft materials. − Hitherto, numerous multiscale modeling schemes have been developed for coarse-graining various polymers (such as dendrimers, , cross-linked networks, , blends, − nanocomposites, − solutions, , etc.). Generally, these schemes share two common steps in order: first, a mapping scheme is chosen to reduce the AA structural model to its CG counterpart; second, the interbead interaction potentials are derived.…”