Introduction
SAFT-γ Mie, a group-contribution equation of state (EoS) rooted in Statistical Associating Fluid Theory1, provides an efficient framework for developing accurate, transferable coarse-grained polymer force fields for molecular dynamics (MD) simulation. Using this EoS, a Mie potential governing intermolecular interactions can be parameterized to reproduce experimental vapor-liquid equilibria (VLE) data of small-molecule analogues over a range of state points. Building on the success of SAFT-γ Mie force fields for small molecules modelled as tangentially bound spheres2,3, we address two key issues in extending the approach to polymers: 1) the treatment of chain rigidity neglected by the first-order thermodynamic perturbation theory used to derive SAFT-γ Mie, and 2) the disparity between the structure of linear chains of tangent spheres and the structure of the real polymers.
Modelling
In our hybrid top-down/bottom-up coarse-graining approach, we use Boltzmann inversion to derive effective bond-stretching and angle-bending potentials mapped from all-atom oligomer MD simulations to the coarse-grained sites, and a fused-sphere version of SAFT-γ Mie as the basis for nonbonded interactions. The introduction of an additional free energy parameter characterizing the degree of overlap between Mie spheres leads to a degeneracy when fitting to monomer VLE data, which we resolve by matching polymer density from coarse-grained MD simulation with that from all-atom simulation. The result is a chain of monomers rigorously parameterized to experimental VLE data and with structural detail consistent with all-atom simulations.
We apply our coarse-graining methodology to poly(ethylene) and poly(vinyl alcohol), and test its limits on a structurally complex copolymer system at an interface with amorphous silica. Interaction forces between monomers and silica slab are mapped from the Optimized Potentials for Liquid Simulations (OPLS) all-atom force field4,5 to an external potential acting on the coarse-grained beads. The tacticity of the underlying chain structure is preserved by assigning stereo-specific angle potentials to triads of coarse-grained beads, and co-monomer sequence-dependent behavior can be studied, features not achievable with SAFT-γ Mie alone. Coarse-grained bulk polymer melt simulations successfully reproduced experimental density, glass transition temperature, and local structural distributions mapped from the all-atom level. For the interfacial system, we investigate the effects of co-monomer sequence distribution on adhesion strength and interfacial structure.
Conclusions
We present a new strategy for developing coarse-grained force fields for polymer melts using the fused-sphere SAFT-γ Mie EoS. Nonbonded interactions parameterized to monomer experimental VLE data and bonded potentials derived from all-atom chains result in a model that is capable of accurately reproducing both thermodynamic and structural properties of polymer melts. We demonstrate the utility of our approach for studying complex copolymer systems in which co-monomer sequence and stereochemistry play important roles.
References
1. Dufal, S. et al. J. Chem. Eng. Data 59, 3272–3288 (2014).
2. Lafitte, T. et al. Mol. Phys. 110, 1189–1203 (2012).
3. Avendaño, C. et al. J. Phys. Chem. B 117, 2717–2733 (2013).
4. Jorgensen, W. L., Maxwell, D. S. & Tirado-Rives, J. J. Am. Chem. Soc. 118, 11225–11236 (1996).
5. Black, J. E., Iacovella, C. R., Cummings, P. T. & McCabe, C. Langmuir 31, 3086–3093 (2015).
Advances in molecular simulation , Interfacial and confined phenomena
