Molecular Dynamics Validation and Applications of the Maximum Entropy Homogenization Procedure for Predicting the Elastic Properties of Gaussian Polymer Networks

Molecular dynamics (MD) simulations are used to obtain direct estimates of the equilibrium shear modulus of 3D periodic microstructures of ideal end-linked Gaussian polymer networks. The same microstructures are employed to estimate the key topological factor Γ of the exact affine network theory (ANT) using the maximum entropy homogenization procedure (MEHP), and the resulting theoretical predictions are validated by comparison with the direct MD estimates. A number of microstructures with different extent of polymerization, stoichiometric imbalance, and loop fraction are generated, and using exact ANT estimates, the validity of the classical phantom network model (PNM), Miller–Macosko nonlinear polymerization theory (MMT), and real elastic network theory (RENT) of Gaussian polymer networks is assessed. It is shown that for the nonswollen (rubber-like) networks the MMT gives good predictions. However, it is also seen that neither PNM nor MMT nor RENT is generally accurate. A novel combination of the MMT and RENT is proposed, and it is shown that for moderate loop fractions, it provides a good description of the numerical ANT estimates. It is surmised that the validated MEHP can help to further advance our understanding of the relationship between the topology and the elastic properties of polymer networks by enabling exact ANT estimates of the elastic properties of detailed 3D network microstructures with entirely specified topology.