All-Atom Molecular Dynamics Simulations of Poly(ethylene glycol) Networks in Water for Evaluating Negative Energetic Elasticity

We performed all-atom molecular dynamics simulations on poly(ethylene glycol) (PEG) hydrogels to microscopically confirm the recently discovered "negative energetic elasticity" [Y. Yoshikawa et al., Phys. Rev. X 2021, 11, 011045], which refers to a negative energetic contribution to the elastic modulus. To scrutinize the force field parameters, we evaluated the densities of aqueous solutions of linear PEG chains at varying concentrations through simulations and compared them with experimental values. We simulated a PEG network consisting of 2(3) unit cells of a diamond lattice with 60 PEG units per strand among numerous water molecules. Subsequently, we examined the temperature (T) dependence of shear stress (sigma(XY)) for each shear strain (gamma) under constant-volume conditions for a simulation duration of 360 ns. Current computational limitations lead to significant errors in sigma(XY). Thus, we employed a statistical approach considering numerous data sets (sigma(XY), gamma, T) based on the multivariate regression of the equation sigma(XY) = A gamma(T - T-E) in a narrow temperature range using fitting parameters A and T-E, where a positive T-E implies a negative energetic elasticity. The magnitude of the negative energetic elasticity (proportional to T-E) was approximately double the overall magnitude (proportional to T - T-E). We confirmed the feasibility of the obtained T-E values via a statistical error analysis. The theoretical prediction of the systematic difference between the T-E values under constant-pressure and constant-volume conditions was confirmed. Our method is effective for evaluating the negative energetic elasticity through T-E for arbitrary PEG concentrations and strand lengths.