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

K Hagita and S Nagahara and T Murashima and T Sakai and N Sakumichi, MACROMOLECULES, 56, 8095-8105 (2023).

DOI: 10.1021/acs.macromol.3c01121

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.

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