Integration of Atomistic Simulation with Experiment Using Time−Temperature Superposition for a Cross-Linked Epoxy Network

Quantitative comparison of atomistic simulations with experiment for glass-forming materials is made difficult by the vast mismatch between computationally and experimentally accessible timescales. Recently, we presented results for an epoxy network showing that the computation of specific volume vs. temperature as a function of cooling rate in conjunction with the time–temperature superposition principle (TTSP) enables direct quantitative comparison of simulation with experiment. Here, we follow-up and present results for the translational dynamics of the same material over a temperature range from the rubbery to the glassy state. Using TTSP, we obtain results for translational dynamics out to 109 s in TTSP reduced time – a macroscopic timescale. Further, we show that the mean squared displacement (MSD) trends of the network atoms can be collapsed onto a master curve at a reference temperature. The computational master curve is compared with the experimental master curve of the creep compliance for the same network using literature data. We find that the temporal features of the two data sets can be quantitatively compared providing an integrated view relating molecular level dynamics to the macroscopic thermophysical measurement. The time-shift factors needed for the superposition also show excellent agreement with experiment further establishing the veracity of the approach

Quantitative Comparison of Atomistic Simulations with Experiment for a Cross-Linked Epoxy: A Specific Volume–Cooling Rate Analysis

Cross-linked epoxy thermosets, like all glass-forming viscoelastic materials, show both a temperature and rate dependence in their thermomechanical properties. However, accounting for rate effects on these properties using molecular dynamics (MD) simulations and making quantitative comparison with experimental measurements has proven to be a difficult task due to the extreme mismatch between experimental and computationally accessible cooling rates. For this reason, the effect of cooling rate on material properties in glass-forming systems (including epoxy networks) has been mostly ignored in computational studies, making quantitative comparison with experimental data nebulous. In this work, we investigate a strategy for modeling rate effects in an epoxy network based on an approach that uses theoretically informed simulation and analysis protocols in combination with material specific time–temperature superposition (TTSP) data obtained from experimental measurements. To illustrate and test the strategy, we build and study an atomistic model of a cross-linked epoxy network. Molecular dynamics simulations are used to model the specific volume as a function of temperature across the glass transition from the rubbery to the glassy state using a total of five computationally accessible cooling rates. From the trends thus identified, we pinpoint the temperatures at which the models show rubbery and glassy behavior and use this information to calculate the values of the glass transition temperature (<i>T</i>_g) for each of the different cooling rates. Comparison with experimental data obtained from the literature (for the identical epoxy network) shows that our computations successfully predict the trends in specific volume in the rubbery and the glassy regions within 0.5%. We then compare the <i>T</i>_g values obtained from the data analysis with those calculated using the TTSP data obtained from the literature. Excellent agreement is found, and the <i>T</i>_g values from the two different methods are within 1.5% for all cooling rates. While our MD simulations do not replicate the experimental cooling rates, the agreement between these two sets of <i>T</i>_g values quantitatively relates the computational and experimental data sets. This agreement indicates that atomistic simulations can reliably capture the molecular mechanisms underlying viscoelasticity in this cross-linked epoxy (even when cooling rates differ by orders of magnitude) and that volume–rate analysis in conjunction with TTSP is a reliable method to computationally characterize certain classes of glass-forming materials. We believe that the general paradigm and protocols developed in this work should in principle be extensible as an efficacious means to integrate theory, computation, and experiment for the analysis of amorphous macromolecular materials