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

Abstract

Cross-linked epoxy thermosets, like all glassforming 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 (T 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 T g values obtained from the data analysis with those calculated using the TTSP data obtained from the literature. Excellent agreement is found, and the T 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 T 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.

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

“…The experimental values of T g range from 399.3 to 407.3 K,15,16 while the computational values range from 489 to 556 K 9. Both experimental and computational values show a strong dependence on q cool 9…”

“…The pressure was maintained at 5 MPa. This value of pressure was used during the v sp ‐ q cool analysis9 to match experimental conditions,15 and we have maintained the same pressure here. Bonds and angles containing hydrogen atoms were constrained by the RATTLE algorithm 33,34.…”

“…Such all‐atom models explicitly account for specific chemical interactions such as hydrogen bonding, that have a significant impact on the thermomechanical properties of such systems 3,4. The creation of realistic all‐atom model structures of cross‐linked epoxy is non‐trivial,5 and two successful strategies have been developed to address the associated challenges: 1) the simulated annealing method (SA)6–9 and 2) the directed diffusion (DD) method 5,9…”

“…Recently,9 we studied an atomistic model for a cross‐linked epoxy network formed by the epoxy monomer Epon 1001F12,13 and the cross‐linker 4,4′‐diaminodiphenyl sulfone (4,4′‐DDS) using MD simulations. We refer to this network as the Epon 1001F/4,4′‐DDS system.…”

“…We discuss the temperature trends of the MSD and the time‐scaling exponent. These trends are then comparatively analyzed with the volumetric behavior from our recent simulation work 9. In Section 4, we present the superposition of the MSD and the exponent trends, and then make a quantitative comparison of the resulting computational master curves with the experimental creep compliance from the literature.…”