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

Simple and convenient mapping of molecular dynamics mechanical property predictions of bisphenol-F epoxy for strain rate, temperature, and degree of cure

It is well-known that all-atom molecular dynamics (MD) predictions of mechanical properties of thermoset resins suffer from multiple accuracy issues associated with their viscoelastic nature. The nanosecond simulation times of MD simulations do not allow for the direct simulation of the molecular conformational relaxations that occur under laboratory time scales. This adversely affects the prediction of mechanical properties at realistic strain rates, intermediate degrees of cure, and elevated temperatures. While some recent studies have utilized a time-temperature superposition approach to relate MD predictions to expected laboratory observations, such an approach becomes prohibitively difficult when simulating thermosets with a combination of strain rates, intermediate degrees of cure, and temperatures. In this study, a phenomenological approach is developed to map the predictions of Young's modulus and Poisson's ratio for a DGEBF/DETDA epoxy system to the corresponding laboratory-based properties for intermediate degrees of cure and temperatures above and below the glass transition temperature. The approach uses characterization data from dynamical mechanical analysis temperature sweep experiments. The mathematical formulation and experimental characterization of the mapping is described, and the resulting mapping of computationally-predicted to experimentally-observed elastic properties for various degrees of cure and temperatures are demonstrated and validated. This mapping is particularly important to mitigate the strain-rate effect associated with MD predictions, as well as to accurately predict mechanical properties at elevated temperatures and intermediate degrees of cure to facilitate accurate and efficient composite material process modeling.

The link between swelling ratios and physical properties of EPDM rubber compound having different oil amounts

This new observation demonstrated that an increase in oil amounts within ethylene propylene diene monomer (EPDM) compounds decreased the crosslink density and the storage modulus but increase the elongation at break after tensile testing. The compounds with high oil amounts were observed to release oil particles when dissolved in toluene solutions and that increased their swell ratios. Consequently, the crosslink density had a perfect negative linear correlation with the elongation at break and a strong power-law correlation with the swell ratios. This work guides the material chemists and engineers during compound formulations when an increase in oil amounts is required.

Predicting Solute Diffusivity in Polymers Using Time-Temperature Superposition

We demonstrate a novel application of the time-temperature superposition (TTS) principle to predict solute diffusivity D in glassy polymers using atomistic molecular dynamics simulations. Our TTS approach incorporates the Debye-Waller factor ⟨u²⟩, a measure of solute caging, along with concepts from thermodynamic scaling methods, allowing us to balance contributions to the dynamics from temperature and ⟨u²⟩ using adjustable parameters. Our approach rescales the solute mean-squared displacement curves at several temperatures into a master curve that approximates the diffusive dynamics at a reference temperature, effectively extending the simulation time scale from nanoseconds to seconds and beyond. With a set of "universal" parameters, this TTS approach predicts D with reasonable accuracy in a broad range of polymer/solute systems. Using TTS greatly reduces the computational cost compared to standard MD simulations. Thus, our method offers a means to rapidly and routinely provide order-of-magnitude estimates of D using simulations.

Atomistic simulation of volumetric properties of epoxy networks: effect of monomer length

Properties of epoxy thermosets can be varied broadly to suit design requirements by altering the chemistry of the component agents. Atomistically-detailed molecular dynamics simulations are well-suited for molecular insight into the structure-property relationship for a rational tailoring of the chemistry. Since the macroscopic properties of interest for applications emerge hierarchically from molecular-scale chemical interactions, seamless integration of experiment, computation, and theory is of great interest. Recently, a Specific Volume-Cooling Rate analysis protocol was successfully developed to quantitatively compare the volumetric properties of an epoxy network model with experimental results in the literature, in spite of the nine orders of magnitude mismatch in the accessible time-scales. Here, we extend the application of the method for two epoxy networks in the same class of chemistry but whose monomers have a higher number of repeating units compared to the previous one for validating the generality of our approach. We observed that atomistic simulations are able to predict the experimental temperature trend of the specific volume within 0.4% for both these networks. Using the William-Landel-Ferry equation to account for rate differences, we also see good agreement between the computational and experimental values of the glass transition temperature.

Systematic Coarse-graining of Epoxy Resins with Machine Learning-Informed Energy Renormalization

A persistent challenge in predictive molecular modeling of thermoset polymers is to capture the effects of chemical composition and degree of crosslinking (DC) on dynamical and mechanical properties with high computational efficiency. We established a new coarse-graining (CG) approach that combines the energy renormalization method with Gaussian process surrogate models of the molecular dynamics simulations. This allows a machine-learning informed functional calibration of DC-dependent CG force field parameters. Taking versatile epoxy resins consisting of Bisphenol A diglycidyl ether combined with curing agent of either 4,4-Diaminodicyclohexylmethane or polyoxypropylene diamines, we demonstrated excellent agreement between all-atom and CG predictions for density, Debye-Waller factor, Young's modulus and yield stress at any DC. We further introduce a surrogate model enabled simplification of the functional forms of 14 non-bonded calibration parameters by quantifying the uncertainty of a candidate set of high-dimensional/flexible calibration functions. The framework established provides an efficient methodology for chemistry-specific, large-scale investigations of the dynamics and mechanics of epoxy resins.

Extending the timescale of molecular simulations by using time-temperature superposition: rheology of ionic liquids

Molecular dynamics simulations are used to determine the temperature dependence of the dynamic and rheological properties of a model imidazolium-based ionic liquid (IL). The simulation results for the volumetric properties of the IL are in good agreement with the experimental results. The temperature dependence of the diffusion coefficient of anions and cations follows the Vogel-Fulcher-Tammann equation over the range of the temperatures studied. The shear viscosity of the IL shows a Newtonian plateau at low shear rates and shear-thinning behavior at high shear rates. The dynamic modulus values indicate that the IL behaves like a viscous liquid at high temperatures and low frequencies, while its viscoelastic response becomes similar to that of an elastic solid at low temperatures and high frequencies. Using the time-temperature superposition (TTS) principle, the dynamic moduli, shear viscosity, and mean squared displacement of cations and anions in the diffusive regime can be collapsed onto master curves by applying a single set of shift factors. Due to the large mismatch in the timescale investigated by the atomistically detailed simulations and experiments, the glass transition temperature predicted in simulations shifts to higher values. When this timescale mismatch is accounted for by using appropriate shift factors, the master curves of the dynamic moduli obtained in simulations closely match those obtained in experiments. This result demonstrates the exciting ability of TTS to overcome the large timescale disparity between simulations and experiments which will enable the use of molecular simulations for quantitatively predicting the rheological property values at frequencies of practical interest.