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

Abstract

For glass‐forming polymers, direct quantitative comparison of atomistically detailed molecular dynamics simulations with thermomechanical experiments is hindered by the vast mismatch between the accessible timescales. Recently, the authors demonstrated the successful application of the time–temperature superposition (TTS) principle to perform such a comparison for the volumetric properties of an epoxy network. Here, the local translational dynamics of the same network is computationally followed‐up and studied. The mean squared displacement (MSD) and time‐scaling exponent trends of select atoms of the network are calculated over a temperature range that spans the glass transition. Using TTS, both trends collapse onto master curves that relate the reduced MSD and time‐scaling exponent to the reduced time at a reference temperature. Because the reduced time of these computational master curves extends to 109 s, they can be directly compared with experimental creep compliance for the same material from the literature. A quantitative comparison of the three master curves is performed to provide an integrated view that relates atomic‐level dynamics with macroscopic thermomechanics. The time‐shift factors needed for TTS in simulation show excellent agreement with experiment in the literature, further establishing the veracity of the approach.

Volumetric and Rheological Properties of Vitrimers: A Hybrid Molecular Dynamics and Monte Carlo Simulation Study

“…The values of b T below the glass transition temperature were set to unity. 61 The rescaled frequency ωp is defined as ωã T , where a T values are the horizontal shift factors. 2 These a T values were determined manually.…”

“…The rescaled moduli were determined by ( ), where b T is the vertical shift factor obtained as b T = T 0 ρ 0 / T ρ (ρ is the density), to construct the master curves of the elastic and loss moduli in the model thermoset. The values of b T below the glass transition temperature were set to unity . The rescaled frequency ω̃ p is defined as ω̃ a T , where a T values are the horizontal shift factors .…”

Thermodynamics, Dynamics, and Rheology of Fuel Surrogates: Application of the Time–Temperature Superposition Principle in Molecular Dynamics Simulations

“…As discussed earlier, the gap between time scales in the AA MD simulations and rheological experiments can be bridged with the aid of the TTS principle. This principle, which originally was proposed for polymers and extended for other complex fluids, has shown great potential in extending the simulation data in determining the creep compliance of cross-linked systems . To test the applicability of TTS in our systems, the viscosity data obtained from simulations were collapsed onto master curves using the following vertical and horizontal shifts where γ̇ p is the reduced shear rate and η p is the reduced viscosity.…”

“…A recent study by Khare and Phelan suggested that the MSD data of a cross-linked network can also be collapsed onto a master curve using similar shift factors, which are obtained from creep compliance measurements (mostly in the linear viscoelastic regime). Here, we have extended the idea to molecular systems, where the MSD shows both subdiffusive and diffusive behaviors, and the nonlinear viscoelastic regime where the fluid is always out of equilibrium.…”

“…TTS has then the potential to bridge the time scale between simulations and experiments. Success in applying TTS in MD simulations has been recently reported for a variety of systems, including asphalts and epoxy polymer networks. ,, Khabaz and Khare successfully implemented this principle in determining the viscoelastic property of a 12-component model of asphalt . Their results showed that a single set of shift factors, which is obtained from shear viscosity, moduli, or creep simulations, can collapse all rheological properties of asphalt onto master curves.…”