(342bf) Ensemble Dependence of Mechanical Relaxations and Their Underlying Correlation Functions

Mechanical properties such as modulus and viscosity have their origin in the interactions among molecules and the extent that molecules relax, either under load conditions or in response to spontaneous stress fluctuations while at equilibrium. Improving the mechanical response of “real world” materials could be enabled by understanding how the presence of additives and adjuvants modifies their properties and relaxations. Classical molecular simulations enable developing physical insights about these mechanisms that underlie the mechanical response. The contributions of individual molecules can be tabulated explicitly, which can aid in interpreting experimental data for systems in which unique contributions cannot be distinguished. The presence of multiple components in a real-world material introduces realism yet complicates the analysis process by adding compositional variability. In a simulation, convergence of numerical results can be plagued by slow relaxations and sizable signal-to-noise barriers that are imposed by large relative nanoscale fluctuations. In this work, we consider the extent that stress time autocorrelation functions depend on the ensemble that is used to carry out the simulations. The storage and loss moduli that can be obtained directly from equilibrium stress fluctuations within molecular dynamics simulations of model bitumens are used as an example. Numerical methods that apply moving averages in the time and frequency domains improve the clarity of the complex modulus results. Use of a window function to screen the time-domain data provides further improvements. Comparisons of stress relaxation functions obtained using ensembles at constant temperature and pressure, temperature, and energy reveal if ensemble-dependent artifacts are present. Very large data sets are required to achieve a sufficient frequency range while simultaneously averaging over the few stress inputs that are available at each time step. Care during computation of the correlation functions is required to achieve both speed and accuracy while maintaining distinct time separations across long simulations. Examples that are enabled by sufficiently accurate results, such as time-temperature superposition across moderate frequency ranges, will be discussed.