Density dependence of the stress relaxation function of a simple fluid

Abstract

We present accurate molecular dynamics calculations of the shear stress relaxation modulus of a simple atomic fluid over a wide range of densities. The high accuracy of the data enables us to study changes in the functional form of the shear relaxation modulus, and the properties that are derived from it, as the density is increased from the ideal gas limit to the upper limit of the fluid range. We show that the shear relaxation modulus of a dilute atomic fluid can be accurately described with a simple functional form consisting of a Gaussian plus a single exponential, whereas the dense fluid exhibits a more complicated relaxation function. The infinite-frequency shear modulus, the zero-shear viscosity, and the zero-shear first normal stress coefficient are calculated from the stress autocorrelation function. The ratio of the first normal stress coefficient to the viscosity is used to calculate the viscoelastic relaxation time. While the viscosity and the infinite-frequency shear modulus both increase monotonically with increasing density, the first normal stress coefficient and the viscoelastic relaxation time both decrease to a minimum at intermediate densities before increasing again. Our results for the viscosity and the first normal stress coefficient in the low-density limit both agree well with the predictions of kinetic theory.

New Possibilities Provided by the Analysis of the Molecular Velocity Autocorrelation Function in Liquids

“…( [10]) are presented in Table 2. As one can see, a quite satisfactory correspondence takes place between the MRT values obtained in work [43] and the results obtained from relation (12). In work [43], the MRT was determined by analyzing the autocorrelation function for transverse stresses.…”

“…As one can see, a quite satisfactory correspondence takes place between the MRT values obtained in work [43] and the results obtained from relation (12). In work [43], the MRT was determined by analyzing the autocorrelation function for transverse stresses. However, the ensemble of 4000 particles, which was used in the cited work, was not sufficiently complete to adequately describe the molecular interaction.…”

Quantifying the sensitivity of the network structure and properties from simultaneous measurements during photopolymerization

“…The other quantity that can change E ∞ is the number density of molecules ρ which does change with DC due to shrinking. Calculation of high frequency modulus for a liquid has been previously performed using Weeks-Chandler-Andersen (WCA) potential 23 . The WCA potential is the entirely repulsive part of the Lennard-Jones (LJ) potential, which is obtained by increasing the value of the LJ potential by the depth of the potential well and setting it to zero for all distances larger than the location of the minimum of the potential 24 .…”

“…As the volumetric shrinkage for these resins is close to 10 % 9 , we can have a corresponding increase in ρ̃ due to curing. The calculations from molecular dynamics simulations 23 show that changing ρ̃ from 0.6 to 0.76 changes by the infinite frequency modulus by a factor of 2. Thus we expect the change in E ∞ to be less than a factor of 2 while curing.…”

Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model

“…A phenomenological way of representing the linear stress response to a time dependent shear rate is to use the Boltzmann superposition principle, [26][27][28] in terms of a time-dependent elastic modulus, C, or "shear stress relaxation function" (SRF), which has units of stress,…”