Microscopic Origins of the Viscosity of a Lennard-Jones Liquid

Efficient single-run implementation of generalized Einstein relation to compute transport coefficients: A binary-based time sampling

A robust and simple implementation of the generalized Einstein formulation using single equilibrium molecular dynamics simulation is introduced to compute diffusion and shear viscosity. The unique features underlying this framework are as follows: (1) The use of a simple binary-based method to sample time-dependent transport coefficients results in a uniform distribution of data on a logarithmic time scale. Although we sample "on-the-fly," the algorithm is readily applicable for post-processing analysis. Overlapping same-length segments are not sampled as they indicate strong correlations. (2) Transport coefficients are estimated using a power law fitting function, a generalization of the standard linear relation, that accurately describes the long-time plateau. (3) The use of a generalized least squares (GLS) fitting estimator to explicitly consider correlations between fitted data points results in a reliable estimate of the statistical uncertainties in a single run. (4) The covariance matrix for the GLS method is estimated analytically using the Wiener process statistics and computed variances. (5) We provide a Python script to perform the fits and automate the procedure to determine the optimal fitting domain. The framework is applied to two fluids, binary hard sphere and a Lennard-Jones near the triple point, and the validity of the single-run estimates is verified against multiple independent runs. The approach should be applicable to other transport coefficients since the diffusive limit is universal to all of them. Given its rigor and simplicity, this methodology can be readily incorporated into standard molecular dynamics packages using on-the-fly or post-processing analysis.

Nuclear induction line shape: Non-Markovian diffusion with boundaries

The dynamics of viscoelastic fluids are governed by a memory function, essential yet challenging to compute, especially when diffusion faces boundary restrictions. We propose a computational method that captures memory effects by analyzing the time-correlation function of the pressure tensor, a viscosity indicator, through the Stokes-Einstein equation's analytic continuation into the Laplace domain. We integrate this equation with molecular dynamics simulations to derive necessary parameters. Our approach computes nuclear magnetic resonance (NMR) line shapes using a generalized diffusion coefficient, accounting for temperature and confinement geometry. This method directly links the memory function with thermal transport parameters, facilitating accurate NMR signal computation for non-Markovian fluids in confined geometries.

Nuclear induction lineshape modeling via hybrid SDE and MD approach

The temperature dependence of the nuclear free induction decay in the presence of a magnetic-field gradient was found to exhibit motional narrowing in gases upon heating, a behavior that is opposite to that observed in liquids. This has led to the revision of the theoretical framework to include a more detailed description of particle trajectories since decoherence mechanisms depend on histories. In the case of free diffusion and single components, the new model yields the correct temperature trends. The inclusion of boundaries in the current formalism is not straightforward. We present a hybrid SDE-MD (stochastic differential equation - molecular dynamics) approach whereby MD is used to compute an effective viscosity and the latter is fed to the SDE to predict the line shape. The theory is in agreement with the experiments. This two-scale approach, which bridges the gap between short (molecular collisions) and long (nuclear induction) timescales, paves the way for the modeling of complex environments with boundaries, mixtures of chemical species, and intermolecular potentials.

Giant slip length at a supercooled liquid-solid interface

The effect of temperature on friction and slip at the liquid-solid interface has attracted attention over the last 20 years, both numerically and experimentally. However, the role of temperature on slip close to the glass transition has been less explored. Here we use molecular dynamics to simulate a bidisperse atomic fluid, which can remain liquid below its melting point (supercooled state), to study the effect of temperature on friction and slip length between the liquid and a smooth apolar wall in a broad range of temperatures. At high temperatures, an Arrhenius law fits well the temperature dependence of viscosity, friction, and slip length. In contrast, when the fluid is supercooled, the viscosity becomes super-Arrhenian, while interfacial friction can remain Arrhenian or even drastically decrease when lowering the temperature, resulting in a massive increase of the slip length. We rationalize the observed superlubricity by the surface crystallization of the fluid, and the incommensurability between the structures of the fluid interfacial layer and of the wall. This study calls for experimental investigation of the slip length of supercooled liquids on low surface energy solids.