Using Molecular Simulation to Compute Transport Coefficients of Molecular Gases

Abstract

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity D, the viscosity η, and the thermal conductivity λ of hard spheres, Lennard-Jones particles, and rough hard spheres agree well with the standard (lowest order) Chapman−Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of polyatomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of polyatomic molecules requires an approximate treatment of their quantized internal modes. We show that a wellknown approximation that relates λ to D and η yields good results. We note that our approach should yield a lower limit to the exact value of D, η, and λ. Interestingly, the most sophisticated (higher-order) Chapman− Enskog results for rough hard spheres seem to violate this bound.

Sampling constrained stochastic trajectories using Brownian bridges

“…With the availability of extremely powerful computers, stochastic simulations have become the main tool to explore a large variety of physical, chemical and biological phenomena such as the spontaneous foldingunfolding of proteins 1 , allosteric transitions 2 , the binding of molecules 3 , or more generally to compute physical observables of complex systems 4 . In some cases, however, the duration of the phenomenon under study can be extremely long, still beyond present computational capabilities.…”