The role of reference frames in the molecular theory of diffusive transport in solutions

Abstract

Starting with the Green–Kubo formulas for the phenomenological coefficients of irreversible thermodynamics, the molecular expression for the distinct diffusion coefficient Dd[R],αβ in any internal reference frame R is derived. It follows that Dd[R],αβ is given by the time integral of a time correlation function (tcf) Λd[R],αβ(t) whose dynamical variables are the velocities of two different particles of species α and β, each relative to a microscopic reference velocity ŵR . These relative dynamic variables have the welcome feature of being orthogonal to the total momentum of the system so that Λd[R],αβ(t) vanishes at long times. Hence the divergence of the barycentric distinct diffusion coefficients, suggested by their usual interpretation in terms of a time correlation function that lacks an explicit dependence on the reference frame, is resolved. The influence of the reference frame on the behavior of the barycentric distinct tcf ’s is analyzed. In great measure this influence is exposed by considering initial values of the tcf ’s; in turn the initial values are decisive in establishing the sign of the distinct diffusion coefficients in ideal or nearly ideal mixtures. Finally, by applying new linear relations connecting the self and distinct tcf ’s, a complete description of some of the barycentric distinct tcf ’s may be given in the limiting cases of a pure fluid and a tracer in a host liquid.