Velocity correlation functions in different reference frames. Their relation with phenomenological and empirical transport coefficients

Abstract

In base of a baricentric expression given by H. Mori and with the introduction of a new set of collective dynamical variables, the ‘mean molecular velocities’ of the components, new Green–Kubo type expressions for the mass-transport phenomenological coefficients of irreversible thermodynamics in any reference frame are obtained. The dynamical variables involved in the time correlation functions are the mean molecular velocities of the components relative to the corresponding ‘microscopic reference velocity’, which is defined by analogy with the usual macroscopic one. The linear dependence of the relative mean molecular velocities determines that the sets of time correlation functions, their time integrals and the phenomenological coefficients are also linearly dependent. Nevertheless, the Onsager reciprocal relations are valid for each set. As the reference velocity appears explicitly, general transformation formulae among different frames for all these quantities are readily obtained at a microscopic level. As an application the expression by time correlation functions of some empirical transport coefficients such as the electric conductivity, transport numbers and ionic conductivities in mixed electrolyte solutions, and the interdiffusion coefficients in non-electrolyte mixtures, are deduced. The new expressions show explicitly the microscopic interpretation of these transport coefficients and their dependence on the reference frame.