Statistical thermodynamics of mixtures of molecules of different sizes

Abstract

The central problem in the theory of mixtures is the calculation of the free energy of mixing of molecules of different sizes. An explicit calculation of this free energy is made for a mixture in which all intermolecular potentials are of the form Uaa(r) = (oaa/r)n, where ccux is a distance characteristic of the interaction of two molecules of species a, and where c a p = $(Daa+cpp) when a#@. This result follows from a solution of Percus-Yevick integral equation for the pair distribution function of a mixture of hard spheres. The form of the free energy provides a criterion by which existing theories can be judged, and it is shown that an approximation of the type originally suggested by van der Waals is superior to approximations based on the concept of random mixing. Molecules that differ only in size mix with a small and negative excess free-energy. The recommended approximation is confirmed by comparison with experiment. * This is the " second rehed version " of the average potential model, in the nomenclature of Bellemans et d 2 O and is the version used throughout this paper.

Are isotopic mixtures ideal?

“…The excess Gibbs energy for the equimolar mixture calculated from the excess vapor pressure is extremely small (0.021 J/mol at 85 K). The calculations based on the vdW-1 fluid theory [24] and 1cLJ perturbation theory [25] yielded G E values, which are in poor agreement with experiments. The theory of isotope effects using the estimated difference between the molar volumes of 36 Ar and 40 Ar (0.23 %) gives G E values, which are much more consistent with the experimental data.…”

“…The vapor pressure differences between the CH 4 /CD 4 mixtures and CH 4 have been determined as a function of concentration and temperature [15]. The G E value obtained from the measured excess vapor pressure is, for example, 0.6 J/mol for the equimolar mixture at 100 K. The theoretical analysis has shown that the models generally used for simple mixtures, the "vdW-1 fluid theory" [24] and "1cLJ perturbation theory" [25], are inadequate in explaining the experimental results, while the isotope effect theory agrees well with experiment ( Table 2). In this isotopic mixture, both external and internal vibrational contributions to G E are important (at 100 K they amount to 67 and 33 % of the total G E , respectively).…”

The Reactivity of Energetic Materials at Extreme Conditions

“…One of the greatest advantages of direct simulation is the ability to go beyond van der Waals 1-fluid theory, which approximately maps the equation of state of a mixture onto that of a single component fluid. 29 In most cases, interactions between unlike molecules are treated with LorentzBerthelot combination rules. 30 These rules specify the interactions between unlike molecules as arithmetic or geometric averages of single molecule pair-interactions.…”

Application of the Van Der Waals One Fluid Theory to Predict Vapor-Liquid Equilibria

“…One is given by assuming Eqs. (20) and (21) for unlike pair interaction parameters. The other is obtained from Eqs.…”