Integral equations for the microstructures of supercritical fluids.

摘要

Molecular interactions and molecular distributions are at the heart of the supercritical behavior of fluid mixtures. The distributions, i.e. structure, can be obtained through any of the three routes: (1) scattering experiments, (2) Monte Carlo or molecular dynamics simulation, and (3) integral equations that govern the relation between the molecular interactions u(r) and the probability distributions g(sub ij)(r). Most integral equations are based on the Ornstein-Zernike relation connecting the total correlation to the direct correlation. The OZ relation requires a (open quotes)closure(close quotes) equation to be solvable. Thus the Percus-Yevick, hypernetted chain, and mean spherical approximations have been proposed. The authors outline the numerical methods of solution for these integral equations, including the Picard, Labik-Gillan, and Baxter methods. Solution of these equations yields the solvent-solute, solvent-solvent, and solute-solute pair correlation functions (pcf's). Interestingly, these pcf's exhibit characteristical signatures for supercritical mixtures that are classified as (open quotes)attractive(close quotes) or (open quotes)repulsive(close quotes) in nature. Close to the critical locus, the pcf shows enhanced first neighbor peaks with concomitant long-range build-ups (sic attractive behavior) or reduced first peaks plus long-range depletion (sic repulsive behavior) of neighbors. For ternary mixtures with entrainers, there are synergistic effects between solvent and cosolvent, or solute and cosolute. These are also detectable on the distribution function level. The thermodynamic consequences are deciphered through the Kirkwood-Buff fluctuation integrals (G(sub ij)) and their matrix inverses: the direct correlation function integrals (DCFI's). These quantities connect the correlation functions to the chemical potential derivatives (macroscopic variables) thus acting as (open quotes)bridges(close quotes) between the two Weltanschauungen.