The new mathematical framework based on the free energy of pure classical fluids presented in [ R. D. Rohrmann , Physica A 347 , 221 ( 2005 ) ] is extended to multi-component systems to determine thermodynamic and structural properties of chemically complex fluids .
Presently , the theory focuses on D -dimensional mixtures in the low-density limit ( packing factor \eta < 0.01 ) .
The formalism combines the free-energy minimization technique with space partitions that assign an available volume v to each particle . v is related to the closeness of the nearest neighbor and provides an useful tool to evaluate the perturbations experimented by particles in a fluid .
The theory shows a close relationship between statistical geometry and statistical mechanics .
New , unconventional thermodynamic variables and mathematical identities are derived as a result of the space division .
Thermodynamic potentials \mu _ { il } , conjugate variable of the populations N _ { il } of particles class i with the nearest neighbors of class l are defined and their relationships with the usual chemical potentials \mu _ { i } are established .
Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically .
The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation .
Several pair distribution functions are introduced and evaluated .
Analytical expressions are also presented for hard spheres with attractive forces due to Kâc-tails and square-well potentials .
Finally , we derive general chemical equilibrium conditions .