Segregation of molecules in binary solvent mixtures without H bonds. A quantitative treatment based on the theory of mobile order and disorder

This treatment applies to binary liquid mixtures of volume fractions phi(1) , and phi(2),, but only in the absence of H bonding or ionisation. An envir onmental layer is defined around the individual volume a, of a given molecu le 1. At a given instant, a fraction alpha(11) of this layer contains atoms belonging to molecules of the same kind as 1 whereas the complementary fra ction alpha(11) contains atoms of molecules of kind 2. Due to the spontaneo us displacements of nu(1), in the liquid, alpha(11), fluctuates between the extreme values 1 and 0. However, after a long time t, the time fraction de fined by the integral gamma(11) drop (1/t)integral(o)(t)alpha(11) dt no lon ger depends on the time and has the same value for all the molecules of the same kind. The four time fractions gamma(11) and gamma(12), gamma(22), gam ma(21) (defined in a similar way) are characteristic of the equilibrium. Th ey are directly related to the partition of the cohesive energy in 11, 22 a nd 12 interactions, xi(11) = gamma(11)phi(1); xi(22) = gamma(22)phi(2); xi( 12) = 2 gamma(12)phi(1) = 2 gamma(21)phi(2). Random mixing occurs when gamm a(11)(rand) = gamma(21)(rand) = phi(1) and gamma(12)(rand)= gamma(22)(rand) = phi(2). In this case (xi(12)(rand))(2)/(xi(11)(rand)xi(22)(rand)) = 4. H owever, in most cases, homogeneous environments are preferred and (xi(12))( 2)/(xi(11)xi(22)) = 4K. The "environmental" constant K is then smaller than unity. K is related to the molar volumes (V) over bar(1) and (V) over bar( 2), and to the differences in standard Gibbs energies between the pure stat e and the state of infinite dilution in the other liquid. K can be estimate d by the geometric mean rule. For liquids of similar polarities, K does not differ markedly from unity, but for mixtures of polar liquids and liquid a lkanes, K is significantly smaller and an important segregation is predicte d. Using the experimental solubilities of solid n-alkanes in pure solvents, the equations predict the solubilities in mixtures of the two solvents wit hout any adapted parameter. The predicted values agree in this case, consid erably better with the experimental ones than do those derived from the hyp othesis of random mixing. The validity of time fractions thermodynamics has thus been experimentally verified.