ABSTRACT

The calculation of non-ideality in a multicomponent solution phase is studied by considering various solution models. The use of an empirical multicomponent solution model is indicated when bulk thermodynamic properties are available for binary solutions. KOHLER has developed an empirical excess free energy model which places no restrictions on the form of binary non-idealities yet it is efficient and is very easily expressed as G^X(K) = ∑^n-1_i=1∑ⁿ_j>i(N_i + N_j)² G^X_ij where G^X_ij is the value of G^X in the binary ij at a normalized composition of N_i/(N_i + N_j). Only binary interactions are considered in this model and because many silicates (solids, liquids) show strong changes in association/dissociation phenomena as additional components are added, KOHLER's model will not be sufficient by itself. It needs to be combined with an empirical multicomponent correction free energy model which takes into consideration a few experimental points. Correction free energy models are meant to describe interactions that involve more than two components and so they should not have the flaw of extending into any binary. Existing ternary correction models have this flaw which can be removed by introducing an exponent. Two so-modified multicomponent correction free energy models are proposed here and the first has n coefficients and is expressed as n G^k = [∑^n-1_i=1∑ⁿ_j>i (1-N_i-N_j)]^γ [∑_i=1 N_iK_i], where γ is the introduced exponent (γ > 1) and K_i are the correction coefficients. This correction, which is based on only n-component experimental data, acts on all subsystems with more than two components. A second correction model has been designed to overcome this subsystem action. This second model accumulates m correction coefficients for every possible 3 ≤ m ≤ n component interaction leading to a total of n2^n-1-n² coefficients. The coefficients of an m-component interaction do not affect the calculations in any m-1 component or smaller subsystem. The model is based on the logic leading to KOHLER's model and is expressed as G^k = ∑_m∑_I(NI)^γm G^k_φ(I) where G^k_φ(I) is the value of G^k in the m-ternary system with components φ(I) at a normalized composition while NI is the sum of N_i in φ(I). KOHLER's model and these two empirical correction models are easily computerized, both in terms G and U_i so that they can be easily incorporated into any computer program that presently assumes ideal mixing of the solution phases.