Development of Higher‐Order Interaction Parameter Formalisms for a Ternary Solution in a Thermodynamically Consistent Manner

Abstract

Wagner's interaction parameter formalism (WIPF), being thermodynamically inconsistent (on truncation) and limited in applicability to a very dilute solution, is modified, ever so often, to extend its utility. In WIPF, the activity coefficients of the solutes present in a solution are represented by Taylor's series. Herein, the analogy between the activity coefficient expression obtained by two different ways, that is, 1) by partially differentiating the (Redlich–Kister) polynomial representing the excess molar free energy and 2) by expressing the truncated Taylor's series (WIPF) along with the special relationships obtained between the interaction parameters by applying Gibbs–Duhem equation, is exhibited. WIPF truncated after the second order along with the special relations obtained by applying Gibbs–Duhem equation and the unified interaction parameter formalism (UIPF) truncated after the first order are identical to the Darken's quadratic formalism which is thermodynamically consistent and restricted to a limited concentration range. Therefore, these formalisms cannot be universal. Higher‐order terms must be included in Redlich–Kister polynomials or in WIPF in a thermodynamically consistent manner to extend its utility for a wide concentration range. Herein, a general quadratic and higher‐order formalisms such as cubic and quartic are developed for a ternary system.