General equation, Redlich-Kister

Guggenheim s polynomial expansion (equation 3.171 Guggenheim, 1937) and the two Redlich-Kister equations (3.172 and 3.173 Redlich and Kister, 1948) are of general applicability for any type of mixture ... 

Taking this process further, more complex composition dependencies to Q can be considered and it is straightforward to show that a general formula in terms of a power series should provide the capability to account for most types of composition dependence (Tomiska 1980). The most common method is based on the Redlich-Kister equation and Eq. (5.19) is expanded to become... 

The Redlich/Kister expansion, the Margules equations, and the van equations are all special cases of a very general treatment based on ratio functions, i.e., on equations for Ge given by ratios of polynomials. These... 

The Redlich/Kister expansion, the Margules equations, and the van Laar equations are all special cases of a general treatment based on rational functions, i.e., on equations for G /x X2RT given by ratios of polynomials. They provide great flexibility in the fitting of VLE data for binary systems. However, they have scant theoretical foundation, and therefore fail to admit a rational basis for extension to multicomponent systems. Moreover, they do not incorporate an explicit temperature dependence for the parameters, though this can be supplied on an ad hoc basis. 

For excess molar volume in real ternary systems, the validity of the Redlich-Kister s (1948) general equation can be assumed. For the description of the composition dependency on the molar volume, the following equation is used... 

For the excess electrical conductivity of the real ternary system, the validity of the general Redlich-Kister s type equation can be proposed. For the description of the composition dependence of electrical conductivity in the ternary system, the following equation could then be used... 

In the second approach, which finds application in real systems, validity of the general Redlich-Kister equation for the excess property is supposed. For description of the composition dependence on the given property Y (molar volume, surface tension) in the system, the following equation is then used (e.g. for a ternary system)... 

Now, some considerations can be written about the Heric s and this last polynomial function. In fact, the interaction terms in Equations 7 and 13 could be formally derived from the more general Redlich-Kister one (39], being the adjustable coefficients derived from this relation truncated at different power terms. However, it should be noted that for these binary mixtures, Heric s equation provides better results if compared with the polynomial one, despite the number of adjustable parameters. 

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