Oishi-Prausnitz Activity Coefficient Model

Here C., is an external degree of freedom parameter for the solvent. 

The combinatorial and residual contributions Qc and QR are identical to the original UNIFAC contributions. 

The Oishi-Prausnitz modification, UNIFAC-FV, is currently the most accurate method available to predict solvent activities in polymers. Required for the Oishi-Prausnitz method are the densities of the pure solvent and pure polymer at the temperature of the mixture and the structure of the solvent and polymer. Molecules that can be constructed from the groups available in the UNIFAC method can be treated. At the present, groups are available to construct alkanes, alkenes, alkynes, aromatics, water, alcohols, ketones, aldehydes, esters, ethers, amines, carboxylic acids, chlorinated compounds, brominated compounds, and a few other groups for specific molecules. However, the Oishi-Prausnitz method has been tested only for the simplest of these structures, and these groups should be used with care. The procedure is described in more detail in Procedure 3C of this Handbook. 

The Oishi-Prausnitz model cannot be defined strictly as a lattice model. The combinatorial and residual terms in the original UNIFAC and UNIQUAC models can be derived from lattice statistics arguments similar to those used in deriving the other models discussed in this section. On the other hand, the free volume contribution to the Oishi-Prausnitz model is derived from the Flory equation of state discussed in the next section. Thus, the Oishi-Prausnitz model is a hybrid of the lattice-fluid and free volume approaches. 

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A final note for these classical activity coefficient models is that, despite the advent of advanced SAFT and other equations of state discussed next (Section 3.4), they are stiU quite popular aud widely used in practical applications. They are also well cited in literature. For example, the historical articles by Flory and Huggins (Refs. [32,33]) are cited 998 (13.5) and 1034 (14) and the citations of the articles by Elbro et al. 164 (6.6), Lindvig et al. 44 (3.4), Kontogeorgis et al." 121 (5.5), and Oishi and Prausnitz" 353 (9.5). The citations are per May 2014 and the numbers in parenthesis are citations per year. 

The UNIFAC (Unified quasi chemical theory of liquid mixtures Functional-group Activity Coefficients) group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures was first introduced by Fredenslund et al. (1975). It is based on the Unified Quasi Chemical theory of liquid mixtures (UNIQUAC) (Abrams and Prausnitz, 1975), which is a statistical mechanical treatment derived from the quasi chemical lattice model (Guggenheim, 1952). UNIFAC has been extended to polymer solutions by Oishi and Prausnitz (1978) who added a free volume contribution term (UNIFAC-FV) taken from the polymer equation-of-state of Flory (1970). 

During the course of preparing this Handbook the available prediction models were evaluated for their ability to accurately predict weight fraction activity coefficients. The methods included were the UNIFAC free volume model (Oishi and Prausnitz, 1978), the Chen et al. (1990) equation of state, and the High-Danner (1990) equation of state. 

Whereas the models given above can be used to correlate solvent activities in polymer solutions, attempts also have been made in the literature to develop concepts to predict solvent activities. Based on the success of the UNIFAC concept for low-molecular liquid mixtures,Oishi and Prausnitz developed an analogous concept by combining the UNIFAC-model with the free-volume model of Flory, Orwoll and Vrij. The mass fraction based activity coefficient of a solvent in a polymer solution is given by ... 

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