Gibbs probability entropy and its implication to combinatorial entropy models

Abstract

We show that the class of combinatorial entropy models, such as the Guggenheim–Staverman model, in which the many conformations of a molecule are taken into account, does not fulfill the Gibbs probability normalization condition. The root cause for this deviation lies in the definition of the pure and mixture state. In the athermal limit, mandatory to define the combinatorial entropy, the number of molecules in a particular conformation does not change upon mixing. Therefore each set of molecules with a particular conformation in the pure state can be regarded as a distinguishable subclass of rigid molecules. When this subdivision is applied to the ‘shape’ models, they fulfill the Gibbs probability normalization condition. The resulting equations simplify to the Flory–Huggins entropy model. Implications of this finding to the existing activity coefficient models are discussed.