Approaches to Polymer Solution Thermodynamics

All of the models developed for predicting and correlating the properties of polymer solutions can be classified into two categories lattice models or van der Waals models. These two approaches can be used to derive activity coefficient models or equations of state. Activity coefficient models are not functions of volume and therefore are not dependent on 

In both the lattice models and the van der Waals models, the behavior of the molecules is described as the sum of two contributions. The first contribution assumes that there are no energetic interactions between the molecules only the size and shape of the molecules need to be considered for this part. This is the contribution that would be predominant at very high temperatures where the kinetic energy of the molecules would be large compared to any interaction energies between the molecules. This interaction-free contribution is generally called the combinatorial or the athermal term. In the case of the van der Waals model, it is frequently referred to as the free volume term. 

In lattice models each molecule (or segment of a molecule in the case of polymers) is assumed to occupy a cell in the lattice. The arrangement of the molecules or segments is assumed to depend upon only the composition and the size and shape of the molecules. In this case, the combinatorial (athermal) contribution is calculated from the number of arrangements statistically possible in the lattice. This contribution is also referred to as the entropic term. 

In the van der Waals model the volume in which the molecules can translate is determined by the total volume of the system less the volume occupied by the molecules. Thus, the term free volume. In this part of the treatment of the system intermolecular attractions are not taken into account, so this free volume term is the combinatorial (athermal) contribution. 

The second contribution in either the lattice or the van der Waals model is that originating from intermolecular attractions. This contribution is commonly referred to as the attractive energy term, the residual term, or the potential energy term. It is also known as the enthalpic contribution since the differences in interaction energies are directly responsible for the heats of mixing. This contribution is calculated by a product of a characteristic energy of interaction per contact and the number of contacts in the system. Van der Waals models use a similar expression for the interaction energy. 

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