The van der Waals-Platteeuw Solid Solution Theory

Characterization of the phase diagram of gas hydrates dominated the early research in gas hydrates. Although the structures, either S-I or S-II, show little variation with the guests, the structural thermodynamic stabilities, in 

The van der Waals and Platteeuw (vdW-P) statistical thermodynamic model was based on the following assumptions  

Consider the simplest case of a clathrate (C) with only one type of cavity. The inclusion of a guest (G) into the host (H) can be described by the process empty cavity -I- G occupied cavity. This can be described as a reversible chemical reaction of binding the guest into the host, 

At thermodynamic equilibrium, for Nq cavities and Nq guests, the Gibbs-Duhem equation requires 

Because Ng = vgNqXg, and i/g is a fraction of the specific type of cavity, in this case, vg = 1. Substituting into Eq. [5] and integrating reference to the chemical potential of the hypothetical empty cavity (Pq), one obtains the important relationship relating the chemical potential of the occupied hydrate to the occupancy (or concentration) of the guest. 

---