Free Volume and the Pressure

One usually distinguishes two types of lattice models. The first type may be called lattice-gas models. In this case, the number of molecules in the system is less than the number of available sites. In other words, there are vacant sites. The second type of lattice models may be called lattice fluids. In this case, all lattice sites are filled exactly by the molecular components in the system the system is considered to be incompressible. It is easily shown that a two-component incompressible lattice fluid model can be mapped on a one-component lattice gas one. In other words, it is possible to interpret vacant sites to be occupied by a ghost  

Below we will see that a sufficiently general model for the lipid bilayer system should account for some free volume (unoccupied lattice sites) in the bilayer core. If this is not done, then the lipid bilayer system will change spontaneously into the gel phase (at all reasonable temperatures). 

For historical reasons, the incompressible lattice-fluid system description is used, even if the distribution of one of the components is coupled to the distribution of vacant sites. Constant pressure SCF calculations are the same as constant chemical potential calculations for the vacant sites. These conditions are used below. 

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