Lattice Fluid Model of Sanchez and Lacombe

Sanchez and Lacombe [15] developed a molecular theory of classical fluids based on a well-defined statistical mechanical model. The model fluid reduces to the classical lattice gas in one special case. It can be characterized as an Ising or lattice fluid. The model fluid undergoes a liquid-vapor transition. Only three parameters are required to describe a fluid. These parameters have been determined and tabulated for several fluids. 

The Gibbs free energy, G, can be expressed in terms of the configurational partition function Z in the pressure ensemble by 

The coordination number of the lattice Z is given by Equation (2.44). Each interior mer of a linear chain is surrounded by the Z-2 nearest nonbonded neighbors and two bonded neighbors. 

The total number of nearest neighbor pairs in the system is (ZI2)N. Only (ZI2)N are nonbonded pairs where 

The large Z limit equation is the Flory approximation. The parameter 8 is independent of temperature and pressure. The closed packed volume rV of a molecule is independent of tanperature and pressure. The closed packed volume of a repeat unit is V. It is also the volnme of a lattice site. The closed packed volume of N, repeat oligomers (no holes) is 

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