Association equation of state (AEOS) based on aggregate formation for pure substance

Based on the statistical mechanical theories and by using the concept of grand canonical ensemble a new equation of state for aggregate formations in the association fluids has been proposed. The compressibility factor for aggregate formation in an association fluid is represented by the following equation:

Z=Z^dis+Z^agg-1$Z=Z^{\text{dis}}+Z^{\text{agg}}-1$

where Z^agg is the aggregate compressibility factor due to aggregate formation by hydrogen bonding of molecules and Z^dis is the dispersed compressibility factor due to dispersion interactions. Each aggregate is considered as an open system in the grand canonical ensemble in which a molecule can enter to form a larger aggregate or leave to form a smaller aggregate. The average number of molecules in an aggregate is used to obtain the compressibility factor Z^agg and M₄ equation of state previously proposed by Mohsen-Nia et al. [M. Mohsen-Nia, H. Modarress, G.A. Mansoori, Fluid Phase Equilibr. 206 (2003) 27.] for non-association compounds is used to obtain Z^dis. The obtained new association equation of state (AEOS) based on the proposed compressibility factor is used for saturated properties calculations of pure well-known association fluids: water, ammonia and methanol. The results indicate that the saturated properties are well correlated by the new AEOS with a reasonable average number of molecules in each aggregate which is in agreement with spectroscopic experimental data and ab initio calculations.