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=Zdis+Zagg-1where Zagg is the aggregate compressibility factor due to aggregate formation by hydrogen bonding of molecules and Zdis 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 Zagg 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 Zdis. 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.