STATISTICAL-MECHANICAL THEORY OF ONE-DIMENSIONAL GASES WITH SHORT-RANGE AND LONG-RANGE INTERMOLECULAR FORCES .5. INTERSECTION AND INVERSION OF ISOTHERMS OF THE WATER TYPE

The detailed behaviour of isotherms is investigated for the one-dimensional gas model proposed and discussed by Ikeda in paper I; the model consists of molecules with hard cores, short-range (square-potential) repulsions and infinitely-long-range-attractions (given by the potential - 2a/L, a = positive constant, L = length of the gas). On the basis of R (region of negative pressure coefficient), the intersection and inversion of isotherms in the P' -l' plane (P' = reduced pressure, l' = reduced specific volume) are studied, in connection with the phase transitions. The interaction constants sigma' and alpha' are so chosen as to represent the features of water. Correspondence between diagrams in the T'-l', P'-T' and P'-l' planes (T' = reduced temperature), including R and R' (region of negative thermal expansivity), is discussed. The behaviour of isotherms in the liquid phase for this model explains the anomalies of liquid water.