potential due to association is given by
√^(r,ω1,ω2) =
if r < rc∙, Θai < θc-, θβ2 < θc
(1.2)
otherwise
Eqn. 1.2 essentially means that if the molecules 1 and 2 are close enough and their as-
sociating sites are oriented towards each other, they associate with the strength of the
association potential given by εas. These positional and orientational constraints are
prescribed by the parameters, rc and θc. respectively. Wertheim introduced separate
singlet densities for each possible associating state of a molecule. For example, for
molecules with one associating site, the individual singlet densities are the densities
of associated molecules and the non-associated molecules. For molecules with mul-
tiple associating sites, the associating state of a molecule increases depending upon
the number of sites that are associated. Using graph theory in statistical mechanics,
Wertheim derived the thermodynamic variables as functionals of the singlet densi-
ties. Additional constraints on the associating molecules were introduced to reduce
the number of graphs, as shown in fig. 1.4.
• If two molecules are associated at their sites A and B respectively, then other
molecules cannot associate at either A or B.
• A site on a molecule cannot associate with two sites on another molecule, si-
multaneously.
• Two sites on a molecule cannot associate with two sites on another molecule,
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