  In this paper we obtain the first general multi-component solution to
thermodynamic perturbation theory for the case that molecules can participate
in cyclic double bonds. In contrast to previous authors, we do not restrict
double bonding molecules to a 2-site association scheme. Each molecule in a
multi-component mixture can have an arbitrary number of donor and acceptor
association sites. The one restriction on the theory is that molecules can have
at most one pair of double bonding sites. We also incorporate the effect of
hydrogen bond cooperativity in cyclic double bonds. We then apply this new
association theory to 2-site and 3 site models for carboxylic acids within the
polar PC-SAFT equation of state. We demonstrate the accuracy of the approach by
comparison to both pure and multi-component phase equilibria data. We also
demonstrate that inclusion of hydrogen bond cooperativity has a substantial
effect on liquid phase hydrogen bonding structure.
