  Conventional gas-liquid phase transitions feature a coexistence line that has
a monotonic and positive slope in line with our intuition that cooling always
leads to condensation. Here we study the inverse phenomenon, condensation of
adsorbed organic molecules into dense domains upon heating. Our considerations
are motivated by recent experiments [Aeschlimann et al., Angew. Chem. (2021)],
which demonstrate the partial dissolution of an ordered molecular monolayer and
the mobilization of molecules upon cooling. We introduce a simple lattice model
in which each site can have three states corresponding to unoccupied and two
discernible molecular conformations. We investigate this model through Monte
Carlo simulations, mean-field theory, and exact results based on the analytical
solution of the Ising model in two dimensions. Our results should be broadly
applicable to molecules with distinct conformations that have sufficiently
different entropies or heat capacities.
