A two-dimensional lattice gas model of network-forming particles on a. tria
ngular lattice is studied by the grand canonical Monte Carlo method. The ef
fects of association and cooperative interactions, which lead to a weakenin
g of the association interaction, are considered. Phase diagrams for severa
l systems are presented. It is shown that the molecular association leads t
o the formation of two different condensed phases characterized by differen
t densities and internal structures. The transition between those two conde
nsed phases appears to be a seldom-observed truly second-order transition a
t finite temperatures.