Interpenetration as a mechanism for liquid-liquid phase transitions

We study simple lattice systems to demonstrate the influence of interpenetrating bond networks on phase behavior. We promote interpenetration by using a Hamiltonian with a weakly repulsive interaction with nearest neighbors and an attractive interaction with second-nearest neighbors. In this way, bond networks will form between second-nearest neighbors, allowing for two (locally) distinct networks to form. We obtain the phase behavior from analytic solution in the mean-field approximation and exact solution on the Bethe lattice. We compare these results with exact numerical results for the phase behavior from grand canonical Monte Carlo simulations on square, cubic, and tetrahedral lattices. All results show that these simple systems exhibit rich phase diagrams with two fluid-fluid critical points and three thermodynamically distinct phases. We also consider including third-nearest-neighbor interactions, which give rise to a phase diagram with four critical points and five thermodynamically distinct phases. Thus the interpenetration mechanism provides a simple route to generate multiple liquid phases in single-component systems, such as hypothesized in water and observed in several model and experimental systems. Additionally, interpenetration of many such networks appears plausible in a recently considered material made from nanoparticles functionalized by single-strands of DNA.