Thermodynamics and ideal glass transition on the surface of a monatomic system modeled as quasi '2-dimensional' recursive lattices

Two quasi 2-dimensional recursive lattices formed by planar elements have been designed to investigate the surface thermodynamics of monatomic Ising glass system with the aim to study the metastability of supercooled liquids and the ideal glass transition. Both lattices are constructed as hybrids of a Husimi lattice representing the bulk and lower dimensional recursive trees representing the surface. The coordination number, i.e. the number of neighbor sites surrounding one site, is designed to be 3 on the surface and 4 inside the bulk to mimic the 2D regular square lattice case. The recursive properties of recursive lattices were adopted to obtain exact thermodynamic calculations without approximation. The model has a strong anti-ferromagnetic interaction to give rise to an ordered phase identified as a crystal, and a metastable solution is also found to represent the amorphous phase. Interactions between particles farther away than the nearest neighbor distance are taken into consideration.;The calculations were done with C/C++ programs. A recursive calculation technique was employed to approach an exact description of the system with the ratio of partial partition functions (PPF) on each site of the lattice. Thermal properties including free energy, energy density and entropy of the ideal crystal and supercooled liquid state of the model on the surface are calculated by the PPF. By analyzing the free energies and entropies of the crystal and supercooled liquid state, we are able to identify the melting transition and the second order ideal glass transition on the surface. The effects of different energy terms that produce competitions between crystallization and glass transition are studied. The results show that due to the coordination number change, the transition temperature on the surface decreases significantly compared to the transition temperature of the bulk system obtained in our previous research. Our theoretical calculation agrees with experiments and computer simulation results on the thermodynamics of surfaces and thin films conducted by others. Comparing to others' work, there are two advantages in our approach: 1) in this work our model focuses on the small molecules system, it reveals the basic dimension origin of transition temperatures reduction without involving the long chain properties of polymer system; 2) the thermodynamics of systems are derived by exact calculation method, the computation time is much shorter than typical simulation methods, usually the calculation of one set of parameters in the interesting temperature region can be done in less than 100 seconds.