Constant Pressure Langevin Dynamics: Theory and Application to the Study of Phase Behaviour in Core-Softened Systems

The principles of statistical mechanics relevant to atomistic computer simulation are reviewed. This is followed by a review of algorithms for generating statistical ensembles. An alternative method for statistical sampling of the isothermal-isobaric ensemble is formulated, based on Langevin dynamics in non-Hamiltonian systems. This is successfully tested on the Lennard-Jones system, and with bond-order models. The potential advantages of this sampling method are discussed. The sampling scheme is then combined with modern Monte-Carlo and other simulation methods such as free energy calculation and meta-dynamics. The resulting suite of simulation tools is validated and used to map phase diagrams for a suitably chosen sequence of core-softened ‘shoulder’ potentials in three-dimensions. These models have possible relevance to the anomalous behaviour of liquid water and the phenomenon of liquid-liquid phase transitions in single component systems. As the sequence evolves from the simple Lennard-Jones potential, a decrease in melting temperature is measured, followed by the emergence of a simple-hexagonal solid phase. This undergoes a phase transition to close-packing at high pressure. The melting temperature of this simple-hexagonal phase can decrease with increasing pressure over an appreciable portion of the phase diagram. A metastable isostructural transition is also mapped, potentially consistent with theories of water-like anomalies. By integrating along paths connecting different parameterisations of the model, values are found which allow this transition to extend into the supercooled liquid. No liquidliquid phase transition is however present and no water-like anomalies are generated. The limitations of the model which prevent formation of a second liquid phase are discussed.