Date of Award
Doctor of Philosophy (PhD)
The most familiar phase transitions observed in nature are associated with a change in the state of matter (solid, liquid, and gas). In some rare cases this may involve the plasma phase. Such transitions are often referred to as first order phase transitions and often occur commonly such as during the melting of snow or freezing of lakes and rivers during winter. This project focuses on the most ubiquitous phase changes such as, liquid-solid and vapor-liquid as well as the less prevalent vapor-solid transitions. These types of phase transitions are also known as classical phase transitions. They usually involve symmetry breaking and can be identified by a singularity in the free energy or one of its derivatives. More modern classification of phase transitions relies on the order parameters as exemplified by the Landau's theory. An order parameter is a quantity that takes a value of zero in the disordered phase and assumes finite values in the ordered phase. In the case of liquid-vapor transition, the order parameter is the density.
The study of phase transitions is often complicated by the amount of time required by these phase changes and the presence of a high free energy barrier. Consequently, changes occurring close to coexistence are hard or even impossible to follow via conventional experimental techniques. Molecular simulation is therefore the method of choice to study these processes. Molecular simulations are numerical experiments carried out on model systems and have a number of advantages over traditional experiments. Simulations do not have any limitation as to the type of molecules or conditions under which they can be applied.
Current simulation methods used to accomplish this task, such as the grand canonical and Gibbs ensemble Monte Carlo methods, employ the concept of particles insertion and deletion moves or requires the knowledge of at least one point at coexistence. These types of moves are extremely inefficient when dense fluids are involved and limit the accuracy of these methods. To circumvent these difficulties, non-Boltzmann sampling methods such as the umbrella sampling and Wang-Landau sampling techniques, have been employed to study these phase transitions.
Vapor-solid and liquid-solid phase transitions were studied using a combination of hybrid Monte Carlo (HMC) and the umbrella sampling on a system of C60 molecules. The crystallization process occurs in two steps, nucleation and growth. The nucleation step is an activated process that involves a high free energy barrier. The free energy barrier is overcome through a series of HMC steps. The growth step on the other hand is studied by means of unconstrained molecular dynamics (MD). This study illustrates that the body centered cubic structure plays no role in the crystallization of C60. This is because only the face centered cubic and the hexagonal closed parked crystal structures were observed in both the nucleation and growth steps. In addition, the growth process is observed to follow a complex mechanism known as cross nucleation. The process of cross nucleation has also been observed in model fluids such as Lennard-Jones fluid and in the experimental study of D-mannitol.
Hybrid Monte Carlo and configurational bias Monte Carlo (CBMC) were combined with the Wang-Landau (WL) sample method to study the vapor-liquid equilibria of Polycyclic aromatic hydrocarbons (PAHs) with four fused benzene rings and &alpha-olefins (C2 - C6 respectively. These studies are conducted in the isothermal-isobaric (NPT) ensemble to avoid the particle insertion and deletion moves that resulted in low acceptance rates in previous simulations. These studies led to the prediction of the critical temperatures, pressures and densities of both systems.
Ndumbe Ngale, Kenneth, "Towards More Efficient Enhanced Sampling Methods To Study Phase Transitions" (2013). Theses and Dissertations. 1460.