Date of Graduation


Document Type


Degree Name

Master of Science in Chemical Engineering (MSChE)

Degree Level



Chemical Engineering


David M. Ford

Committee Member

Gregory J. Thoma

Second Committee Member

Mahmoud Moradi


Machine learning, small systems, phase transitions, phase behavior examinations


Under the umbrella of statistical mechanics and particle-based simulations, two distinct problems have been discussed in this study. The first part included systems of finite clusters of three and 13 particles, where the particles are interacting via Lennard Jones potential. A machine learning technique, Diffusion Maps (DMap), has been employed to the large datasets of thermodynamically small systems from Monte Carlo simulations in order to identify the structural and energetic changes in these systems. DMap suggests at most three dimensions are required to describe and identify the systems with 9 (N = 3) and 39 (N = 13) dimensions. At the end of the study, a model has been proposed to functionalize the potential energy in terms of geometric variables that are identified with a heuristic screening. Investigation of the thermodynamics of bulk systems was another major focus of this thesis. The phase diagrams of the pure square-well solids and binary mixture of square-well and hard-disk particles, under the assumption of a pseudo-single- component model, have been constructed, and the phase equilibria behaviors were discussed. The datasets were also created in Monte Carlo simulations. The results showed isostructural solid-solid phase transition, which was previously identified that the pure square-well system with a very short range of attraction undergoes, also occurs in the presence of additional hard-disk components, namely for the binary mixture of square-well and hard-disk systems.