Monte Carlo methods are used to explore vapor-liquid phase transitions. However, current models are computationally expensive when identifying these phase transitions. Traditionally, Monte Carlo simulations are run across a range of temperatures at a fixed number of atoms/molecules. The Number Monte Carlo method (NMC), our proposed Monte Carlo method, runs simulations at a constant temperature across a range of atoms/molecules. In this thesis, NMC was run using a modified version of Stochastic Approximation Monte Carlo (SAMC).
NMC was able to simulate the square-well fluid at a reduced volume of 100 across a range of four reduced temperatures (0.8, 0.9, 1, 1.1). The liquid-to-vapor phase transition was observed at all temperatures except the reduced temperature of 0.8. Using the NMC phase transitions, a phase diagram was constructed and compared to one built from National Institutes of Standards and Technology (NIST) data. The comparison revealed that the two phase diagrams roughly agree. The simulations demonstrate the validity of NMC as a faster method of finding a single-phase transition. However, simulations with a higher volume are needed to test the accuracy of the model. Additionally, NMC is not found to yield any improvement in constructing a phase diagram.