# Phase Equilibria of Diatomic Lennard-Jones Molecules Using Monte Carlo Simulation

Title: | Phase Equilibria of Diatomic Lennard-Jones Molecules Using Monte Carlo Simulation |

Author: | Galbraith, Aysa Lamia |

Advisors: | Orlin Velev, Committee Member Keith E. Gubbins, Committee Member Carol K. Hall, Committee Chair Peter K. Kilpatrick, Committee Member |

Abstract: | The overall aim of this research is to use computer simulations to study vapor-liquid and solid-liquid phase behavior of simple nonspherical molecules with a special focus on determining how the differences in the components' molecular size and intermolecular interactions affect the type of phase diagrams observed. We first calculate vapor-liquid phase diagrams for binary mixtures of diatomic Lennard-Jones molecules using Monte Carlo simulations and the Gibbs-Duhem integration method. We plot pressure versus composition vapor-liquid phase diagrams for the binary mixtures O₂-N₂, CO₂-C₂H₆ and N₂-C₂H₆ at different temperatures. We then add a quadrupole term to the two-center Lennard-Jones potential model and we observe that this further improves the agreement with experimental data. We also investigate the dependence of Henry's constant on the temperature, pressure and binary interaction parameter. We explore the effect of varying the molecular size ratio from σ₁₁/σ₂₂=1.0 to 1.40, intermolecular attraction ratio from ε₁₁/ε₂₂=0.70 to 1.20 and binary interaction parameter from δ₁₂=0.70 to 1.10 on the dumbbell mixture's phase behavior. We then examine the solid-liquid phase equilibria for systems containing pure Lennard-Jones dumbbell molecules and their mixtures. We begin by calculating the equations of state for systems containing C₂H₆, CO₂ and F₂, all of which are modeled by two-center Lennard-Jones potential for linear diatomic molecules. We then use the Frenkel-Ladd thermodynamic integration method to calculate the free energies. The equations of state and the free energies are used to obtain solid-liquid coexistence points which are needed to start the Gibbs-Duhem integration. The solid-liquid phase equilibria for pure and binary mixtures of Lennard-Jones dumbbells are predicted using the Gibbs-Duhem integration method. We use three model Lennard-Jones binary mixtures with varying bondlengths, σ₁₁/σ₂₂, ε₁₁/ε₂₂ ratios to calculate the solid-liquid phase diagram. Mixtures I, II and III show solid solution, azeotrope and eutectic phase diagrams, respectively. We then investigate the effects of molecular size and intermolecular attractions on the solid-liquid phase diagrams of binary Lennard-Jones mixtures using our three model mixtures. |

Date: | 2006-08-06 |

Degree: | PhD |

Discipline: | Chemical Engineering |

URI: | http://www.lib.ncsu.edu/resolver/1840.16/3185 |

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