Undergraduate Thesis Or Project
 

Freezing a Softly Repulsive Fluid : Monte Carlo Methods and the Weeks-Chandler-Andersen Potential

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  • The equation of state for a fluid described by the Weeks-Chandler-Andersen (WCA) potential was solved to determine at what pressures and temperatures the fluid will theoretically freeze. A Monte Carlo (MC) algorithm was used to sample a system of 256 spheres for a set of thermodynamic averages to locate and confirm a phase transition. A thorough discussion of the basics of the Metropolis MC algorithm and the derivation of thermodynamic averages for WCA are developed. The phase transitions over varying densities and temperatures were found and used to plot a pair of phase diagrams which describe the equation of state. The WCA potential is a modification of the Lennard-Jones potential and it treats intermolecular potentials as fully repulsive which means there is no liquid state. Its implementation into density functional theory (DFT) has been of interest to the Roundy research group for some time, and to determine whether or not the DFT is accurate the group needs to compare results with the MC. The WCA potential is used as a model for crystal growth kinetics and dendrimers, so simulations that better model the properties of those categories of materials can provide greater insight into their behavior.
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  • Roundy Research Group
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