An investigation of the dynamics of phase transitions in Lennard-Jones fluids

Abstract

This thesis reports the development, validation and application of a method to simulate external heat addition in molecular dynamics simulations of Lennard-Jones fluids. This simulation capability is very important for both purely theoretical and practical applications. Here we examine one theoretical application, namely the evaporation of clusters of liquid Argon under constant pressure. The algorithm is based on modified equations of motion derived from Newton's equations with the use of what is known in the literature as Gauss' least constraint principle. The modified equations of motion satisfy the constraint of linear (in time) energy addition to all the system molecules. The first part of the thesis presents the validation of the heat addition algorithm: the method is useful only if it does not adversely affect the properties of the simulated material. The validation consists of a series of simulations of a Lennard-Jones fluid in a two-dimensional channel bounded between two parallel (molecular) walls. The walls are kept at constant temperature, while the fluid is externally heated using the new simulation method. The temperature profile solution for this problem is, according to (the exact) continuum theory, parabolic. Given the heat addition rate, estimates for the value of the thermal conductivity can be obtained from the curvature of the temperature profile. The estimates for the thermal conductivity are compared to experimental data for the fluid, and simulation data based on the Newtonian (exact) equations of motion for the same fluid. We find that the thermal conductivity estimates obtained from our simulations are in agreement with the baseline results utilizing the Newtonian equations of motion. The second part of the thesis reports on the investigation of the phase change of fluid clusters at constant pressure in real time using the heat addition algorithm. This has not been attempted before; results exist in the literature only for quasistatic simulations whereby the phase change behavior of a Lennard-Jones fluid is recovered by performing a series of equilibrium simulations at varying temperatures. The results obtained through the newly proposed, developed, and validated time dependent method are in agreement with the results of the quasistatic simulations as linear response theory predicts. We conclude with the interpretation of our results using homogeneous nucleation theory. We find that our results are consistent with homogeneous nucleation which predicts that phase separation starts at the nanoscopic level with critical radii of the order of a few nanometers for both evaporation and condensation. The critical nuclei for evaporation, which are gaseous, are predictably larger than the nuclei for condensation, which are in the liquid state. Our results are in good agreement with experimental data. This work can form the basis for the investigation of open problems related to nucleation theory and nucleation kinetics, such as metastable cluster lifetimes, and nucleation frequencies. Alternative phase change mechanisms, such as spinodal decomposition, can also be investigated.