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Chapter 6: CONCLUSION |
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In this thesis, we estimated the free energy of the homogeneous nucleation in the supersaturated Lennard-Jones vapor phase by using the Monte Carlo simulations. The MC simulations are performed on the various numbers of particles and volumes per particle at 128 states. From the MC results, we assumed an equation of state for the free energy of the homogeneous nucleation as a function of the number of particles, the temperature, and the volume per particle. The EOS clarified the characteristics of the nucleation energy against these variables. The results obtained in this work are concluded as follows. First, we focused a specific N-particle nucleation, and daringly simplified the nucleation as the phase transition between the two extremes of the N-particle system, i.e., from the monomer phase to the cluster phase. In the former, the N particles scatter as the supersaturated vapor phase, while in the latter, on contrary, the N particles connect together as a unity cluster. If the free energies of the monomer phase and the cluster phase in the N-particle system are estimated independently, which difference obtains the N-particle nucleation free energy. In the simulations of the cluster phase, we restricted the system configuration to keep a unity cluster in the whole range of the simulated temperature by the Stillinger's cluster criterion. In which the all particles of the system should be connected together, and the connection is decided by a threshold value of the interparticle distance. We obtained the interaction part of the Helmholtz free energy under constant volume per particle as sum of the interaction energy and the interaction entropy term. The interaction entropy was estimated by the thermodynamic integration from the interaction energy, as the relative value from the low temperature. Secondly, the Helmholtz free energy gave a maximum (the critical nucleus) against the number of cluster particles under representative temperature (near the triple point temperature of the LJ fluid) and volume per particle. That has been studied widely by the small- and large-scale simulations, in which the critical nuclei were similarly obtained. Thirdly, we designed the equation of state for the Helmholtz free energy of the homogeneous nucleation by the results of MC simulations at the 128 states. From the EOS, we suggested a reason what the nucleation energy has a maximum against the number of particles; that is caused by competition between the internal energy term and the entropy term of the nucleation energy. Lastly, we suggested a method that rearranges the EOS for estimating Gibbs free energy of the homogeneous nucleation as a function of the number of particles, the temperature, and the pressure. The EOS gave the maximum and behaved similarly to the one of the Helmholtz free energy in which low-pressure/low-density region. Though the EOS still has unsatisfied problems as the overestimation of the nucleation energy in which high-pressure/high-density region, it is variable as a technique for estimating the EOS of the Gibbs free energy of the homogeneous nucleation from the microscopic MC simulations with the simplified model. |
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