Molecular Dynamics: an Investigation Into Heat Capacity with Respect to Temperature of a Lennard Jones Fluid.
The simulation and analysis of liquid droplets with respect to heat capacity and droplet size
Abstract
Define
Using Molecular dynamic simulation a cluster of particles was modelled and their behaviour analysed with respect to temperature change. As proof of a specific state i.e. solid, the Mean squared displacement was calculated and illustrated with respect to time. This occurred for varying temperatures. From the internal energy of the system per time step, the heat capacity was determined. Heat capacity was then plotted against temperature in order to view phase transitions. The results show almost independence of heat capacity-temperature curves with respect to the number of particles. That is, for all numbers of particles in said range the heat capacity rises with respect to temperature and then plateaus at temperatures where the cluster changes state. Knowledge of this change of state was found by other means and the shape of these curves was backed by the theory of gradual phase change. There were no visible peaks in these curves which would be an indicator for specific temperatures where state changes occur abruptly. From the simulations and these results it was clear that there was also co-existence of states.
The investigation:
With the birth of Quantum mechanics came uncertainty at the particle level and it began to dominate the microscopic world. Nonetheless, today a lot still needs to be learnt from the classical world. The numerical solutions of N-body problems are something that Molecular dynamics solves elegantly. Molecular Simulations then allowed for these particles to be viewed in certain environments without real experimentation. This investigation was done on clusters as it was clear from that start that the results obtained would be beneficial. This is in the sense that, although there have been many studies done on clusters, with respect to state transition there is not a definite conclusion. Thus this investigation was
Abstract
Define
Using Molecular dynamic simulation a cluster of particles was modelled and their behaviour analysed with respect to temperature change. As proof of a specific state i.e. solid, the Mean squared displacement was calculated and illustrated with respect to time. This occurred for varying temperatures. From the internal energy of the system per time step, the heat capacity was determined. Heat capacity was then plotted against temperature in order to view phase transitions. The results show almost independence of heat capacity-temperature curves with respect to the number of particles. That is, for all numbers of particles in said range the heat capacity rises with respect to temperature and then plateaus at temperatures where the cluster changes state. Knowledge of this change of state was found by other means and the shape of these curves was backed by the theory of gradual phase change. There were no visible peaks in these curves which would be an indicator for specific temperatures where state changes occur abruptly. From the simulations and these results it was clear that there was also co-existence of states.
The investigation:
With the birth of Quantum mechanics came uncertainty at the particle level and it began to dominate the microscopic world. Nonetheless, today a lot still needs to be learnt from the classical world. The numerical solutions of N-body problems are something that Molecular dynamics solves elegantly. Molecular Simulations then allowed for these particles to be viewed in certain environments without real experimentation. This investigation was done on clusters as it was clear from that start that the results obtained would be beneficial. This is in the sense that, although there have been many studies done on clusters, with respect to state transition there is not a definite conclusion. Thus this investigation was
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