Natarajan, S; (2007) Stability of small molecular clusters modelled with stochastic and deterministic dynamics. Doctoral thesis , UCL (University College London).

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Abstract

This investigation concerns the transition pathway of the condensation phase transition. Under certain conditions condensation is initiated by nucleation events, which are driven by fluctuations or instabilities in the vapour phase. This involves the spontaneous formation of groups of particles, which we refer to as clusters. The clusters have a highly unstable nature and exist momentarily, before breaking up. This makes them difficult to study experimentally and model mathematically, in comparison to larger more stable systems. The aim of this study is to explore the stability of these tiny molecular clusters that exist momentarily within their environment, in terms of the time taken for the cluster to lose particles (decay). To do this we employ a microscopic cluster model of n-nonane molecules in which the cluster is treated in isolation from the vapour particles that would normally surround it. The interactions between cluster particles are modelled using empirical potentials. The cluster's dynamics is modelled using deterministic molecular dynamics simulations. The simulations generate a time evolved trajectory of all the positions, velocities and forces of all the atoms in the cluster. The process of cluster decay in n-nonane clusters is modelled using a Langevin interpretation of the decay mechanism. This treatment views cluster decay as a process of single particle escape from a confining potential of mean force, driven by a particle's interactions with the surrounding cluster particles. The motion of a cluster particle is modelled using a Langevin equation, which is parameterised using the MD generated data in order to extract the decay related parameters. The decay parameters are used to evaluate an Arrhenius type equation for the kinetic decay rate. This is used to calculate the mean timescale of cluster decay for n-nonane clusters, which we refer to as the mean cluster lifetime. We compare the dynamically generated lifetimes calculated from the model to those predicted by experimental measurements, as well as classically derived lifetimes. We discover the dynamical model predicts lifetimes that compare well to experimental predictions. The cluster decay model allows us to predict cluster decay timescales without decay events actually occurring. This makes it an essential tool for systems with long decay timescales, for which decay events can not be feasibly observed through MD simulations alone. Finally, the last chapter presents recent work that has been conducted on ice cluster embryos. The ice embryos emerge during the freezing transition of supercooled water into ice I. Unlike the previous method of treating clusters in isolation from their surroundings, this study involves the treatment of ice clusters in coexistence with their environment. We utilise a molecular dynamics trajectory of supercooled water freezing into ice, which is used to identify and extract ice cluster embryos. It is evident from the MD simulations that at the initial stages of freezing the clusters are very amorphous and disordered. We investigate cluster properties such as the size distribution and molecular connectivity, and explore whether we are able to quantify the potential of mean force in order to estimate the mean lifetime of disordered ice cluster embryos.

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