Doctoral Degrees (Physics)

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Browsing Doctoral Degrees (Physics) by browse.metadata.advisor "Boonzaaier, Leandro"

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    Particle diffusion in elastically coupled narrow parallel channels
    (Stellenbosch : Stellenbosch University, 2014-12) Mateyisi, Mohau Jacob; Muller-Nedebock, Kristian K.; Boonzaaier, Leandro; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: We investigate a model system for particle diffusion in elastically coupled one-dimensional narrow channels. The elastic coupling of the channels is such that channels mutually affect the stochastic dynamics of particles. This kind of constrained and coupled stochastic diffusion may occur in supramolecular lattices where pore occupancy by guest particles may induce a reversible mechanical deformation of the lattice hence, affecting particle evolution in neighbouring pores. The model is explored first for out-of-equilibrium conditions, where we look mainly at the kinetic properties of the system, and thereafter under equilibrium conditions, where we try to understand the nature of dynamic correlation within the coupled channel system. For an out-of-equilibrium version of the model the focus is placed on the steady state behaviour of the two elastically coupled finite channels. The channels are kept in contact with particle reservoirs at the boundaries. Three current-density regimes of different distinct behaviour are identified using a simulation experiment. The sensitivity of the system mean occupancy profile and the steady state particle flux to small and large coupling parameter strength are explored. We find that, for small coupling strength, the system steady state profile and flux behaviour can be approximated by a simple mean field theory ignoring density-density correlations. We present the analytic description of the system using a cellular automaton formalism and then we generalize the theory for a multi-coupled channel system using a hopping particle dynamics approach. For small coupling parameter values, the analytic results are confirmed by the stochastic simulation. From the equilibrium perspective, we model the elastically coupled channel system as a system of infinite narrow channels having a uniform guest particle occupancy and we calculate density fluctuation correlation functions. The elastic coupling between channels is modelled as short range interacting potential and the particle evolution is modelled through Langevin dynamics. The dynamics are cast into the functional integral formalism expressed in terms of the collective particle number density, current density and the associated density response fields. The resulting generating functional takes these fields into consideration within the random phase approximation (RPA) up to second order. For a short range interaction potential, we uncover the behaviour of the system by looking at the influence of the inter-channel interaction strength on the dynamic density-density correlation functions. We conclude that the system long time limit effective friction coefficient is reduced with increase in the coupling parameter values while the strength of thermal forces for the effective system becomes renormalized. We also find out that the RPA breaks down under certain conditions, signalling a transition to a behaviour that is no longer characterised by a homogeneous density. The work presented here provides the beginnings for microscopic insights into the filling, filtering and storage processes for which certain types of microporous materials can be utilised.