Diffusion In Highly Confined Channels: A Transition State Theory for Hopping
Date
2019-09-16
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ORCID
Type
Thesis
Degree Level
Doctoral
Abstract
Brownian particles restricted to narrow, quasi-one dimensional channels exhibit a dynamic transition from single file diffusion (SFD) to normal diffusion for tracer particle diffusion as the channels' confinement becomes less severe and the pore diameter is wide enough for the particles to hop past each other. The dynamics of a tracer particle in the crossover regime can be described in terms of a hopping time, that measures the average time for a tagged particle to escape the cage formed by its immediate left and right neighbors. The hopping time contains all the details of the systems such as the density, particle-particle and particle-wall interactions and has a potential to lead to a better understanding of diffusion and the control of transport in confined single file fluids.
The main goal of this thesis is to develop a Transition State Theory (TST) approach to the calculation of the hopping time in Single file fluids. The method rigorously transforms the process of a particle escaping its cage, in a many particle single- file system, into a problem involving two particles attempting to pass each other in a small system isobaric-isothermal ensemble. The validity of this approach is examined theoretically and computationally for a system of two-dimensional ideal gas particles and a two-dimensional hard disc system. The proposed method correctly predicts the hopping times for the full range of pore radii studied for the ideal gas system. For the case of hard discs, inclusion of the prefactor calculations is necessary, because of its dependency on the channels' diameter, and leads to a quantitative prediction of hopping time.
To demonstrate the effect particle-particle interactions have on diffusion in single file fluids, the hopping time and TST barriers are calculated for a system of soft repulsive discs. The result shows the method overestimates the hopping time for the narrower channels and underestimates it for the wider channels, which could be related to the assumptions made in deriving the partition function for the system, and also the kinetic prefactor calculations. Nevertheless, the method resulted in a quantitative prediction of hopping times within a factor of two.
It has previously shown that various components of a mixture may experience di fferent hopping barriers, leading to differences in tracer particle mobility. This thesis explores the possibility that enantiomers confined to a chiral channel exhibit different hopping times. The free energy barriers for the R- and S- enantiomers of Bromochlorofluoromethane, CHFClBr, inside carbon nanotubes are calculated using the TST isothermal-isobaric ensemble method, but are found to exhibit no difference. However, when the molecule, channel shapes, and interactions are modified to enhance the chiral interaction, the R- and S- enantiomers exhibit differences in their free energy barriers. In addition, reversing the chirality of the modified nanotube, reverses the relative heights of the barrier obtained for the two pairs of enantiomers, confirming that the chirality plays an important role in controlling the hopping barrier heights.
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Keywords
Single file system, single file diffusion, brownian particles, tracer particle, narrow channels, hopping time, diffusion coefficient, transition state theory, isobaric-isothermal ensemble, separation, enantiomers, hopping barrier, chirality, carbon nanotube
Citation
Degree
Doctor of Philosophy (Ph.D.)
Department
Chemistry
Program
Chemistry