Doctoral Degrees (Physics)

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Browsing Doctoral Degrees (Physics) by Author "Boonzaaier, Leandro"

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    Confined counterions surrounding a Macroion : a field theoretic approach
    (Stellenbosch : Stellenbosch University, 2011-12) Boonzaaier, Leandro; Muller-Nedebock, Kristian K.; Scholtz, Frederik G.; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: Several experiments [1, 2, 3, 4] have shown that e ective attractive interactions exist between con ned like-charged macromolecules. Theoretical approaches have not reached consensus as to precisely what the mechanism for the attraction is, but it is agreed that comprehending the role of the counterion arrangement around macromolecules is crucial for understanding the e ective macromolecule interactions. It is generally assumed that attraction only occurs in the limit of strong electrostatic coupling and is driven by correlation e ects that are neglible in a mean- eld approach, which is valid in the weak-coupling limit. However, in some experimental situations attraction occurs even in the limit of weak-coupling. We consider a eld-theoretic approach that includes uctuations to study the Coulomb interactions of con ned counterions with a single exible charged spherical macromolecule that can expand or collapse uniformly by changing its radius. We show how the linearised eld-theory (valid in the weak-coupling limit) is mapped onto the square-well potential of Quantum Mechanics. The con nement leads to bound states being present in the spectrum at all times. Bound states are non-perturbative and we investigate the role they play in the physics of the system. Some of the e ects are rather counter-intuitive. Firstly, upon expanding the macromolecule in a xed con nement volume, the uctuation part of the free energy favours a decrease in the free energy. Secondly, upon increasing the temperature to high but nite values, the uctuation contribution does not dominate the free energy as would be expected. The mathematical origins of these e ects are dicussed in detail and as part of the analysis we introduce a novel regularisation scheme for computing the functional determinant arising in the model considered where the cut-o is speci ed unambiguously in terms of physical parameters.