Thesis (PhD)--Stellenbosch University, 2011. / 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. / AFRIKAANSE OPSOMMING: Verskeie eksperimente [1, 2, 3, 4] toon dat makro-ione met gelyksoortige ladings, in `n
eindige volume, `n e ektiewe aantrekkende krag ondervind. Alhoewel daar nog geen
konsensus oor die presiese meganisme vir die aantrekking bereik is nie, is dit duidelik dat
die rol van \counter-ion" rangskikking rondom die makro-ione belangrik is om die
e ektiewe wisselwerkings te verstaan. Dit word algemeen aanvaar dat die aantrekkende
krag slegs in die limiet van sterk elektrostatiese koppeling plaasvind en dat dit `n gevolg
van \counter-ion" korrelasies is wat weglaatbaar is in `n gemiddelde veld benadering, wat
geldig is in die limiet van swak elektrostatiese koppeling. Daar bestaan egter
eksperimentele situasies waar die aantrekking in die limiet van swak elektrostatiese
koppeling waargeneem word. Ons bestudeer die Coulomb wisselwerking tussen
\counter-ions" en `n enkele rekbare sferiese makro-ioon vanuit `n veld-teoretiese
beskouing wat
uktuasies in ag neem. Die sferiese makro-ioon kan vergroot of verklein
deur sy radius uniform te verander. Ons toon aan dat die gelineariseerde veldeteorie
(geldig in die limiet van swak elektrostatiese koppeling) op die eindige-diepte put
Kwantummeganiese model afgebeeld kan word. Die eindige volume van die sisteem het
tot gevolg dat daar altyd gebonde toestande in die spektrum voorkom. Gebonde
toestande is `n suiwer nie-steuringsteoretiese e ek en ons ondersoek die rol wat dit speel
in die sika van die sisteem. Die teenwoordigheid van die gebonde toestande in die
spektrum het `n paar teen-intuitiewe e ekte tot gevolg. Eerstens word die vrye energie
verlaag soos die makro-ioon in `n eindige volume vergroot. Tweedens oorheers die
uktuasie bydrae nie die vrye energie met toenemende temperatuur soos verwag sou
word nie. Ons bespreek die wiskundige oorsprong van hierdie e ekte. As deel van die
analise ontwikkel ons `n nuwe regulariseringstegniek vir die berekening van
funksionaalintegrale waar die regulariseringsparameter ondubbelsinnig in terme van
siese hoeveelhede uitgedruk kan word.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/17853 |
| Date | 12 1900 |
| Creators | Boonzaaier, Leandro |
| Contributors | Muller-Nedebock, Kristian K., Scholtz, Frederik G., Stellenbosch University. Faculty of Science. Dept. of Physics. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 57 p. |
| Rights | Stellenbosch University |
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