Confined counterions surrounding a Macroion : a field theoretic approach

[摘要] ENGLISH ABSTRACT: Several experiments [1, 2, 3, 4] have shown that e ective attractive interactions existbetween con ned like-charged macromolecules. Theoretical approaches have not reachedconsensus as to precisely what the mechanism for the attraction is, but it is agreed thatcomprehending the role of the counterion arrangement around macromolecules is crucialfor understanding the e ective macromolecule interactions. It is generally assumed thatattraction only occurs in the limit of strong electrostatic coupling and is driven bycorrelation e ects that are neglible in a mean- eld approach, which is valid in theweak-coupling limit. However, in some experimental situations attraction occurs even inthe limit of weak-coupling. We consider aeld-theoretic approach that includesuctuations to study the Coulomb interactions of con ned counterions with a singleexible charged spherical macromolecule that can expand or collapse uniformly bychanging its radius. We show how the linearisedeld-theory (valid in the weak-couplinglimit) is mapped onto the square-well potential of Quantum Mechanics. The con nementleads to bound states being present in the spectrum at all times. Bound states arenon-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 themacromolecule in axed con nement volume, the uctuation part of the free energyfavours a decrease in the free energy. Secondly, upon increasing the temperature to highbutnite values, the uctuation contribution does not dominate the free energy as wouldbe expected. The mathematical origins of these e ects are dicussed in detail and as partof the analysis we introduce a novel regularisation scheme for computing the functionaldeterminant arising in the model considered where the cut-ois speci ed unambiguouslyin terms of physical parameters.

[发布机构] Stellenbosch University