Long-range electrostatic interactions between like-charged colloids: steric and confinement effects

Within the framework of a Modified Poisson-Boltzmann theory accounting for steric effects of microions, we prove analytically that the effective pair interactions between like-charge colloids immersed in a confined electrolyte are repulsive. Our approach encompasses and extends previously known results to the case of complete confinement, and further incorporates the finite size of the microions which is absent in the standard Poisson-Boltzmann theory.Comment: 5 pages, 1 figure, to appear in Physical Review

Sine-Gordon theory for the equation of state of classical hard-core Coulomb systems. II. High-temperature expansion

We perform a high-temperature expansion of the grand potential of the restrictive primitive model of electrolytes in the frame of the extended sine-Gordon theory exposed in the companion paper. We recover a result already obtained by Stell an Lebowitz (J. Chem. Phys., 49, 3706 (1968)) by means of diagrammatic expansions

On geometric aspects of diffuse groups

Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric point of view from Bowditch's paper. In particular, we discuss fundamental groups of flat and hyperbolic manifolds. The appendix settles an open question by providing an example of a group which is diffuse but not left-orderable.Comment: 37 pages, main text by Kionke and Raimbault, appendix by Dunfield. v2 : updated ancillary files and added url to the reference