Counter-ion condensation and Kosterlitz–Thouless transition

Abstract

The similarity between counter-ion condensations in polyelectrolyte rod systems andKosterlitz–Thouless phase transitions in two-dimensional systems is discussed at the levelof mean-field theory. Based on the similarity, the renormalization group theory is applied topolyelectrolyte liquid systems aligned in parallel. It is found that the critical separationbetween monovalent charges for the counter-ion condensation is renormalized inpolyelectrolyte liquid systems and becomes shorter than the Bjerrum length which is thecritical separation predicted by the mean-field theory for a dilute solution of polyelectrolyterods.