We investigate the effect of counterion fluctuations in a single
polyelectrolyte brush in the absence of added salt by systematically expanding
the counterion free energy about Poisson-Boltzmann mean field theory. We find
that for strongly charged brushes, there is a collapse regime in which the
brush height decreases with increasing charge on the polyelectrolyte chains.
The transition to this collapsed regime is similar to the liquid-gas
transition, which has a first-order line terminating at a critical point. We
find that for monovalent counterions the transition is discontinuous in theta
solvent, while for multivalent counterions the transition is generally
continuous. For collapsed brushes, the brush height is not independent of
grafting density as it is for osmotic brushes, but scales linear with it.Comment: 9 pages, 9 figure
