  The effective elasticity of highly charged stiff polyelectrolytes is studied
in the presence of counterions, with and without added salt. The rigid polymer
conformations may become unstable due to an effective attraction induced by
counterion density fluctuations. Instabilities at the longest, or intermediate
length scales may signal collapse to globule, or necklace states, respectively.
In the presence of added-salt, a generalized electrostatic persistence length
is obtained, which has a nontrivial dependence on the Debye screening length.
It is also found that the onset of conformational instability is a re-entrant
phenomenon as a function of polyelectrolyte length for the unscreened case, and
the Debye length or salt concentration for the screened case. This may be
relevant in understanding the experimentally observed re-entrant condensation
of DNA.
