  The experimentally observed swelling and collapse response of weakly charged
polymers to the addition of specific salts displays quite convoluted behavior
that is not easy to categorize. Here we use a minimalistic implicit solvent /
explicit salt simulation model with a focus on ion-specific interactions
between ions and a single weakly charged polyelectrolyte to qualitatively
explain the observed effects. In particular, we demonstrate ion-specific
screening and bridging effects cause collapse at low salt concentrations
whereas the same strong ion-specific direct interactions drive re-entrant
swelling at high concentrations. Consistently with experiments, a distinct salt
concentration at which the salting-out power of anions inverts from the reverse
to direct Hofmeister series is observed. At this, so called 'isospheric point',
the ion-specific effects vanish. Furthermore, with additional simplifying
assumptions, an ion-specific mean-field model is developed for the collapse
transition which quantitatively agrees with the simulations. Our work
demonstrates the sensitivity of the structural behavior of charged polymers to
the addition of specific salt and shall be useful for further guidance of
experiments.
