  The interaction between charged objects in an electrolyte solution is a
fundamental question in soft matter physics. It is well-known that the
electrostatic contribution to the interaction energy decays exponentially with
object separation. Recent measurements reveal that, contrary to the
conventional wisdom given by classic Poisson-Boltzmann theory, the decay length
increases with ion concentration for concentrated electrolytes and can be an
order of magnitude larger than the ion diameter in ionic liquids. We derive a
simple scaling theory that explains this anomalous dependence of the decay
length on ion concentration. Our theory successfully collapses the decay
lengths of a wide class of salts onto a single curve. A novel prediction of our
theory is that the decay length increases linearly with the Bjerrum length,
which we experimentally verify by surface force measurements. Moreover, we
quantitatively relate the measured decay length to classic measurements of the
activity coefficient in concentrated electrolytes, thus showing that the
measured decay length is indeed a bulk property of the concentrated electrolyte
as well as contributing a mechanistic insight into empirical activity
coefficients.
