  Screening of a surface charge by electrolyte and the resulting interaction
energy between charged objects is of fundamental importance in scenarios from
bio-molecular interactions to energy storage. The conventional wisdom is that
the interaction energy decays exponentially with object separation and the
decay length is a decreasing function of ion concentration; the interaction is
thus negligible in a concentrated electrolyte. Contrary to this conventional
wisdom, we have shown by surface force measurements that the decay length is an
increasing function of ion concentration and Bjerrum length for concentrated
electrolytes. In this paper we report surface force measurements to test
directly the scaling of the screening length with Bjerrum length. Furthermore,
we identify a relationship between the concentration dependence of this
screening length and empirical measurements of activity coefficient and
differential capacitance. The dependence of the screening length on the ion
concentration and the Bjerrum length can be explained by a simple scaling
conjecture based on the physical intuition that solvent molecules, rather than
ions, are charge carriers in a concentrated electrolyte.
