  Ion channels play a key role in regulating cell behavior and in electrical
signaling. In these settings, polar and charged functional groups -- as well as
protein response -- compensate for dehydration in an ion-dependent way, giving
rise to the ion selective transport critical to the operation of cells.
Dehydration, though, yields ion-dependent free-energy barriers and thus is
predicted to give rise to selectivity by itself. However, these barriers are
typically so large that they will suppress the ion currents to undetectable
levels. Here, we establish that graphene displays a measurable dehydration-only
mechanism for selectivity of $\mathrm{K}^+$ over $\mathrm{Cl}^-$. This
fundamental mechanism -- one that depends only on the geometry and hydration --
is the starting point for selectivity for all channels and pores. Moreover,
while we study selectivity of $\mathrm{K}^+$ over $\mathrm{Cl}^-$, we find that
dehydration-based selectivity functions for all ions, i.e., cation over cation
selectivity (e.g., $\mathrm{K}^+$ over $\mathrm{Na}^+$). Its likely detection
in graphene pores resolves conflicting experimental results, as well as
presents a new paradigm for characterizing the operation of ion channels and
engineering molecular/ionic selectivity in filtration and other applications.
