  We present a scaling behavior of a rectifying bipolar nanopore as a function
of the parameter $\xi=R_{\mathrm{P}}/(\lambda z_{\mathrm{if}})$, where
$R_{\mathrm{P}}$ is the radius of the pore, $\lambda$ is the characteristic
screening length of the electrolyte filling the pore, and
$z_{\mathrm{if}}=\sqrt{z_{+}|z_{-}|}$ is a scaling factor that makes scaling
work for electrolytes containing multivalent ions ($z_{+}$ and $z_{-}$ are
cation and the anion valences). By scaling we mean that the rectification of
the pore (defined as the ratio of currents in the forward and reversed biased
states) depends on pore radius, concentration, $c$, and ion valences via the
parameter $\xi$ implicitly. This feature is based on the fact that
rectification depends on the voltage-sensitive appearance of depletion zones
that, in turn, depend on the relation of $R_{\mathrm{P}}$ to the rescaled
screening length $\lambda z_{\mathrm{if}}$. In this modeling study, we use the
Poisson-Nernst-Planck (PNP) theory and a particle simulation method, the Local
Equilibrium Monte Carlo (LEMC). The latter can compute ion correlations that
are ignored in the mean-field treatment of PNP and that are very important for
multivalent ions (we show results for 1:1, 2:1, 3:1, and 2:2 electrolytes). In
addition to the $z_{\mathrm{if}}$ factor, we show that one must choose a
screening length appropriate to the system, in our case the Debye length for
$\lambda$ for PNP and the screening length given by the Mean Spherical
Approximation for LEMC.
