  In this paper we study the electrostatic properties of `Janus' spheres with
unequal charge densities on both hemispheres. We introduce a method to compare
primitive-model Monte Carlo simulations of the ionic double layer with
predictions of (mean-field) nonlinear Poisson-Boltzmann theory. We also derive
practical DLVO-like expressions that describe the Janus-particle pair
interactions by mean-field theory. Using a large set of parameters, we are able
to probe the range of validity of the Poisson-Boltzmann approximation, and thus
of DLVO-like theories, for such particles. For homogeneously charged spheres
this range corresponds well to the range that was predicted by
field-theoretical studies of homogeneously charged flat surfaces. Moreover, we
find similar ranges for colloids with a Janus-type charge distribution. The
techniques and parameters we introduce show promise for future studies of an
even wider class of charged-patterned particles.
