  We theoretically investigate the nucleation of liquid droplets from vapor in
the presence of a charged spherical particle. Due to field gradients,
sufficiently close to the critical point of the vapor--gas system, the charge
destabilizes the vapor phase and initiates a phase transition. The fluid's free
energy is described by the van der Waals expression augmented by electrostatic
energy and a square-gradient term. We calculate the equilibrium density profile
at arbitrary temperatures, particle charges, and vapor densities. In contrast
to classical nucleation theory, here, both liquid and vapor phases are
different from the bulk phases because they are spatially nonuniform. In
addition, the theory applies to both sharp and diffuse interfaces and
calculates the surface tension self-consistently. We find the composition
profiles and integrate them to get the adsorption near the particle. We find
that the adsorption changes discontinuously at a first-order phase transition
line. This line becomes a second-order phase transition at high enough
temperatures. We describe the transition point numerically and provide
approximate analytical expressions for it. Similarly to prewetting, the
adsorption diverges at the binodal phase boundary. We construct a phase diagram
indicating changes in the binodal, spinodal, and critical temperature. It is
shown that the field gradient enlarges the range of temperature and vapor
density where liquid can nucleate.
