Ion-induced nucleation in polar one-component fluids

The free energy due to the polarization and the charge¹² is $Fe=∫dr(P2∕2χ+E2∕8π)$ with $∇∙(E+4πP)=4πρ$⁠. For $P=χE$ we obtain Eqs. (2.1) and (2.5). If $P=0$⁠, it is equal to the vacuum result $Z2e2∕2RB$ for a single ion. If $P=χE$ without electrostriction, it is equal to $ΔΩBorn$ in Eq. (2.17). In literature (Refs. 5 and 10) the difference of these two quantities is the Born formula for the solvation free energy.

In discussing the droplet growth we need to consider the inhomogeneity of the temperature induced by latent heat absorption or generation at the interface (Ref. 21).

In Eq. (2.17) we obtain $RB=(5∕6)Ri$ from Eq. (2.5) if the integration is performed also in the region $r<Ri$ (Ref. 13).

In dynamics growing or shrinking of the droplet occurs depending on whether the added particle number is positive or negative. For example, this can be verified if we assume the time-evolution equation $∂n∕∂t=∇2δ(ΔΩ′)∕δn$⁠.

Near the critical point we obtain $RR∕ξ∼(1−T∕Tc)(ν+β)∕3$⁠, where $ξ∝(1−T∕Tc)−ν$ is the correlation length with $ν≅0.63$ and $β≅0.33$ being the critical exponents (Ref. 21). The interface thickness is of the order $ξ$⁠.