M. Labowsky et al., A continuum model for ion evaporation from a drop: effect of curvature andcharge on ion solvation energy, ANALYT CHIM, 406(1), 2000, pp. 105-118
A drop of liquid is treated as a continuum medium with surface tension gamm
a and dielectric constant epsilon. The energy Delta (surface + electrostati
c) required to extract a solvated ion from the drop can then be determined
as part of a well posed problem as a function of the initial number z + 1 o
f elementary charges in the drop and its initial radius R'. Instead of a di
rect numerical attack on the full model, a geometrically simpler situation
is analyzed, in which the drop and the solvated ion are taken to be either
spheres or spherical caps after or prior to detachment, respectively. This
simplified model is closely related to the full continuous problem when the
radius R-i of the solvated ion is small (R-i/R' << 1), and the main drop i
s not near the Rayleigh limit. This model problem is solved analytically in
the limit epsilon << 1. When z = 0 and 1/R' = 0 one recovers Born's result
, where Delta = 2.7 eV for monovalent ions in water, which exceeds by some
0.3 eV the experimental value for the alkali ions. In the limit of small io
ns one recovers the results of Gamero et al. [5], Delta = Delta G(Born) - e
(2)[F(z)+alpha]/(4 pi epsilon(0)R'), though surface tension effects shift t
he constant cr from 4/5 to 2/3, The effect of finite ion diameter is determ
ined numerically for the two-spheres model. When the solvation energy at ze
ro curvature and charge is Delta G(born), small ions do not evaporate from
water drops. When this value is reduced to fit available experimental data,
a narrow ion evaporation window appears for drops charged near the Rayleig
h limit with z similar to 12 or less. The domain in (z, R') space leading t
o ion evaporation is broader for the case of formamide. The micro-hydrodyna
mic process of escape of a singly charged nanodrop from a larger drop requi
res a large activation energy. It is hence indistinguishable from Iribarne-
Thomson ion evaporation, and radically different from a Coulomb explosion.
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