406 research outputs found
Charge regulation: a generalized boundary condition?
The three most commonly-used boundary conditions for charged colloidal
systems are constant charge (insulator), constant potential (conducting
electrode) and charge regulation (ionizable groups at the surface). It is
usually believed that the charge regulation is a generalized boundary condition
that reduces in some specific limits to either constant charge or constant
potential boundary conditions. By computing the disjoining pressure between two
symmetric planes for these three boundary conditions, both numerically (for all
inter-plate separations) and analytically (for small inter-plate separations),
we show that this is not, in general, the case. In fact, the limit of charge
regulation is a separate boundary condition, yielding a disjoining pressure
with a different characteristic separation-scaling. Our findings are supported
by several examples demonstrating that the disjoining pressure at small
separations for the charge regulation boundary-condition depends on the details
of the dissociation/association process.Comment: 6 pages, 3 figure
Surface Tension of Electrolyte Solutions: A Self-consistent Theory
We study the surface tension of electrolyte solutions at the air/water and
oil/water interfaces. Employing field-theoretical methods and considering
short-range interactions of anions with the surface, we expand the Helmholtz
free energy to first-order in a loop expansion and calculate the excess surface
tension. Our approach is self-consistent and yields an analytical prediction
that reunites the Onsager-Samaras pioneering result (which does not agree with
experimental data), with the ionic specificity of the Hofmeister series. We
obtain analytically the surface-tension dependence on the ionic strength, ionic
size and ion-surface interaction, and show consequently that the
Onsager-Samaras result is consistent with the one-loop correction beyond the
mean-field result. Our theory fits well a wide range of concentrations for
different salts using one fit parameter, reproducing the reverse Hofmeister
series for anions at the air/water and oil/water interfaces.10.1029Comment: 5 pages, 2 figure
Constructing families of moderate-rank elliptic curves over number fields
We generalize a construction of families of moderate rank elliptic curves
over to number fields . The construction, originally
due to Steven J. Miller, \'Alvaro Lozano-Robledo and Scott Arms, invokes a
theorem of Rosen and Silverman to show that computing the rank of these curves
can be done by controlling the average of the traces of Frobenius, the
construction for number fields proceeds in essentially the same way. One
novelty of this method is that we can construct families of moderate rank
without having to explicitly determine points and calculating determinants of
height matrices.Comment: Version 1.0, 4 pages, sequel to arXiv:math/040657
Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions
We study, by incorporating short-range ion-surface interactions, ionic
profiles of electrolyte solutions close to a non-charged interface between two
dielectric media. In order to account for important correlation effects close
to the interface, the ionic profiles are calculated beyond mean-field theory,
using the loop expansion of the free energy. We show how it is possible to
overcome the well-known deficiency of the regular loop expansion close to the
dielectric jump, and treat the non-linear boundary conditions within the
framework of field theory. The ionic profiles are obtained analytically to
one-loop order in the free energy, and their dependence on different
ion-surface interactions is investigated. The Gibbs adsorption isotherm, as
well as the ionic profiles are used to calculate the surface tension, in
agreement with the reverse Hofmeister series. Consequently, from the
experimentally-measured surface tension, one can extract a single adhesivity
parameter, which can be used within our model to quantitatively predict hard to
measure ionic profiles.Comment: 14 pages, 6 figure
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