1,358 research outputs found
Non-linear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes
From a multiple scale analysis, we find an analytic solution of spherical and
cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent co-ions,
divalent counter-ions) and a 2:1 (reversed situation) electrolyte. Our approach
consists in an expansion in powers of rescaled curvature , where
is the colloidal radius and the Debye length of the electrolytic
solution. A systematic comparison with the full numerical solution of the
problem shows that for cylinders and spheres, our results are accurate as soon
as . We also report an unusual overshooting effect where the
colloidal effective charge is larger than the bare one.Comment: 9 pages, 11 figure
Onsager-Manning-Oosawa condensation phenomenon and the effect of salt
Making use of results pertaining to Painleve III type equations, we revisit
the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff
linear polymers, in the mean-field approximation with salt. We obtain
analytically the associated critical line charge density, and show that it is
severely affected by finite salt effects, whereas previous results focused on
the no salt limit. In addition, we obtain explicit expressions for the
condensate thickness and the electric potential. The case of asymmetric
electrolytes is also briefly addressed.Comment: to appear in Phys. Rev. Let
Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile
We complement a recent exact study by L. Samaj on the properties of a guest
charge immersed in a two-dimensional electrolyte with charges . In
particular, we are interested in the behavior of the density profiles and
electric potential created by the charge and the electrolyte, and in the
determination of the renormalized charge which is obtained from the
long-distance asymptotics of the electric potential. In Samaj's previous work,
exact results for arbitrary coulombic coupling were obtained for a
system where all the charges are points, provided and .
Here, we first focus on the mean field situation which we believe describes
correctly the limit but large. In this limit we can
study the case when the guest charge is a hard disk and its charge is above the
collapse value . We compare our results for the renormalized charge
with the exact predictions and we test on a solid ground some conjectures of
the previous study. Our study shows that the exact formulas obtained by Samaj
for the renormalized charge are not valid for , contrary to a
hypothesis put forward by Samaj. We also determine the short-distance
asymptotics of the density profiles of the coions and counterions near the
guest charge, for arbitrary coulombic coupling. We show that the coion density
profile exhibit a change of behavior if the guest charge becomes large enough
(). This is interpreted as a first step of the counterion
condensation (for large coulombic coupling), the second step taking place at
the usual Manning--Oosawa threshold
Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
The two-dimensional one-component plasma (2dOCP) is a system of mobile
particles of the same charge on a surface with a neutralising background.
The Boltzmann factor of the 2dOCP at temperature can be expressed as a
Vandermonde determinant to the power . Recent advances in
the theory of symmetric and anti-symmetric Jack polymonials provide an
efficient way to expand this power of the Vandermonde in their monomial basis,
allowing the computation of several thermodynamic and structural properties of
the 2dOCP for values up to 14 and equal to 4, 6 and 8. In this
work, we explore two applications of this formalism to study the moments of the
pair correlation function of the 2dOCP on a sphere, and the distribution of
radial linear statistics of the 2dOCP in the plane
The Ideal Conductor Limit
This paper compares two methods of statistical mechanics used to study a
classical Coulomb system S near an ideal conductor C. The first method consists
in neglecting the thermal fluctuations in the conductor C and constrains the
electric potential to be constant on it. In the second method the conductor C
is considered as a conducting Coulomb system the charge correlation length of
which goes to zero. It has been noticed in the past, in particular cases, that
the two methods yield the same results for the particle densities and
correlations in S. It is shown that this is true in general for the quantities
which depend only on the degrees of freedom of S, but that some other
quantities, especially the electric potential correlations and the stress
tensor, are different in the two approaches. In spite of this the two methods
give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge
Description beyond the mean field approximation of an electrolyte confined between two planar metallic electrodes
We study an electrolyte confined in a slab of width composed of two
grounded metallic parallel electrodes. We develop a description of this system
in a low coupling regime beyond the mean field (Poisson--Boltzmann)
approximation. There are two ways to model the metallic boundaries: as ideal
conductors in which the electric potential is zero and it does not fluctuate,
or as good conductors in which the average electric potential is zero but the
thermal fluctuations of the potential are not zero. This latter model is more
realistic. For the ideal conductor model we find that the disjoining pressure
is positive behaves as for large separations with a prefactor that is
universal, i.e. independent of the microscopic constitution of the system. For
the good conductor boundaries the disjoining pressure is negative and it has an
exponential decay for large . We also compute the density and electric
potential profiles inside the electrolyte. These are the same in both models.
If the electrolyte is charge asymmetric we find that the system is not locally
neutral and that a non-zero potential difference builds up between any
electrode and the interior of the system although both electrodes are grounded.Comment: 16 pages, 5 figures, added a new appendix B and a discussion on ideal
conductors vs. good conductor
Integración de las construcciones rurales en el paisaje: encuestas y conclusiones
Design and integration of rural buildings in landscape: surveys and conclusions. The visual and aesthetic aspect of any object is defined by its characteristics of colour, form, line and texture. Any elements of compositive reference such as its scale and spatial character could also be added. This research applies a new method for predicting the value of the integration of buildings into the landscape, based on psychological aspects and the capacities of modern computers that are able to analyse easily these attributes. The designer can analyse the visual elements, all of them divided and studied in the properties that define them
A comparative study between single gas and mixed gas permeation of polyether-block-amide type copolymer membranes
We analyze the gas separation performance of five polyether-block-amide type copolymers (Pebax® 1657, Renew®, 2533, 3533 and 4533). These codes are composed of different hard and rubbery segments with different proportions. Dense membranes were prepared by the casting-solution method and studied by elemental, thermogravimetric and X-ray diffraction analyses, FTIR-ATR spectroscopy and single and mixed gas permeation. Codes with the best separation performance are those of polyethylene oxide as the soft phase (Pebax® 1657 and Renew®) due to the more intense interactions of this segment with CO2, which increases the CO2/N2 solubility selectivity (17.5 and 30.5 for Pebax® 1657 and Renew®, respectively) and hence the CO2/N2 separation selectivity of the membrane (36 and 37 for Pebax® 1657 and Renew®, respectively, obtained from mixed gas permeation). It is also noticeable that the proportion of the soft phase in the copolymer determines the permeability of CO2. It was found that the codes with a greater soft/hard segment ratio (Pebax® 2533 and 3533) have also a greater permeability value (239 and 220 Barrer for Pebax® 2533 and 3533, respectively, measured by mixed gas permeation). Pebax® Renew® was the polymer with the best separation performance with CO2 permeabilities of 167 and 164 Barrer and CO2/N2 selectivities of 41 and 37, measured by single and mixed gas permeation, respectively. The comparison between the single and mixture gas permeation results revealed a relatively good correspondence between both for most of the Pebax® codes tuned by the solubility and diffusion properties of the polymers. © 2022 The Authors
Equation of state in the fugacity format for the two-dimensional Coulomb gas
We derive the exact general form of the equation of state, in the fugacity
format, for the two-dimensional Coulomb gas. Our results are valid in the
conducting phase of the Coulomb gas, for temperatures above the
Kosterlitz-Thouless transition. The derivation of the equation of state is
based on the knowledge of the general form of the short-distance expansion of
the correlation functions of the Coulomb gas. We explicitly compute the
expansion up to order in the activity . Our results are in
very good agreement with Monte Carlo simulations at very low density
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