10 research outputs found
Ground state of classical bilayer Wigner crystals
We study the ground state structure of electronic-like bilayers, where
different phases compete upon changing the inter-layer separation or particle
density. New series representations with exceptional convergence properties are
derived for the exact Coulombic energies under scrutiny. The complete phase
transition scenario --including critical phenomena-- can subsequently be worked
out in detail, thereby unifying a rather scattered or contradictory body of
literature, hitherto plagued by the inaccuracies inherent to long range
interaction potentials
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
Anomalous Effects of "Guest" Charges Immersed in Electrolyte: Exact 2D Results
We study physical situations when one or two "guest" arbitrarily-charged
particles are immersed in the bulk of a classical electrolyte modelled by a
Coulomb gas of positive/negative unit point-like charges, the whole system
being in thermal equilibrium. The models are treated as two-dimensional with
logarithmic pairwise interactions among charged constituents; the
(dimensionless) inverse temperature is considered to be smaller than 2
in order to ensure the stability of the electrolyte against the collapse of
positive-negative pairs of charges. Based on recent progress in the integrable
(1+1)-dimensional sine-Gordon theory, exact formulas are derived for the
chemical potential of one guest charge and for the asymptotic large-distance
behavior of the effective interaction between two guest charges. The exact
results imply, under certain circumstances, anomalous effects such as an
effective attraction (repulsion) between like-charged (oppositely-charged)
guest particles and the charge inversion in the electrolyte vicinity of a
highly-charged guest particle. The adequacy of the concept of renormalized
charge is confirmed in the whole stability region of inverse temperatures and
the related saturation phenomenon is revised.Comment: 21 pages, 1 figur
Wigner-Crystal Formulation of Strong-Coupling Theory for Counter-ions Near Planar Charged Interfaces
International audienceWe present a new analytical approach to the strong electrostatic coupling regime (SC), that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity etc. Two geometries are analyzed in detail: one charged wall first, and then, two parallel walls at small distances, that can be likely or oppositely charged. In all cases, one type of mobile counter-ions only is present, and ensures electroneutrality (salt free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counter-ions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte-Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counter-ion mediated like-charge attraction, and the opposite-charge repulsion
Planar screening by charge polydisperse counterions
We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), n(q). We work out analytically the one-plate and two-plate cases, at the level of non-linear PoissonBoltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full PoissonBoltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions n(q), for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous n(q) behaviour are already featured by discrete mixtures with a relatively small number of constituents