292 research outputs found
The Dielectric Constant of Ionic Solutions: A Field-Theory Approach
We study the variation of the dielectric response of a dielectric liquid
(e.g. water) when a salt is added to the solution. Employing field-theoretical
methods we expand the Gibbs free-energy to first order in a loop expansion and
calculate self-consistently the dielectric constant. We predict analytically
the dielectric decrement which depends on the ionic strength in a complex way.
Furthermore, a qualitative description of the hydration shell is found and is
characterized by a single length scale. Our prediction fits rather well a large
range of concentrations for different salts using only one fit parameter
related to the size of ions and dipoles.Comment: 5 pages, 2 figure
Electrostatic Interactions of Asymmetrically Charged Membranes
We predict the nature (attractive or repulsive) and range (exponentially
screened or long-range power law) of the electrostatic interactions of
oppositely charged and planar plates as a function of the salt concentration
and surface charge densities (whose absolute magnitudes are not necessarily
equal). An analytical expression for the crossover between attractive and
repulsive pressure is obtained as a function of the salt concentration. This
condition reduces to the high-salt limit of Parsegian and Gingell where the
interaction is exponentially screened and to the zero salt limit of Lau and
Pincus in which the important length scales are the inter-plate separation and
the Gouy-Chapman length. In the regime of low salt and high surface charges we
predict - for any ratio of the charges on the surfaces - that the attractive
pressure is long-ranged as a function of the spacing. The attractive pressure
is related to the decrease in counter-ion concentration as the inter-plate
distance is decreased. Our theory predicts several scaling regimes with
different scaling expressions for the pressure as function of salinity and
surface charge densities. The pressure predictions can be related to surface
force experiments of oppositely charged surfaces that are prepared by coating
one of the mica surfaces with an oppositely charged polyelectrolyte
Attractive instability of oppositely charged membranes induced by charge density fluctuations
We predict the conditions under which two oppositely charged membranes show a
dynamic, attractive instability. Two layers with unequal charges of opposite
sign can repel or be stable when in close proximity. However, dynamic charge
density fluctuations can induce an attractive instability and thus facilitate
fusion. We predict the dominant instability modes and timescales and show how
these are controlled by the relative charge and membrane viscosities. These
dynamic instabilities may be the precursors of membrane fusion in systems where
artificial vesicles are engulfed by biological cells of opposite charge
Statistical mechanics of budget-constrained auctions
Finding the optimal assignment in budget-constrained auctions is a
combinatorial optimization problem with many important applications, a notable
example being the sale of advertisement space by search engines (in this
context the problem is often referred to as the off-line AdWords problem).
Based on the cavity method of statistical mechanics, we introduce a message
passing algorithm that is capable of solving efficiently random instances of
the problem extracted from a natural distribution, and we derive from its
properties the phase diagram of the problem. As the control parameter (average
value of the budgets) is varied, we find two phase transitions delimiting a
region in which long-range correlations arise.Comment: Minor revisio
Interfaces of Modulated Phases
Numerically minimizing a continuous free-energy functional which yields
several modulated phases, we obtain the order-parameter profiles and
interfacial free energies of symmetric and non-symmetric tilt boundaries within
the lamellar phase, and of interfaces between coexisting lamellar, hexagonal,
and disordered phases. Our findings agree well with chevron, omega, and
T-junction tilt-boundary morphologies observed in diblock copolymers and
magnetic garnet films.Comment: 4 page
The Phase Behavior of Mixed Lipid Membranes in Presence of the Rippled Phase
We propose a model describing liquid-solid phase coexistence in mixed lipid
membranes by including explicitly the occurrence of a rippled phase. For a
single component membrane, we employ a previous model in which the membrane
thickness is used as an order parameter. As function of temperature, this model
properly accounts for the phase behavior of the three possible membrane phases:
solid, liquid and the rippled phase. Our primary aim is to explore extensions
of this model to binary lipid mixtures by considering the composition
dependence of important model parameters. The obtained phase diagrams show
various liquid, solid and rippled phase coexistence regions, and are in
quantitative agreement with the experimental ones for some specific lipid
mixtures.Comment: 8pages, 5figure
Topography and instability of monolayers near domain boundaries
We theoretically study the topography of a biphasic surfactant monolayer in
the vicinity of domain boundaries. The differing elastic properties of the two
phases generally lead to a nonflat topography of ``mesas'', where domains of
one phase are elevated with respect to the other phase. The mesas are steep but
low, having heights of up to 10 nm. As the monolayer is laterally compressed,
the mesas develop overhangs and eventually become unstable at a surface tension
of about K(dc)^2 (dc being the difference in spontaneous curvature and K a
bending modulus). In addition, the boundary is found to undergo a
topography-induced rippling instability upon compression, if its line tension
is smaller than about K(dc). The effect of diffuse boundaries on these features
and the topographic behavior near a critical point are also examined. We
discuss the relevance of our findings to several experimental observations
related to surfactant monolayers: (i) small topographic features recently found
near domain boundaries; (ii) folding behavior observed in mixed phospholipid
monolayers and model lung surfactants; (iii) roughening of domain boundaries
seen under lateral compression; (iv) the absence of biphasic structures in
tensionless surfactant films.Comment: 17 pages, 9 figures, using RevTeX and epsf, submitted to Phys Rev
Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation
The adsorption of large ions from solution to a charged surface is
investigated theoretically. A generalized Poisson--Boltzmann equation, which
takes into account the finite size of the ions is presented. We obtain
analytical expressions for the electrostatic potential and ion concentrations
at the surface, leading to a modified Grahame equation. At high surface charge
densities the ionic concentration saturates to its maximum value. Our results
are in agreement with recent experiments.Comment: 4 pages, 2 figure
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