880 research outputs found
Nonlinear screening of charged macromolecules
We present several aspects of the screening of charged macromolecules in an
electrolyte. After a review of the basic mean field approach, based on the
linear Debye-Huckel theory, we consider the case of highly charged
macromolecules, where the linear approximation breaks down and the system is
described by full nonlinear Poisson-Boltzmann equation. Some analytical results
for this nonlinear equation give some interesting insight on physical phenomena
like the charge renormalization and the Manning counterion condensation
Long range polarization attraction between two different likely charged macroions
It is known that in a water solution with multivalent counterions (Z-ions),
two likely charged macroions can attract each other due to correlations of
Z-ions adsorbed on their surfaces. This "correlation" attraction is
short-ranged and decays exponentially with increasing distance between
macroions at characteristic distance A/2\pi, where A is the average distance
between Z-ions on the surfaces of macroions. In this work, we show that an
additional long range "polarization" attraction exists when the bare surface
charge densities of the two macroions have the same sign, but are different in
absolute values. The key idea is that with adsorbed Z-ions, two insulating
macroions can be considered as conductors with fixed but different electric
potentials. Each potential is determined by the difference between the entropic
bulk chemical potential of a Z-ion and its correlation chemical potential at
the surface of the macroion determined by its bare surface charge density. When
the two macroions are close enough, they get polarized in such a way that their
adjacent spots form a charged capacitor, which leads to attraction. In a salt
free solution this polarization attractive force is long ranged: it decays as a
power of the distance between the surfaces of two macroions, d. The
polarization force decays slower than the van der Waals attraction and
therefore is much larger than it in a large range of distances. In the presence
of large amount of monovalent salt, when A/2\pi<< d<< r_s (r_s is the
Debye-H\"{u}ckel screening radius), this force is still much stronger than the
van der Waals attraction and the correlation attraction mentioned above.Comment: 12 pages, 7 figures. Small change in the text, no change in result
Nonlinear effects in charge stabilized colloidal suspensions
Molecular Dynamics simulations are used to study the effective interactions
in charged stabilized colloidal suspensions. For not too high macroion charges
and sufficiently large screening, the concept of the potential of mean force is
known to work well. In the present work, we focus on highly charged macroions
in the limit of low salt concentrations. Within this regime, nonlinear
corrections to the celebrated DLVO theory [B. Derjaguin and L. Landau, Acta
Physicochem. USSR {\bf 14}, 633 (1941); E.J.W. Verwey and J.T.G. Overbeck, {\em
Theory of the Stability of Lyotropic Colloids} (Elsevier, Amsterdam, 1948)]
have to be considered. For non--bulklike systems, such as isolated pairs or
triples of macroions, we show, that nonlinear effects can become relevant,
which cannot be described by the charge renormalization concept [S. Alexander
et al., J. Chem. Phys. {\bf 80}, 5776 (1984)]. For an isolated pair of
macroions, we find an almost perfect qualitative agreement between our
simulation data and the primitive model. However, on a quantitative level,
neither Debye-H\"uckel theory nor the charge renormalization concept can be
confirmed in detail. This seems mainly to be related to the fact, that for
small ion concentrations, microionic layers can strongly overlap, whereas,
simultaneously, excluded volume effects are less important. In the case of
isolated triples, where we compare between coaxial and triangular geometries,
we find attractive corrections to pairwise additivity in the limit of small
macroion separations and salt concentrations. These triplet interactions arise
if all three microionic layers around the macroions exhibit a significant
overlap. In contrast to the case of two isolated colloids, the charge
distribution around a macroion in a triple is found to be anisotropic.Comment: 10 pages, 9 figure
Effective interactions in the colloidal suspensions from HNC theory
The HNC Ornstein-Zernike integral equations are used to determine the
properties of simple models of colloidal solutions where the colloids and ions
are immersed in a solvent considered as a dielectric continuum and have a size
ratio equal to 80 and a charge ratio varying between 1 and 4000. At an infinite
dilution of colloids, the effective interactions between colloids and ions are
determined for ionic concentrations ranging from 0.001 to 0.1 mol/l and
compared to those derived from the Poisson-Boltzmann theory. At finite
concentrations, we discuss on the basis of the HNC results the possibility of
an unambiguous definition of the effective interactions between the colloidal
molecules.Comment: 26 pages, 15 figure
Screening of charged spheroidal colloidal particles
We study the effective screened electrostatic potential created by a
spheroidal colloidal particle immersed in an electrolyte, within the mean field
approximation, using Poisson--Botzmann equation in its linear and nonlinear
forms, and also beyond the mean field by means of Monte Carlo computer
simulation. The anisotropic shape of the particle has a strong effect on the
screened potential, even at large distances (compared to the Debye length) from
it. To quantify this anisotropy effect, we focus our study on the dependence of
the potential on the position of the observation point with respect with the
orientation of the spheroidal particle. For several different boundary
conditions (constant potential, or constant surface charge) we find that, at
large distance, the potential is higher in the direction of the large axis of
the spheroidal particle
The Electric Double Layer Structure Around Charged Spherical Interfaces
We derive a formally simple approximate analytical solution to the
Poisson-Boltzmann equation for the spherical system via a geometric mapping.
Its regime of applicability in the parameter space of the spherical radius and
the surface potential is determined, and its superiority over the linearized
solution is demonstrated.Comment: 7 pages, 5 figure
Discrete solvent effects on the effective interaction between charged colloids
Using computer simulations of two charged colloidal spheres with their
counterions in a hard sphere solvent, we show that the granular nature of the
solvent significantly influences the effective colloidal interaction. For
divalent counterions, the total effective force can become attractive generated
by counterion hydration, while for monovalent counterions the forces are
repulsive and well-described by a solvent-induced colloidal charge
renormalization. Both effects are not contained in the traditional "primitive"
approaches but can be accounted for in a solvent-averaged primitive model.Comment: 4 pages, 3 figure
Colloidal ionic complexes on periodic substrates: ground state configurations and pattern switching
We theoretically and numerically studied ordering of "colloidal ionic
clusters" on periodic substrate potentials as those generated by optical
trapping. Each cluster consists of three charged spherical colloids: two
negatively and one positively charged. The substrate is a square or rectangular
array of traps, each confining one such cluster. By varying the lattice
constant from large to small, the observed clusters are first rod-like and form
ferro- and antiferro-like phases, then they bend into a banana-like shape and
finally condense into a percolated structure. Remarkably, in a broad parameter
range between single-cluster and percolated structures, we have found stable
supercomplexes composed of six colloids forming grape-like or rocket-like
structures. We investigated the possibility of macroscopic pattern switching by
applying external electrical fields.Comment: 14 pages, 13 figure
Modulation and correlations lengths in systems with competing interactions
We examine correlation functions in the presence of competing long and short
ranged interactions to find multiple correlation and modulation lengths. We
calculate the ground state stripe width of an Ising ferromagnet, frustrated by
an arbitrary long range interaction. In large systems, we demonstrate that
for a short range system frustrated by a general competing long range
interaction, the crossover temperature veers towards the critical
temperature of the unfrustrated short range system (i.e., that in which the
frustrating long range interaction is removed). We also show that apart from
certain special crossover points, the total number of correlation and
modulation lengths remains conserved. We derive an expression for the change in
modulation length with temperature for a general system near the ground state
with a ferromagnetic interaction and an opposing long range interaction. We
illustrate that the correlation functions associated with the exact dipolar
interactions differ substantially from those in which a scalar product form
between the dipoles is assumed.Comment: 17 pages, 9 figure
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