382 research outputs found
Electrostatic image effects for counter-ions between charged planar walls
We study the effect of dielectric inhomogeneities on the interaction between
two planparallel charged surfaces with oppositely charged mobile charges in
between. The dielectric constant between the surfaces is assumed to be
different from the dielectric constant of the two semiinfinite regions bounded
by the surfaces, giving rise to electrostatic image interactions. We show that
on the weak coupling level the image charge effects are generally small, making
their mark only in the second order fluctuation term. However, in the strong
coupling limit, the image effects are large and fundamental. They modify the
interactions between the two surfaces in an essential way. Our calculations are
particularly useful in the regime of parameters where computer simulations
would be difficult and extremely time consuming due to the complicated nature
of the long range image potentials.Comment: 21 pages, 8 figure
Counterion-mediated Electrostatic Interactions between Helical Molecules
We study the interaction of two cylinders with helical charge distribution
mediated by neutralizing counterions, by analyzing the separation as well as
the azimuthal angle dependence of the interaction force in the weak and strong
coupling limit. While the azimuthal dependence of the interaction in the weak
coupling limit is overall small and mostly negligible, the strong coupling
limit leads to qualitatively new features of the interaction, among others also
to an orientationally dependent optimal configuration that is driven by angular
dependence of the correlation attraction. We investigate the properties of this
azimuthal ordering in detail and compare it to existing results.Comment: 11 pages, 12 figure
Tensorial conservation law for nematic polymers
We derive the "conservation law" for nematic polymers in tensorial form valid
for quadrupolar orientational order in contradistinction to the conservation
law in the case of polar orientational order. Due to microscopic differences in
the coupling between the orientational field deformations and the density
variations for polar and quadrupolar order, we find that respective order
parameters satisfy fundamentally distinct constraints. Being necessarily scalar
in its form, the tensorial conservation law is obtained straightforwardly from
the gradients of the polymer nematic tensor field and connects the spatial
variation of this tensor field with density variations. We analyze the
differences between the polar and the tensorial forms of the conservation law,
present some explicit orientational fields that satisfy this new constraint and
discuss the role of singular "hairpins", which do not affect local quadrupolar
order of polymer nematics, but nevertheless influence its gradients.Comment: 10 pages, 6 figure
Field theoretic description of charge regulation interaction
In order to find the exact form of the electrostatic interaction between two
proteins with dissociable charge groups in aqueous solution, we have studied a
model system composed of two macroscopic surfaces with charge dissociation
sites immersed in a counterion-only ionic solution. Field-theoretic
representation of the grand canonical partition function is derived and
evaluated within the mean-field approximation, giving the Poisson-Boltzmann
theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations
around the mean-field are then analyzed in the lowest order correction that we
calculate analytically and exactly, using the path integral representation for
the partition function of a harmonic oscillator with time-dependent frequency.
The first order (one loop) free energy correction gives the interaction free
energy that reduces to the zero-frequency van der Waals form in the appropriate
limit but in general gives rise to a mono-polar fluctuation term due to charge
fluctuation at the dissociation sites. Our formulation opens up the possibility
to investigate the Kirkwood-Shumaker interaction in more general contexts where
their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ
Continuous Crystallization in Hexagonally-Ordered Materials
We demonstrate that the phase transition from columnar-hexagonal liquid
crystal to hexagonal-crystalline solid falls into an unusual universality
class, which in three-dimensional allows for both discontinuous transitions as
well as continuous transitions, characterized by a single set of exponents. We
show by a renormalization group calculation (to first order in ) that the critical exponents of the continuous transition are precisely
those of the XY model, which gives rise to a continuous evolution of elastic
moduli. Although the fixed points of the present model are found to be
identical to the XY model, the elastic compliance to deformations in the plane
of hexagonal order, , is nonetheless shown to critically influence the
crystallization transition, with the continuous transition being driven to
first order by fluctuations as the in plane response grows weaker, .Comment: 4 pages, 2 figures (revised version
New Approach on the General Shape Equation of Axisymmetric Vesicles
The general Helfrich shape equation determined by minimizing the curvature
free energy describes the equilibrium shapes of the axisymmetric lipid bilayer
vesicles in different conditions. It is a non-linear differential equation with
variable coefficients. In this letter, by analyzing the unique property of the
solution, we change this shape equation into a system of the two differential
equations. One of them is a linear differential equation. This equation system
contains all of the known rigorous solutions of the general shape equation. And
the more general constraint conditions are found for the solution of the
general shape equation.Comment: 8 pages, LaTex, submit to Mod. Phys. Lett.
Influence of heat treatment and KIc/HRc ratio on the dynamic wear properties of coated high speed steel
The aim of this work was to determine the impact of various heat treatments on the KIc/HRc ratio and subsequently on the wear properties of coated high-speed steel under dynamic impact loading. The results showed that hardness and improvement in the fracture toughness have significant influence on the adhesion and impact wear properties of the coated high-speed steel
Coupling between Smectic and Twist Modes in Polymer Intercalated Smectics
We analyse the elastic energy of an intercalated smectic where
orientationally ordered polymers with an average orientation varying from layer
to layer are intercalated between smectic planes. The lowest order terms in the
coupling between polymer director and smectic layer curvature are added to the
smectic elastic energy. Integration over the smectic degrees of freedom leaves
an effective polymer twist energy that has to be included into the total
polymer elastic energy leading to a fluctuational renormalization of the
intercalated polymer twist modulus. If the polymers are chiral this in its turn
leads to a renormalization of the cholesteric pitch.Comment: 8 pages, 1 fig in ps available from [email protected] Replaced
version also contains title and abstract in the main tex
Role of Multipoles in Counterion-Mediated Interactions between Charged Surfaces: Strong and Weak Coupling
We present general arguments for the importance, or lack thereof, of the
structure in the charge distribution of counterions for counterion-mediated
interactions between bounding symmetrically charged surfaces. We show that on
the mean field or weak coupling level, the charge quadrupole contributes the
lowest order modification to the contact value theorem and thus to the
intersurface electrostatic interactions. The image effects are non-existent on
the mean-field level even with multipoles. On the strong coupling level the
quadrupoles and higher order multipoles contribute additional terms to the
interaction free energy only in the presence of dielectric inhomogeneities.
Without them, the monopole is the only multipole that contributes to the strong
coupling electrostatics. We explore the consequences of these statements in all
their generality.Comment: 12 pages, 3 figure
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