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 $\epsilon = 4-d$) 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, $\mu$, 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, $\mu \to 0$.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.

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

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

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

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