Electrostatics of quadrupolarizable media

The classical macroscopic Maxwell equations are approximated. They are a corollary of the multipole expansion of the local electrostatic potential up to dipolar terms. But quadrupolarization of the medium should not be neglected if the molecules which build up the medium possess large quadrupole moment or do not have any dipole moment. If we include the quadrupolar terms in Maxwell equations we obtain the quadrupolar analogue of Poisson's equation: $\nabla^2 \phi - L^2_Q\nabla^4 \phi = - \rho / \varepsilon$. This equation is of the fourth order and it requires not only the two classical boundary conditions but also two additional ones: continuous electric field and the relation of the jump of the normal quadrupolarizability at the surface to the intrinsic normal surface dipole moment. The account of the quadrupole moment of the molecules leads to significant differences compared to the classical electrostatic theory

Quadrupole terms in the Maxwell equations: Born energy, partial molar volume and entropy of ions. Debye-Hückel theory in a quadrupolarizable medium

A new equation of state relating the macroscopic quadrupole moment density $Q$ to the gradient of the field $\nabla E$ in an isotropic fluid is derived: $Q = \alpha_Q(\nabla E - U \nabla.E/3)$, where the quadrupolarizability $\alpha_Q$ is proportional to the squared molecular quadrupole moment. Using this equation of state, a generalized expression for the Born energy of an ion dissolved in quadrupolar solvent is obtained. It turns out that the potential and the energy of a point charge in a quadrupolar medium are finite. From the obtained Born energy, the partial molar volume and the partial molar entropy of a dissolved ion follow. Both are compared to experimental data for a large number of simple ions in aqueous solutions. From the comparison the value of the quadrupolar length $L_Q$ is determined, $L_Q = \sqrt{\alpha_Q/3\epsilon}= 1-2 {\AA}$. Further, the extended Debye-H\"uckel model is generalized to ions in a quadrupolar solvent. If quadrupole terms are allowed in the macroscopic Coulomb law, they result in suppression of the gradient of the electric field. In result, the electric double layer is slightly expanded. The activity coefficients obtained within this model involve three characteristic lengths: Debye length, ion radius and quadrupolar length $L_Q$. Comparison to experimental data shows that minimal distance between ions is equal to the sum of their bare ion radii; the concept for ion hydration as an obstacle for ions to come into contact is not needed for the understanding of the experimental data

The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential.

The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension-of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of the bulk phases and the intrinsic polarization of the interface. The coefficient of the dielectro-Marangoni effect (surface flow due to gradient of the normal electric field) is found. A model of the Langevin type for the surface dipole moment and the intrinsic surface polarizability is presented.The work is funded by National Science fund through Contract No. 162 from 2015 with Sofia Universit

Normal metal to ferromagnetic superconductor tunneling

We study the point-contact tunneling between normal metal and ferromagnetic superconductor. In the case of magnon-induced pairing the tunneling conductance is continuous and smooth function of the applied voltage. For small values of the applied voltage the Ohm law holds. We show that one can obtain the magnetization and the superconducting order parameter from the tunneling conduc- tance. In the case of paramagnon-induced superconductivity the tunneling does not depend on the magnetization. We argue that tunneling experiment can unambiguously determine the correct pairing mechanism in the ferromagnetic superconductors.Comment: 6 pages, 4 figur

Comment on “A spherical cavity model for quadrupolar dielectrics” [J. Chem. Phys. 144, 114502 (2016)]

The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ε and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsager’s theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures

Nanomaterials and Coatings for Managing Antibiotic-Resistant Biofilms

Biofilms are a global health concern responsible for 65 to 80% of the total number of acute and persistent nosocomial infections, which lead to prolonged hospitalization and a huge economic burden to the healthcare systems. Biofilms are organized assemblages of surface-bound cells, which are enclosed in a self-produced extracellular polymer matrix (EPM) of polysaccharides, nucleic acids, lipids, and proteins. The EPM holds the pathogens together and provides a functional environment, enabling adhesion to living and non-living surfaces, mechanical stability, next to enhanced tolerance to host immune responses and conventional antibiotics compared to free-floating cells. Furthermore, the close proximity of cells in biofilms facilitates the horizontal transfer of genes, which is responsible for the development of antibiotic resistance. Given the growing number and impact of resistant bacteria, there is an urgent need to design novel strategies in order to outsmart bacterial evolutionary mechanisms. Antibiotic-free approaches that attenuate virulence through interruption of quorum sensing, prevent adhesion via EPM degradation, or kill pathogens by novel mechanisms that are less likely to cause resistance have gained considerable attention in the war against biofilm infections. Thereby, nanoformulation offers significant advantages due to the enhanced antibacterial efficacy and better penetration into the biofilm compared to bulk therapeutics of the same composition. This review highlights the latest developments in the field of nanoformulated quorum-quenching actives, antiadhesives, and bactericides, and their use as colloid suspensions and coatings on medical devices to reduce the incidence of biofilm-related infections