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 α_Q of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of α_Q 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 a 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.

Liquid oxygen is an example for a quadrupolar medium—a dense fluid made of nonpolar molecules carrying a significant quadrupolar moment. In this work, we present a method for the computation of the macroscopic quadrupolarizability of such a quadrupolar liquid. As a first step, the quadrupole moment and the molecular quadrupolarizability of O₂ are calculated from first principles. Next, we apply a model generalizing Onsager’s dielectric cavity theory to compute the macroscopic quadrupolarizability of liquid oxygen under a wide range of conditions. Literature data for the density and dielectric permittivity of oxygen are used to determine the cavity size independently.

This is the problem of the 8th International Experimental Physics Olympiad (EPO8). The task of the EPO8 is to determine Planck constant ħh/2 using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items – they are instructive for physics education in general. Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best.

Nearby interfaces, polar-quadrupolar molecules are orientated by image forces. This produces a macroscopic normal dipole moment and is the reason for the surface potential of liquids like water. The theory of the effect requires higher-order multipole expansion of both the image interactions and the macroscopic equations of electrostatics. The quadrupolar Coulomb law predicts the formation of a dipolar double layer (DDL) at the surface, with an adsorbed layer of dipoles orientated by image forces and oppositely polarized diffuse layer formed as a response to the field of the adsorbed dipoles. We relate the surface dipolar potential to the molecular properties (dipole and quadrupole moments and molecular polarizability), the medium properties (dielectric permittivity and macroscopic quadrupolarizability), and structural characteristics of the surface layer (distance between equimolecular and dielectric surfaces, thickness of the adsorbed layer, and cavity size). The thickness of the DDL is set by the quadrupolar length of the fluid, a quantity analogous to the Debye length. Molecules on the gas-phase side of the Gibbs equimolecular surface have a large contribution to the adsorbed dipole, especially for water. The surface layer is thick enough to produce a diffuse dipole layer also on the gas-phase side of the surface, i.e., three layers of dipoles exist, in agreement with recent simulations data. The calculated unperturbed surface polarization of the adsorbed layer for water agrees with estimates from point of zero dipole of alcohol monolayers. The calculated surface potential of water (between -15 and -85 mV, depending on the assumptions; oxygen toward the gas phase) agrees with existing experimental estimates.

When a liquid film is thinning, the charge and the potential of its surfaces change simultaneously due to the interaction between the two surfaces. This phenomenon is an example for charge regulation and has been known for half a century for systems featuring aqueous solutions in contact with metals, salts, biological surfaces covered by protolytes, etc. Few studies, however, investigated regulation in foam and emulsion films, where the charge is carried by soluble ionic surfactants. This work presents an analysis of the phenomenon for surfactants that follow the classical Davies adsorption isotherm. The electrostatic disjoining pressure Π_el was analyzed, and the Davies isotherm was shown to lead to Π_el ∝ h^−1/2 behavior at a small film thickness h. As usual, the charge regulation regime (constant chemical potential of the surfactant) corresponded to a dependence of Π_el on h between those for constant charge and constant electric potential regimes. The role of the background electrolyte was also studied. At the water–air interface, many ionic surfactants exhibit a surface phase transition. We show that the interaction between the two surfaces of a foam film can trigger the phase transition (i.e., the film changes its charge abruptly), and two films of different h values can coexist in equilibrium with each other—one covered by surfactant in the 2D gaseous state and another in the 2D liquid state.