Rigorous treatment of pairwise and many-body electrostatic interactions among dielectric spheres at the Debye–Hückel level

Electrostatic interactions among colloidal particles are often described using the venerable (two-particle) Derjaguin–Landau–Verwey–Overbeek (DLVO) approximation and its various modifications. However, until the recent development of a many-body theory exact at the Debye–Hückel level (Yu in Phys Rev E 102:052404, 2020), it was difficult to assess the errors of such approximations and impossible to assess the role of many-body effects. By applying the exact Debye–Hückel level theory, we quantify the errors inherent to DLVO and the additional errors associated with replacing many-particle interactions by the sum of pairwise interactions (even when the latter are calculated exactly). In particular, we show that: (1) the DLVO approximation does not provide sufficient accuracy at shorter distances, especially when there is an asymmetry in charges and/or sizes of interacting dielectric spheres; (2) the pairwise approximation leads to significant errors at shorter distances and at large and moderate Debye lengths and also gets worse with increasing asymmetry in the size of the spheres or magnitude or placement of the charges. We also demonstrate that asymmetric dielectric screening, i.e., the enhanced repulsion between charged dielectric bodies immersed in media with high dielectric constant, is preserved in the presence of free ions in the medium. Graphic abstract

Validation of Fresnel–Kirchhoff Integral Method for the Study of Volume Dielectric Bodies

In this work, we test a nondestructive optical method based on the Fresnel–Kirchhoff integral, which could be applied to different fields of engineering, such as detection of small cracks in structures, determination of dimensions for small components, analysis of composition of materials, etc. The basic idea is to apply the Fresnel–Kirchhoff integral method to the study of the properties of small-volume dielectric objects. In this work, we study the validity of this method. To do this, the results obtained by using this technique were compared to those obtained by rigorously solving the Helmholtz equation for a dielectric cylinder of circular cross-section. As an example of the precision of the method, the Fresnel–Kirchhoff integral method was applied to obtain the refractive index of a hair by fitting the theoretical curve to the experimental results of the diffraction pattern of the hair measured with a CCD camera. In a same manner, the method also was applied to obtain the dimensions of a crack artificially created in a piece of plastic.

High-accuracy quasistatic numerical model for bodies of revolution tailored for RF measurements of dielectric parameters

We have developed rotationally symmetrical coaxial chambers for measurements of dielectric parameters of disk-shaped samples, in the frequency range from 1 MHz to several hundred MHz. The reflection coefficient of the chamber is measured and the dielectric parameters are hence extracted utilizing a high-accuracy quasistatic numerical model of the chamber and the sample. We present this model, which is based on the method of-moments solution of a set of integral equations for composite metallic and dielectric bodies. The equations are tailored to bodies of revolution. The model is efficient and accurate so that the major contribution of the measurement uncertainty comes from the measurement hardware.

Применение метода продолженных граничных условий к решению задачи дифракции волн на рассеивателях сложной геометрии, расположенных в однородной и неоднородной средах

Based on the method of continued boundary conditions, a technique is proposed that allows modeling the scattering characteristics for bodies of arbitrary geometry. The two-dimensional problem of the diffraction of a plane wave by dielectric bodies with complex section geometry, in particular, by fractal-like bodies, is considered. Comparison of numerical algorithms for solving the diffraction problem based on systems of integral equations of the 1st and 2nd kind is carried out. The method is generalized to the problem of diffraction by a cylindrical body located in a homogeneous magnetodielectric half-space. The correctness of the method is confirmed by checking the fulfillment of the optical theorem for various bodies and by comparing it with the results of calculations obtained by the modified method of discrete sources.