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The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a sense, as the gravitational shock wave. In this paper we show how some very important features of the double layer equations of motion can be extracted straight from the least action principle.

TFDC (Thomas-Fermi-Dirac-Cheng) electron theory is applied to analyzing the characteristics of the electrons inside the double layer of the nanometer composite thin films. This paper proposes the new mechanism about the high capacity in both theoretical analysis and experimental measurement.

We consider a double-layer system made of two parallel bilayer graphene sheets separated by a dielectric medium. We calculate the finite-temperature electrical conductivity of the first layer due to charged impurities located in two layers. We study the effects of temperature, interlayer distance, dielectric constants and impurity concentration, carrier concentration on the electrical conductivity. We show the importance of charged impurities located in layer II in determining electrical conductivity of the first layer for small interlayer distance. The results in this paper give us more understanding about the long-range charged impurity scattering in bilayer graphene under the effect of the second one.

This paper is devoted to the analysis of physical processes in composite matrix materials whose properties are greatly affected by the interphase interaction of the matrix and the modifier. Contribution of this interaction to thermodynamic and dielectric properties of such materials is investigated by the example of a model system which is a colloid solution of solid particles with charged surface in a polar liquid. Mechanisms underlying formation and stabilization of specific structures near the interphase boundaries of the examined system are discussed. Special attention is paid to the assessment of additional contribution to the internal energy and heat capacity related to the electric interaction of solid and liquid components. Results obtained within the proposed model show that for a certain concentration of liquid (about several percent) the interphase energy in a unit of volume magnificently increases to the values of about 10⁷–10⁸ J/m³ and therefore exceeds heat motion energy of polar molecules. Moreover it was revealed that the electrical part of heat capacity is comparable to self-capacity of the liquid matrix provided that the surface charge density of solid particles is high enough.

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the “external pressure” and the “external flow” components of the surface energy–momentum tensor together with the Lichnerowicz conditions serve to find the hypersurface itself, while the remaining ones define arbitrary functions that arise due to the implicit presence of the delta function derivative. It turns out that neither double layers nor thin shells exist for the quadratic Gauss–Bonnet term. It is shown that there is no “external pressure” for null singular hypersurfaces. The Lichnerowicz conditions imply the continuity of the scalar curvature in the case of spherically symmetric null singular hypersurfaces. These hypersurfaces must be thin shells if the Lichnerowicz conditions are necessary. It is shown that for this particular case the Lichnerowicz conditions can be completely removed therefore a spherically symmetric null double layer exists. Spherically symmetric null singular hypersurfaces in conformal gravity are explored as application.

Several elliptic integrals related to the interaction energy between two dissimilar parallel plates (the potentials on the two plates are of the same sign) are expanded in several fast convergent series for lower and higher surface potentials, respectively. The number of series terms required to obtain the interaction energy with six significant figures is not more than four for the dimensionless surface potential from 0 to 20 if the series fit for the lower potential is combined with the series fit for the higher potential. The approximate expressions with different precisions can be obtained by retaining different series terms. The results of Devereux and de Bruyn are discovered to be incorrect when the surface potential is very low or very high.

A novel, simple, and efficient method to calculate the interaction energies of double layers, λ parameter method, is presented by introducing a parameter λ in the elliptical integral. The interaction energies between two similar plane parallel double layers are expanded in the power series with such a method. The series converge very fast. When the dimensionless surface potential of double layers is less than or equal to 30, the number of the series terms required does not exceed 3 to obtain the interaction energies with six significant digits.

AFM was used to study the evolution of double layer on SiO₂ surface and self-assembly monolayer induced by the polarization with DC voltages. Approach force curves were recorded when external DC voltages were applied between solution and SiO₂ or aminopropyltriethoxysilane (APTES) modified SiO₂ surfaces in electrolyte solution. The results showed that the reversing of tip–surface interaction forces between attraction and repulsion could take place only by adjusting DC voltages. It is very useful for biotechnology because the adsorption of biomolecules could be controllable by DC voltages. A model was proposed to explain the behavior of double layer under DC voltages.