Dielectric and Elastic Characterization of Nonlinear Heterogeneous Materials

Abstract

This review paper deals with the dielectric and elastic characterization of composite materials constituted by dispersions of nonlinear inclusions embedded in a linear matrix. The dielectric theory deals with pseudo-oriented particles shaped as ellipsoids of revolution: it means that we are dealing with mixtures of inclusions of arbitrary aspect ratio and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. Each ellipsoidal inclusion is made of an isotropic dielectric material described by means of the so-called Kerr nonlinear relation. On the other hand, the nonlinear elastic characterization takes into consideration a dispersion of nonlinear (spherical or cylindrical) inhomogeneities. Both phases are considered isotropic (actually it means polycrystalline or amorphous solids). Under the simplifying hypotheses of small deformation for the material body and of small volume fraction of the embedded phase, we describe a theory for obtaining the linear and nonlinear elastic properties (bulk and shear moduli and Landau coefficients) of the overall material.

Electric Polarization Properties of Single Bacteria Measured with Electrostatic Force Microscopy

“…We first note that the value of ε r,eff measured with EFM differs in general from the effective dielectric constant that would be obtained by considering an isolated core–shell bacteria in an uniform external electric field (see section S6 in the Supporting Information). In our previous work with very small core–shell objects like viruses of ∼60 nm in diameter, the electric field was approximately uniform for the entirety of object and analytical models for uniform external electric fields could be used .…”

“…We consider the relationship of this parameter to the intrinsic dielectric constants of the different cell components using a simple coreÀshell model (see inset in Figure 5a for geometry), in which the core represents the cytoplasm region and the shell the bacterial envelope (which includes the plasma membrane, the cell wall, the periplasmic space, and, in the case of Gram-negative bacteria, the outer membrane). We first note that the value of ε r,eff measured with EFM differs in general from the effective dielectric constant that would be obtained by considering an isolated coreÀshell bacteria in an uniform external electric field 13 (see section S6 in the Supporting Information). In our previous work with very small coreÀshell objects like viruses of ∼60 nm in diameter, the electric field was approximately uniform for the entirety of object and analytical models for uniform external electric fields could be used.…”

Suppressed terahertz dynamics of water confined in nanometer gaps

“…Next, we incorporate an effective medium theory combined with a three-layer capacitor model with two interfacial layers and one residual layer, and assumed that the decrease in dielectric permittivity is primarily attributed to the interfacial layer ( 59 ). However, we find that this three-layer model, which is widely accepted at the static regime, is inadequate to explain the observed decrease in dielectric permittivity in THz frequencies due to the intricate collective phenomena involved ( 58 ) (see fig.…”

Dielectric properties and lamellarity of single liposomes measured by in-liquid scanning dielectric microscopy

“…To facilitate the analysis, we propose a phenomenological analytical expression for dC/dz, following our previous analysis of the tipnanoparticle electrical interaction in air environment [25]. The phenomenological tip-liposome capacitance gradient relation is of the form Here, ε eq * is the equivalent homogeneous complex permittivity of a spheroidal liposome in a uniform external ac electric field [47,48] with the height and width being equal to the ones of the absorbed liposome (see Additional file 1: S3 for explicit expressions of ε eq * for uni-and bi-lamellar liposomes). Here, α and β are two phenomenological parameters that depend on the size of the liposome and of the tip, and on the tip-sample distance, among other parameters.…”