Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor

An analytical model of the electrostatic force between the tip of a non-contact Atomic Force Microscope (nc-AFM) and the (001) surface of an ionic crystal is reported. The model is able to account for the atomic contrast of the local contact potential difference (CPD) observed while nc-AFM-based Kelvin Probe Force Microscopy (KPFM) experiments. With the goal in mind to put in evidence this short-range electrostatic force, the Madelung potential arising at the surface of the ionic crystal is primarily derived. The expression of the force which is deduced can be split into two major contributions: the first stands for the coupling between the microscopic structure of the tip apex and the capacitor formed between the tip, the ionic crystal and the counter-electrode; the second term depicts the influence of the Madelung surface potential on the mesoscopic part of the tip, independently from its microscopic structure. These short-range electrostatic forces are in the range of ten pico-Newtons. When explicitly considering the crystal polarization, an analytical expression of the bias voltage to be applied on the tip to compensate for the local CPD, i.e. to cancel the short-range electrostatic force, is derived. The compensated CPD has the lateral periodicity of the Madelung surface potential. However, the strong dependence on the tip geometry, the applied modulation voltage as well as the tip-sample distance, which can even lead to an overestimation of the real surface potential, makes quantitative KPFM measurements of the local CPD extremely difficult.

https://hal.archives-ouvertes.fr/docs/00/29/42/67/PDF/manuscript_Electrostat-model.pdf

Analytical Approach to the Local Contact Potential Difference on (001) Ionic Surfaces:~Implications for Kelvin Probe Force Microscopy

Because of the increasing use of dielectrophoresis in the dielectric characterization and sorting of living cells or their parts, it has become important to establish carefully the theoretical backgrounds for this effect. A comparison with experiment is made of the several versions of the theory for the dielectrophoretic force exerted by nonuniform electric fields upon a neutral object. The three fundamental approaches: the Maxwell-Strattonstress tensor, the effective dipole moment, and the ‘Helmholtz’ energy approach are presented along with the general solution given earlier by Pohl and Crane. These are found to agree closely with experiment in predicting the dielectrophoretic force upon various rods hung in specially shaped (isomotive) field distributions. On the other hand, an alternative formulation based upon a debatable assignment of fields local to the dipoles gave a good fit to the experimental data only for materials of very low permittivity, and fitted poorly in the case of highly polarizable materials. An improved derivation of the theory for stable dielectrophoretic levitation is also presented. This phenomenon is of particular interest in that it is based upon an apparent violation of the Earnshaw's theorem, and is useful in the study of the dielectric properties of individual living cells.

Dielectrophoretic force: A comparison of theory and experiment

A Schlieren optical system has been used to measure the pressure Δp (by its effect on the refractive index) induced in non-polar isotropic liquid dielectrics by the application of an electric field E. All the results agree with the equation which is derived from the theory due to Helmholtz, Δp = E2(-1)(+2)/24π where is the permittivity of the liquid, and not with the equation based on the theory of Livens.

E. Durand

Papers

Électrostatique et magnétostatique