Nonlinear electrical effects, analysis

Both theoretical analysis and dipole moment measurements indicated that sulfonyl-substituted compounds may have ft coefficients similar in magnitude to their nitro analogues. Therefore, we have measured p for several sulfonyl- and nitro-substituted compounds using electric-field-induced second-harmonic generation method (EFISH) (11,25). In this experiment, one measures an effective third-order nonlinearity rEFISH for a solution containing the compound of interest, given by... 

In much of the above analysis, the relative magnitude of the surface and bulk contribution to the nonlinear response has not been addressed in any detail. As noted in Section 3.1, in addition to the surface dipole terms of Eq. (3.9), there are also nonlocal electric-quadrupole-type nonlinearities arising from the bulk medium. The effective polarization is made of a combination of surface nonlinear polarization, PNS (2co) (Eq. (3.9)), and bulk nonlinear polarization (Eq. (3.8)) which contains bulk terms y and . The bulk term y is isotropic with respect to crystal rotation. Since it appears in linear combination with surface terms (e.g. Eq. (3.5)), its separate determination is not possible under most circumstances [83, 129, 130, 131]. It mimics a surface contribution but its magnitude depends only upon the dielectric properties of the bulk phases. For a nonlinear medium with a high index of refraction, this contribution is expected to be small since the ratio of the surface contribution to that from y is always larger than se2(2co)/y. The magnitude of the contribution from depends upon the orientation of the crystal and can be measured separately under conditions where the anisotropic contribution of vanishes. 

Lubricants have a nonlinear viscosity coefficient against temperature. At very low or very high temperature this nonlinearity can create significant measurement failures. A careful analysis will show this effect within the transmission chain. Sticking is the worst case. It can happen that frozen water makes a short cut in torque sensors. In most cases damping factors are based on the electrical filter circuits (Fig. 7.12.13). 

Koh et al. [6] have rigorously modeled the electromechanics of this interaction for the simplified case of uniform biaxial stretching of an incompressible polymer film including many important effects such as the nonlinear stiffness behavior of the polymer film and the variation in breakdown field with the state of strain. With regard to the latter effect, Pelrine et al. [5] showed the dramatic effect of prestrain on the performance of dielectric elastomers (specifically silicones and acrylics) as actuators. We would expect the same breakdown enhancement effects to be involved with regard to power generation. There are many additional effects that may be important, such as electrical and mechanical loss mechanisms, interaction with the environment or circuits, frequency, and temperature-dependent effects on material parameters. The analysis by Koh provides the state equations... 

Compared to the vast literature on linear electrophoresis, the study of nonlinear electrokinetic motion is still its early stages. As indicated above, much remains to be done, in both making theoretical predictions and systematically testing them (or discovering new effects) in experiments. Modern mathematical methods and computational power now allow more sophisticated analysis, going beyond linear and weakly nonlinear approximations, as well as large-scale simulations of interacting colloidal particles. Similarly, the advent of microfluidics provides new opportunities to observe and exploit nonlinear electrokinetic phenomena, since polarizable particles can now be fabricated with complicated shapes and material properties and electric fields controlled with submicron precision. 

Accurate mass measurements with ESI are performed in combination with an FT-ICR instrument [6,7]. This instrument currently yields the highest resolving power and the most accurate mass measurement of any mass spectrometry instrument. The space-charge effects and nonlinearity of the trapping electric fields limit the current accuracy in mass measnrement. Use of an internal calibrant can minimize this effect. By bracketing the nnknown mass with two references, an accuracy of less than 3 ppm for the elemental analysis can be achieved [7]. ESI has also been combined with qnadmpoles, provided that the compound is pure [2] or online with HPLC [9]. 

Barnik et al. observed the same effect but deduced a much smaller nonlinear susceptibility from the measurements than Arakelyan et al. They provided a different interpretation as well in their opinion SHG was due to electric- quadrupole effects. (Quadrupole effects originate from the coupling between the polarization P and the spatial derivatives of the electric field.) As second-order quadrupole effects are not forbidden by the existence of an inversion centre the interpretation of Barnik et ai is compatible with the generally accepted symmetry properties of nematics. A detailed theoretical analysis of the problem was given by Ou-Yang et Their results indicate also that the quadrupole mechanism is responsible for SHG in MBBA rather than the existence of noncentrosymmetric blocks. 

Experimentally, the fraction of free counterions in salt-free polyelectrolyte solutions is believed to give the main contribution to the system osmotic pressure. In the framework of the two-state models, the osmotic pressure is equal to the osmotic pressure of the free counterions. The more accurate analysis of the counterion effect on the solution osmotic pressure can be done in the framework of the Poisson-Boltzmann approach and its two-zone model simplification. In order to obtain an expression for the osmotic pressure in the framework of the two-zone model, one has to know the counterion concentration at the outer boundary of the spherical region. This requires knowledge of the electrostatic potential within the spherical zone. However, one can avoid solving the nonlinear Poisson-Boltzmann equation and use the relation between the local pressure P(r) and the electric field (r). To obtain this relation, one has to combine the differential form of the Gauss law ... 

For further information on ceramic actuators, see Uchino (1993). It has been recognized that in modern multilayer piezoelectric actuators (MPAs), the combination of thermal, electrical and mechanical loads during service may affect the functional integrity of the devices. As the details of these effects and their synergistic coupling are still unknown, modeling of the nonlinear behavior of these temperature-sensitive functional properties and their implementation into finite element analysis (FEA) tools has been performed recently (Griinbichler et al., 2008). 

When a polymer is subject to an intense sinusoidal electric field such as that due to an intense laser pulse, Fourier analysis of the polarization response can be shown to contain not only terms in the original frequency co, but also terms in 2(0 and 3nonlinear response depends on the square of the intensity of the incident beam for 2co, and the third power for 3 . For the second-order effects, the system must have some asymmetry, as discussed previously. For poling, this means both high voltage and a chemical organization that will retain the resulting polarization for extended periods of time. Polymeric systems investigated have been of three basic types ... 

The first observation of natural optical anisotropy was made in 1669 by Bartolinius in calcite crystals, in which light travels at different velocities depending on the direction of propagation relative to the crystal structure. The electrooptic effect, electric-field-induced anisotropy, was first observed in glass in 1875 by J. Kerr. Kerr found a nonlinear dependence of refractive index on applied electric field. The term Kerr effect is used to describe the quadratic electrooptic effect observed in isotropic materials. The linear electrooptic effect was first observed in quartz crystals in 1883 by W. Rontgen and A. Kundt. Pockels broadened the analysis of this relationship in quartz and other crystals, which led to the term Pockels effect to describe linear behavior. In the 1960s several developments... 

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