Electric field, transformed

Guggenheim s characteristic free energy in electric fields, transformed Gibbs free energy Conversion factors Kirkwood correlation factor Ionic strength (mol dm )... 

External electric fields transform as the regular solid spherical harmonics, (p), for which the Laplacian vanishes, V r Yemi, v) = 0. There is therefore no spin-free correction of 0(c ) to the property operator, and the operator can be written as... 

Point nuclear electric fields transform as the irregular solid spherical harmonics for which the Laplacian is a generalized delta function. For finite... 

The most important materials among nonlinear dielectrics are ferroelectrics which can exhibit a spontaneous polarization PI in the absence of an external electric field and which can spHt into spontaneously polarized regions known as domains (5). It is evident that in the ferroelectric the domain states differ in orientation of spontaneous electric polarization, which are in equiUbrium thermodynamically, and that the ferroelectric character is estabUshed when one domain state can be transformed to another by a suitably directed external electric field (6). It is the reorientabiUty of the domain state polarizations that distinguishes ferroelectrics as a subgroup of materials from the 10-polar-point symmetry group of pyroelectric crystals (7—9). 

Electroporation. When bacteria are exposed to an electric field a number of physical and biochemical changes occur. The bacterial membrane becomes polarized at low electric field. When the membrane potential reaches a critical value of 200—300 mV, areas of reversible local disorganization and transient breakdown occur resulting in a permeable membrane. This results in both molecular influx and efflux. The nature of the membrane disturbance is not clearly understood but bacteria, yeast, and fungi are capable of DNA uptake (see Yeasts). This method, called electroporation, has been used to transform a variety of bacterial and yeast strains that are recalcitrant to other methods (2). Apparatus for electroporation is commercially available, and constant improvements in the design are being made. 

One type of material that has transformed electronic displays is neither a solid nor a liquid, but something intermediate between the two. Liquid crystals are substances that flow like viscous liquids, but their molecules lie in a moderately orderly array, like those in a crystal. They are examples of a mesophase, an intermediate state of matter with the fluidity of a liquid and some of the molecular order of a solid. Liquid crystalline materials are finding many applications in the electronics industry because they are responsive to changes in temperature and electric fields. 

The last problem of this series concerns femtosecond laser ablation from gold nanoparticles [87]. In this process, solid material transforms into a volatile phase initiated by rapid deposition of energy. This ablation is nonthermal in nature. Material ejection is induced by the enhancement of the electric field close to the curved nanoparticle surface. This ablation is achievable for laser excitation powers far below the onset of general catastrophic material deterioration, such as plasma formation or laser-induced explosive boiling. Anisotropy in the ablation pattern was observed. It coincides with a reduction of the surface barrier from water vaporization and particle melting. This effect limits any high-power manipulation of nanostructured surfaces such as surface-enhanced Raman measurements or plasmonics with femtosecond pulses. 

Figure 2 (a) The optimized electric field as a function of time for the H2(v = 0,) = 0) — H2 (v = 0,7 = 2) rotational excitation process, (b) Absolute value of the Fourier transform of the optimized electric field, (c) The change in populations of the ground-and target excited-state shown as a function of time. Taken from Ref [24] with permission from Qinghua Ren, Gabriel G. Balint-Kurti, Frederick R. Manby, Maxim Artamonov, Tak-San Ho, and Herschel Rabitz, 7. Chem. Phys. 124, 014111 (2006). Copyright 2006, American Institute of Physics. 

The inclusion of (nonrelativistic) property operators, in combination with relativistic approximation schemes, bears some complications known as the picture-change error (PCE) [67,190,191] as it completely neglects the unitary transformation of that property operator from the original Dirac to the Schrodinger picture. Such PCEs are especially large for properties where the inner (core) part of the valence orbital is probed, for example, nuclear electric field gradients (EEG), which are an important... 

In the case of resonance absorption of synchrotron radiation by an Fe nucleus in a polycrystalline sample, the frequency dependence of the electric field of the forward scattered radiation, R(oj), takes a Lorentzian lineshape. In order to gain information about the time dependence of the transmitted radiation, the expression for R(oj) has to be Fourier-transformed into R(t) [6]. 

Moriya et al. first demonstrated that anisotropic structure in blends can be generated by applying ac electric fields to solvent-free blends of PEO and PS [60]. A similar morphology transformation induced by electric fields has been detected in PEO/PS/cyclohexane systems [61-63]. During solvent evaporation,... 

It is, of course, usual in discussing the electrochemical interface to use a dielectric constant, which is the ratio of the electric displacement to the electric field. By Fourier transforming the dielectric function e(k), one would obtain an effective dielectric constant, which would, however, depend on position. In fact,48 the screening... 

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

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