Electric fields, dynamic static

Even if the use of electric fields, either static or dynamic, to improve chemical processes has long been known, only more recently it has been applied for process intensification. The application of an electric field in liquid-liquid systems induces an increase in the mass transfer (up to a factor 10), due to a higher degree of turbulence within and around the dispersed phase, as a result of interaction between the field and the interface [109]. Four different mechanisms are noted ... 

At the molecular level, the application of an external electric field F of high intensity induces changes in the dipole moment of the individual molecules, which can be expressed by the Taylor series in the electric field amplitudes. Thus, in the presence of electric fields containing static and dynamic (oscillating) contributions, the z-component of the dipole moment reads ... 

We only consider static response properties in this chapter, which arise from fixed external field. Their dynamic counterparts describe the response to an oscillating electric field of electromagnetic radiation and are of great importance in the context of non-linear optics. As an entry point to the treatment of frequency-dependent electric response properties in the domain of time-dependent DFT we recommend the studies by van Gisbergen, Snijders, and Baerends, 1998a and 1998b. 

When a molecular system is placed in static and/or dynamic external electric fields, a perturbation term has to be added to the unperturbed time independent Hamiltonian, Hg ... 

In addition to these static problems with M junctions, once a device is operating, dynamic perturbations may arise during a given area of device operation, as illustrated in Fig. 7. The major cause of perturbations would be the onset of extremely high electric fields across the junction, e.g., 5 x 10 V m for an... 

The multiplier structures may be divided into two main types (1) dynamic and (2) static. The dynamic multiplier in its simplest form consists of two parallel dynode surfaces with an alternating electric field applied between them. Elections leaving one suiface at the piopei phase, of the applied field are accelerated to the other surface where they knock out secondary electrons. These electrons, in turn, are accelerated back to the first plate when the field reverses, creating still more secondary electrons. Eventually, the secondary electrons are collected by an anode placed in... 

D. M. Bishop, Rev. Mod. Phys., 62, 343 (1990). Molecular Vibrational and Rotational Motion in Static and Dynamic Electric Fields. 

In the absence of external fields the suspension under consideration is macroscopically isotropic (W = const). The applied field h (we denote it in the same way as above but imply the electric field and dipoles as well as the magnetic ones), orienting, statically or dynamically, the particles, thus induces a uniaxial anisotropy, which is conventionally characterized by the orientational order parameter tensor (Piin h)) defined by Eq. (4.358). (We remind the reader that for rigid dipolar particles there is no difference between the unit vectors e and .) As in the case of the internal order parameter S2, [see Eq. (4.81)], one may define the set of quantities (Pi(n h)) for an arbitrary l. Of those, the first statistical moment (Pi) is proportional to the polarization (magnetization) of the medium, and the moments with / > 2, although not having meanings of directly observable quantities, determine those via the chain-linked set [see Eq. (4.369)]. 

Nonpolar and dipolar altitudinal rotors (compounds 2 and 3 in Fig. 17.3) have been synthesized. 19F NMR spectroscopy showed that the barrier to rotation in 3 was extremely low in solution. Both systems have then been immobilized on Au(l 11) surfaces and studied with a variety of techniques.57 The results obtained indicated that for a fraction of molecules the static electric field from the scanning tunneling microscopy (STM) tip could induce an orientation change in the dipolar rotor but not in the nonpolar analog (for a recent example of an azimuthal molecular rotor controlled by the STM tip, see Reference 58). Compound 3 can exist as three pairs of helical enantiomers because of the propeller-like conformation of the tetra-arylcyclobutadienes. For at least one out of the three diastereomers, an asymmetric potential energy surface can be predicted by molecular dynamics simulations on application of an alternating electric field.55... 

Matrix asymmetry is linked to the existence of anisotropic spin-orbit coupling,123 and the presence of sufficiently low-symmetry electric fields (static and dynamic). 

To end this section and the review, we mention briefly the first results from the simulation on laboratory-frame cross-correlation of the type (v(f)J (0)). Here v is the molecular center-of-mass linear velocity and J is the molecular angular momentum in the usual laboratory frame of reference. For chiral molecules the center-of-mass linear velocity v seems to be correlated directly in the laboratory frame with the molecule s own angular momentum J at different points r in the time evolution of the molectilar ensemble. This is true in both the presence and absence of an external electric field. These results illustrate the first direct observation of elements of (v(r)J (0)) in the laboratory frame of reference. The racemic modification of physical and molecular dynamical properties depends, therefore, on the theorem (v(r)J (0)) 0 in both static and moving frames of reference. An external electric field enhances considerably the magnitude of the cross-correlations. 

Figure 12 The molecular contributions to the electric field gradient (EFG) can be correlated. Hence the EFG-TCF can be divided into molecular self-EFG-TCF and cross-EFG-TCF terms (See equation (25)). The static quenching of the EFG is due to the momentary symmetry in the solvation shell. The cross EFG-TCF has a different decay that the self-EFG-TCF which results in a dynamic quenching of the molecular contributions.

Molecular electric properties give the response of a molecule to the presence of an applied field E. Dynamic properties are defined for time-oscillating fields, whereas static properties are obtained if the electric field is time-independent. The electronic contribution to the response properties can be calculated using finite field calculations , which are based upon the expansion of the energy in a Taylor series in powers of the field strength. If the molecular properties are defined from Taylor series of the dipole moment /x, the linear response is given by the polarizability a, and the nonlinear terms of the series are given by the nth-order hyperpolarizabilities ()6 and y). 

Equation (8.159) is strictly valid for a Gaussian distribution of electric fields. The electric field autocorrelation function is related to the dynamic structure factor S q, t) [compare it with the static scattering function S q) in Eq. (3.121)] ... 

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