Electric perturbation

The iterative scheme for the second-order coefficients, consistent with (49)-(52), is (in the case of electric perturbation there is no... 

The electron density of a molecule in the presence of electric perturbation is a scalar field with perturbation expansion [6], [11]... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

Whether a given field is to be considered as strong or weak depends on the ratio of the corresponding electric perturbation to the relativistic. As the expressions for the relativistic doublet and for the Stark effect are almost the same in the old and the new theory, we have, roughly speaking, the same criterion in both of them. ... 

Of course, electrochemical systems can be perturbed in a large number of ways, e.g. pressure and temperature variation and the application of a time-dependent illumination leading to responses that are of an electrical nature (current or voltage). The discussions to follow will be restricted to electrical perturbations leading to responses that are also electrical. 

In a recent work [43], Martem Yanov and Grafov, envisaged also the effect of hydrodynamic fluctuations on the electrochemical current, proposing to call it a hydroelectrochemical impedance, with the same definitions as those given above (see Section 1.3). Their approach is basically the same as that described in Section 1.3 in that they consider the hydrodynamic and electrical perturbations from a unified position. More precisely, for the kinetic situation described in Section 4.2 they show that an equation such as Eq. (4-7), obtained in a simplified version (i.e. no convective diffusion and a qualitative analysis of the fluctuating flow field) can be written as... 

One of the most fruitful trends in the comprehension and control of electrochemical reaction kinetics and electrocatalysis has been the development of modified electrodes to achieve redox mediators of solution processes. This strategy is based on the electrochemical activation (through the application of an electrical perturbation to the electrode) of different sites at a modified surface. As a result of this activation, the oxidation or the reduction of other species located in the solution adjacent to the electrode surface (which does not occur or occurs very slowly in the absence of the immobilized catalyst) can take place4 [40, 69, 70]. 

The electrostatic embedding approach appears reasonable in cases of weak interactions, with negligible intermolecular charge transfer, provided that the interactions can be described as some average electric perturbation. By properly modifying the disposition of the point charges more realistic embedding schemes could also be introduced. 

Diffusion time (diffusion time constant) — This parameter appears in numerous problems of - diffusion, diffusion-migration, or convective diffusion (- diffusion, subentry -> convective diffusion) of an electroactive species inside solution or a solid phase and means a characteristic time interval for the process to approach an equilibrium or a steady state after a perturbation, e.g., a stepwise change of the electrode potential. For onedimensional transport across a uniform layer of thickness L the diffusion time constant, iq, is of the order of L2/D (D, -> diffusion coefficient of the rate-determining species). For spherical diffusion (inside a spherical volume or in the solution to the surface of a spherical electrode) r spherical diffusion). The same expression is valid for hemispherical diffusion in a half-space (occupied by a solution or another conducting medium) to the surface of a disk electrode, R being the disk radius (-> diffusion, subentry -> hemispherical diffusion). For the relaxation of the concentration profile after an electrical perturbation (e.g., a potential step) Tj = L /D LD being - diffusion layer thickness in steady-state conditions. All these expressions can be derived from the qualitative estimate of the thickness of the nonstationary layer... 

Potential sweep rate — is the rate of an electrical perturbation to the system in which the potential is changed linearly with time at a certain sweep (scan) rate. 

The raw data was strings of storage modulus, G, and frequency, w, at various temperature levels. Data reduction was carried out with linear temperature, T, Y = log G, and X = log (w/100). The reduced scale for X was used so that intercepts at X=0 would correspond to 100 Hz frequency and fall within the experimental range. There was noise in the modulus data attributable to mechanical and electrical perturbations. These small perturbations were removed by smoothing with simple linear and second order polynomial functions. 

As pointed out earlier, the equivalent circuit shown in Fig. 4A is meant to represent the simplest situation only. It does not take into account factors such as mass transport, heterogeneity of the surface and the occurrence of reaction intermediates absorbed at the surface. Some of these factors are discussed later. Even in the simplest cases, in which this circuit does represent the response of the interphase to an electrical perturbation reasonably well, one should bear in mind that... 

In this analysis and in that of the next section, the vibrational motion effects presume a field source that is rotating with the molecule, such as when the electrical perturbation is due to a weakly complexed partner molecule. A freely rotating molecule in a laboratory-fixed field source, however, is different, and then evaluations of electrical properties should account for rotational state dependence as well [114, 115]. 

Obviously enough, the external radiation can only induce forced oscillations of the electron distribution, whose mean position is fixed in space. Thus, for instance, for the electric perturbation, averaging the terms depend-ing on E over a period one finds... 

The second question is more difficult to answer. Indeed, since the electrical perturbation extends only over a few angstroms from the electrode surface, the medium in which the electrogenerated intermediates react is identical to the bulk of the solution, which favors a positive answer. On the other hand, they react under essentially nonisotropic conditions because of the existence of concentration profiles, that is, of concentration changes with distance of the electrode (see Fig. 15). Yet this is a situation identical to that encountered when heterogeneous reagents or polyphasic conditions are used in usual homogeneous chemistry. A more serious difference is related to the nature of the media... 

As explained earlier, in transient electrochemical methods an electrical perturbation (potential, current, charge, and so on) is imposed at the working electrode during a time period 0 (usually less than 10 s) short enough for the diffusion layer 8 (2D0) to be smaller than the convection layer (S onv imposed by natural convection. Thus the electrochemical response of the system investigated depends on the exact perturbation as well as on the elapsed time. This duality is apparent when one considers a double-pulse potentiostatic perturbation applied to the electrode as in the double-step chronoampero-metric method. 

E. Levart and D. Schuhmann, "General Determination of Transition Behavior of a Rotating Disc Electrode Submitted to an Electrical Perturbation of Weak Amplitude," Journal of Electroanalytical Chemistry, 28 (1970) 45. 

Conditions in Strong Fields.—It will be necessary to discuss this case, though only our method of approach is new, while the results were known from Bohr s and Kramers work. If the electric perturbation dominates over the relativistic, our process of successive approximations must start from considering the electric terms. As we have pointed out, the most important one among them is the degenerate term (11). Our second step will be, therefore, the consideration of the Hamiltonian equation... 

If we wish to go a step farther, and to study the change of this motion produced by the electric field, we have to proceed exactly as in section 3. Again we may expect a material change of coordinates only for the degenerate terms, which in this case will depend only on the variable qi. However, we have pointed out that all the terms of the expansion of the electric perturbation depend either on qz or on q2. From our new point of view there will be no degenerate terms at all. This means that our system of polar coordinates will remain the adequate system for quantization even if we take into account the electric perturbation. 

Application of an electrical perturbation (current, potential) to an electrical circuit causes a response. In this chapter, the system response to an arbitrary perturbation and later to an ac signal, is discussed. Knowledge of the Laplace transform technique is assumed, but the reader may consult numerous books on the subject if necessary. 

The distribution of electric charge in a molecule is intimately related to its structure and reactivity. Knowledge of the distribution gives us a feeling for the physical and chemical properties of the molecule and provides a valuable assessment of the accuracy of approximate molecular wavefunctions. The charge distribution in the nth stationary state is determined by the many-electron wave function 0 of the free molecule. If the molecule interacts with an external electric perturbation E, the wave function determines the distortion and,... 

Bloch electrons in a perfect periodic potential can sustain an electric current even in the absence of an external electric held. This infinite conductivity is limited by the imperfections of the crystals, which lead to deviations from a perfect periodicity. The most important deviation is the atomic thermal vibration from the equilibrium position in the lathee however, electric perturbations can also promote this type of vibration. A quantitative treatment of the external electric perturbation of a crystal, therefore, starts with the observation of the change in the lattice vibrations [1] ... 

Since the electric perturbation vibrates along a unique axis, that is, perpendicular to the surface of the electrode, a simplified contribution of the new wave function with the interlayer distance is expected. This fact leads to longitudinal waves having an u(r) atomic displacement in the lattice. However, in spite of the absence of the other transversal components, three modes of propagation are expected one longitudinal and the other two degenerating in a single transversal mode. 

In the ordinary theory of the dispersion interaction the electric perturbation term Hs. alone is included. The dispersion energy is then given by... 

We must distinguish between two cases. For an electric perturbation fi is diagonal in the upper and lower components... 

Information about an electrochemical system is often gained by applying an electrical perturbation to the system and observing the resulting changes in the characteristics of the system. In later sections of this chapter and later chapters of this book, we will encounter such experiments over and over. It is worthwhile now to consider the response of the IPE system, represented by the circuit elements and in series, to several common electrical perturbations. 

Acoustic wave devices use piezoelectric materials for excitation and detection of acoustic waves (Figure 4.5). The nature of all of the parameters involved with sensor applications concerns either mechanical or electrical perturbations [23,24]. An acoustic device is thus sensitive mainly to the physical parameters, which may interact with the mechanical properties of the wave and/or its associated electrical field. For chemical or biosensing applications, a transduction (sensing) layer is used to convert... 

In the following sections, perturbation theory approach as well as precise numerical technique such as finite elements are used to study the effect of various mechanical and electrical perturbations on SAW sensor response and are shown to yield useful information for efficient sensor design and material characterization. 

Simulations involving SAW sensor typically generate responses of SAW device to various mechanical and electrical perturbations. Variations in the mass loading, elastic constants, and conductivity are some of the factors, which contribute to the velocity change of the surface acoustic wave. The change in velocities results in a... 

Under the assumption of LTE a rather simple method consists in measuring the dynamic pressure of the gas with a probe. But, in that case, the probe disturbs the plasma flow, even if it is precisely profiled <> >. Another technique consists of the observation of a small electrical perturbation superimposed on the discharge 106) jijg ygg Qf pulsed laser now offers new opportunities for this type of measurement Figure 34 shows the velocity of an argon and nitrogen plasma jet at the nozzle exit as a function of the gas flow rate. A third technique uses very small particles injected into the plasma. In HF plasma the particles velocity, supposed to be the same as the gas flow, is measured by laser anemometry However for DC... 

Figure 4 Image of a typical reversing (bipolar) electric perturbation pulse (100 ns per data point). The fall time of polarity reversal is < 0.5 (Reprinted with permission from Ref 40. Copyright 1995 American Chemical Society.)...

The oxygen remains adsorbed on the metal. This negatively charged adsorbed phase is the cause of an electric perturbation at the Sn02-metal interface. 

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