Response Debye

In order to explain the non-Debye response (134) it is possible to use the memory function approach [22,23,31,266-268]. Thus, the normalized dipole correlation function k(f) (22) corresponding to a nonexponential dielectric relaxation process obeys the equation... 

Schwan emphasized the concept of dispersion in the field of dielectric spectroscopic analysis of biomaterials. Dispersion has already been introduced in Section 3.4.1 dispersion means frequency dependence according to relaxation theory. Biological materials rarely show a single time constant Debye response as described in Section 3.4.2. Knowing how complex and heterogeneous living tissue is, the concept of a distribution of... 

The Nyquist plot in Figure 9 is a classical Debye response. Debye response is the dielectric response of an ideal, non-interacting population of dipoles to an alternating external electric field. It involves only a single relaxation time because the dipoles do not interact with each other or induce other dipoles surrounding it. They aligned tliemselves with the direction of external field within the same time. This relaxation model was introduced by Peter Debye in 1913. 

The Nyquist plots of many real electrolyte systems deviate from the ideal Debye response, they tend to show distorted or depressed semicircles, tilted or curved spikes. The deviations can be fitted if a CPE replaces the capacitor in the equivalent circuit. A CPE is viewed as a leaky capacitor with impedance given by ... 

An overview on the topic of IS, with emphasis on its application for electrical evaluation of polymer electrolytes is presented. This chapter begins with the definition of impedance and followed by presenting the impedance data in the Bode and Nyquist plots. Impedance data is commonly analyzed by fitting it to an equivalent circuit model. An equivalent circuit model consists of elements such as resistors and capacitors. The circuit elements together with their corresponding Nyquist plots are discussed. The Nyquist plots of many real systems deviate from the ideal Debye response. The deviations are explained in terms of Warburg and CPEs. The ionic conductivity is a function of bulk resistance, sample... 

Equations (1.23a), (1.23b) and (1.23c) are, respectively, Cole-Cole (C-C) (0Davidson-Cole (D-C) (0Havriliak-Negami (0empirical laws. The calculations of permittivity on the base of Eq. (1.22) with relaxation function corresponding to KWW law (see Eq. 1.20) yield Eq. (1.23c) with y8 = a - [30]. Expression (1.23c) delivers pretty good description of experimental data obtained by dielectric spectroscopy, radiospectroscopy and quasielastic neutron scattering. It can be shown, that the physical mechanism, underlying the expressions (1.23) is the distribution of relaxation times in a system. Namely, Equation (1.23) can be derived by the averaging of simple Debye response (1.21) with properly tailored distribution function of relaxation times F(x) ... 

Interfacial or Maxwell-Wagner polarization is a special mechanism of dielectric polarization caused by charge build-up at the interfaces of different phases, characterized by different permittivities and conductivities. The simplest model is the bilayer dielectric [1,2], (see Fig. 1.) where this mechanism can be described by a simple Debye response (exponential current decay). The effective dielectric parameters (unrelaxed and relaxed permittivities, relaxation time and static conductivity) of the bilayer dielectric are functions of the dielectric parameters and of the relative amount of the constituent phases ... 

An important characteristic of plasma is that the free charges move in response to an electric field or charge, so as to neutralize or decrease its effect. Reduced to its smaUest components, the plasma electrons shield positive ionic charges from the rest of the plasma. The Debye length, given by the foUowing ... 

Figure 4 shows the measured angle of 105° between the hydrogens and the direction of the dipole moment. The measured dipole moment of water is 1.844 debye (a debye unit is 3.336 x 10 ° C m). The dipole moment of water is responsible for its distinctive properties in the Hquid state. The O—H bond length within the H2O molecule is 0.96 x 10 ° m. Dipole—dipole interaction between two water molecules forms a hydrogen bond, which is electrostatic in nature. The lower part of Figure 4 (not to the same scale) shows the measured H-bond distance of 2.76 x 10 ° m or 0.276 nm. 

Identify the most negatively-charged and most positively-charged regions in each molecule. (Ignore the phenyl rings attached to triafulvene.) The dipole moments of these molecules have been measured as 6.3, 0 and 0.8 debyes. Which molecule is responsible for which dipole moment Explain the trend in dipole moments. 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

According to the model, a perturbation at one site is transmitted to all the other sites, but the key point is that the propagation occurs via all the other molecules as a collective process as if all the molecules were connected by a network of springs. It can be seen that the model stresses the concept, already discussed above, that chemical processes at high pressure cannot be simply considered mono- or bimolecular processes. The response function X representing the collective excitations of molecules in the lattice may be viewed as an effective mechanical susceptibility of a reaction cavity subjected to the mechanical perturbation produced by a chemical reaction. It can be related to measurable properties such as elastic constants, phonon frequencies, and Debye-Waller factors and therefore can in principle be obtained from the knowledge of the crystal structure of the system of interest. A perturbation of chemical nature introduced at one site in the crystal (product molecules of a reactive process, ionized or excited host molecules, etc.) acts on all the surrounding molecules with a distribution of forces in the reaction cavity that can be described as a chemical pressure. 

Raicu, V. 1999. Dielectric dispersion of biological matter Model combining Debye-type and universal responses. Phys. Rev. E 60 4667-80. 

Truhlar model ). Electrostatics may be responsible. The dipole moment for the endo transition state is slightly larger than that for the exo transition state (3.4 vs. 3.2 debyes), meaning that a polar medium will stabilize it to greater extent. 

Hartree-Fock, local density, density functional and MP2 models provide a credible account of dipole moments in hydrocarbons. Even STO-3G and 3-2IG (Hartree-Fock) models appear to be suitable. Not only is the mean absolute error very low (0.1 debye or less), but all models properly account for a variety of subtle trends in the experimental data, for example, the increase in dipole moment in cyclopropene in response to methyl substitution on the double bond. Finally, note that there is very little difference in the performance of any of the models with 6-3IG and 6-311+G basis sets. 

The electrostatic term, AFgiggtrostatiC is the change in electrostatic free energy when the protein goes from the crystalline state to the solution state. Melander and Horvath have expressed this term by combining the proper terms from the Debye-Huckel and Kirkwood theories (7). This term is always positive, and is responsible for salTing in. 

If each normal mode is equally weighted in the total response, equations identical in form to (2.18) and (2.19) also hold for the cubic array since the connection between x and v obtains regardless of dimensionality. Here, g(v) — g3 (v) may be approximated by the familiar Debye equation ... 

Let us summarize by modeling the velocity autocorrelation function using Debye-Huckel type interactions between charged point defects in ionic crystals, one can evaluate the frequency-dependent conductivity and give an interpretation of the universal dielectric response. 

Onsager Theory for C(t) for Non-Debye Solvents. Generally solvents have more complex dielectric responses than described by the Debye equation (Eq. (18)). To obtain the time dependence of the reaction field R from Eqs. (12, (15), (16) and (7) an appropriate model for dielectric behavior of a specific liquid should be employed. One of the most common dielectric relaxation is given by the Debye-type form, which is applicable to normal alcohols. 

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