Frequency dependence dielectric properties

Dielectric measurements on poly(vinyl acetate) were obtained utilizing a Fourier transform dielectric spectrometer developed in our laboratory (6). A voltage step pulse was applied to the sample and the time dependent Integrated current response, Q(t), was collected by computer. The frequency dependent dielectric properties, e and e" were then obtained from the Fourier trans-... 

Dielectric relaxation results are proven to be the most definitive to infer the distinctly different dynamic behavior of the hydration layer compared to bulk water. However, it is also important to understand the contributions that give rise to such an anomalous spectrum in the protein hydration layer, and in this context MD simulation has proven to be useful. The calculated frequency-dependent dielectric properties of an ubiquitin solution showed a significant dielectric increment for the static dielectric constant at low frequencies but a decrement at high frequencies [8]. When the overall dielectric response was decomposed into protein-protein, water-water, and water-protein cross-terms, the most important contribution was found to arise from the self-term of water. The simulations beautifully captured the bimodal shape of the dielectric response function, as often observed in experiments. 

In another recent study of dielectric properties of a protein-water system, Loeffler et al. ° presented a rigorous derivation of a theory for the calculation of the frequency-dependent dielectric properties of each component of a system which, in their example, consisted of the HIV-1 zinc finger peptide, water, and one zinc and two chloride ions. A 13.1 ns molecular dynamics simulation was performed, and, from it, dielectric constants for the various components of the system were extracted. It was discovered that the first hydration layer had a much lower dielectric response (47) than that of ordinary bulk water (80). The... 

The optical properties of metal nanoparticles have traditionally relied on Mie tlieory, a purely classical electromagnetic scattering tlieory for particles witli known dielectrics [172]. For particles whose size is comparable to or larger tlian tire wavelengtli of the incident radiation, tliis calculation is ratlier cumbersome. However, if tire scatterers are smaller tlian -10% of tire wavelengtli, as in nearly all nanocrystals, tire lowest-order tenn of Mie tlieory is sufficient to describe tire absorjDtion and scattering of radiation. In tliis limit, tire absorjDtion is detennined solely by tire frequency-dependent dielectric function of tire metal particles and the dielectric of tire background matrix in which tliey are... 

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

From frequency dependent dielectric loss measurements, the transitions associated with solvent dipole reorientations occur on a timescale of 10-n -10-13 s. By contrast, the time response of the electronic contribution to the solvent polarization is much more rapid since it involves a readjustment in electron clouds . The difference in timescales for the two types of polarization is of paramount importance in deciding what properties of the solvent play a role in electron transfer. The electronic component of the polarization adjusts rapidly and remains in equilibrium with the charge distribution while electron transfer occurs. The orientational component arising from solvent dipoles must adopt a non-equilibrium distribution before electron... 

Polymer properties are very often dependent on the polymer preparation. So, a good monitoring of the polymerization process is the key step to obtaining good and reproducible materials. The extent of the polymerization can be controlled in different ways. IR is the most usual [27,30] but is not very accurate and requires the extraction of samples to analyze. Recently, an in situ monitoring of PMR-15 processing has been provided by means of frequency-dependent dielectric measurements [33,34]. This non-destructive technique allows the characterization of all the steps of the curing process and thus they can be optimized. 

We have presented response methods that provide procedures for calculating frequency-dependent molecular properties for a molecular subsystem coupled to a stmctured environment. We have shown that the molecular subsystem is treated on a quantum mechanical level and the stmctured environment as a classical subsystem. We have presented the stmctured environment, classical subsystem, as a heterogeneous dielectric media or a molecular mechanics force field. We have demonstrated that the interactions between the quantum mechanical and classical subsystems are part of the energy functional used for optimizing the MCSCF electronic wave function. 

Representing the diffusive flow as Eq. (574) allows one to draw an analogy between the diffusion of a particle including inertial effects and the frequency dependent dielectric and viscoelastic properties. 

Nelson, S. O. and P. G. Bartley. 2000. Measuring frequency- and temperatnre-dependent dielectric properties of food materials. Transactions oftheASAE 43 1733-1736. 

Depending on the frequency of the field and the relaxation time band in relation to the temperature considered, one can observe three general changes of dielectric properties with temperature. Figure 1.11 gives the three-dimensional curves depicting the dependence dielectric properties on frequency and temperature [70]. 

Dipole-dipole interaction between molecules placed in an oscillating electric field results in energy being transferred from the oscillating field to the sample. This phenomenon manifests itself as a frequency dependent dielectric constant and is a property common to all materials. The physical basis of the measurement is expressed by Equation 3. 

The optical properties of dispersions of spherical particles can be predicted by Mie theory. This theory provides expressions for the extinction cross section of spherical particles with a frequency dependent dielectric function e = e -I- ie", embedded in a medium of dielectric function Sm, as [142-144]... 

A wide variety of molecular properties can be accurately obtained with ADF. The time-dependent DFT implementation " yields UV/Vis spectra (singlet and triplet excitation energies, as well as oscillator strengths), frequency-dependent (hyper)polarizabilities (nonlinear optics), Raman intensities, and van der Waals dispersion coefficients. Rotatory strengths and optical rotatory dispersion (optical properties of chiral molecules ), as well as frequency-dependent dielectric functions for periodic structures, have been implemented as well. NMR chemical shifts and spin-spin couplingsESR (EPR) f-tensors, magnetic and electric hyperfme tensors are available, as well as more standard properties like IR frequencies and intensities, and multipole moments. Relativistic effects (ZORA and spin-orbit coupling) can be included for most properties. 

Frequency dependent dielectric measurements made over many decades of frequency (Hz to MHz) provide a sensitive, convenient means for characterising processing properties of thermosets and thermoplastics [882]. DIES contributes to the understanding of the dynamics of complex solid polymer systems such as blends, of polymer solutions, and of polymerisation and curing or drying reactions. On-line in situ dielectric sensing is applied in monitoring the polymerisation step in the production of... 

Impedance spectroscopy (IS) is a versatile and powerfiil characteization technique for the investigation of frequency dependent electrical properties of materials and interfaces. It can be used to investigate the dynamics of boimd or mobile charge, both in the bulk and in interfacial regions of any kind of soUd or Uquid material with electronic, ionic, semiconducting, mixed electronic-ionic conductivity or even dielectric properties (Macdonald, 1987a). 

A typical example for the frequency- and temperature-dependent dielectric properties of a piezoelectric polymer is given in Fig. 7 that displays the a-relaxation, related the dynamic glass transition, of a polyvinylidene fluoride (PVDF) film along with an upswing of the dielectric loss at low frequencies due to electrical conduction. 

The electric permittivity determines the polarization (dipole moment per unit volume) induced in a material by an electric field. If the applied field varies with time, then the frequency dependence of the permittivity is an additional property of the material. A complication with any time-dependent response is that it may not be in-phase with the applied field. Thus to describe the frequency-dependent dielectric response of a... 

In order to investigate the origin and the physical properties of SPPs, we consider a metal-dielectric interface described by the plane z = 0 (see Fig. 1.6). The local frequency-dependent dielectric function is supposed to change in a stepwise manner from the dielectric with e z) = (for z > 0) to the metal with c(z) =... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

The same idea was actually exploited by Neumann in several papers on dielectric properties [52, 69, 70]. Using a tin-foil reaction field the relation between the (frequency-dependent) relative dielectric constant e(tj) and the autocorrelation function of the total dipole moment M t] becomes particularly simple ... 

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