Permitivity frequency dependence

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

Frequency-dependent measurements of the materials dielectric impedance as characterized by its equivalent capacitance, C, and conductance, G, are used to calculate the complex permitivity, e = d — id, where co = 2nf, f is the measurement frequency, and C0 is the equivalent air replacement capacitance of the sensor. 

A practical consequence of architecture is to permit acoustical performances to large numbers of listeners by enclosing the sound source within walls. This dramatically increases the sound energy to listeners, particularly those far from the source, relative to free field conditions. A measure of the resulting frequency dependent gain of the room can be obtained from the EDR evaluated at time 0. This frequency response can be considered to be an equalization applied by the room, and is often easily perceived. 

The use of a parallel combination of R2 and C2, as in Fig. 1, is attractive because the value of C2 needed to compensate for the capacitance of the cell is quite low, and small capacitors are cheaper, more accurate, and less frequency dependent than large ones. By adjusting C2, and thus compensating for the phase shift in the cell, one can improve the balance of the bridge. The ideal detector is an oscilloscope since this permits separate observation of both the capacitive and the resistive balance and can also reveal any waveform distortion that might occur if there is serious polarization of the electrodes. 

The curves showing the frequency dependence of loss functions [tan 5, G"(g)), or / (to)] permit the detection in the frequency domain, at temperatures just slightly above the glass transition temperature, of a prominent absorption or a process. The unavailability of experimental devices to measure mechanical viscoelastic functions at high frequencies impedes the detection of a fast process or P relaxation in the high frequency region. This latter process is usually detected in the glassy state at low frequencies. 

This method is valid only in the static field limit (zero frequency), which is a weakness. However, recent advances of a derived procedure (Coupled Perturbed Hartree-Fock) permit the frequency dependence of hyperpolarizabilities to be computed. The FF method mainly uses MNDO (modified neglect of diatomic differential overlap) semi-empirical algorithm and the associated parametrizations of AM-1 and PM-3, which are readily available in the popular MOPAC software package. ... 

The application of relaxation time measurements to study segmental motion (in polymers) as well as diffusional chain motion is very well documented but is still a subject of study, particularly using the frequency dependence of relaxation times to test the detailed predictions of models (McBriety and Packer 1993). The anisotropy of reorientation can also be studied conveniently, and recent interest in motion of molecules on surfaces (e.g. water on porous silica) has been investigated with great sueeess (Gladden 1993). Since the dipolar interaction is usually both intermolecular and intramolecular, the relaxation of spin- /2 nuclei (e.g. H) in the same molecule as a quadrupolar nucleus (e.g. H) can permit a complete study of reorientation and translation at a microscopic level (Schmidt-Rohr and Spiess 1994). 

The determination of radioelectric parameters on a wide frequency range permits calculation of the exponents of frequency dependencies. S and S", and thus goes back to the radioelectric value for any point situated inside the linearity zone. Results obtained on samples doped with PTSA and NDSA have also been reported [47]. The curves obtained have qualitatively the same form as for HCl doped samples and are not given here. 

The proposed model of the carrier multiplication process in quantum dots permits to explain a possibility to create with considerable probability three electron-hole pairs. It shows the way to the two steps with creation of four and five e-h pairs. It can explain the existence of the threshold on the frequency dependence of the CM quantum efficiency, when two pairs and a Raman scattered photon are created. 

The above results permit to present a model for the kinetics of counter-ion site binding. This model rests primarily (1) on the similarity which has been found for the frequency dependence of the absorptions due to site binding and to ion-pair formation and (2) on Manning s theory [16] for counter-ion condensation in polyelectrolyte solutions. In this model, site binding between a counter-ion C and a part P of the polyion writes ... 

Perhaps the most important stress factor affecting corrosion fatigue is the frequency of the cyclic stress. Since corrosion is an essential component of the failure mechanism and since corrosion processes typically require time for the interaction between the metal and its environment, the corrosion-fatigue life of a metal depends on the frequency of the cyclic stress. Relatively low-stress frequencies permit adequate time for corrosion to occur high-stress frequencies may not allow sufficient time for the corrosion processes necessary for corrosion... 

This model permits one to immediately relate the bath frequency spectrum to the rate-constant temperature dependence. For the classical bath (PhoOc < 1) the Franck-Condon factor is proportional to exp( —with the reorganization energy equal to... 

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