Dielectric problem

When Barriol begun with his laboratory, he inherited what had been left from the ancient laboratory of Donzelot, the laboratory of physical chemistry. [12] But because the laboratories were poorly equipped in this after-war time, the spectroscopic equipment had already been taken by other laboratories. There remained little at the laboratory of physical chemistry, only something such as a spiritual inheritance and a tradition that wanted to found theoretical speculations on experiment. Two topics were further pursued Raman spectrography, or, more generally, the studies of vibrations inside the molecule, and dielectric problems. The first assistants had to build their own installation for the measurement of dipolar moments, and a part of an installation for the measurement of the refractive index in order to determine the atomic polarization. 

We shall consider two extreme kinds of systems. In the first kind, the system is a conductor and by application of a voltage between two electrodes (for the sake of simplicity the two electrodes will be taken parallel) a current flows from one electrode to another. The failure occurs when the current density becomes larger than a threshold value. Consequently, the system becomes nonconducting. The system behaves exactly as a fuse which is destroyed when the current is too large. We shall call this failure the fuse failure. In the second case, the system is a perfect insulator and a voltage is applied between the two electrodes. Again, beyond a definite (threshold) value of the electric field, the system breaks down and becomes conducting. This phenomenon is well-known in the physics of dielectrics, since it limits the application of dielectrics as insulators. We shall talk about the dielectric problem for this kind of failure. 

In the present work, we shall not discuss the exact nature of the failure, i.e. its microscopic mechanism. In the fuse problem, the mechanism of the failure is very well-known (it is merely the Joule effect), but in the dielectric problem the mechanism is much more complicated (O Dwyer 1973). The reason is that we intend to attack the problem from a point of view which is of tremendous importance for statistical analysis. If the sample is perfectly homogeneous the failure will take place in all the portions of the sample. In the first case the current density is uniform in the sample and in the second, the electric field is the same everywhere. If the threshold value is reached, the failure will be general and the sample will explode. In fact, this never happens. The failure always begins as a local event and progressively becomes general. This is because there are weak points in the system. The failure always begins at these weak points. The existence of weak points is due to the fact that solids are never homogeneous. This means that the... 

Fig. 2.2. Failure paths, (a) In the dielectric problem, the failure path gives the possibility for a current to flow from one electrode to the other, (b) In the fuse problem, the failure path is made of insulating elements and it prevents the current across the sample.

One can ask, what exactly is Vb or If First, we have to imagine how the sample looks after the failure. In the dielectric problem, after the failure has taken place, there is a conducting path composed of conducting portions which connects the two electrodes (Fig. 2.2a). In the fuse problem, after the failure, the current cannot flow since there is now an insulating path more or less perpendicular to the current direction (Fig. 2.2b). It is also possible that other parts of the sample, which do not belong to the failure... 

Thus we see that the current density is equal in magnitude to the field E, but is rotated by 90 from the dielectric problem. It is also easy to see that... 

Fig. 2.13. Comparison of constant current lines in the fuse problem and the equipotential lines in the dielectric problem in two dimensions. The two figures are identical but rotated by 90°.

We can visualise the equivalence of the two problems by comparing Fig. 2.3(b) and Fig. 2.12(b), which we draw again in Fig. 2.13. We see that the current is zero inside a defect (fuse problem) while the field is nil inside a defect (dielectric problem). Also, we see that the regions with enhancement of the field are located perpendicularly to those with enhancement of the current density. 

There are of course problems, common to any analyses requiring numerical Fourier transformations, of aliasing, truncation, and time referencing. Happily, these can be handled quite readily for dielectric problems because the pulse forms to be transformed are relatively simple and because effects of apparatus response characteristics and unwanted reflections can be eliminated or minimized by judicious apparatus design and use. In the sections that follow, we present basic analysis of TDS measurements, useful sample cell designs and working equations, methods for evaluation of transforms involved, and representative results. 

While for the exact dielectric problem only multipolar expansions are available, the COSMO approximation allows for the analytical calculation of the Green function in the case of a spherical cavity. Nevertheless, all implementations of COSMO are developed for the general case of a molecular shaped cavity, since any restriction to regular cavities such as spheres or ellipsoids is too severe a limitation. In this case the COSMO screening charges have to be calculated numerically. This requires a discretization of the cavity surface into... 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

This perturbation method is claimed to be more efficient than the fluctuating dipole method, at least for certain water models [Alper and Levy 1989], but it is important to ensure that the polarisation (P) is linear in the electric field strength to avoid problems with dielectric saturation. 

In some cases particles have been added to electrical systems to improve heat removal, for example with an SF -fluidized particulate bed to be used in transformers (47). This process appears feasible, using polytetrafluoroethylene (PTFE) particles of low dielectric constant. For a successful appHcation, practical problems such as fluidizing narrow gaps must be solved. 

There are two general weaknesses associated with capacitance systems. First, because it is dependent on a process medium with a stable dielectric, variations in the dielectric can cause instabiUty in the system. Simple alarm appHcations can be caUbrated to negate this effect by cahbrating for the lowest possible dielectric. Multipoint and continuous output appHcations, however, can be drastically affected. This is particularly tme if the dielectric value is less than 10. Secondly, buildup of conductive media on the probe can cause the system to read a higher level than is present. Various circuits have been devised to minimize this problem, but the error cannot be totally eliminated. 

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