Dielectric constant time-dependent

In a manner similar to the dielectric constant, frequency-dependent Cp co) is defined as a dynamic susceptibility. Under equilibrium conditions, the heat that the system can adsorb from its surroundings during a AT change isq = H = CpAT, that is, the change in enthalpy per volume H. If the system contains (t) relaxing degrees of freedom after a T change, H = H t). For a time-dependent T variation, AT t) in a time interval 0 < < t is... 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

At low frequencies when power losses are low these values are also low but they increase when such frequencies are reached that the dipoles cannot keep in phase. After passing through a peak at some characteristic frequency they fall in value as the frequency further increases. This is because at such high frequencies there is no time for substantial dipole movement and so the power losses are reduced. Because of the dependence of the dipole movement on the internal viscosity, the power factor like the dielectric constant, is strongly dependent on temperature. 

Treating the free electrons in a metal as a collection of zero-frequency oscillators gives rise51 to a complex frequency-dependent dielectric constant of 1 - a>2/(co2 - ia>/r), with (op = (47me2/m)l/2 the plasma frequency and r a collision time. For metals like Ag and Au, and with frequencies (o corresponding to visible or ultraviolet light, this simplifies to give a real part... 

Relaxation processes are probably the most important of the interactions between electric fields and matter. Debye [6] extended the Langevin theory of dipole orientation in a constant field to the case of a varying field. He showed that the Boltzmann factor of the Langevin theory becomes a time-dependent weighting factor. When a steady electric field is applied to a dielectric the distortion polarization, PDisior, will be established very quickly - we can say instantaneously compared with time intervals of interest. But the remaining dipolar part of the polarization (orientation polarization, Porient) takes time to reach its equilibrium value. When the polarization becomes complex, the permittivity must also become complex, as shown by Eq. (5) ... 

Time-domain reflectometry (TDR) involves the use of two or more substantial metal rods inserted into soil. The rods are parallel and are attached to a signal generator that sends an electrical input down the rods. The time it takes the signal to travel down the rods is dependent on the soil s apparent dielectric constant, which, in turn, is proportional to the amount of water in the soil. Upon reaching the end of the rods, the signal is dissipated and the amount of... 

Additional drawbacks to the use of polyimide insulators for the fabrication of multilevel structures include self- or auto-adhesion. It has been demonstrated that the interfacial strength of polyimide layers sequentially cast and cured depends on the interdiffusion between layers, which in turn depends on the cure time and temperature for both the first layer (Tj) and the combined first and second layers (T2) [3]. In this work, it was shown that unusually high diffusion distances ( 200 nm) were required to achieve bulk strength [3]. For T2 > Tj, the adhesion decreased with increasing T. However, for T2 < Tj and Tj 400 °C, the adhesion between the layers was poor irrespective of T2. Consequently, it is of interest to combine the desirable characteristics of polyimide with other materials in such a way as to produce a low stress, low dielectric constant, self-adhering material with the desirable processabiHty and mechanical properties of polyimide. 

The electrical properties of materials are important for many of the higher technology applications. Measurements can be made using AC and/or DC. The electrical properties are dependent on voltage and frequency. Important electrical properties include dielectric loss, loss factor, dielectric constant, conductivity, relaxation time, induced dipole moment, electrical resistance, power loss, dissipation factor, and electrical breakdown. Electrical properties are related to polymer structure. Most organic polymers are nonconductors, but some are conductors. 

When restrictions are not placed on the amount of time or the amount of material, different solvents or different quantities of acid or base are usually used as variables. It is not only important to know the solubility of the compounds in aqueous solutions but also in other solvents to which the compound might be exposed during synthesis and formulation. The solvents usually have a wide range of dielectric constants and the experimental results provide a solubility profile which can be utilized in the selection of appropriate solvents to use during the development of the compound. Since the compounds almost always selected for development are either weak acids or weak bases, the solubilities of the compounds will be pH-dependent. The use of different amounts of acid or base with an excess amount of compound permits the determination of a pH-solubility profile. 

Figure 14 (a) Time-dependent behavior of cation radicals in liquid -dodecane monitored at 790 nm. The dotted and the solid lines represent the experimental curve and the simulation curve, respectively. The parameters of the electron dilfusion coefficient (De) = 6.4 x 10 " cm /sec, the cation radical diffusion coefficient (D + ) = 6.0 x 10 cm /sec, the relative dielectric constant e = 2.01, the reaction radius R = 0.5 nm, and the exponential function as shown in Eq. (19) with ro = 6.6 nm were used, (b) Time-dependent distribution function obtained from fitting curve of (a), r indicates the distance between the cation radical and the electron. The solid line, dashed line, and dots represent the distribution of cation radical-electron distance at 0, 30, and 100 psec after irradiation, respectively. 

While it is not clear how the constant frequency low field dielectric relaxation measurements mentioned above should be applied to reactions in liquids, save for a complete time-dependent theory of liquids, these effects are very significant. At short times (<10ps) the effective Onsager distance may be 20 nm, even in methanol or ethanol, but over the next two or three decades of time reduce to more nearly 2 nm. Such a change can reduce the rate of reaction much more rapidly than that which occurs by decay of the transient time dependence discussed in the previous sub-section. 

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