Properties dielectric

Dielectrics are insulating materials, and the dielectric behaviour of a solid is its behaviour in an electric field. When ordinary insulators are exposed to an externally applied electric field the negative electrons and positive atomic nuclei are displaced in opposite directions, so that electric dipoles develop where none existed before. (An electric dipole occurs in a crystal when a 

In some dielectrics, such as pyroelectric and ferroelectric materials, permanent electric dipoles exist in the absence of an external electric field. In these latter types of materials, dielectric properties are related to the way in which the permanent electric dipoles, as well as the other electrons and atomic nuclei, respond to the applied electric field. 

It is clear that if the effect of internal electric dipoles in a crystal is to be observed externally, as 

A polar direction in a crystal is a direction [ yir] that is not related by symmetry to the opposed direction [nvw]. The two senses of the direction are physically different. No polar direc- 

Crystal class directions polar axis effect group activity possible 

Dielectric properties of FLCs strongly depend on the temperature (especially near phase transition points) and frequency of the field. The dielectric 

Two modes contribute to the value of the averaged polarization (P). The first of them (soft mode) is induced due to the amplitude change of the polarization, i.e., variation of the tilt angle 6. This mode is the most important near the phase transition point of the FLC phase and results in the electroclinic eflFect [19, 20, 36]. The second mode, called the Goldstone mode, is responsible for the variation of the phase of polarization, i.e., the azimuthal director angle (p. 

Characteristic times and relaxation frequencies of FLCs can be measured by plotting the Cole-Cole diagrams (see Chapter 2) [32, 46-49]. The dielectric response of the smectic A, near the phase transition, into smectic C phase is approximately one order of magnitude weaker than the corresponding response of the ferroelectric phase. The only contribution to the smectic A response is made by the soft mode with characteristic relaxation frequency [46-48] 

At the A C phase transition point the characteristic frequency of the dielectric relaxation does not tend to zero and is defined by the Goldstone mode [4, 46-48]. The characteristic frequency of the Goldstone mode 

Here K2 is the elastic coefiicient related to deformation of the helix, and qo = 2 k/Rq and 7 are the helix wave vector and rotational viscosity. Typical values for the Goldstone mode relaxation frequency is 100 Hz-1 kHz [12, 46-48]. 

The dielectric properties of a material are characterized by its permittivity e, or more commonly by its relative permittivity (or dielectric constant) where 

With alternating voltages, the charge stored on a dielectric has both real (in-phase) and imaginary (out-of-phase) components caused by resistive leakage or dielectric absorption respectively. The dielectric permittivity is therefore a complex quantity 

A dielectric with capacitance C and dielectric loss tan has an equivalent 

The noise voltage produced by this conductance is given by the expression for Johnson noise in a resistor  

Values of tan can be calculated from conductance measurements or obtained directly using modern capacitance bridges. Polymers are comparatively lossy dielectrics. Typical room-temperature values of tan dg for PVDF range from 0.015 to 0.02 at 1 kHz and for VDF TrFE from 0.015 to 0.025, compared with values of 10 for some ferroelectric ceramics such as lithium tantalate and lead germanate. 

The heating characteristics of a particular material (for example, a solvent) under microwave irradiation conditions are dependent on the dielectric properties of the material. The ability of a specific substance to convert electromagnetic energy into heat at a given frequency and temperature is determined by the so-called loss tangent, tan 5. The loss factor is expressed as the quotient tan (3 = / , where e is the dielectric loss, indicative of the efficiency with which electromagnetic radiation is 

According to definition, the penetration depth is the point where 37% (1/e) of the initially irradiated microwave power is still present [6]. The penetration depth is in- 

Tga — Tg of uncrosslinked polymer is a constant and a is the conversion. This equation is for pre-gel in the absence of substantial crosshnking. 

X is the crosshnk density or fraction of all (Eco/Eo — Coo/Cq)X segments crosslinked, E is the lattice energy, 

C is the segment mobility. This gives a good fit for many systems. 

Fgo is the Tg of polymer at a = 0. This is good for many systems except for highly crosslinked multifunctional epoxy-resin moulding compounds (Hale 1991). 

Ej is the activation eneregy of transition from the glassy to the rubbery state, 

A magnetic field produces lines of force that penetrate the medium to which the field is applied. These lines of force appear, for example, when you scatter iron filings on a piece of paper covering a bar magnet. The density of these lines of force is known as the magnetic flux density. In a vacuum, the magnetic field and the magnetic flux density are related by the permeability of free space, po- 

FIGURE 9.1 Flux density in (a) a diamagnetic and (b) a paramagnetic sample. 

The field of the sample in the applied field is known as its magnetisation, M. The magnetic flux density is now given by Equation (9.2). 

The magnetisation is usually discussed in terms of the magnetic susceptibility, y, where 

FIGURE 9.2 Variation of magnetic susceptibility with temperature for (a) a paramagnetic substance, (b) a ferromagnetic substance, and (c) an antiferromagnetic substance. 

As in previous chapters we work in the continuum limit employing quantities averaged over macroscopically infinitesimal volume elements and disregarding microscopic local variations associated with the molecular structure (see Brown 1956). These considerations will be limited to processes sufficiently slow to restrict the treatment to time independent or quasistatic fields. The validity of Maxwell s equations of electrostatics is presupposed. The basic electric state variables are the electric field strength vector E, the electric flux density (or electric displacement) vector D, and the electric polarization vector P, related by 

Material properties are characterized by the permittivity tensor Sy or the dielectric susceptibility tensor Xij describing relations between the field quantities by 

In tables on material properties usually the relative permittivities e,y/eo are listed, formerly also called (relative) dielectric constants. Symbol eo designates the electric field constant which, regrettably, frequently is called permittivity of vacuum . 

Since eo is entirely a consequence (and, therefore, dependent on) the particular system of measuring units (in this case the SI) on which the formulation is based, this latter designation is misleading and has nothing to do with a plysical property of vacuum. 

Equations (4.2) and (4.3) suggest a direct proportionality between D and P with E. This is obviously oidy an approximation (sometimes excellent, in other cases rather poor) similar to Hooke s law in the case of elasticity. Deviations from this linearity are discussed elsewhere in this volume. 

In general, the polarization response of a material to an electric field occurs with time lag. This is caused by the mass effect and viscous resistance with dipole rotation and change in electric charge, which are the causes of polarization. Hence, a distribution of responses will be observed 

If this electric field is applied to a sample, change of electricity D widi phase lag d is observed  

From the ratio of D to E, complex dielectric constant e can be obtained  

Both ionic polarization (where the positive and negative charges move in opposite directions) and electronic polarization (where the electrons move 

If it is taken into consideration that the potential energy of a dipole in an electric field is much smaller than the thermal energy, then the time variation of the orientation polarization P of N dipoles having dipole moment p is found to follow a linear differential equation  

The above data are a clear evidence of the facilitated local mobility of the imide cycles in the PI matrix of PNC, which could be explained by a looser molecular packing of the PI chain fragments adjacent to the organosilicon nanophase. Obviously, this effect (i.e., the apparent density decrease in the PI matrix) should become stronger at higher MTS contents however, the reliable estimate of its magnitude remains the object of further studies. 

As can be seen in Table 3, the values of e (at a fixed frequency/= 1 kHz) for the PNC decreased with the rise in the MTS content. This latter result was consistent with other relevant data and was regarded as a further evidence of the invalidity of the reasonable expectation of an increase in dielectric permittivity from e 3.18 for the precursor (PAAS) to e = 3.8-4.0 for the bulk silica. 

A more quantitative assessment of the above data was attempted within the frame of several theoretical treatments of dielectric permittivity-composition relationships in composite materials, by the implicit assumption that the dielectric permittivities of the matrix and of spherical inclusions (e and e, respectively) 

The apparent values of estimated by different theoretical models (Table 3) exhibited a similar dependence on the PNC composition, remaining considerably lower than the dielectric permittivity of bulk silica. This result was explained by the assumtion that the organosilicon nanophase is made up of nanoparticles of silica (e =3.8-4.0) fused together into loose spatial aggregates with a considerable fraction, tp, of empty inner pockets (e- 1). 

The crosslinked organosilicon nanophase formed by the sol-gel procedure possesses a rather loose inner structure, characterized by an enhanced water diffusivity and by mean-square electron density fluctuations and dynamic elasticity moduli comparable to those of the pristine, glassy PI. 

In this equation, C is the film capacitance, Tg thickness of any oxide layo present on the metal electrodes, Tlb layer i avaage thickness of a monolayer, A is the 

Rubner and associates [19,30] have shown that electrically conducting LB films fabricated from polypyrrole/30DOP monolayers exhibit unusually large dielectric constants over a wide frequency range. The large dielectric constants are believed to be 

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Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

Microwaves from the waveguide are coupled into the resonator by means of a small coupling hole in the cavity wall, called the iris. An adjustable dielectric screw (usually machined from Teflon) with a metal tip adjacent to the iris pennits optimal impedance matching of the cavity to the waveguide for a variety of samples with different dielectric properties. With an appropriate iris setting the energy transmission into the cavity is a maximum and simultaneously reflections are minimized. The optimal adjustment of the iris screw depends on the nature of the sample and is found empirically. 

Barker J A and Watts R O 1973 Monte Carlo studies of the dielectric properties of water-like models Mol. Phys. 26 789-92... 

Figure C2.17.13. A model calculation of the optical absorjDtion of gold nanocrystals. The fonnalism outlined in the text is used to calculate the absorjDtion cross section of bulk gold (solid curve) and of gold nanoparticles of 3 mn (long dashes), 2 mn (short dashes) and 1 mn (dots) radius. The bulk dielectric properties are obtained from a cubic spline fit to the data of [237]. The small blue shift and substantial broadening which result from the mean free path limitation are...

Electron transfer reaction rates can depend strongly on tire polarity or dielectric properties of tire solvent. This is because (a) a polar solvent serves to stabilize botli tire initial and final states, tluis altering tire driving force of tire ET reaction, and (b) in a reaction coordinate system where the distance between reactants and products (DA and... 

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 ... 

On one hand, there are the dielectric properties, which are especially important for polai solvents like water. Bulk properties can, on the other hand, only be modeled by using a supermolecule approach with explicitly defined solvent molecules. 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

Alper H E and R M Levy 1989. Computer Simulations of the Dielectric Properties of Water - Studies of the Simple Point-Charge and Transferable Intermolecular Potential Models. Journal of Chemical Physics 91 1242-1251. 

Ah initio calculations of polymer properties are either simulations of oligomers or band-structure calculations. Properties often computed with ah initio methods are conformational energies, polarizability, hyperpolarizability, optical properties, dielectric properties, and charge distributions. Ah initio calculations are also used as a spot check to verify the accuracy of molecular mechanics methods for the polymer of interest. Such calculations are used to parameterize molecular mechanics force fields when existing methods are insulficient, which does not happen too often. 

Finally, the dielectric properties of a nonpolar polymer are modified by inclusion of even small amounts of a polar comonomer. In coatings applications the presence of polar repeat units in an otherwise nonpolar polymer reduces the tendency for static buildup during manufacture, printing, and ultimate use. On the other hand, in dielectric applications this increases the power loss and must be kept to a minimum, even to the exclusion of polar initiator fragments. 

In air, PTFE has a damage threshold of 200—700 Gy (2 x 10 — 7 x 10 rad) and retains 50% of initial tensile strength after a dose of 10" Gy (1 Mrad), 40% of initial tensile strength after a dose of 10 Gy (10 lad), and ultimate elongation of 100% or more for doses up to 2—5 kGy (2 X 10 — 5 X 10 rad). During irradiation, resistivity decreases, whereas the dielectric constant and the dissipation factor increase. After irradiation, these properties tend to return to their preexposure values. Dielectric properties at high frequency are less sensitive to radiation than are properties at low frequency. Radiation has veryHtde effect on dielectric strength (86). 

A combination of excellent chemical and mechanical properties at elevated temperatures results in rehable, high performance service to the chemical processing and related industries. Chemical inertness, heat resistance, toughness and flexibiUty, stress-crack resistance, excellent flex life, antistick characteristics, Htfle moisture absorption, nonflammability, and exceptional dielectric properties are among the characteristics of these resins. 

Some electrical properties are shown in Table 3. Values of other parameters have been pubflshed (146). Polymorphism of the PVDF chains and the orientation of the two distinct dipole groups, —CF2— and —CH2—, rather than trapped space charges (147) contribute to the exceptional dielectric properties and the extraordinarily large piezoelectric and pyroelectric activity of the polymer (146,148,149). 

Electrical Properties. Like unfluorinated siHcone counterparts, fluorosihcone elastomers have inherently good electrical insulating properties. The dielectric properties remain relatively unchanged when the elastomer is exposed to severe environments. 

The low molecular weight materials produced by this process are used as lubricants, whereas the high molecular weight materials, the polyisobutylenes, are used as VI improvers and thickeners. Polybutenes that are used as lubricating oils have viscosity indexes of 70—110, fair lubricating properties, and can be manufactured to have excellent dielectric properties. Above their decomposition temperature (ca 288°C) the products decompose completely to gaseous materials. 

Another important use of dielectrics is as intermetal dielectrics (IMDs), where the dielectrics insulate metal lines from each other. The dielectric material must fill small gaps with high aspect ratios (depth to width) while maintaining all other dielectric properties. It is essential that the IMDs are void-free at submicrometer dimensions for both performance and rehabiUty. 

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