Properties, electrical

Electrically, ferrites can be classified as somewhere between semiconductors and insulators. In many applications, this is their main advantage over ferromagnetic metals, because their high resistivity results in low energy losses. When an ac field is applied to a conductive material, the fraction of the field absorbed to excite the conduction electrons becomes increasingly important as the frequency increases, at the expense of the field fraction used to magnetise the sample effectively. An accurate calculation of eddy-current losses is extremely complex, because it depends on the detailed domain structure. However, an approximate comparison can be illustrative. Eddy-current losses can be expressed as  

Eddy currents appear as a consequence of Faraday s law of electromagnetic induction. Consider a cylindrical sample of material. Fig. 4.64. As the current flows in the coil, an ac magnetic field H is applied to the 

In polycrystalline ferrites, grain boundaries can also have an influence on eddy-current losses. In high-permeability Mn-Zn ferrites, for instance, CaO and SiOj are used as additives to decrease the Fe content and increase the grain boundary resistivity (Berger et ai, 1989), both processes limiting eddy-current losses. 

The measurement of electrical properties as a function of frequency and their analysis by complex impedance methods (impedance spectroscopy) allow a separation of contributions to impedance from grains, grain boundaries and electrode polarisation (Jonscher, 1983 MacDonald, 1987). This technique therefore permits the separation of the electrical 

The electrical resistivity of p-type Cu S films which show optimum photovoltaic performance lies in the range between about 10 to Qcm. This value corresponds to a carrier density 

Such properties are required in the processing of semiconductor devices, and coupled with the advantage of fine control of layer thickness, these materials have much potential in microelectronics applications. 

The excellent insulating properties of LB films of fatty acid salts are well known, with film resistance being directly proportional to the number of layers n. Studies of electrical tunnelling through monolayers of thickness / have produced good agreement between theory and experiment [39], where the conductivity a is given by 

Tetrathiotetracenes (25), poly aromatic-based materials, form stable cationic salts when suitably doped. The most frequently used doping technique involves oxidizing deposited multilayers by exposing the grown LB film according to one of the following methods  

Gaseous oxidation involving exposure to an oxidizing gas such as CI2, Br2 or I2. 

Applications based upon derivatives of (25) are particularly interesting, since not only do these materials possess a high degree of electrical 

Electrical properties of one form or another are included in virtually all specifications for insulating oils. 

The electric strength or dielectric breakdown test method (ASTM D-877) indicates the absence, or presence, of free or suspended water and other contaminant matter that will conduct electricity. A high electric strength gives no indication of the purity of an oil in the sense of degree of refinement or the absence of most types of oil-soluble contaminants. This test method is of some assistance, when applied to an otherwise satisfactory oil, to indicate that the oil is free of contaminants of the type indicated above in practice, this ensures that the oil is dry. 

The test for stability (gas evolution) under electric stress must not be confused with tests for the gas content of insulating oil (ASTM D-831, ASTM D-1827, ASTM D-2945). These tests are largely factory control tests to ensure that oils intended for filling equipment have been adequately degassed (because dissolved gas, like gas evolved under stress, could cause void formation). 

Electrical properties such as volume resistivity and surface resistivity of blend samples are furnished. Blend with 30 phr carbon black was found to be overloaded in terms of both volume resistivity and surface resistivity. That is, the resistivity of these formulations was lower than the limit of the testing equipment. This is an effect of the quasigraphitic microstmcture of the carbon black this makes the blend more electrically conductive. The higher the surface/volume resistivity, the lower the leakage current and the less conductive the material is. The major application of carbon black 

Properties NECO NEC3 NEC5 NEC7 NECIO NEC20 NEC30 

and NEC30 are 70 30 NR/EPDM blends with carbon black content 0, 3, 5, 7, 10, 20, and 30 phr, respectively, b—the resistivities were lower than the limit of the testing equipment. 

Electrical properties of polymers that are subject to low electric field strengths can be described by their electrical conductivity, dielectric constant, dissipation factor, and triboelectric behavior. Materials can be classified as a function of their conductivity (k) in (Q/cm)- as follows conductors, O-IO dissipatives, and insulators, lO or lower. Plastics are considered nonconductive materials (if the newly developed conducting plastics are not included). The relative dielectric constant of insulating materials (s) is the ratio of the capacities of a parallel plate condenser with and without the material between the plates. A correlation between the dielectric constant and the solubility parameter (6) is given by 6 7.0s. There is also a relation between resistivity R (the inverse of conductivity) and the dielectric constant at 298 K log R = 23 - 2s. 

The insulating properties of polyethylene compare favourably with those of any other dielectric material. As it is a non-polar material, properties such as power factor and dielectric constant are almost independent of temperature and frequency. Dielectric constant is linearly dependent on density and a reduction of density on heating leads to a small reduction in dielectric constant. Some typical data are given in Table 10.6. 

Oxidation of polyethylene with the formation of carbonyl groups can lead to a serious increase in power factor. Antioxidants are incorporated into compounds for electrical applications in order to reduce the effect. 

Properties of Polyethylene 227 Table 10.6 Electrical properties of polyethylene 

The electrical properties of silicon oxide play a critical role in many phenomena on sihcon electrodes, particularly in the growth of anodic films. Anodic oxides can 

TABLE 3.3. Values of the Electronegativity and Charge Transfer in the Electron/Bond for Interface Bonds at the Si/SiOi Interface  

Compound Electronegativity Charge transfer, electron/bond 

Finally, the surface state charge or the fixed oxide charge illustrated in Fig. 3.26d is a result of an oxide growth process that has the following characteiislics  

It cannot be charged or discharged over a wide range bending of the silicon energy band. 

The electrical properties of polymers are of considerable importance in various applications—the insulation of electrical or telecommunication cables, electrical components, electrical appliances and accessories, printed circuits, radar and electronics. Semiconductors based on polymers should also be mentioned. It is also possible to use electrical properties for monitoring or tests without fracture on stmcture or properties such as sequence of polymerization, degradation, and transition temperatures. Let s discuss briefly some major electrical properties. 

The electrical properties of composites that are of interest include the relative permittivity or dielectric constant, e, the dissipation factor, tan 5, the dielectric strength (kV/mm) and the surface and volume resistivities. These properties will depend upon the constitution of the composite, the alignment of the fibres, the temperature and other enviromental conditions, and upon the frequency at which the measurement is made. 

There is a certain amount of information available for the fibres and matrices and this is also included here. 

Some electrical properties of fibres are given in Table 7.6. 

The differences in resistivity among the various types of fibre are very great. Particularly noticeable is the range of resistivities provided by the 

A fascinating study of electrical polarizabilities is that reported by Hurst et al. on polyenes. Using carefully selected but rather small basis sets, they computed dipole polarizabilities and second hyperpolarizabilities for a series of polyenes through C22H24, a major feat for ab initio technology. These 

Our own calculations on hydrocarbons have involved a small part of the series of polyacetylenes, C2 H2. Geometries for the first three members of the series were fully optimized at the DZ/SCF level, and these were extrapolated to select the bond lengths for the next two members of the series. These geometries are given in Table 4. A number of basis sets were tested for the first two members of the series, ranging from double-zeta sets to the triply polarized ELP (electrical properties) sets. The polarizabilities were evaluated with DHF, and the results are in Table 5. 

From a computational standpoint, an important difference between electrical and magnetic properties is the problem of gauge effects in the evaluation 

Tossell, Lazzeretti, and co-workers have provided a number of interesting examples of what comes from direct calculation of magnetic properties. One problem is PF5, which, as a trigonal bipyramid, has inequivalent fluorine centers, and yet only one resonance struaure has been observed. Calculations of the chemical shift revealed a difference between the axial and equatorial fluorine s of only 7 ppm, which is minute compared to how wide fluorine 

Basis set type With gauge at H With gauge at C IGLO 

Resistance is a familiar electrical property. The volume resistivity pj is the resistance in ohms of a material 1 cm thick, t, and 1 cm in area, A (Table 11.4). The resistance R of any other conflgnration is given by 

Volume resistivity is the ohmic resistance of the bulk dielectric material measured as though the material were a conductor The resistance is expressed as the resistance of a cube 1 cm on a side measured between faces. This value is measured according to ASTM D257. It is dependent on temperature, frequency, and voltage, and will vary with the conditioning of the material. 

Dielectric strength is defined as the potential per unit of thickness that will cause catastrophic failure of a dielectric material. This value is measured according to ASTM DI49. The value is dependent on the method of application of potential the nature of the potential dc or frequency of ac, and the temperature, and it varies with the conditioning of the specimen, all of which must be specified with the value. 

Arc resistance is the time in seconds that an are may play across the surface of a material without rendering it conductive. The property is measured according to ASTM D495 with the low-current, high-voltage arc. The failure may occur by carbonization, heating, and other means, and it is dependent on temperature, frequency, and conditioning, which, as well as the type of failure, must be specified. 

Dielectric constant is defined as the ratio of the capacity of a condenser made with a particular dielectric to the capacity of the same condenser with air as the dielectric. The test method for plastics is ASTM DC150. The value is frequency and temperature dependent, and varies with conditioning, all of which must be specified with the value. 

Undoped BN films exhibit low electrical conductivities. Ronning et al. [81] determined for ion beam deposited films resistivities of 10 -10 Qcm and the I-U curves were best approximated assuming a Frenkel-Poole conduction mechanism. These resistivities are near to the expected bulk value (up to 10 flcm [82]). Furthermore the dielectric constant was estimated as e — 8-10. 

The resistivities of films sputter deposited with a boron carbide target were lower (10 -10 n cm). Comparing the results of lateral and sandwich measuring arrangements, no essential differences were found [55]. 

Obviously the conductivity of BN films can be decreased by doping, for example with magnesium to prepare a p-type semiconductor [83]. 

The Nature and Appreciation of Electrical Phenomena in Polymers , in Advances in 

Blythe, Electrical Properties of Polymers, Cambridge University Press, 1979. 

Though the elastomers with high electrical conductivity (s) are critical for their applications in sensor skills, flexible display, wearable electronics, etc., the insulating behavior of SR limits its application in the above fields. Recently, this barrier has been overcome by introducing different nanofillers in SR, e.g., multi-walled carbon nanotubes [124, 127, 157, 160, 162, 163, 168], carbon nanofiber [165, 167], graphite, etc. [39, 128, 137]. These studies have shown that the SR nanocomposites exhibit a low percolation threshold. It is also suggested that the conductivity of these nanocomposites depends on the filler type, aspect ratio and extent of the dispersion of the filler in SR. 

Chua et al. [124] observed that the incorporation of 0.5 to 2.0 vol % of unmodified-MWNT (U-MWNTs) increases a in PDMS from 5.25x10 to 1.83x10S/cm. On the contrary, the values of a in PDMS composites filled with diphenyl-carbinol-functionalized MWNT (D-MWNTs) and silane-grafted diphenyl-carbinol-functionahzed MWNT (SD-MWNT) are lesser compared to U-MWNT-filled nanocomposite. This is attributed to the presence of organic layer wrapping of non-conducting diphenyl-carbinol and silane on the MWNT surfaces, which resists 

Electrical conductivity of CNF/silicone nanocomposites has been investigated by few researchers [165, 167]. Roy et al. [165] observed that the percolation threshold is attained at 4 phr in-situ and ex-situ prepared CNF/PDMS nanocomposites. When amine-modified CNF is used as filler in PDMS, the percolation threshold appears at lower filler loading (1 phr). These studies have also shown that the electrical conductivity of PDMS and its nanocomposites follow the order neat PDMS (10 S cm ) ex-situ PDMS/1 phr CNF (10 S cm ) in-situ PDMS/1 phr CNF (10 S cm ) in-situ PDMS/amine modified 1 phr CNF (10 S cm ). The higher electrical conductivity of amine-modified CNF-based PDMS nanocomposites could be assigned to the better dispersion of CNF facilitating the formation of conducting network. 

Two groups of electrical properties of polymers are of interest. The first group of properties is usually assessed from the behaviour of the polymer at low electric field strengths. To this group belong the dielectric constant, the dissipation factor, the static electrification, and the electrical conductivity. 

The second group consists of properties that are important at very high electric field strengths, such as electric discharge, dielectric breakdown and arc resistance. They may be regarded as the ultimate electrical properties. Properties of the first group are directly related to the chemical structure of the polymer those of the second are greatly complicated by additional influences in the methods of determination. 

Only the dielectric constant can be estimated by means of additive quantities. 

The application of an electric field to a material can produce two effects. It may cause the charges within the material to flow on removal of the field the flow ceases but does not reverse. In this case the material is called an electric conductor. 

Alternatively the field may produce field changes in the relative positions of the electric charges, which change is of the nature of an electric displacement and is completely reversed when the electric field is removed. In this case the material is called a dielectric. 

Only the liquid phase in a foam possesses electrical conductivity. The specific conductivity of a foam, xTp depends on the liquid content and its specific conductivity 

Matter can be classified according to its specific electrical conductivity o into electrical insulators (a = cm ), semiconductors (a = 

Macromolecules with certain constitutional characteristics possess semiconductor properties (Section 13.2). The majority of the commercially used polymers, however, are insulators (Section 13.1). A consequence of their limited conductivity is that these polymers readily become electrostatically 

When an electrical field is applied, the groups, atoms, or electrons of the insulator molecules are polarized. With stronger fields, electrons are displaced, giving rise to ions. With even stronger fields, the conductivity of the ions finally becomes so great that the material no longer shows any electrical resistance It discharges. Electrical conduction need not only take place in the interior, it can also occur on the surface. 

The electrical conductivity is the reciprocal of the electrical resistance. Since electrical resistance is measured in ohms, the unit of conductivity is often written as mho instead of ohm in American scientific literature. 

Macromolecules with certain constitutional characteristics possess semiconductor properties (Section 14.2). The majority of the commercially used polymers, however, are insulators (Section 14.1). A consequence of their limited conductivity is that these polymers readily become electrostatically charged (Section 14.1.5). Specific conductivities are, for example, 10 ohm cm for poly(ethylene), 10 ohm cm for poly-(styrene), and 10 ohm cm for polyamides (containing water ). 

It is only the liquid phase in a foam that possesses electrical conductivity. That is why the specific electrical conductivity of a foam kf (or its specific electrical resistance pF ) depends on the liquid content and on its specific electrical conductivity Kl (or its specific resistance pi) 

Theoretical and semi-empirical equations were derived for gas emulsions (as well as for suspensions of non-conducting spherical particles and O/W emulsion), specifying Eq. (8.33) . A relation for coefficient B can be derived from Maxwell-Wagner equation [45,46] 

A brief review on the electrical conductivity of diluted disperse systems and analysis of the expressions for the coefficient B is presented in [46]. 

Two other relations about B have been proposed in [46,48,49] 

In a polyhedral foam the liquid is distributed between films and borders and for that reason the structure coefficient B depends not only on foam expansion ratio but also on the liquid distribution between the elements of the liquid phase (borders and films). Manegold [5] has obtained B = 1.5 for a cubic model of foam cells, assuming that from the six films (cube faces) only four contribute to the conductivity. He has also obtained an experimental value for B close to the calculated one, studying a foam from a 2% solution of Nekal BX. Bikerman [7] has discussed another flat cell model in which a raw of cubes (bubbles) is shifted to 1/2 of the edge length and the value obtained was B = 2.25. A more detailed analysis of this model [45,46] gives value for B = 1.5, just as in Manegold s model. 

Wang and Chung [186] have observed apparent negative electrical resistance in interfaces between layers of carbon fibers in composite material in a direction perpendicular to the fiber layers. 

The magneto-resistance of carbon fibers made from coal tar mesophase pitch treated at 2500°C becomes lower and Lc (002) becomes smaller as the diameters get smaller [187]. 

A patent by Matthews and Ko [188] describes how the electrical resistivity of a PAN based carbon fiber heat treated at 650°-1050°C increases with time when aged in air and the magnitude of this increase is proportional to the initial resistance— the higher the initial resistance, greater is the increase. BASF established that the stability ean be enhanced by treatment in air for 8 8 h at 260-285°C. 

Lerner [189] found that oxidized PAN fibers subjected to heat treatment temperatures of 715-945 K are semiconductors. The room temperature conductivity is dominated by the contributions of impurity states, but these are not related to defects in the polymer. There is a decrease in conductivity on ageing in air caused by a decrease in the electron-phonon scattering time. The conductivity increases at temperatures above 473 K, as the samples aged in air outgas. 

The electrical resistance of cfrp was found to be closely related to the mechanical deformation and damage due to a change of cross-sectional area and length [190]. 

Electrons are driven to move by electric force when an electrical potential difference exists in a material. The resistance R to this force depends on the cross-sectional area A, the length l, and the conductivity a of an object as 

The electrical conductivity a is defined as the electrical current density or the amount of charges passing through a unit cross-sectional area per second in an electrical field with strength E of 1 V/m. The electrical conductivity can be determined from the particle number concentration n, the charge on a particle q, and the mobility of a particle p by 

The mobility here is the average velocity of a particle that accelerates between successive collisions under unit electric driving force (i.e., electric field strength E of 1 V/m). 

For metallic materials, charges are conducted by electrons or holes because most of the energy bands of metals are partially filled. A common equation for the electrical conductivity of metals can be derived from the following simple model. Applying Newton s second law to an electron in a crystal, it yields 

Therefore, the electrical conductivity of metals is obtained from Eqs. (1.66) and (1.69) as 

As electrical insulators, PET and PEN have very similar properties. The major difference between them is the long-term thermal ageing of the respective films and the effect that such ageing has on continuous use at various temperatures. Standard PET films have a continuous-use temperature of 105 °C, as measured 

Film type RTF -electrical (°C) RTF-mechanical w/ob impact (°C) Reference UL file number 

In addition, PEN has better resistance to moisture absorption than PET and polyurethane [44], All of these properties endow PEN film with better electrical resistant properties than any other polymer. 

Polymers, both uncompounded and compounded, are used in many electrical applications, often as primary electrical insulation. In other cases, such plastics may have primarily a structural function, but also an electrical function. 

The electrical properties of polymers must be understood and taken into account for many different applications (1-8). The electrical behavior of insulating materials is influenced by temperature, time, moisture and other contaminants, geometric relationships, mechanical stress and electrodes, and frequency and magnitude of the applied voltage. These factors interact in a complex fashion. 

The electrical properties of plastics are measured (1-8) to determine performance capability in electrical applications evaluate characteristics other than electrical provide quahty assurance serve as a means of identification and as a research tool and provide a basis for the buyer-seller relationship. 

In the United States, ASTM Committee D 09, on Insulating Materials, and Committee D 20 on plastics, have the primary responsibility of issuing standards for the evaluation and specification of plastics. Pertinent ASTM test methods and specifications pertaining to the electrical properties of plastics are given in Table 1. 

In addition to ASTM, several other groups, such as the National Electrical Manufacturers Association (NEMA), the Underwriters Laboratories (UL), the Institute of Electrical and Electronics Engineers (IEEE), and several US. government agencies issue plastics specifications, as do German (VDE and DIN) and British (BSD agencies. International standards are coordinated and written by the International Electrotechnical Commission (lEC). Despite such extensive and useful standardization activity, relatively little emphasis has been placed on the 

Insulation resistance, volume resistance, surface resistance of electrical insulating, solid materials can be determined by methods described in ASTM standard. Special standard was developed to determine permittivity (dielectric constant) and AC loss characteristics of solid electrical insulation.  

In metals, the primary mechanisms of both thermal conductivity and electrical conductivity are the same. Accordingly, the mechanisms of electron-lattice interaction described in the previous section for thermal conductivity apply equally well to electrical conductivity. Superconductivity also depends upon the electron-lattice interaction, albeit in a much more subtle way. A brief discussion of superconductivity completes this section. 

Metals. An electrical field applied to a metal produces a drift of free electrons. The resistance that this flow encounters is due to the scattering of 

The effect of temperature on resistance can be deduced by considering the effect of temperature on these two resistance mechanisms, that is, the collision of electrons with phonons and with imperfections in the crystal lattice. The first is a dynamic scattering mechanism, the second, static. As in the case of thermal conductivity, these scattering mechanisms can be considered reasonably independent, permitting the electrical resistivity p to be approximated by 

Since the lattice vibrations (phonons) are temperature dependent, p, will have a temperature dependence. Since the numbers of defects and impurities are not a function of temperature, p will have no temperature dependence. 

The temperature dependence of p, can be defined from what is already known about the effect of temperature on phonon activity. If thermal conductivity is used as an index of the phonon effect, Eq. (3.20) gives a 1/T dependence for thermal conductivity. Since thermal conductivity and electrical conductivity in metals are due to the same carriers (electrons), it follows that electrical conductivity will also have a l/T dependence. Since electrical resistance is the reciprocal of electrical conductivity, it follows that p,- will have a linear dependence on T. 

Reproduced with permission from Handbook of Polyolefins Synthesis and Properties, 1st Edition, Eds., C. Vasile and R.B. Seymour, Marcel Dekker, New York, NY, USA, 1993. Copyright Marcel Dekker, 1993. 

The historical interest in the electrical properties of polymers revolved aroimd their insulating and low dielectric properties. The vast majority of polymer applications involving electrical properties relies on their insulating characteristics, such as with wire and cable insulation as well as general apphance utility where insulating housings are desired. The dielectric properties of polymer blends has been covered earlier as a valuable method for characterization 

Polymer Volume resistivity (Ohm-cm) Dielectric constant 60 Hz 1M Hz Dissipation factor 60 Hz 1M Hz Dielectric strength (V/mil) 

Ionic conductivity of alkali metal salt complexes of poly(ethylene oxide) was noted in studies three decades ago by Wright [217, 218]. The interest in this observation has surged, due to the commercial success of lithium ion batteries. Poly(ethylene oxide) plus lithium salts have been the preferred system for solid polyelectrolyte layers, although the commercial systems 

ASTM D 1304-69 (1983) Methods of Testing Adhesives Relative to Their Use as Electrical Insulation. 

DIN 53482 Now DIN VDE 0303 Part 3 Methods of test for materials for electrical purposes measuring of the electrical resistance of non-metallic materials. 

DIN 53483 Testing of insulting materials Determination of dielectric properties measuring cells for liquids for frequencies up to 100 MHz. 

ASTM D1304-99 Standard methods of testing adhesives relative to their use as electrical insulation. 

Polymeric materials usually have low dielectric breakdown voltages. Fortunately, the electrical insulation property of PDMS is sufficient (R 1015 O/cm) [159]. Moreover, the use of a lower electric field ( 1100 V/cm) helps alleviate this 

Some of the discussed additives may affect electrical properties of the materials. There is not much information published on this subject. It is known from literature that fluoropolymer additives made dramatic improvement in processing rates of several polymers (ethylene oxide epichlorohydrin copolymer, silicone, polyacrylate, nitrile butadiene mbber, and ethylene propylene diene terpolymer) without affecting dielectric constant and dissipation factors. It can be assumed that similar effect can be obtained with some silicone additives, but in remaining cases these properties have to be analyzed if of importance. 

The only class of lanthanidomesogens for which electrical properties have been investigated in detail, are the bis(phthalocyaninato)lanthanide(III) sandwich complexes. As already described in Section 8, the free electron in these complexes is associated with the extensive re-system of the phthalocyanine macrocycles. The individual Pc2Lu units can be considered nominally as Lu Pc2 The bis(phthalocyaninato)lutetium(III) complexes are intrinsic molecular semiconductors. The generation of charge carriers can be represented by the reaction AAA A free carriers, where A is the molecular unit. The ionized pair A A is photochemically or thermally activated. 

Electric studies were later extended by the same authors to [(Ci2H250)gPc]2-Lu, and the oxidized species [(Ci2H250)gPc]2Lu+BF4 , obtained by oxidation of the parent compound with nitrosyl tetrafluoroborate (Belarbi et al., 1989). The electrical properties were determined in the frequency range between 10 and 

Q cm Mt was shown that the frequency dependence of the electrical conduc- 

Polyurethanes can be used in applications where electrical properties are important. They are not normally used for high-voltage insulation. Polyurethanes are often used directly or in combination with epoxies for encapsulation. The addition of antistatic agents to polyurethane gives a product with the correct electrical properties while retaining the excellent wear needed for a number of roller-type applications. 

Testing of polyurethanes for their electrical properties due to the voltages required must be carried out using properly designed equipment. The electrical tests that are normally carried out are resistivity, insulation resistance, electric strength, tracking resistance, power factor, and permittivity. 

Volume and surface resistivity tests for conductive and antistatic materials include  

Antistatic and conductive products Determination of electrical resistance 

Standard test method for rubber property-volume resistivity of electrically conductive and antistatic products Specification for electrical properties of conducting and antistatic products made from flexible polymeric material 

Another consequence of the molecular structure of water is its extremely high dielectric constant, which lowers the electrical forces between charged solutes in aqueous solutions. To quantify the magnitude of electrical effects in a fluid, let us consider two ions having charges Ql and Q2 and separated from each other by a distance r. The electrical force exerted by one ion on the other is expressed by Coulomb s law  

Unlike the transition-metal nitrides and unlike boron carbide and silicon carbide, the covalent nitrides are excellent electrical insulators. Their electrons are strtmgly and covalently bonded to the nucleus and are not available for metallic bonding (see Sec. 3.1 of Ch. 4). 

electrical conductivity, thermal conductivity, Seebeck effect and Hall effect are some of the common electron-transport properties of solids that characterize the nature of charge carriers. On the basis of electrical properties, solid materials may be classified into metals, semiconductors, and insulators where the charge carriers move in band states (Fig. 6.1) there are other semiconductors and insulators where charge carriers are localized and their motion involves a diffusive process (Honig, 1981). We shall briefly present the important relations involved in interpreting the transport phenomena in solids. 

An expression for the electrical conductivity of a metal can be derived in terms of the free-electron theory. When an electric field E is applied, the free carriers in a solid are accelerated but the acceleration is interrupted because of scattering by lattice vibrations (phonons) and other imperfections. The net result is that the charge carriers acquire a drift velocity i j given by 

Equation (6.24) expresses Ohm s law, where the proportionality constant between J 

In semiconductors, where the number of carriers is small, all the carriers respond to the applied field. The average kinetic energy can be equated to kT and thus 

For intrinsic semiconductors, in which both electrons and holes are present 

PP is an excellent electrical insulator, as can be expected from a non-polar hydrocarbon. The electrical properties of PP are very similar to those of PE and are compared in Table 19. 

The following terms are commonly used to describe the electrical properties of a material  

Typical electrical application of PP is in insulating power cable, particularly for telephone wires. The other functional requirements for this application are high impact strengths at low temperature and heat stabilisation for use in contact with copper. However, with the increasing use of optical fibres, the use of PP in this application is limited. 

The dissipation factor of PP is low and is hardly affected by temperature and frequency. The low dissipation factor rules out the use of high frequency heating and welding of PP. Hence, special techniques are required for welding of PP, discussed in Section 7.1. 

Dielectric properties are related to the capability of a material to be polarized under the influence of an externally applied electrical field. The polarizability of a material depends on its structure and molecular properties and therefore dielectric measurements can provide information in this respect. The study of dielectric properties of various substances is an Important tool for investigating their molecular structure and a rapid method to follow up the compatibility of the blends before and after the addition of different types of compatlblllzers. Moreover, the materials with a high dielectric constants are good Insulators [30, 31]. 

In continuation to our previous reported studies, the dielectric properties of the cellulose ether-transition metal complexes were examined [18]. The aim of this investigation was to find the relation between the dielectric measurements [permittivity and relaxation time] with the previous proposed structures, and ligand field parameters. The polymer complexes chosen for this study were prepared from cellulose ethers [CMC and HEC] with transition metals CuCl2, NiCl2, C0CI2 and FeCls. The dielectric properties were studied over a frequency range 0.1-80 kHz, at 25°C. Example of the relation between the permittivity [c ] and dielectric loss 

From this figure, it was clear that the values of e in the lower frequency range seem to be high, including the presence of dc conductivity. 

From the values of resistance [K] obtained for the different investigated systems, the dc conductivity was calculated, according to the equation reported in [32] and listed in Table 7.10. After subtracting the dc losses from the measured s values, the results showed a well-defined absorption region [Fig. 7.3) according to the Frohlich equation [33]. Table 7.11 shows these values in the 

For the case of HEC-metal complexes (Table 7.11), the relaxation times (r) were found to be less than that detected for different CMC-metal complexes. This view was realized to the presence of polyhydroxyethyl groups on the cellulose backbone, which result in inter-chain spaces and consequently reduce the effect of volume expansion due to the chelation of HEC with metal ions [18]. 

A plot of log p = f l/T) thus yields straight lines (Fig. 3.4-19). Because of the relatively small differences in slope for most glasses, the electrical insulation of glasses is often defined only hy the temperature at which the resistivity is 10 2 cm. According to DIN 52326, this temperature is denoted hy Tjtioo. The international convention is to quote volume resistivities at 250 and 350 °C (Table 3.4-11, second page, second column), from which the constants A and B 

The dielectric dissipation factor tan S is frequency-and temperature-dependent. Owing to the diverse mechanisms which cause dielectric losses in glasses, there is a minimum of tan 3 in the region of 10 -10 Hz, and increasing values at lower and higher frequencies (Fig. 3.4-21). 

At 10 Hz, the dissipation factors tanS for most glasses lie between 10 and 10 fused silica, with a value of 10 , has the lowest dissipation factor of all glasses. The special glass 8248 has relatively low losses, and in this cases tan S increases only slightly up to 5.5 GHz (where tan 5 = 3 x 10 ). 

The steep increase in dielectric losses with increasing temperature (Fig. 3.4-22) can lead to instability, i. e. overheating of the glass due to dielectric loss energy in the case of restricted heat dissipation and corresponding electrical power. 

4-20 Dielectric constant r of electrotechnical glasses as a function of temperature, measured at 1 MHz 

UHMWPEs exhibit excellent dielectric and insulating properties. The base polymer is an effective electrical insulator with a dielectric constant of 2.3 at 2 MHz. The high surface resistivity may cause electrostatic discharges. It can be reduced by the addition of carbon black. 

Sintered alumina possesses excellent insulating properties. Therefore, it is used as an insulator in electrical and electronic industries. The electrical conductivity is some 20 orders of magnitude smaller than metallic conductors. As an insulator, sintered alumina is used at frequencies in the kilocycle to megacycle range. Impurities in the material tend to increase its conductivity. 

Alumina can also be doped to use it as a semiconductor. At temperatures greater than 1500°C, alumina behaves as an intrinsic semiconductor. The activation energy then is found to be 5.5 eV [16]. Below this temperature, it behaves as an extrinsic semiconductor with an activation energy in the range of 2.5-5.5 eV. 

Nonconductive fillers are employed with electrical-grade epoxy adhesive formulations to provide assembled components with specific electrical properties. Metallic fillers generally degrade electrical resistance values, although they could be used to provide a degree of conductivity as discussed above. 

The effect of electrical-grade fillers (e.g., silica) on the electrical properties of the adhesive is usually marginal. Generally fillers are not used to improve electrical resistance characteristics such as dielectric strength. The unfilled epoxy is usually optimal as an insulator. Also under conditions of high humidity, fillers may tend to wick moisture and considerably degrade the electrical resistance properties of the adhesive. 

The one exception where certain fillers can provide electrical property improvement is in arc resistance. Here hydrated aluminum oxide and hydrated calcium sulfates will improve arc resistance if cure is sufficiently low to prevent dehydration of the filler particles. Electrical-grade fillers generally improve the arc resistance of cured epoxy systems, as indicated in Table 9.10. 

As would be expected from their structures, most plastics, at least in the solid state, are very poor conductors of electricity indeed, some are amongst the best insulators known. Dielectric properties—relative permittivity and power factor (or loss factor)—are typical of those found in low-molecular-weight organic materials, although the fine structure of such properties is affected by features associated with the structure. Conversely, the measurement of dielectric properties, which can be made with high precision over very wide frequency ranges, provides a powerful means of probing polymer structure. 

The insulation afforded by plastics materials with the poorest properties, such as polyamide 6.6 or plasticized PVC, is still more than adequate, except for the most critical uses. This is exemplified by the use of the former by British Rail as an insulant in automatic track signalling, and of the latter in domestic cable insulation. 

The intrinsic electrical strength of most plastics is higher by a factor of a thousand than the breakdown strength of air, so that in most practical situations breakdown is dominated by the breakdown of the air. 

It is well known since the middle of the 20th century that PE composites show interesting electrical properties, which are responsible for their use as sensors and to faul current limits. Also PE/carbon blend composites show a strong PTC, positive temperature coefficient. The behaviour of PE nanocomposites in this phenomenon depends both on the crystallinity degree of the PE matrix, as well as on the properties of the filler [162]. Dispersion of the EDH layers in electrically active polymeric matrices increases the thermal stability of the nanocomposite. [163], Schonhals et al. [164] have studied the changes observed in the electrical properties of a LDPE 

In the past three decades, several types of rr-electron systems have shown very interesting features in the electrical transport properties. The charge-transfer complexes [e.g., tetrathiafulvale-nium tetracyanoquinodimethane (TTT-TCNQ), etc.], consisting of electron-donating (donors, TTF, etc.) and electron-withdrawing (acceptors, TCNQ, etc.) organic molecules, have a wide range of 

The electrical and optical properties of polyacetylene (CH) , polyaniline (PANI), polypyrrole (PPy), polythiophene (PT), po-ly(p-phenylene vinylene) (PPV), poly(p-phenylene) (PPP), and poly(thienylene vinylene) (PTV) are some of the extensively studied conducting polymers [3,1049]. 

By the early 1990s, several groups have started making high-quality materials of PPV, PPy, PANI, and polyalkylthiophene (PAT) [3]. In doped oriented PPV samples, room-temperature conductivity values on the order of 10 S cm were observed [1117]. In high-quality PF6-doped PPy and PT samples, prepared by low-temperature electrochemical polymerization, the conductivity was nearly 500 S cm [1118]. In these samples, for the first time in doped conducting polymers, a positive temperature coefficient of resistivity (TCR) was observed at temperatures below 20 K, demonstrating the real metallic qualities. 

In general, conducting polymers can be considered as a special type of semiconducting material. The conductivity of undoped polyconjugated systems is 10 -10 S cm , hence, it can be considered at the semiconductor-insulator boundary. The bandgaps of known polyconjugated systems vary from 0.8 to 4 eV [3]. The bandwidths, parallel and perpendicular to the chain axis, in a typical polyconjugated system like (CH) c are nearly 10 and 

The main sources of disorder in conducting polymers are the sp defects in the chain, chain ends, chain entanglements, voids. 

The application of molybdenum disulphide and other dichalcogenides has become important in electrical brushes, especially in spacecraft, and its electrical properties are of considerable interest. It is therefore surprising to find that there is no clear agreement about its electrical conductivity. 

It is usual to state that molybdenum disulphide is a p type semiconductor, while niobium diselenide is a conductor, However Mikhailov has shown that pure molybdenum disulphide is a conductor and that only specimens having a developed film of oxidised material on the surface of the lamellae show semiconductor properties. Correspondingly a composite containing 15% was found to have a specific contact resistance of only 0.4 m.ohm.cm. compared with 0.7 m.ohm.cm  

The resistance depends to some extent on the direction of the current flow in relation to the crystal structure. At 70 C interpolated results were approximately 17 ohms parallel and 10 ohms perpendicular to the C-axis, but at 19 C the value was 29 ohms in both directions. 

The resistance also varies with the applied potential, with pressure, and with light . No detailed study has been made of the interactions between these various influences, but none of them seems sufficient to account for the wide range of measured values. It is probable that impurities have a dominant influence on the 

The composition and performance of compacts and composites used electrical brushes are considered in some detail in Chapter 12. 

Plastics and composites offer the designer a great degree of freedom in the design and manufacture of products requiring specific electrical properties (see Fig. 3-94). Their combination of mechanical and electrical properties makes them an ideal choice for everything from tiny electronic components to large electrical equipment enclosures. The 

Polyacetylene with iodine Polypyrrole with phenylsulfonate Polystyrene 

Acetate Epoxy Resins, Polyesters Urea Formaldehyde Cast Phenolics Polyvinyl Bulyral Plastics 

Material Resistivity Dielectric Constant/Dissipation Factor  

differences in test measurements and samples configurations make comparisons difficult. The ASTM has a relatively new standard that defines the methods for stabilizing materials measurement, thus allowing relative measurements to be repeated in any laboratory. These procedures permit relative performance ranking, so that comparisons of materials can also be made. Nonetheless, the designer will still have to confirm the 

As opposed to diamond, DLC has a variable electrical conductivity, which is a function of hydrogen content. It may not be a suitable semiconductor material since it has a relatively low bandgap, generally low resistivity, and low operating temperature, although semiconducting properties have been reported.0 1 

An outstanding property of DLC is its hardness. Vickers hardness ranges from 2000 to 9000 kg/mm. The large spread is due in part to the difficulty of testing thin coatings by indentation such as the Vickers test, since it is difficult to eliminate the substrate effect. Hardness also varies with the structure and composition. 

In this Section, the derivation of useful expressions for the calculation of first-order properties at the quasi-relativistic level of theory will be outlined. The electric field gradient at the nucleus is chosen to represent first-order electrical properties. The relativistic corrections to the electric field gradients are large since the electric field gradient operator is proportional to r. The electric field gradient operator is thus mainly sampling the inner part of the electronic density distribution. 

First-order electrical properties can conveniently be determined from expressions derived by using gradient theory. The Hamiltonian is augmented with an operator representing the studied property. By calculating the first derivative of the total energy with respect to the strength parameter of the property operator, one obtains an expression for the calculation of the specified first-order property. 

In this case, the perturbation term is e.g. proportional to the tensor component of the electric field gradient operator (43) times the nuclear quadrupole moment or is actually multiplied by a perturbation-strength parameter, Q, which is linearly proportional to the nuclear quadrupole moment. 

The quadrupole coupling term is added to the interaction potential V r) and when one proceeds as outlined in Sections 2 and 3, one obtains a quasi-relativistic Hamiltonian (44) which considers the quadrupole coupling interaction between the electrons and the nuclei. 

Qq is the nonrelativistic operator considering the quadrupole coupling. The relativistic correction terms that will contribute to the final expression are X that explicitly includes an additional Q dependent term and Y which contributes indirectly since it affects the orthonoimalization condition. The X operator defined in equation (45) contains the interaction terms originating from the lower half of the Dirac equation. 

PAEK can be used as good electrical insulators in a wide range of environments and over a wide range of temperatures. The polar nature of the carbonyl group means that materials such as fluoropolymers have superior dielectric constants and dissipation factors. However, relative to fluoropolymers, PAEK insulation offers lower toxicity in fire situations and more resistant mechanical properties. PAEK can have a relatively low comparative tracking index which measures susceptibility to electrical breakdown on the surface of an insulator. Possibly this reflects the relatively easy degradation of PAEK to carbonaceous char. 

To a good approximation, the more extensively studied azides are mostly ionic compounds with band gaps in excess of 3 eV, and they behave as insulators at room temperature. With such materials, it is not a simple matter to distinguish between contributions from ionic conductivity and electronic conductivity. Brief descriptions of the standard kinds of measurements appear below to point out some of the difficulties inherent in interpreting electrical experiments on ionic insulating materials. 

Alternatively, a metal insulator junction is an ohmic contact for electron flow if X (for hole flow if and if the interface state density in the insulator band gap is sufficiently small that the metal Fermi energy will not be pinned in the insulator band gap [125]. The accumulation layer which then forms can act as a virtual cathode for electrons ( x) or anode for holes (  

Distinguishing between interface-dominated currents and bulk-dominated (ohmic) currents often requires a self-consistent interpretation of a variety of electrical conductivity measurements. These may be steady-state and transient, equilibrium and nonequilibrium, and can use a variety of electrode materials and sample geometries. 

The most common sample forms used for the measurement of electrical properties are pressed pellets, thin films, and single crystals. Electrical measurements on pellets are often difficult to interpret because of the presence of polycry staUinity, grain boundaries, large surface area, and unknown amounts of adsorbed gases. Films are useful in some instances, but in many cases also cause uncertainties because of poly cry staUinity. Electrical properties are most easUy and reUably interpreted with single crystals free from unintentional impurities and solvent occlusions. 

The bulk ohmic conductivity a of a sample of thickness L, with parallel electrodes of area A is 

All commodity polymers (that is those manufactured and sold in high volume) act as insulators because they have no free electrons to conduct electricity. Some low-volume polymers such as polyacetylene, are conductive or semi-conductive, but their applications are specialized and their use limited. In this section, we shall concentrate on the properties of commodity polymers, because these materials represent the vast majority of polymers used in electrical applications. 

We can divide commodity plastics into frvo classes excellent and moderate insulators. Polymers that have negligible polar character, typically those containing only carbon-carbon and carbon-hydrogen bonds, fall into the first class. This group includes polyethylene, polypropylene, and polystyrene. Polymers made from polar monomers are typically modest insulators, due to the interaction of their dipoles with electrical fields. We can further divide moderate insulators into those that have dipoles that involve backbone atoms, such as polyvinyl chloride and polyamides, and those with polar bonds remote from the backbone, such as poly(methyl methacrylate) and poly(vinyl acetate). Dipoles involving backbone atoms are less susceptible to alignment vith an electrical field than those remote from the backbone. 

Most important is, however, the fact that Pr strongly depends on VF2 content. This is because the copolymers adopt the all-trans highly polar conformation (see Sect 3) and with increasing number of VF2 units the resulting dipole moment within each crystal increases. In fact, it has been shown that the electric polarization in these copolymers increases with the fraction of ferroelectric crystals in the material 

Another technique used for obtaining macroscopically polar films involves mechanical extension of the material. Uniaxial plastic deformation induces a destruction of the original spherulitic structure into an array of crystallites in which the molecules are oriented in the deformation direction. In case of PVF2 when such deformation takes place below 90 °C the original tg+ tg chains are forced into their most extended possible conformation which is all-trans [32]. 

In general, it is accepted that recombination of electrons and holes, trapping of electrons by oxygen deficiency sites and a low mobility of the holes, cause a low conductivity and accordingly a low photoresponse for hematite. Electron mobility in the range 0.01 [60] to 0.1 cm2/V-s [17] has been reported. In the latter case, it was found that the electron mobility was independent of donor concentration. More recently, an electron mobility of about 0.1 cm2/V-s has been measured with doped single crystals and the mobility was also here independent of donor concentration [5]. A diffusion length of holes has been determined to be only of 2-4 nm [6], which is about 100 times lower than many other (III-V) oxides. 

Interstitial ions always favor ferromagnetic ordering of the principal cation sublattice. If the principal sublattice is antiferromagnetic, the interstitials are undoubtedly shifted from the center of symmetry of their bipyramidal interstice into the tetrahedral environment nearer one of the two neighboring cation basal planes. The 

Direct confirmation of these conclusions has been obtained by neutron diffraction for CrSb, MnTe, FeS and by susceptibility measurements (see Table VIII). It is significant that the titanium compounds show Pauli paramagnetism, indicative of collective electrons, since 3.15 A Rtt(c axis) 3.23 A. This is in agreement with equation 174, which calls for Rc 3.2 A in the more polarizable anion sublattices. 

Experiment appears to confirm the essential features of this model. 

All the ferromagnetic NiAs compounds contain 3d4 cations (CrTe, MnAs, MnSb, and MnBi). 

The paramagnetic susceptibility of MnAs gives Meff 4.9m per 3d4 cation. 

More recent studies have focussed on the characterization of the conductive polymer, polypyrrole, and its use as a coating for acoustic wave vapor sensors [74-77]. One advantage of polypyrrole is that it can be generated directly on an 

The single designation indicates that the response is from an individual SAW sensor (i.e., no reference sensor was employed). (Reprinted with permission. See Ref, [671. 1985 Elsevier F lblishers.) 

Product Deflection temperature (0.45 MPa) IS075-1, -2 (°C) Vicat softening temperature ISO306 (B50, 50c C/h50N) (°C) CLTE parallel to flow ISOl 1359-1, —2 (cm/cm/ C) 

Product Relative permittivity IEC250 (KP/Hz) Dissipation (loss) factor IEC250 (106/Hz) Volume resistivity IEC93 (ohm cm) Surface resistivity IEC93 (ohm) 

The conductivity of the PAn/HA emeraldine salts (ES) is dependent upon the temperature9 as well as humidity and, hence, polymer water content.10-11 In general, attachment of functional groups decreases the conductivity, whereas the formation of copolymers between aniline and functionalized aniline results in polymers with intermediate conductivity. In addition, the preparation conditions,12-13 particularly as 

FIGURE 5.1 The doping of emeraldine base with protons to form the conducting emeral-dine salt form of polyaniline (a polaron lattice). 

Even so, the occurrence of a charge exchange phenomenon is necessary to produce the conductivity levels observed, even in 50% doped PAn, because of the presence of structural defects other than those caused by inadequate protonation of the nitrogen sites. It is proposed that this involves interchain or intrachain proton exchange as well as electron transport. This explains the observed dependence of conductivity on the ambient humidity, as the presence of water within the polymer lattice would facilitate this proton-exchange phenomenon.16 

Other phenolic compounds have also been shown to cause similar changes in conformation and physical properties of PAn/HCSA salts.24-28 Most of these, for example, m-cresol, are highly corrosive and toxic, limiting their desirability for processing and enhancing the electrical conductivity of PAn s. However, we have recently found that the structurally related molecules thymol 2 and carvacrol 3, which are much less toxic than m-cresol, can also function as effective secondary dopants for PAn/(+)-HCSA films and increase the electrical conductivity by up to two orders of magnitude.28 

FIGURE 5.2 UV-visible spectrum for PAn/( )-HCSA obtained by doping EB with ( )-HCSA in carvacrol. 

Ideally, PPV should exhibit a thoroughly r-conjugated structure for electronic applications. In practice, this cannot be achieved. Saturated defects interrupt the tr-conjugated structure and thus the length of conjugation. On the other hand, ethynylene moieties instead of vinylene moieties may act as traps of charge carriers. The trapping may occur at either radiative or non-radiative trap states. In fact, there are two types of defects  

Structural defects include grain boundaries, crystallographic defects, chain ends and oxidative defects. In contrast, chemical defects may either be due to impurities incorporated during material processing, or in the polymer backbone itself. 

Photoluminescence (PL) and EL spectroscopy can be used to determine the presence of traps. Other techniques include current voltage measurements, capacitance voltage measurements, capacitance transient spectroscopy, and admittance spectroscopy. Under favorite conditions, the identification of the nature of the trap is possible. 

The incorporation of a fire retardant additive, in the case of some polymers, produces a deterioration in surface arc resistance and tracking resistance. 

This has been observed in the case of diallyl phthalate, PA-6,6 and PBT A slight deterioration in dissipation factor was also observed for PBT, PPO and PP. 

The incorporation of 10% to 30% of glass fibre into the non-fire retardant and fire retardant PPO formulations causes a decrease in dielectric strength. 

Microwave dielectric measurements confirm the ferroelectric nature of order phases, the dipoles being related to the orientation of the protonic species and not to the proton ordering, according to the small temperature shift on H/D substitution (Table 17.1). The extrapolated Curie-Weiss temperature of the first order I - II transition is located below the actual 

Effect of fiber treatment Chemical modification of fibers decreased the dielectric constant of OPF-sisal fiber-NR hybrid composites [59]. This was due to the decrease in orientation polarization of the composites upon treatment. Chemical treatment results in reduction of hydrophilicity of the fibers leading to lowering of orientation polarization and subsequently dielectric constant. Alkali treatment yielded higher dielectric constant comparing to silane treatment. However, higher concentration of alkali 

The high tonnage, commercially important polymers are, in general, excellent insulators with resistivities in the range 10 - 10 Q-cm [22], The top three polymers in volume terms (in descending order) PE, PP and PVC are all used extensively as cable insulation. There are some intrinsically conductive polymers [39-41] such as polyaniline [42, 43] polythiophene and polypyrrole [43], but these are relatively expensive, intractable, niche materials, that must be modified to impart processability [44-46]. 

Neurons Projecting Through the Carotid Sinus Nerve (CSN) 

Intracellular recordings from identified cat PG baroreceptor neurons, with myelinated axons, show that they respond to electrically imposed short depolariza- 

Marcel Dekker, Inc. 270 Madison Avenue. New York, New Yoric 10016 

The MSe compounds with trivalent rare earth cations (all except M = Sm, Eu, and Yb) exhibit low room temperature resistivities and positive temperature coefficients of resistance and appear to be degenerate semiconductors, or metallic in nature. The high conductivity is believed to result from the excess valence electron (formulated as [1]) which does 

As noted before the polystannanes are good conductors and conductivity has been found for a mmiber of other tin-containing polymers. 

Theoretical calculations predict significant anisotropy in effective hole masses for the different valence bands of GaN, though the various calculations differ in the predicted magnitude of the anisotropy in each band [113-115]. Direct measurements of hole masses are, however, very difficult and most reported experimental values are indeed inferred from luminescence, magneto-optical studies of exciton luminescence, infrared reflectance and transmittance studies of polar materials, which are often isotropically averaged and thus not informative about the anisotropy. Directionally dependent Hall-effect measurements in m-plane GaN films grown on m-plane SiC substrates 

The conductivity of PEDOTPSS layers is usually determined by depositing uniform thin films onto a nonconductive substrate. The sheet resistance, is measured via four-point or two-point probes. The resistivity, p, or its inverse, the conductivity, o, are calculated by multiplying times the layer thickness, d, according to 

The conductivity of PEDOTPSS films can be altered by various means The modification of the ratio of PEDOT to PSS will have direct impact on the 

Changing the pH value of the solution will also have an impact on conductivity as reported by Aleshin et al. The highest conductivity was found at pH values between 0 and 3. 

First attempts to unravel the mechanisms of conductivity in PEDOT PSS films have been made by Aleshin et al. The authors studied the conductivity and magnetoresistance of PEDOT PSS as a function of temperature and found that both parameters increase with temperature. The temperature dependence of conductivity was discussed using the model of variable range hopping (VRH)i  

In the meantime there have been several reports focusing on the temperature dependence of the conductivity of PEDOT PSS. i All results are discussed within the framework of the VRH model. The results differ with 

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IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Chemical properties of deposited monolayers have been studied in various ways. The degree of ionization of a substituted coumarin film deposited on quartz was determined as a function of the pH of a solution in contact with the film, from which comparison with Gouy-Chapman theory (see Section V-2) could be made [151]. Several studies have been made of the UV-induced polymerization of monolayers (as well as of multilayers) of diacetylene amphiphiles (see Refs. 168, 169). Excitation energy transfer has been observed in a mixed monolayer of donor and acceptor molecules in stearic acid [170]. Electrical properties have been of interest, particularly the possibility that a suitably asymmetric film might be a unidirectional conductor, that is, a rectifier (see Refs. 171, 172). Optical properties of interest include the ability to make planar optical waveguides of thick LB films [173, 174]. 

Some aspects of adsorption on oxides and other semiconductors can be treated in terms of the electrical properties of the solid, and these are reviewed briefly here. More details can be found in Refs. 84 and 182. 

Some electric properties of molecules are described in section Al.5.2.2 because the coefficients of the powers of Mr turn out to be related to them. The electrostatic, mduction and dispersion energies are considered m turn in section Al.5.2.3, section Al.5.2.4 and section Al.5.2.5, respectively. 

Rasaiah J C 1987 Theories of electrolyte solutions The Liquid State and its Electrical Properties (NATO Advanced Science Institute Series Vol 193) ed E E Kunhardt, L G Christophous and L H Luessen (New York Plenum)... 

Atmospheric ions are important in controlling atmospheric electrical properties and conmumications and, in certain circumstances, aerosol fomiation [128. 130. 131. 138. 139, 140. 141. 142, 143, 144 and 145]. In addition, ion composition measurements can be used to derive trace neutral concentrations of the species involved in the chemistry. Figure A3.5.11 shows the total-charged-particle concentration as a frmction of... 

Salmeron M, Neubauer G, Folch A, Tomitori M, Ogletree D F and Sautet P 1993 Viscoelastic and electrical properties of self-assembled monolayers on Au(111) films Langmuirs 3600... 

Procarione W L and Kauffman J W 1974 The electrical properties of phospholipid bilayer Langmuir films Chem. Phys. Lipids 12 251-60... 

Black phosphorus is formed when white phosphorus is heated under very high pressure (12 000 atmospheres). Black phosphorus has a well-established corrugated sheet structure with each phos phorus atom bonded to three neighbours. The bonding lorces between layers are weak and give rise to flaky crystals which conduct electricity, properties similar to those ol graphite, it is less reactive than either white or red phosphorus. 

The dielectric constant is concerned with the electrical properties of a material. The dielectric constant for a solid is a 3 x 3 matrix with different components according to the Cartesian axes. These elements are given by ... 

Thus far the importance of carbon cluster chemistry has been in the discovery of new knowl edge Many scientists feel that the earliest industrial applications of the fullerenes will be based on their novel electrical properties Buckminsterfullerene is an insulator but has a high electron affinity and is a superconductor in its reduced form Nanotubes have aroused a great deal of interest for their electrical properties and as potential sources of carbon fibers of great strength... 

It resembles polytetrafiuoroethylene and fiuorinated ethylene propylene in its chemical resistance, electrical properties, and coefficient of friction. Its strength, hardness, and wear resistance are about equal to the former plastic and superior to that of the latter at temperatures above 150°C. 

This thermoplastic shows good tensile strength, toughness, low water absorption, and good frictional properties, plus good chemical resistance and electrical properties. 

It is a very lightweight rubber and has very good weathering and electrical properties, excellent adhesion, and excellent ozone resistance. 

Polysulfide rubbers possess excellent resistance to weathering and oils and have very good electrical properties. 

Silicone rubbers have excellent ozone and weathering resistance, good electrical properties, and good adhesion to metal. 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

Physical Properties Electrical. Electrical properties have been the main focus of study of organic semiconductors, and conductivity studies on organic materials have led to the development of materials with extremely low resistivities and large anisotropies. A discussion of conductivity behaviors for various classes of compounds follows. 

Electrica.1 Properties. The bulk electrical properties of the parylenes make them excellent candidates for use in electronic constmction. The dielectric constants and dielectric losses are low and unaffected by absorption of atmospheric water. The dielectric strength is quoted for specimens of 25 p.m thickness because substantially thicker specimens cannot be prepared by VDP. If the value appears to be high in comparison with other materials, however, it should be noted that the usual thickness for such a measurement is 3.18 mm. Dielectric strength declines with the square root of increasing... 

Fig. 6. Variation of electrical properties of Parylenes N and C with temperature.

Electrical properties of acetal resin are collected in Table 3. The dielectric constant is constant over the temperature range of most interest (—40 to 50°C). Table 3. Electrical Properties of Acetal Resins... 

Many grades of acetal resins are Hsted in Underwriters Eaboratories (UL) Kecogni d Component Directory. UL assigns temperature index ratings indicating expected continuous-use retention of mechanical and electrical properties. UL also classifies materials on the basis of flammability characteristics homopolymer and copolymer are both classified 94HB. 

A VinylcarbaZole. Vinylation of carba2ole proceeds in high yields with alkaline catalysts (212,213). The product, 9-ethenylcarba2ole, [1484-13-5] forms rigid high-melting polymers with outstanding electrical properties. 

Electrical Properties. (See Table 1.) A new family of ABS products exhibiting electrostatic dissipative properties without the need for nonpolymeric additives or fillers (carbon black, metal) is now also commercially available (2). 

Differential heats of adsorption for several gases on a sample of a polar adsorbent (natural 2eohte chaba2ite) are shown as a function of the quantities adsorbed in Figure 5 (4). Consideration of the electrical properties of the adsorbates, included in Table 2, allows the correct prediction of the relative order of adsorption selectivity ... 

Perovskite-type compounds, especially BaTiO, have the abiUty to form extensive soHd solutions. By this means a wide variety of materials having continuously changing electrical properties can be produced ia the polycrystaUine ceramic state. By substituting ions for ions, T can be... 

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