Bartnikas, R. “Dielectrics and Insulators” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 55 Dielectrics and Insulators 55.1Introduction 55.2Dielectric Losses 55.3Dielectric Breakdown 55.4Insulation Aging 55.5Dielectric Materials Gases?Insulating Liquids?Solid Insulating Materials? Solid-Liquid Insulating Systems 55.1 Introduction Dielectrics are materials that are used primarily to isolate components electrically from each other or ground or to act as capacitive elements in devices, circuits, and systems. Their insulating properties are directly attributable to their large energy gap between the highest filled valence band and the conduction band. The number of electrons in the conduction band is extremely low, because the energy gap of a dielectric (5 to 7 eV) is sufficiently large to maintain most of the electrons trapped in the lower band. As a consequence, a dielectric, subjected to an electric field, will evince only an extremely small conduction or loss current; this current will be caused by the finite number of free electrons available in addition to other free charge carriers (ions) associated usually with contamination by electrolytic impurities as well as dipole orientation losses arising with polar molecules under ac conditions. Often the two latter effects will tend to obscure the miniscule contribution of the relatively few free electrons available. Unlike solids and liquids, vacuum and gases (in their nonionized state) approach the conditions of a perfect insulator—i.e., they exhibit virtually no detectable loss or leakage current. Two fundamental parameters that characterize a dielectric material are its conductivity s and the value of the real permittivity or dielectric constant ?￠. By definition, s is equal to the ratio of the leakage current density J l to the applied electric field E, (55.1) Since J l is in A cm –2 and E in V cm –1 , the corresponding units of s are in S cm –1 or V –1 cm –1 . Alternatively, when only mobile charge carriers of charge e and mobility m, in cm 2 V –1 s –1 , with a concentration of n per cm 3 are involved, the conductivity may be expressed as s = emn (55.2) The conductivity is usually determined in terms of the measured insulation resistance R in V; it is then given by s = d/RA, where d is the insulation thickness in cm and A the surface area in cm 2 . Most practical insulating materials have conductivities ranging from 10 –6 to 10 –20 S cm –1 . Often dielectrics may be classified in terms of their resistivity value r, which by definition is equal to the reciprocal of s. s= J E l R. Bartnikas Institut de Recherche d’Hydro-Québec ? 2000 by CRC Press LLC The real value of the permittivity or dielectric constant e￠ is determined from the ratio (55.3) where C represents the measured capacitance in F and C o is the equivalent capacitance in vacuo, which is calculated for the same specimen geometry from C o = e o A/d; here e o denotes the permittivity in vacuo and is equal to 8.854 3 10 –14 F cm –1 (8.854 3 10 –12 F m –1 in SI units) or more conveniently to unity in the Gaussian CGS system. In practice, the value of e o in free space is essentially the same as that for a gas (e.g., for air, e o = 1.000536). The majority of liquid and solid dielectric materials, presently in use, have dielectric constants extending from approximately 2 to 10. 55.2 Dielectric Losses Under ac conditions dielectric losses arise mainly from the movement of free charge carriers (electrons and ions), space charge polarization, and dipole orientation [Bartnikas and Eichhorn, 1983]. Ionic, space charge, and dipole losses are temperature- and frequency-dependent, a dependency which is reflected in the measured values of s and e￠. This necessitates the introduction of a complex permittivity e defined by e = e′ – je2 (55.4) where e2 is the imaginary value of the permittivity, which is equal to s/w. Note that the conductivity s determined under ac conditions may include the contributions of the dipole orientation, space charge, and ionic polarization losses in addition to that of the drift of free charge carriers (ions and electrons) which determine its dc value. The complex permittivity, e, is equal to the ratio of the dielectric displacement vector D to the electric field vector E, i.e., e = D/E. Since under ac conditions the appearance of a loss or leakage current is manifest as a phase angle difference d between the D and E vectors, then in complex notation D and E may be expressed as D o exp [j (vt – d)] and E o exp[jvt], respectively, where v is the radial frequency term, t the time, and D o and E o the respective magnitudes of the two vectors. From the relationship between D and E, it follows that (55.5) and (55.6) It is customary under ac conditions to assess the magnitude of loss of a given material in terms of the value of its dissipation factor, tand; it is apparent from Eqs. (55.5) and (55.6), that (55.7) Examination of Eq. (55.7) suggests that the behavior of a dielectric material may also be described by means of an equivalent electrical circuit. It is most commonplace and expedient to use a parallel circuit representation, consisting of a capacitance C in parallel with a large resistance R as delineated in Fig. 55.1. Here C represents ￠=e C C o ￠=ed D E o o cos ￠ =ed D E o o sin tand e e s we = ￠￠ ￠ = ￠ ? 2000 by CRC Press LLC the capacitance and R the resistance of the dielectric. For an applied voltage V across the dielectric, the leakage current is I l = V/R and the displacement current is I C = jvCV ; since tand = I l /I C , then (55.8) It is to be emphasized that in Eq. (55.8), the quantities R and C are functions of temperature, frequency, and voltage. The equivalence between Eqs. (55.7) and (55.8) becomes more palpable if I l and I C are expressed as we2C o V and jwe￠C o V, respectively. Every loss mechanism will exhibit its own characteristic tand loss peak, centered at a particular absorption frequency, v o for a given test temperature. The loss behavior will be contingent upon the molecular structure of the material, its thickness, and homogeneity, and the temperature, frequency, and electric field range over which the measurements are performed [Bartnikas and Eichhorn, 1983]. For example, dipole orientation losses will be manifested only if the material contains permanent molecular or side-link dipoles; a considerable overlap may occur between the permanent dipole and ionic relaxation regions. Ionic relaxation losses occur in dielectric structures where ions are able to execute short-range jumps between two or more equilibrium positions. Interfacial or space charge polarization will arise with insulations of multilayered struc- tures where the conductivity and permittivity is different for the individual strata or where one dielectric phase is inter- spersed in the matrix of another dielectric. Space charge traps also occur at crystalline-amorphous interfaces, crystal defects, and oxidation and localized C-H dipole sites in polymers. Alternatively, space charge losses will occur with mobile charge carriers whose movement becomes limited at the electrodes. This type of mechanism takes place often in thin-film dielectrics and exhibits a pronounced thickness effect. If the various losses are considered schematically on a logarithmic frequency scale at a given temperature, then the tand and e￠ values will appear as functions of frequency as delineated schematically in Fig. 55.2. For many materials the dipole and ionic relaxation losses tend to predominate over the frequency range extending from about 0.5 to 300 MHz, depending upon the molecular structure of the dielectric and temperature. For example, the absorption peak of an oil may occur at 1 MHz, while that of a much lower viscosity fluid such as water may appear at approximately 100 MHz. There is considerable overlap between the dipole and ionic relaxation loses, because the ionic jump distances are ordinarily of the same order of magnitude as the radii of the permanent dipoles. Space charge polarization losses manifest themselves normally over the low-frequency region extending from 10 –6 Hz to 1 MHz and are characterized by very broad and intense peaks; this behavior is apparent from Eq. (55.7), which indicates that even small conductivities may lead to very large tand values at very low frequencies. The nonrelaxation-type electronic conduction losses are readily perceptible over the low-frequency spectrum and decrease monotonically with frequency. The dielectric loss behavior may be phenomenologically described by the Pellat-Debye equations, relating the imaginary and real values of the permittivity to the relaxation time, t, of the loss process (i.e., the frequency at which the e2 peak appears: f o = 1/2 pt), the low-frequency or static value of the real permittivity, e s , and the high- or optical-frequency value of the real permittivity, e ‘ . Thus, for a loss process characterized by a single relaxation time (55.9) tand w = 1 RC FIGURE 55.1(a) Parallel equivalent RC circuit and (b) corresponding phasor diagram. ￠=+ - + ￥ ￥ ee ee wt s 1 22 ? 2000 by CRC Press LLC and (55.10) In practice Eqs. (55.9) and (55.10) are modified due to a distribution in the relaxation times either because several different loss processes are involved or as a result of interaction or cooperative movement between the discrete dipoles or the trapped and detrapped charge carriers in their own particular environment. Since the relaxation processes are thermally activated, an increase in temperature will cause a displacement of the loss peak to higher frequencies. In the case of ionic and dipole relaxation, the relaxation time may be described by the relation (55.11) where h is the Planck constant (6.624 3 10 –34 J s –1 ), k the Boltzmann constant (1.38 3 10 –23 J K –1 ), DH the activation energy of the relaxation process, R the universal gas constant (8.314 3 10 3 J K –1 kmol –1 ), and DS the entropy of activation. For the ionic relaxation process, t may alternatively be taken as equal to 1/2G, where G denotes the ion jump probability between two equilibrium positions. Also for dipole orientation in liquids, t may be approximately equated to the Debye term h/4pr 3 T, where h represents the macroscopic viscosity of the liquid and r is the dipole radius [Bartnikas, 1994]. With interfacial or space charge polarization, which may arise due to a pile-up of charges at the interface of two contiguous dielectrics of different conductivity and permittivity, Eq. (55.10) must be rewritten as [von Hippel, 1956] (55.12) FIGURE 55.2 Schematic representation of different absorption regions [Bartnikas, 1987]. ￠￠ = - + ￥ e eewt wt () s 1 22 t= é ? ê ê ù ? ú ú - é ? ê ê ù ? ú ú h kT H RT S R exp exp DD ￠￠ =+ + ? è ? ? ? ÷ ￥ ee t wt t wt wt 12 22 1 K ? 2000 by CRC Press LLC where the Wagner absorption factor K is given by (55.13) where t 1 and t 2 are the relaxation times of the two contiguous layers or strata of respective thicknesses d 1 and d 2 ; t is the overall relaxation time of the two-layer combination and is defined by t = (e￠ 1 d 2 1e￠ 2 d 1 )/(s 1 d 2 1s 2 d 1 ), where e￠ 1 , e￠ 2 , s 1 , and s 2 are the respective real permittivity and conductivity parameters of the two discrete layers. Note that since e￠ 1 and e￠ 2 are temperature- and frequency-dependent and s 1 and s 2 are, in addition, also voltage-dependent, the values of t and e2 will in turn also be influenced by these three variables. Space charge processes involving electrons are more effectively analyzed, using dc measurement techniques. If retrap- ping of electrons in polymers is neglected, then the decay current as a function of time t, arising from detrapped electrons, assumes the form [Watson, 1995] (55.14) where n(E) is the trap density and n is the attempt jump frequency of the electrons. The electron current displays the usual t –1 dependence and the plot of i(t)t versus kTln(nt) yields the distribution of trap depths. Eq. (55.14) represents an approximation, which underestimates the current associated with the shallow traps and overcompensates for the current due to the deep traps. The mobility of the free charge carriers is determined by the depth of the traps, the field resulting from the trapped charges, and the temperature. As elevated temperatures and low space charge fields, the mobility is proportional to exp[–DH/kT] and at low temperatures to (T) 1/4 [LeGressus and Blaise, 1992]. A high trapped charge density will create intense fields, which will in turn exert a controlling influence on the mobility and the charge distribution profile. In polymers, shallow traps are of the order of 0.5 to 0.9 eV and deep traps are ca. 1.0 to 1.5 eV, while the activation energies of dipole orientation and ionic conduction in solid and liquid dielectrics fall within the same range. It has been known that most charge trapping in the volume occurs in the vicinity of the electrodes; this can now be confirmed by measurement, using thermal and electrically stimulated acoustical pulse methods [Bernstein, 1992]. In the latter method this involves the application of a rapid voltage pulse across a dielectric specimen. The resulting stress wave propagates at the velocity of sound and is detected by a piezoelectric transducer. This wave is assumed not to disturb the trapped charge; the received electrical signal is then correlated with the acoustical wave to determine the profile of the trapped charge. Errors in the measurement would appear to be principally caused by the electrode surface charge effects and the inability to distinguish between the polarization of polar dipoles and that of the trapped charges [Wintle, 1990]. Temperature influences the real value of the permittivity or dielectric constant e￠ insofar as it affects the density of the dielectric material. As the density diminishes with temperature, e￠ falls with temperature in accordance with the Clausius-Mossotti equation (55.15) where [P] represents the polarization per mole, M the molar mass, d o the density at a given temperature, and e￠ = e s . Equation (55.14) is equally valid, if the substitution e￠ = (n￠) 2 is made; here n￠ is the real value of the index of refraction. In fact, the latter provides a direct connection with the dielectric behavior at optical frequencies. In analogy with the complex permittivity, the index of refraction is also a complex quantity, and its imaginary value n2 exhibits a loss peak at the absorption frequencies; in contrast with the e￠ value which can only fall with frequency, the real index of refraction n￠ exhibits an inflection-like behavior at the absorption frequency. This is illustrated schematically in Fig. 55.2, which depicts the kn￠ or n2 and n￠ 21 values as a function of frequency over the optical frequency regime. The absorption in the infrared results from atomic K = +- -()tt tttt tt 12 12 12 it kT vt nE()= () [] () () P M d o = ￠ - ￠ + e e 1 2 ? 2000 by CRC Press LLC resonance that arises from a displacement and vibration of atoms relative to each other, while an electronic resonance absorption effect occurs over the ultraviolet frequencies as a consequence of the electrons being forced to execute vibrations at the frequency of the external field. The characterization of dielectric materials must be carried out in order to determine their properties for various applications over different parts of the electromagnetic frequency spectrum. There are many techniques and methods available for this purpose that are too numerous and detailed to attempt to present here even in a cursory manner. However, Fig. 55.3 portrays schematically the different test methods that are commonly used to carry out the characterization over the different frequencies up to and including the optical regime. A direct relationship exists between the time and frequency domain test methods via the Laplace transforms. The frequency response of dielectrics at the more elevated frequencies is primarily of interest in the electrical communications field. In contradistinction for electrical power generation, transmission, and distribution, it is the low-frequency spectrum that constitutes the area of application. Also, the use of higher voltages in the electrical power area necessarily requires detailed knowledge of how the electrical losses vary as a function of the electrical field. Since most electrical power apparatus operates at a fixed frequency of 50 or 60 Hz, the main variable apart from the temperature is the applied or operating voltage. At power frequencies the dipole losses are generally very small and invariant with voltage up to the saturation fields which exceed substantially the operating fields, being in the order of 10 7 kV cm –1 or more. However, both the space charge polarization and ionic losses are highly field-dependent. As the electrical field is increased, ions of opposite sign are increasingly segregated; this hinders their recombination and, in effect, enhances the ion charge carrier concentration. As the dissociation rate of the ionic impurities is further augmented by temperature increases, combined rises in temperature and field may lead to appreciable dielectric loss. Thus, for example, for a thin liquid film bounded by two solids, tand increases with voltage until at some upper voltage value the physical boundaries begin to finally limit the amplitude of the ion excursions, at which point tand commences a downward trend with voltage (B?ning–Garton effect). The interfacial or space charge polarization losses may evince a rather intricate field dependence, depending upon the manner in which the discrete conductivities of the contiguous media change FIGURE 55.3Frequency rangse of various dielectric test methods [Bartnikas, 1987]. ? 2000 by CRC Press LLC with applied voltage and temperature [as is apparent from the nature of Eqs. (55.12) and (55.13)]. The exact frequency value at which the space charge loss exhibits its maximum is contingent upon the value of the relaxation time t. Figure 55.4 depicts typical tand versus applied voltage characteristics for an oil-impregnated paper-insulated cable model at two different temperatures, in which the loss behavior is primarily governed by ionic conduction and space charge effects. The monotonically rising dissipation factor with increasing applied voltage at room temperature is indicative of the predominating ionic loss mechanism, while at 85°C, an incipient decrease in tand is suggestive of space charge effects. 55.3 Dielectric Breakdown As the voltage is increased across a dielectric material, a point is ultimately reached beyond which the insulation will no longer be capable of sustaining any further rise in voltage and breakdown will ensue, causing a short to develop between the electrodes. If the dielectric consists of a gas or liquid medium, the breakdown will be self-healing in the sense that the gas or liquid will support anew a reapplication of voltage until another breakdown recurs. In a solid dielectric, however, the initial breakdown will result in a formation of a permanent conductive channel, which cannot support a reapplication of voltage. The dielectric breakdown processes are distinctly different for the three states of matter. In the case of solid dielectrics the breakdown is dependent not only upon the molecular structure and morphology of the solid but also upon extraneous variables such as the geometry of the material, the temper- ature, and the ambient environment. Since breakdown often occurs along some fault of the material, the breakdown voltage displays a readily perceptible decrease with area and thickness of the specimen due to increased incidence of faults over larger volumes. This is indeed part of the reason why thin-film inorganic dielectrics, which are normally evaluated using small-diameter dot counter electrodes, exhibit exceptionally high dielectric strengths. With large organic dielectric specimens, recessed electrodes are used to minimize electrode edge effects, leading to greatly elevated breakdown strengths in the order of 10 6 to 10 7 kV cm –1 , a range of values which is considered to represent the ultimate breakdown strength of the material or its intrinsic breakdown strength; as the intrinsic breakdown occurs in approximately 10 –8 to 10 –6 s, an electronic mechanism is implicated. The breakdown strength under dc and impulse conditions tends to exceed that at ac fields, thereby suggesting the ac breakdown process may be partially of a thermal nature. An additional factor, which may lower the ac breakdown strength, is that associated with the occurrence of partial discharges either in void inclusions or at the electrode edges; this leads to breakdown values very much less than the intrinsic value. In practice, the breakdowns are generally of an extrinsic nature, and the intrinsic values are useful conceptually insofar as they provide an idea of an upper value that can be attained only under ideal conditions. The intrinsic breakdown theories were essentially developed for crystalline dielectrics, for which it was assumed that a very small number FIGURE 55.4Loss characteristics of mineral oil-impregnated paper. ? 2000 by CRC Press LLC of thermally activated electrons can be thermally excited to move from the valence to the conduction band and that under the influence of an external field they will be impelled to move in the direction of the field, colliding with the lattice of the crystalline dielectric and dissipating their energy by phonon interactions [Bartnikas and Eichhorn, 1983]. Accordingly, breakdown is said to occur when the average rate of energy gain by the electrons, A(E, T, T e , j), exceeds that lost in collisions with the lattice, B(T, T e , j). Hence, the breakdown criterion can be stated as A(E, T, T e , j) = B(T, T e , j) (55.16) where E is the applied field, T the lattice temperature, T e the electron temperature, and j an energy distribution constant. Thus in qualitative terms as the temperature is increased gradually, the breakdown voltage rises because the interaction between the electrons and the lattice is enhanced as a result of the increased thermal vibrations of the lattice. Ultimately, a critical temperature is attained where the electron–electron interactions surpass in importance those between the electrons and the lattice, and the breakdown strength commences a monotonic decline with temperature; this behavior is borne out in NaCl crystals, as is apparent from Fig. 55.5 [von Hippel and Lee, 1941]. However, with amorphous or partially crystalline polymers, as for example with polyethylene, the maximum in breakdown strength is seen to be absent and only a decrease is observed [Oakes, 1949]; as the crystalline content is increased in amorphous-crystalline solids, the breakdown strength is reduced. The electron avalanche concept has also been applied to explain breakdown in solids, in particular to account for the observed decrease in breakdown strength with insulation thickness. Since breakdown due to electron avalanches involves the formation of space charge, space charges will tend to modify the conditions for breakdown. Any destabilization of the trapping and detrapping process, such as may be caused by a perturbation of the electrical field, will initiate the breakdown event [LeGressus and Blaise, 1992]. The detrapping of mobile charge carriers will be accompanied by photon emission and formation of the plasma breakdown channel, resulting in the dissi- pation of polarization energy. If dipole interaction is neglected, the polarization energy due to a trapped charge is of the order of 5c eV, where c is the dielectric susceptibility. The release of the polarization energy will be accompanied by electrical tree growth in and melting of the polymer. The breakdown process in gases is relatively well understood and is explained in terms of the avalanche theory. A free electron, occurring in a gas due to cosmic radiation, will be accelerated in a field and upon collision with neutral molecules in its trajectory will eject, if its energy is sufficient, other electrons that will in turn undergo additional collisions resulting in a production of more free electrons. If the electric field is sufficiently high, the number of free electrons will increase exponentially along the collision route until ulti- mately an electron avalanche will form. As the fast-moving electrons in the gap disappear into the anode, they leave behind the slower-moving ions, which gradually drift to the cathode where they liberate further electrons with a probability g. When the height of the positive ion avalanche becomes sufficiently large to lead to a regeneration of a starting electron, the discharge mechanism becomes self-sustaining and a spark bridges the two electrodes. The condition for the Townsend breakdown in a short gap is given by g[exp(ad) 21] = 1 (55.17) where d is the distance between the electrodes and a represents the number of ionizing impacts per electron per unit distance. The value of g is also enhanced by photoemission at the cathode and photon radiation in FIGURE 55.5 Dielectric breakdown characteristics of sodium chloride [von Hippel and Lee, 1941] and polyethylene [Oakes, 1949]. ? 2000 by CRC Press LLC the gas volume by the metastable and excited gas atoms or molecules. In fact, in large gaps the breakdown is governed by steamer formation in which photon emission from the avalanches plays a dominant role. Break- down characteristics of gases are represented graphically in terms of the Paschen curves, which are plots of the breakdown voltage as a function of the product of gas pressure p and the electrode separation d. Each gas is characterized by a well-defined minimum breakdown voltage at one particular value of the pd product. The breakdown process in liquids is perhaps the least understood due to a lack of a satisfactory theory on the liquid state. The avalanche theory has been applied with limited success to explain the breakdown in liquids, by assuming that electrons injected from an electrode surface exchange energy with the atoms or molecules of the liquid, ultimately causing the atoms and molecules to ionize and thus precipitating breakdown. Recent investigations, utilizing electro-optical techniques, have demonstrated that breakdown involves steamers with tree- or bushlike structures that propagate from the electrodes [Bartnikas, 1994]. The negative streamers emerging from the cathode form due to electron emission, while positive steamers originating at the anode are due to free electrons in the liquid itself. The breakdown of liquids is noticeably affected by electrolytic impurities as well as water and oxygen content; also, macroscopic particles may form bridges between the electrodes along which electrons may hop with relative ease, resulting in a lower breakdown. As in solids, there is a volume effect and breakdown strength decreases with thickness; a slight increase in breakdown voltage is also observed with viscosity. In both solid and liquid dielectrics, the breakdown strength under dc and impulse fields is markedly greater than that obtained under ac fields, thus suggesting that under ac conditions the breakdown may be partially thermal in nature. Thermal breakdown occurs at localized hot spots where the rate of heat generated exceeds that dissipated by the surrounding medium. The temperature at such hot spots continues to rise until it becomes sufficiently high to induce fusion and vaporization, causing eventually the development of a channel along which breakdown ensues between the opposite electrodes. Since a finite amount of time is required for the heat buildup to occur to lead to the thermal instability, thermally induced breakdown is contingent upon the time of the alternating voltage application and is thus implicated as the leading cause of breakdown in many dielectrics under long-term operating conditions. However, under some circumstances thermal instability may develop over a very short time; for example, some materials have been found to undergo thermal breakdown when subjected to very short repetitive voltage pulses. In low-loss dielectrics, such as polyethylene, the occur- rence of thermal breakdown is highly improbable under low operating temperatures, while glasses with signif- icant ionic content are more likely to fail thermally, particularly at higher frequencies. The condition for thermal breakdown may be stated as KA DT/l = ve￠E 2 tand (55.18) where the left-hand side represents the heat transfer in J s –1 along a length l (cm) of sectional area A (cm 2 ) of the dielectric surface in the direction of the temperature gradient due to the temperature difference DT, in °C, such that the units of the thermal conductivity constant K are in J °C –1 cm –1 s –1 . The right-hand side of Eq. (55.18) is equal to the dielectric loss dissipated in the dielectric in J s –1 , where E is the external field, e￠ the real value of the permittivity, and tand the dissipation factor at the radial frequency v. Other causes of extrinsic breakdown are associated with particular defects in the dielectric or with the environmental conditions under which the dielectric material is employed. For example, some dielectrics may contain gas-filled cavities that are inherent with the porous structure of the dielectric or that may be inadvert- ently introduced either during the manufacturing process or created under load cycling. If the operating electrical field is sufficiently elevated to cause the gas within the cavities to undergo discharge, the dielectric will be subjected to both physical and chemical degradation by the partial discharges; should the discharge process be sustained over a sufficiently long period, breakdown will eventually ensue. With overhead line insulators or bushings of electrical equipment, breakdown may occur along the surface rather than in the bulk of the material. Insulator surfaces consisting of porcelain, glass, or polymeric materials (usually elastomers), may become contaminated by either industrial pollutants or salt spray near coastal areas, leading to surface tracking and breakdown below the normal flashover voltage. Surface tracking is enhanced in the presence of moisture, which increases the surface conductivity, particularly in the presence of ionic contaminants [Bartnikas, 1987]. The latter is measured in S or V –1 and must be distinguished from the volume ? 2000 by CRC Press LLC conductivity whose units are stated in S cm –1 or V –1 cm –1 . Surface tracking may be prevented by cleaning the surface and by applying silicone greases. When insulators are employed under a vacuum environment, charge accumulation will occur in the surface because the charged surface will no longer be able to discharge due to the finite breakdown strength of an ambient gas. Space charge will thus play a dominant role in the surface breakdown mechanism [Miller, 1993]. 55.4 Insulation Aging All insulating materials will undergo varying degrees of aging or deteriorating under normal operating condi- tions. The rate of aging will be contingent upon the magnitude of the electrical, thermal, and mechanical stresses to which the material is subjected; it will also be influenced by the composition and molecular structure of the material itself as well as the chemical, physical, and radiation environment under which the material must perform. The useful life of an insulating system will thus be determined by a given set and subset of aging variables. For example, the subset of variables in the voltage stress variable are the average and maximum values of the applied voltage, its frequency, and the recurrence rate of superposed impulse or transient voltage surges. For the thermal stress, the upper and lower ambient temperatures, the temperature gradient in the insulation, and the maximum permissible operating temperature constitute the subvariable set. Also, the character of the mechanical stress will differ, depending upon whether torsion, compression, or tension and bending are involved. Furthermore, the aging rate will be differently affected if all stresses (electrical, thermal, and mechan- ical) act simultaneously, separately, or in some predetermined sequence. The influence exerted on the aging rate by the environment will depend on whether the insulation system will be subjected to corrosive chemicals, petroleum fluids, water or high humidity, air or oxygen, ultraviolet radiation from the sun, and nuclear radiation. Organic insulations, in particular, may experience chemical degradation in the presence of oxygen. For example, polyethylene under temperature cycle will undergo both physical and chemical changes. These effects will be particularly acute at the emergency operating temperatures (90–130°C); at these temperatures partial or complete melting of the polymer will occur and the increased diffusion rate will permit the oxygen to migrate to a greater depth into the polymer. Ultimately the antioxidant will be consumed, resulting in an embrittlement of polymer and in extreme cases in the formation of macroscopic cracks. Subjection of the polymer to many repeated overload cycles will be accompanied by repeated melting and recrystallization of the polymer—a process that will inevitably cause the formation of cavities, which, when subjected to sufficiently high voltages, will undergo discharge, leading eventually to electrical breakdown. There is a general consensus that electrically induced aging involves the mechanisms of treeing, partial discharge, and dielectric heating. Dielectric heating failures are more characteristic of lossy insulations or when highly conductive contaminants are involved. In the treeing mechanism, a distinction must be made between electrical and water trees [Bartnikas and Eichhorn, 1983]. The former refers to growth, resembling a tree, that occurs under dry conditions in the presence of an electric field; its branches or channels are hollow. In contrast, water trees require the presence of moisture, and their branches consist of fine filamentary channels, joining small cavities, all of which contain water; when placed in a dry environment, they eventually disappear. In a translucent dielectric, water trees are invisible and are rendered visible only when stained with a die, whereas electrical trees once formed remain readily discernible. Water trees are intrinsic to solid polymeric insulation, while electrical trees may occur in both solid and impregnated insulating systems. The actual failure path, when the breakdown current is limited to prevent destruction of evidence, invariably, even in liquids, consists of an electrical treelike structure. Both electrical and water trees tend to propagate from electrical stress enhancement points, with water trees requiring appreciably lower stresses for their inception (ca. 2 kV/mm). Whereas the electrical tree mechanism usually involves partial discharges, the occurrence of the latter is conspicuously absent in water trees. The fact that water trees may bridge the opposite electrodes without precipitating failure infers a nonconductive nature of the filamentary channels or branches. Yet water trees are implicated in the overall degradation and aging process of the dielectric because of their presence in areas of failure as well as because of the often-observed phenomenon of an electrical tree emerging from some point along a water tree and causing abrupt failure. The presence of voids or cavities within a solid or solid-liquid insulating system will almost invariably lead to eventual failure, with the proviso that the electrical field is sufficiently elevated to induce them to undergo ? 2000 by CRC Press LLC either continuous or regularly recurring, though at times intermittent, discharge. Electrical trees may readily ensue from charge injection sites adjacent to discharging cavity inclusions. The time required for electrical tree initiation may be defined quasi-empirically as [Fothergill et al., 1994], (55.19) where N c denotes the critical number of impact ionizations necessary for tree channel formation, l is the avalanche or newly formed tree length, n o is the number of initiating electrons and b is a constant dependent on the frequency, f. The deterioration rate due to partial discharges is proportional to the power dissipated P by the discharges, which may be expressed as [Bartnikas and McMahon, 1979] (55.20) where n ij is the recurrence rate of the jth discharge in the ith cavity and DQ ij is its corresponding charge release at an applied voltage V ij . Under ac conditions the discharges will tend to recur regularly in each cycle due to the capacitative voltage division across the void. Under dc conditions the discharge rate will be controlled by the time constant required to recharge the cavity following a discharge. The physical damage arising from discharges consists of surface erosion and pitting and is caused by the ion and electron bombardment incident on the void’s walls at a given discharge site. Chemical degradation results from molecular chain scission due to particle bombardment of the surface and the reactions between the ambient ionized gases and the gases released due to the molecular chain scission processes. The final chemical composition of the reaction product is generally varied, depending primarily on the molecular structure of the dielectric materials involved and the composition of the ambient ionized gases; one discharge degradation product common to many polymers exposed to discharges in air is that of oxalic acid. Oxalic acid, as a result of its elevated conductivity, when deposited upon the cavity’s walls may change the nature of the discharge (e.g., from a spark to a glow type) or may even ultimately extinguish the discharge (i.e., replace the discharge loss by an I 2 R-type loss along the cavity’s walls). A number of aging models have been propounded to predict insulation aging under different types of stress. However, there are essentially only two models whose usefulness has been substantiated in practice and which have, therefore, gained wide acceptance. One of these is Dakin’s classical thermal degradation model, which is based upon the approach used in chemical reaction rate theory [Bartnikas, 1987], t = A exp[DH/kT] (55.21) where t represents the time to breakdown, A is a constant, DH is the activation energy of the aging process, T is the absolute temperature, and k is the Boltzmann constant (1.38 3 10 –23 J K –1 ). If the log t versus 1/T plot represents a straight line that is obtained when the insulation aging is accelerated at various temperatures above the operating temperature, extrapolation of the line to the operating temperature may yield a rudimentary estimate of the aging time or the service life that can be anticipated from the insulation system when operated under normal temperature and load conditions. Deviations from straight-line behavior are indicative of more than one thermal aging mechanism; for example, a polymeric insulation will exhibit such behavior when thermally stressed beyond its melting or phase transition temperature. Another extremely useful model, applicable to accelerated aging studies under electrical stress, is the so- called inverse power law relationship given by [Bartnikas, 1987] t = BE –n (55.22) t N bfn l c o = - ( ) [] 21exp a PnQV ij j m i l ij ij = == ?? 11 D ? 2000 by CRC Press LLC where t is the time to breakdown under an electric stress E, B is a constant, and n is an exponent parameter. The relationship is essentially empirical in nature, and its proof of validity rests primarily on experiment and observation. It is found that a single type of electrically induced aging process will generally result in a straight- line relationship between log t and log E. Consequently, aging data obtained at higher electrical stresses with correspondingly shorter times to breakdown when extrapolated to longer times at stresses in the vicinity of the operating stress should yield the value of the effective service life under the operating stress. The slope of the line determines the exponent n, which constitutes an approximate indicator of the type of aging involved. For example, with polymer insulation water treeing ordinarily results in n values less than 4, while under conditions that may involve discharges and electrical trees, the n values may approach 10 or greater. 55.5 Dielectric Materials Dielectric materials comprise a variety of solids, liquids, and gases. The breakdown strength generally increases with the density of the material so that dielectric solids tend to have higher dielectric strengths than gases. The same tendency is observed also with the dielectric loss and permittivity; for example, the dielectric losses in gases are virtually too small to be measurable and their dielectric constant in most practical applications can be considered as unity. In this section we will describe a number of the more common insulating materials in use. Gases The 60-Hz breakdown strength of a 1-cm gap of air at 25°C at atmospheric pressure is 31.7 kV cm –1 . Although this is a relatively low value, air is a most useful insulating medium for large electrode separations as is the case for overhead transmission lines. The only dielectric losses in the overhead lines are those due to corona discharges at the line conductor surfaces and leakage losses over the insulator surfaces. In addition, the highly reduced capacitance between the conductors of the lines ensures a small capacitance per unit length, thus rendering overhead lines an efficient means for transmitting large amounts of power over long distances. Nitrogen, which has a slightly higher breakdown strength (33.4 kV cm –1 ) than air, has been used when compressed in low-loss gas-insulated capacitors. However, as air, which was also used in its compressed form in circuit breakers, it has been replaced by sulfur hexafluoride, SF 6 . The breakdown strength of SF 6 is ca. 79.3 kV cm –1 . Since the outside metal casing of metal-clad circuit breakers is ordinarily grounded, it has become common practice to have much of the substation interconnected bus and interrupting switching equipment insulated with SF 6 . To achieve higher breakdown strengths, the SF 6 gas is compressed at pressures on the order of 6 atm. The use of SF 6 in substation equipment has resulted in the saving of space and the elimination of line insulator pollution problems; however, its extensive usage has also posed some environmental concerns in regard to its flourine content. The breakdown strength of gases is little affected with increasing frequency until the period of the wave becomes comparable to the transit time of the ions and, finally, electrons across the gap. At this point a substantial reduction in the breakdown strength is observed. Insulating Liquids Insulating liquids are rarely used by themselves and are intended for use mainly as impregnants with cellulose or synthetic papers. The 60-Hz breakdown strength of practical insulating liquids exceeds that of gases and for a 1-cm gap separation it is of the order of about 100 kV cm –1 . However, since the breakdown strength increases with decreasing gap length and as the oils are normally evaluated using a gap separation of 0.254 cm, the breakdown strengths normally cited range from approximately 138 to 240 kV cm –1 . The breakdown values are more influenced by the moisture and particle contents of the fluids than by their molecular structure (cf. Table 55.1). Mineral oils have been extensively used in high-voltage electrical apparatus since the turn of the century. They constitute a category of hydrocarbon liquids that are obtained by refining petroleum crudes. Their composition consists of paraffinic, naphthenic, and aromatic constituents and is dependent upon the source of the crude as well as the refining procedure followed. The inclusion of the aromatic constituents is desirable ? 2000 by CRC Press LLC because of their gas absorption and oxidation characteristics. Mineral oils used for cable and transformer applications have low polar molecule contents and are characterized by dielectric constants extending from about 2.10 to 2.25 with dissipation factors generally between 2 3 10 –5 and 6 3 10 –5 at room temperature, depending upon their viscosity and molecular weight. Their dissipation factors increase appreciably at higher temperatures when the viscosities are reduced. Oils may deteriorate in service due to oxidation and moisture absorption. Filtering and treatment with Fullers’ earth may improve their properties, but special care must be taken to ensure that the treatment process does not remove the aromatic constituents which are essential to maintaining the gas-absorption characteristics of the oil. Alkyl benzenes are used as impregnants in high-voltage cables, often as substitutes of the low-viscosity mineral oils in self-contained oil-filled cables. They consist of alkyl chains attached to a benzene ring having the general formula C 6 H 5 (CH 2 ) n CH 3 ; however, branched alkyl benzenes are also employed. Their electrical properties are comparable to those of mineral oils, and they exhibit good gas inhibition characteristics. Due to their detergent character, alkyl benzenes tend to be more susceptible to contamination than mineral oils. Polybutenes are synthetic oils that are derived from the polymerization of olefins. Their long chains, with isobutene as the base unit, have methyl group side chains with molecular weights in the range from 300 to 1350. Their electrical properties are comparable to those of mineral oils; due to their low cost, they have been used as pipe cable filling oils. Higher viscosity polybutenes have been used as capacitor impregnants. Mixtures of polybutenes and alkyl benzenes have been used to obtain higher ac breakdown strength with impregnated paper systems. They are also compatible and miscible with mineral oils. Since the discontinued use of the nonflammable polychlorinated biphenyls (PCBs), a number of unsaturated synthetic liquids have been developed for application to capacitors, where due to high stresses evolved gases may readily undergo partial discharge. Most of these new synthetic capacitor fluids are thus gas-absorbing low- molecular-weight derivatives of benzene, with permittivities ranging from 2.66 to 5.25 at room temperature (compared to 3.5 for PCBs). None of these fluids have the nonflammable characteristics of the PCBs; however, they do have high boiling points [Bartnikas, 1994]. Halogenated aliphatic hydrocarbons are derived by replacing the hydrogens by either chlorine or fluorine or both; they may also contain nitrogen and oxygen in their molecular structure. Their dielectric constants range from 1.8 to 3.0, the higher value reflecting some polarity due to molecular asymmetry as a result of branching. They have superior thermal properties to mineral oils and are highly flame-resistant. Fluorocarbons have been used in large power transformers, where both flammability and heat removal are of prime concern. TABLE 55.1 Electrical Properties of a Number of Representative Insulating Liquids [Bartnikas, 1994; Encyclopedia Issue, 1972] Viscosity Dielectric Dissipation Breakdown cSt Constant Factor Strength, Liquid (37.8°C) (at 60 Hz, 25°C) (at 60 Hz, 100°C) (kV cm–1) Capacitor oil 21 2.2 0.001 >118 Pipe cable oil 170 2.15 0.001 >118 Self-contained 49.7 2.3 0.001 >118 cable oil Heavy cable oil 2365 2.23 0.001 >118 Transformer oil 9.75 2.25 0.001 >128 Alkyl benzene 6.0 2.1 0.0004 >138 Polybutene 110 2.14 0.0003 >138 pipe cable oil (SUS) (at 1 MHz) Polybutene 2200 2.22 0.0005 >138 capacitor oil (SUS (at 1 MHz) at 100°C) Silicone fluid 50 2.7 0.00015 >138 Castor oil 98 3.74 0.06 >138 (100°C) C 8 F 16 O 0.64 1.86 <0.0005 >138 fluorocarbon ? 2000 by CRC Press LLC Silicone liquids consist of polymeric chains of silicon atoms alternating with oxygen atoms, with methyl side groups. For electrical applications, polydimethylsiloxane fluids are used, primarily for transformers as substi- tutes for the PCBs due to their inherently high flash and flammability points and reduced environmental concerns. They have lower tand values than mineral oils but somewhat higher dielectric constants because of their moderately polar nature. The viscosity of silicone fluids exhibits relatively little change with temperature, which is attributed to the ease of rotation about the Si–O–Si bond, thereby overcoming close packing of molecules and reducing intermolecular forces. There are a large number of organic esters, but only a few are suitable for electrical applications. Their properties are adversely affected by hydrolysis, oxidation, and water content. Due to their reduced dielectric losses at elevated frequencies, they have been used in high-frequency capacitors. Castor oil has found specialized application in energy storage capacitors due to its exceptional resistance to partial discharges. The dielectric constants of esters are substantially higher than those for mineral oils. Solid Insulating Materials Solid insulating materials may be classified into two main categories, organic and inorganic. There are an extremely large number of solid insulants available, but in this section only the more commonly representative solid insulants will be considered. Inorganic Solids Below are described a number of the more prevalent inorganic dielectrics in use; their electrical and physical properties are listed in Table 55.2. Alumina (Al 2 O 3 ) is produced by heating aluminum hydroxide or oxyhydroxide; it is widely used as a filler for ceramic insulators. Further heating yields the corundum structure, which in its sapphire form is used for dielectric substrates in microcircuit applications. Barium titanate (BaTiO 3 ) is an extraordinary dielectric in that below 120°C it behaves as a ferroelectric. That is, the electric displacement is both a function of the field as well as its previous history. Due to spontaneous polarization of the crystal, a dielectric hysteresis loop is generated. The dielectric constant is different in the x and z axis of the crystal (e.g., at 20°C, e￠ > 4000 perpendicular to the z axis and e￠ < 300 in the x-axis direction. Porcelain is a multiphase ceramic material that is obtained by heating aluminum silicates until a mullite (3Al 2 O 3 · 2SiO 2 ) phase is formed. Since mullite is porous, its surface must be glazed with a high-melting-point glass to render it smooth and impervious and thus applicable for use in overhead line insulators. For high- frequency applications, low-loss single-phase ceramics, such as steatite (3MgO · 4SiO 2 · H 2 O), are preferred. Magnesium oxide (MgO) is a common inorganic insulating material, which due to its relatively high thermal conductivity is utilized for insulating heating elements in ovens. The resistance wire elements are placed concentrically within stainless steel tubes, with magnesium oxide packed around them to provide the insulation. Electrical-grade glasses consist principally of SiO 2 , B 2 O 3 , and P 2 O 5 structures that are relatively open to permit ionic diffusion and migration. Consequently, glasses tend to be relatively lossy at high temperatures, though at low temperatures they are suitable for use in overhead line insulators and in transformer, capacitor, and circuit breaker bushings. At high temperatures, their main application lies with incandescent and fluorescent lamps as well as electronic tube envelopes. Most of the mica used in electrical applications is of the muscovite [KAl 2 (OH) 2 Si 3 AlO 10 ] type. Mica is a layer-type dielectric, and mica films are obtained by the splitting of mica blocks. The extended two-dimen- sionally layered strata of mica prevent the formation of conductive pathways across the mica, resulting in a high dielectric strength. It has excellent thermal stability and due to its inorganic nature is highly resistant to partial discharges. It is used in sheet, plate, and tape form in rotating machines and transformer coils. For example, a mica-epoxy composite is employed in stator bar insulation of rotating machines. In metal-oxide-silicon (MOS) devices, the semiconductor surface is passivated by thermally growing a silicon dioxide, SiO 2 , film (about 5000 ?) with the semiconductor silicon wafer exposed to an oxygen ambient at 1200°C. The resulting SiO 2 dielectric film has good adhesion properties, but due to its open glassy structure is not impervious to ionic impurities (primarily sodium). Accordingly, a denser film structure of silicon nitride, Si 3 N 4 , is formed in a reaction between silane and ammonia and is pyrolytically deposited on the SiO 2 layer. ? 2000 by CRC Press LLC ? 2000 by CRC Press LLC T ABLE 55.2 Elect r ical and Ph ysical P r oper ties of Some C o mmon Solid I n sulating M a t e r ials [Bar t nikas and E i c hhor n , 1983; I n sulation C i r cuits , 1972] M axim um Dielect r ic C o nstant Dissipation F a ct or Oper ating AC Specific T emper a tur e 20 ° C2 0 ° C D ielect r ic Str e ngth M a t e r ial G r a v it y ( ° C) 60 Hz 1 kHz 1 MHz 60 Hz 1 kHz 1 MHz (kV cm–1) Alumina (Al 2 O 3 ) 3.1–3.9 1950 8.5 8.5 8.5 1 3 10 2 3 1 3 10 2 3 1 3 10 2 3 98–157 P o r c elain (m ullit e) 2.3–2.5 1000 8.2 8.2 8.2 1.4 3 10 2 3 5.7 3 10 2 4 2 3 10 2 4 94–157 St eatit e 3MgO · 4S iO 2 · H 2 O 2.7–2.9 1000–1100 5.5 5.0 5.0 1.3 3 10 2 3 4.5 3 10 2 4 3.7 3 10 2 4 200 M a g nesium o xide (MgO) 3.57 <2800 9.65 9.65 9.69 <3 3 10 2 4 <3 3 10 2 4 <3 3 10 2 4 >2000 Glass (soda lime) 2.47 110–460 6.25 6.16 6.00 5.0 3 10 2 3 4.2 3 10 2 3 2.7 3 10 2 3 4500 M ica (K Al 2 (OH) 2 Si 3 AlO 10 ) 2.7–3.1 550 6.9 6.9 5.4 1.5 3 10 2 3 2.0 3 10 2 4 3.5 3 10 2 4 3000–8200 Si O 2 film <900 3.9 7 3 10 2 4 1000–10,000 Si 3 N 4 <1000 12.7 <1 3 10 2 4 1000–10,000 Ta 2 O 5 8.2 <1800 28 1 3 10 2 2 Hf O 2 4700 ° F3 5 1 3 10 2 2 Lo w-densit y P E (densit y : 0.910–0.925 70 2.3 2.3 2.3 2 3 10 2 4 2 3 10 2 4 2 3 10 2 4 181–276 g cm 2 3 ) M e dium-densit y P E (densit y : 0.926–0.940 70 2.3 2.3 2.3 2 3 10 2 4 2 3 10 2 4 2 3 10 2 4 197–295 g cm 2 3 ) H i g h-densit y P E (densit y : 0.941–0.965 70 2.35 2.35 2.35 2 3 10 2 4 2 3 10 2 4 2 3 10 2 4 177–197 g cm 2 3 ) XLP E ( densit y : 0.92g cm 2 3 ) 9 0 2.3 2.28 3 3 10 2 4 4 3 10 2 4 217 ? 2000 by CRC Press LLC EPR 0.86 300–350 ° F 3.0–3.5 4 3 10 2 3 354–413 P o ly pr op ylene 0.90 128–186 2.22–2.28 2.22–2.28 2.22–2.28 2–3 3 10 2 4 2.5–3.0 3 10 2 4 4.6 3 10 2 4 295–314 PTFE 2.13–2.20 <327 2.0 2.0 2.0 <2 3 10 2 4 <2 3 10 2 4 <2 3 10 2 4 189 Glass-r einfor c e d 1.8–2.3 265 5.3–7.3 5.0 2 6.4 1–4 3 10 2 2 0.8–2.2 3 10 2 2 90.6–158 p o ly est er pr emix Ther moplastic 1.31–1.58 250 3.3–3.8 1.5–2.0 3 10 2 3 232–295 poly est er (100 Hz) P o ly imide 1.43–1.49 480 ° F 3.4 1–5 3 10 2 3 220 poly est er (100 kHz) (100 kHz) P o ly car bonat e 1.20 215 3.17 2.96 9 3 10 2 4 1 3 10 2 2 157 E p o xy (w ith 1.6–1.9 200 4.4–5.6 4.2–4.9 4.1–4.6 1.1–8.3 3 10 2 2 0.19–1.4 3 10 2 1 0.13–1.4 3 10 2 1 98.4–158 miner al filler) (dec omposition t e mper atur e) E p o xy (w ith 1.6–2.0 200 3.2–4.5 3.2–4.0 3.0–3.8 0.8–3.0 3 10 2 2 0.8–3.0 3 10 2 2 2–4 3 10 2 2 158–217 silica filler) (dec omposition t e mper atur e) S ilic one r u bber 1.1–1.5 700 ° F 3.3–4.0 3.1–3.7 1.5–3.0 3 10 2 2 3.0–5.0 3 10 2 3 158–197 T ABLE 55.2 (c ont i n u ed) Elect r ical and Ph ysical P r oper ties of Some C o mmon Solid I n sulating M a t e r ials [Bar t nikas and E i c hhor n , 1983; I n sulation C i r cuits , 1972] M axim um Dielect r ic C o nstant Dissipation F a ct or Oper ating AC Specific T emper a tur e 20 ° C2 0 ° C D ielect r ic Str e ngth M a t e r ial G r a v it y ( ° C) 60 Hz 1 kHz 1 MHz 60 Hz 1 kHz 1 MHz (kV cm–1) The thin film of Si 3 N 4 is characterized by extremely low losses, and its relatively closed structure does not provide any latitude for free sodium movement, thereby providing complete passivation of the semiconductor device. The high dielectric strength of the double film layer of SiO 2 and Si 3 N 4 renders it dielectrically effective in field-effect transistor (FET) applications. In integrated circuit devices, a number of materials are suitable for thin-film capacitor applications. In addition to Al 2 O 3 , tantalum pentoxide, Ta 2 O 5 , has been extensively utilized. It is characterized by high-temper- ature stability and is resistant to acids with the exception of hydrofluoric acid (HF). The high dielectric constant material hafnia (HfO 2 ) has also been used in thin-film capacitors. Organic Solids Solid organic dielectrics consist of large polymer molecules, which generally have molecular weights in excess of 600. Primarily, with the exception of paper, which consists of cellulose that is comprised of a series of glucose units, organic dielectric materials are synthetically derived. Polyethylene (PE) is perhaps one of the most common solid dielectrics, which is extensively used as a solid dielectric extruded insulant in power and communication cables. Linear PE is classified as a low- (0.910–0.925), medium- (0.926–0.940), or high- (0.941–0.965) density polymer (cf. Table 55.2). Since PE is essentially a long- chain hydrocarbon material in which the repeat unit is –CH 2 –CH 2 –, a low-density PE necessarily implies a high degree of branching. Decreased branching increases the crystallinity as molecules undergo internal folding, which leads to improved stiffness, tear strength, hardness, and chemical resistance. Cross linking of PE produces a thermosetting polymer with a superior temperature rating, improved tensile strength, and an enhanced resistance to partial discharges. Most of the PE used on extruded cables is of the cross-linked polyethylene (XLPE) type. Ethylene-propylene rubber (EPR) is an amorphous elastomer, which is synthesized from ethylene and propylene. As an extrudent on cables its composition has filler contents up to 50%, comprising primarily clay, with smaller amounts of added silicate and carbon black. The dielectric losses are appreciably enhanced by the fillers, and, consequently, EPR is not suitable for extra-high-voltage applications, with its use being usually confined to lower and intermediate voltages (￡138 kV) and also where high cable flexibility due to its rubber properties may be additionally desired. Polypropylene has a structure related to that of ethylene with one added methyl group. It is a thermoplastic material having properties similar to high-density PE, though due to its lower density it has also a lower dielectric constant. It has many electrical applications both in bulk form as in molded and extruded insulations as well as in film form in taped capacitor, transformer, and cable insulations. Polytetrafluoroethylene (PTFE) or Teflon is a fully fluorinated version of PE, having a repeat unit of [–CF 2 –CF 2 –]. It is characterized by a low dielectric constant, extremely low losses, and has excellent temperature stability and is resistive to chemical degradation. It has been extensively used in specialized applications on insulators, wires and cables, transformers, motors, and generators. Its relatively high cost is attributable to both the higher cost of the fluorinated monomers as well as the specialized fabrication techniques required. Polyesters are obtained most commonly by reacting a dialcohol with a diester; they may be either thermo- setting or thermoplastic. The former are usually employed in glass laminates and glass-fiber-reinforced mold- ings, while thermoplastic polyesters are used for injection-molding applications. They are used in small and large electrical apparatus as well as in electronic applications. Polyimides (kaptons), as nylons (polyamides), have nitrogen in their molecular structure. They constitute a class of high-temperature thermoplastics that may be exposed to continuous operation at 480°F. When glass- reinforced, they may be exposed to temperatures as high as 700°F; they are used in molded, extruded wire, and film form. Polycarbonates are thermoplastics that are closely related to polyesters. They are primarily employed in the insulation of electrically powered tools and in the casings of electrical appliances. Polycarbonates may be either compression- or injection-molded and extruded as films or sheets. Epoxy resins are prepared from an epoxide monomer. The first step involves a reaction between two comono- mers, and in the subsequent step the prepolymer is cured by means of a cross-linking agent. Epoxy resins are characterized by low shrinkage and high mechanical strength; they may be reinforced with glass fibers and mixed with mica flakes. Epoxy resins have many applications such as, for example, for insulation of bars in the stators of rotating machines, solid-type transformers, and spacers for compressed-gas-insulated busbars and cables. ? 2000 by CRC Press LLC Silicone rubber is classified as an organic-inorganic elastomer, which is obtained from the polymerization of organic siloxanes. They are composed of dimethyl-siloxane repeat units, (CH 3 ) 2 SiO–, with the side groups being methyl units. Fillers are added to obtain the desired silicone rubber compounds; cross linking is carried out with peroxides. Since no softeners and plasticizers are required, silicone rubbers are resistant to embrittlement and may be employed for low- temperature applications down to –120°F. Continuous operation is possible up to 500°F, with intermittent usage as high as 700°F. Solid-Liquid Insulating Systems Impregnated-paper insulation constitutes one of the earliest insulating systems employed in electrical power apparatus and cables. Although in some applications alternate solid- or compressed-gas insulating systems are now being used, the impregnated-paper system still constitutes one of the most reliable insulating systems available. Proper impregnation of the paper results in a cavity-free insulating system, thereby eliminating the occurrence of partial discharges that inevitably lead to deterioration and breakdown of the insulating system. The cellulose structure of paper has a finite acidity content as well as a residual colloidal or bound water, which is held by hydrogen bonds. Consequently, impregnated cellulose base papers are characterized by somewhat more elevated tand values in the order of 2 3 10 –3 at 30 kV cm –1 . The liquid impregnants employed are either mineral oils or synthetic fluids. Since the dielectric constant of these fluids is normally about 2.2 and that of dried cellulose about 6.5–10, the resulting dielectric constant of the impregnated paper is approximately 3.1–3.5. Lower-density cellulose papers have slightly lower dielectric losses, but the dielectric breakdown strength is also reduced. The converse is true for impregnated systems utilizing higher-density papers. The general chemical formula of cellulose paper is C 12 H 20 O 10 . If the paper is heated beyond 200°C, the chemical structure of the paper breaks down even in the absence of external oxygen, since the latter is readily available from within the cellulose molecule. To avert this process from occurring, cellulose papers are ordinarily not used beyond 100°C. In an attempt to reduce the dielectric losses in solid-liquid systems, cellulose papers have been substituted in some applications by synthetic papers (cf. Table 55.3). For example in extra-high-voltage cables, cellulose paper–polypropylene composite tapes have been employed. A partial paper content in the composite tapes is necessary both to retain some of the impregnation capability of a porous cellulose paper medium and to maintain the relative ease of cellulose-to-cellulose tape sliding capability upon bending. In transformers the synthetic nylon or polyamide paper (nomex) has been used both in film and board form. It may be continuously operated at temperatures up to 220°C. Defining Terms Conductivity s: Represents the ratio of the leakage current density to the applied electric field density. In general its ac and dc values differ because the mechanisms for establishing the leakage current in the two cases are not necessarily identical. Dielectric: A material in which nearly all or a large portion of the energy required for its charging can be recovered when the external electric field is removed. TABLE 55.3Electrical Properties of Taped Solid-Liquid Insulations Impregnating Average tand at Room tand at Operating Tape Liquid Voltage Stress (kV cm –1 ) Temperature Temperature Kraft paper Mineral oil 180 3.8 3 10 –3 5.7 3 10 –3 at 23°C at 85°C Kraft paper Silicone liquid 180 2.7 3 10 –3 3.1 3 10 –3 at 23°C at 85°C Paper-polypropylene-paper (PPP) Dodecyl benzene 180 9.8 3 10 –4 9.9 3 10 –4 at 18°C at 100°C Kraft paper Polybutene 180 2.0 3 10 –3 2.0 3 10 –3 at 25°C at 85°C ? 2000 by CRC Press LLC Dielectric constant ?￠: A quantity that determines the amount of electrostatic energy which can be stored per unit volume per unit potential gradient. It is a real quantity and in Gaussian–CGS units is numerically equal to the ratio of the measured capacitance of the specimen, C, to the equivalent geometrical capac- itance in vacuo, C o . It is also commonly referred to as the real value of the permittivity. Note that when the SI system of units is employed, the ratio C/C o defines the real value of the relative permittivity e￠ r . Dielectric loss: The rate at which the electrical energy supplied to a dielectric material by an alternating electrical field is changed to heat. Dielectric strength: Represents the value of the externally applied electric field at which breakdown or failure of the dielectric takes place. Unless a completely uniform field gradient can be assured across the dielectric specimen, the resulting breakdown value will be a function of the specimen thickness and the test electrode geometry; this value will be substantially below that of the intrinsic breakdown strength. Dissipation factor (tand): Equal to the tangent of the loss angle d, which is the phase angle between the external electric field vector E and the resulting displacement vector D. It is numerically equal to the ratio of the imaginary permittivity e2 to the real permittivity, e￠; alternatively, it is defined by the ratio of the leakage current to the displacement (charging or capacitive) current. Related Topics 54.1 Introduction ? 58.4 Material Properties Conducive for Smart Material Applications References R. Bartnikas and R. M. Eichhorn (eds.), Engineering Dielectrics, Vol. II A, Electrical Properties of Solid Insulating Materials: Molecular Structure and Electrical Behavior, STP 783, Philadelphia: ASTM, 1983. R. Bartnikas (ed.), Engineering, Dielectrics, Vol. III, Electrical Insulating Liquids, Monograph 2, Philadelphia: ASTM, 1994. A. von Hippel, Dielectrics and Waves, New York: Wiley, 1956. P. K. Watson, IEEE Trans. on Dielectrics and Electrical Insulation, 2, 915–924, 1995. C. LeGressus and G. Blaise, IEEE Trans. on Electrical Insulation, 27, 472–481, 1992. J. B. Bernstein, Ibid., pp. 152–161. H. J. Wintle, IEEE Trans. on Electrical Insulation, 25, 27–44, 1990. A. von Hippel and G.M. Lee. Phys. Rev., 59, 824–826, 1941. W.G. Oakes, Proc. IEE, 90(I), 37–43, 1949. R. Bartnikas (ed.), Engineering Dielectrics, Vol. II B, Measurement Techniques, STP 926, Philadelphia: ASTM, 1987. H. C. Miller, IEEE Trans. on Electrical Insulation, 28, 512–527, 1993. R. Bartnikas and E.J. McMahon (eds.), Engineering Dielectrics, Vol. I, Corona Measurement and Interpretation, STP 669, Philadelphia: ASTM, 1979. J. C. Fothergill, L. A. Dissado, and P. J. J. Sweeny, IEEE Trans. on Dielectrics and Electrical Insulation, 1, 474–486, 1994. Encyclopedia Issue, Insul. Circuits, June/July 1972. Further Information The IEEE Dielectrics and Electrical Insulation Society publishes regularly its IEEE Transactions on Dielectrics and Electrical Insulation, wherein many new developments in the field of dielectrics are recorded in permanent form. It also sponsors on either an annual or a biennial basis a number of conferences, which provide a forum for rapid dissemination of both the applied and fundamental work carried out on dielectrics and electrical insulating systems. The reader may wish to consult the IEEE Conference Records on the Annual Report, Conference on Electrical Insulation and Dielectric Phenomena, the IEEE International Symposium on Electrical Insulation, and the Electrical/Electronics Insulation Conference. Also, a description of the different test methods on dielectric materials may be found in the ASTM Book on Standards. ? 2000 by CRC Press LLC