The Complex Nature of Dielectric Absorption and Dielectric Loss

T H E CORlPLEX NATURE O F DIELECTRIC ABSORPTIOIC AND DIELECTRIC LOSS K i t h Particular Reference to the Influence of Ions adsorbed on Inner Surfaces. B Y E. J. MURPHY AXD H. H. LOWRY

Introduction I n recent years many facts have been discovered which indicate that in most solid dielectrics direct-current conduction does not take place uniformly through the material as a whole but’ along paths of higher conductivity than the main part of the dielectric. Since t’hese paths are of sub-microscopic dimensions the interfacial area of their boundaries should be large in comparison with their voIume, and it would consequently be expected that the ions adsorbed by the interface between the conducting medium and the insulating medium may have important effects on the electrical properties of dielectrics. The following discussion is primarily an inquiry into the nature of the effects which the ions in a dielectric would have upon dielectric absorption (Le., the formation of a residual charge) and dielectric loss‘ on the assumption that besides free ions solid dielectrics may contain ions adsorbed by the above-mentioned inner surfaces, or associated in some equivalent way with neutral molecules. Consideration of the physical, chemical, and electrical properties of dielectrics also suggests that it would be advantageous in general to divide dielectric absorption and dielectric loss into components based upon different physical mechanisms, where there are independent evidences of the existence of these mechanisms. The characteristics of dielectric absorption and loss are therefore discussed here on the basis of a division of these quantities into components due to free ions, to adsorbed ions, and to neutral molecules. The relative prominence of each of these components should depend on the nature of the dielectric, t,he temperature and other factors. Before discussing the characteristics of dielectric absorption and loss, it seems desirable to discuss the general picture of the structure of dielectrics which appears to be warranted by recent data, and to outline the electrical properties which materials with such a structure would be expected to have. 1 The most recent discussions of these subjects have been given by Whitehead: J. Am. Inst. El. Eng., 45, 515 (1926); Whitehead and Marvin: 48, 186 (1929); Kitchen: 48 281 (1929); Kitchen and Muller: Phys. Rev., ( 2 ) , 32, 929 (1928); Schiller: 2. Physik,’ 42, 246(1927);,50,577 (1928);Ann.Physik (4),81,88 (1926); Joff6:“PhysicsofCrystals” (1928); Ann. Physik, 72, 495 (1923); Z. Physik, 48, 288 (1928); Sinlelnikoff and Ralther: 40, 786 (1927); Seumann: 45, 717 (1927); Hartshorn: J. Inst. El. Eng., 64, 1152 (1926); K. W. Wagner: Schering’s “Die Isolierstoffe der Elektrotechnik ” ( 1924).

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Evidences for the General Occurrence of “Interstitial Conduction” The work of A. Smekal2 in the past few years has shown that in crystalline dielectrics a t ordinary temperatures, or a t least in those which are ionic conductors, the ions which take part in conduction are concentrated in positions in the crystal where lattice imperfections are present. It is suggested also that these ions are produced by thermal dissociation within the spaces bounded by the inner crystalline surfaces and move in an adsorbed condition along paths formed by these crystalline fissures. This mechanism of conduction is supported by indirect evidences provided by the mechanical and optical properties of crystals, as well as by the form of the conductivitytemperature curve for such crystals, by the conductivity-voltage relationship, and by the influence of impurities. The theory proposed by Smekal has recently been the subject of several investigations, the majority of which favor it.3 While the gross structure of the moisture-absorbing dielectrics differs from that of the crystalline dielectrics studied by Smekal and others, the assumption that conduction takes place through water which occupies spaces between the insulating micelles of the main constituent of the material also gives consistent plausible explanations of their electrical behaviors4 The structure recently given by Meyer and Markj for cellulose and a variety of similar materials, based on a review of existing rontgenographic and other evidence is in agreement TTith the structure which has been proposed to explain the electrical properties of these materials. Thus both types of dielectric, though quite different in some respects, have the common property that conduction takes place through conducting paths distributed in an insulating medium; such a system may perhaps appropriately be called an “interstitial conduction” system because it consists of conducting paths dispersed in the interstices between relatively non-conducting structural units of the material. These interstitial spaces are not in general to be regarded as accidental occurrences-though it may not be proven beyond question that they are not accidental-but as a normal part of the structure of the materials. Smeka1,G from a study of a large number of substances, estimates that the ideal part of the lattice in a crystal unit contains 104 to 105 atoms or molecules. This is supported by Zwicky’ who attributes t o crystals a mosaic structure in which the dimensions of the elements are about 508. Even in Smekal: Physik. Z., 26, 707 (1925);Anz. Akad. Wiss. W e n . , 63, 195 (1926);Z.techn. Physik, 8, 72, 203, j61 (1927);Ann. Physik, (4)83, 1202 (1927);Z. Physik, 45,869 (1927). Bltih and Jost: Z. physik. Chem, B1,270 (1929);Gingold: Z. Physik, 50, 633 (1928); Gyulai and Hartley: 51, 376 (1928);Cf. also Traube and v. Behren: Z. physik, Chern., A138, 85 (1928);Zwicky: Proc. S a t . Acad. Sci., 15, 253 (1929);v. Hevesy: Z. physik. Chern., 101,337 (1922);127,401 (1927);Joffe: loc. cit., ref. I. Murphy: J. Phys. Chem., 32, 1761 (1928);33, 197,509 (1929). hleyer and Mark: Ber., 61,593 (1928). Smekal: Ann. Physik, (4)83, 1202 (1927). Zwicky: loc. cit., ref. 3.

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some liquids, particularly those with a mesomorphic phase,* there is a tendency for aggregates of about 105molecules to form.9 These facts all appear to support Smekal’s conclusions regarding the existence of crystal imperfections and their importance in explaining the phenomena associated with electrical conduction in crystals. With an analogous picture of the conducting paths in moisture absorbing dielectrics, we have also obtained qualitative agreement with the mechanism of electrical conduction in textiles. As already mentioned it is highly probable that in such interstitial conduction systems the adsorption of ions at the boundary surfaces between the conducting paths and the insulating structural elements of the dielectric would have important effects owing to the large ratio of interfacial area to volume which would characterize conducting paths of submicroscopic dimensions. Since therefore it is necessary to consider the adsorption of ions in discussing electrical properties, it may be advantageous to recall certain properties characteristic of an adsorption system. For instance, if the total number of ions in such a system remains constant an increase in temperature will decrease the number of adsorbed ions, thereby increasing the number of free ions. As a result of this one might expect that the electrical properties determined by the number of adsorbed ions might become relatively less important as the temperature increases. Another common effect of temperature is to increase the total concentration of ions, which in turn wjll increase the number of adsorbed jons. Since, however, there is no strict proportionality between the total concentrations of ions and the number of adsorbed ions-the number of adsorbed ions being proportional to a fractional power of the concentration-at low concentrations an increase in the total number of ions may result in an enhancement of the electrical effects due to the adsorbed ions, while a t higher concentrations the effect of the free ions may predominate. General Electrical Properties of an Interstitial Conduction System The preceding discussion of the structure of dielectrics suggests that the essential form of the internal structures in the dielectric may be schematically illustrated as in Fig. I-A. It will be noted that the conducting paths do not consist of smooth channels running parallel to the direction of the applied field, a form which would have quite different properties from those about to be described, but that the idealized element of structure consists of an insulating micelle or crystallite (assumed spherical in shape, though any other form would do for our purpose) surrounded by a conducting skin as shown in Fig. I-B. I n crystals the skin may be of the same material as the sphere, *Friedel: Ann. Physik, (4) 18, 273 (1922). Stewart: Phys. Rev., (2),32, 558 (1928);Krishnamurti: Indian J. Physics, 2, 5 0 1 (1928); Kate: Z. angew. Chem., 41, 329 (1928);Naturwissenschaften, 16, 758 (1928); Kate and Selman: Z. Physik, 46, 392 (1928);Ornstein: Phpsik. Z.,29, 668 (1928); Ann. Physik, (4)74,&5 (1924);Kast: Physik. Z.,29, 293 (1928);Magnus: Z.anorg. Chem., 171, 73 (1928);Jetheys: Proc. Camb. Phil. SOC.,24, 19 (1928). 9


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but less dense, but in moisture absorbing materials it is to be regarded as a filmof water containing a certain concentration of ions. The ions in this skin near the interface between the insulating micelle and the conducting layer will be attracted toward the interface, i.e., adsorbed. The electrical behavior of such an adsorption system may be quite complex, but the literature on adsorption gives support for attributing to the system the following properties, which are considered the most essential for

C

A FIG.I

Illustration of an interstitial conduction system showing the effect of the electric field on the distribution of adsorbed ions. A. Section of an interstitially conducting dielectric represented schematically. Conduction takes place through the medium which occuxies the interstices between the insulating spheres. Each sphere is surrounded by an atmosphere” of adsorbed ions extending for a small distance away from its surface with gradually decreasing density. B. This sketch shows the distribution of adsorbed ions around two adjacent insulating spheres in the schematic structure shown in .1 before the application of the electric field. Three concentric layers of ions are shown to illustrate a possible distribution of adsorbed ions in the absence of an impressed electric field. The density of ions in each layer is uniform but is less the greater the distance from the interface. The only significance of the outer circles is to indicate the limits of the atmospheres of adsorbedions surrounding each sphere. For the present purpose it is not essential that the distribution of the adsorbed ions should be as illustrated, for it is only the change in distributlon produced by the electric field which is important. C. The same as B after the application of the field for a sufficient time for the adsorbed ions to assume a polarized distribution under the influence of the electric field. The direction of the field is indicated by the arrow.

the purpose of deriving in a qualitative way the effect of the adsorption of ions on the electrical properties of a dielectric: (a) the adsorbed ions are not rigidly fixed to certain points on the adsorbing surface, but can move over the surface under the influence of an ext,ernally applied electric field;l0 (b) they cannot leave the particular structural unit by which they are adsorbed unless a certain threshold voltage gradient, which may be called the “desorption voltage,” is exceeded;“ (c) not all of the ions are adsorbed equally ‘OVolrner and Estermann: Z. Physik, 7, 13 (1921); Estermann: 33, 320 (19zj). Polanyi: Verh. deutsch. physik. Ges., 18, 5 5 (1916); Z. Elektrochemie, 26, 370 (1920).

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strongly owing to there being several layers of ions,12i.e., a decreasing gradient of concentration of adsorbed ions as a function of distance from the interface, as shown by Fig. 2-A. The result would be essentially the same for our purposes whether ions of only one sign or both signs are adsorbed.'S One effect of these properties is that when a voltage is applied the least strongly adsorbed ions-those in the outer layers-will become desorbed and join the conduction current, thereby increasing the conductivity. As the voltage gradient is increased, more adsorbed ions would join the conduction current; this explains the increase of conductivity with increasing field strength which is a prominent characteristic of solid dielectrics. This explanation of the voltage effect is equivalent, except for the details of the physical picture, to the mechanism proposed by Smekal. A second result is that when an electric field is applied the adsorbed ions will move over the surface of the micelle, or crystallite, and accumulate at its poles,-for convenience, defining the axis of these interstitial conduction units as the direction of the electric field-as shown in Fig. I-C.* This process of accumulation will continue until the effect of the repulsive forces between like ions equals that of the applied electric field. After the electric field is removed, the adsorbed ions will return to the equilibrium distribution which existed in the absence of the field. The movement of the adsorbed ions on the surface of the micelle or crystallite under the influence of the electric field is equivalent to a condenser charging current and their return to the equilibrium distribution in the absence of the field (Le., uniform distribution in the case of a spherical micelle, for instance) to a discharge current; the reversible change in the distribution of ions produced by the application of a field may be regarded as equivalent in effect to dielectric polarization, Le., to the orientation of dipoles in a field and their return to random orientation on its removal, or to the displacement by the field of the charges within a molecule and their return to their normal positions after the removal of the field. I n the polarization of the charges within a molecule the internal forces of the molecule are involved, while in the polarization, or redistribution of ions on the surface of a micelle or crystallite the external forces which cause cohesion and adsorption are the bonds which prevent the ions from moving freely in the electric field but allow an elastic displacement of charge. Each micelle or crystallite whose atmosphere of adsorbed ions has been given a polarized distribution by an externally applied electric field may be regarded as an induced dipole. It is recognized that the ions of opposite sign may be in alternate layers, as suggested by Eucken,I3 and that the outermost layers of ions may be considered practically free. I n any case, owing to the fact 1z Gouy: Ann. Phys., 7, 129 (1916);Eucken: Verh. deutsch. physik. Ges., 16, 345 (1914); Po!any: loc. cit. IaEucken: 2. physik. Chem., A138, 375 (1928). * If the conduction paths were smooth channels of uniform resistance running through the dielectnc in the same direction as the applied electric field, there would be no accumulation of charge either due to the ions adsorbed by the walls or t o free ions; but such a representation of the conduction paths would be erroneous since conduction paths running only in the direction of the applied field would not normally occur in d.dectncs.


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that the dielectric is solid, the micelle or crystallite with its adsorbed ions cannot move as a whole in the electric field even where this unit is not neutral and the electrical effect is therefore similar to that of a large dipole. This means that the ions adsorbed on the inner surfaces of a dielectric can produce a displacement current without producing a space charge. Free ions could not produce a displacement currentI4 without producing a space chargels a t the same time. The mechanism described above differs from most theories of the effect of ions on dielectric absorption in that the ions do not form a space charge but produce a modified type of dielectric polarization. I n a series of recent papers Boningi6 has studied the effects of adsorbed ions on the electrical properties of dielectrics and has developed expressions for a number of relationships assuming that the adsorbed ions are rigidly fixed to points on the walls of the conducting paths. When the ions of opposite sign to the adsorbed ions are removed from the dielectric by the current, he considers that there results a space charge of uniform density. The fact that the mechanism proposed by Boning results in a modified form of space charge while the present one results in a modified type of dielectric polarization is due largely to the fact that Boning considers the adsorbed ions as fixed, while we consider them as capable of movement in the electric field, though only over the surface of the particular micelle or crystallite by which they are adsorbed. A third property of adsorbed ions which will be important in the consideration of the electrical effects is the existence in general of more than one layer of adsorbed ions, each successive layer in the conducting medium being less strongly adsorbed the greater its distance from the interface in accordance with the theories of Gouy, Polanyi, and Eucken.'* The rapidity of movement of the adsorbed ions over the surface of an interstitial conduction unit under the influence of the applied electric field will depend on the resistance to motion of the ions. It may be assumed that adsorption reduces the mobility of the ions even in a direction on the average parallel to the surface of the unit." The electric circuit equivalent to the micelle or crystallite with its adsorbed ions would therefore be a capacity in series with a resistance, the magnitude of the resistance being determined by the resistance offered to the motion of the adsorbed ions as they move in the electric field and accumulate at the poles of the structural unit. But if the adsorption of the ions decreases their mobility in the electric field, the amount of the decrease will be smaller the greater the distance of the layer of ions from the interface. Further, if the adsorptive force is a necessary condition for the accumulation of l4 Except that involved in the ionic atmospheres of the Debye-Falkenhagen theory or unless there were non-uniform resistances on the molecular scale in the conduction paths. As the term is used here there is no space charge when the potential distribution in the dielectric is uniform on a macroscopic scale. Boning: Z. Fernmeldetechnik, 8, 162 (1927); Arch. Elektrotech., 20, 88 (1928);Z. techn. Physik., 9, 2 1 2 (1928);10,20 (1929). Perhaps because of an increase in the density of the conducting medium near the interface, or for other reasons such as the energy of the ion moving in the electric field being partly lost by inelastic collision with adsorption centers into which it falls.

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ions, and if it is assumed that it is possible t o consider each layer of ions separately, the amount of the accumulation should be less the greater the distance from the interface of the layer of ions considered. The same conclusion may be reached if one considers that owing to the lower desorption voltage of ions in the outer layers they could not accumulate to the same extent as those in the inner layers. These considerations lead to the representation of the equivalent electrical circuit for the structural unit with its adsorbed ions as in Fig. zB, where each layer of adsorbed ions is represented by a capacity in series with a

A

B

FIG.2 Representation of adsorbed ion displacements by equivalent electric circuit, showing the asaumed relation of density of ions to relaxation time. A. This curve represents the density of adsorbed ions vs. distance from the interface as calculated from observed data on the basis of Polanyi’s theory. It is Fig. 4 of Polanyi’s pa er in Verh. deutsch. physik, Ges., 18, 55 (1916). 6 is the, density in mol/liters. (p is the vogme in liters, and is a function of the distance from the Interface. B. Diagram of circuit equivalent in conductance and capacjty to the units of the interstitial conduction system of Fig. I . C m is the capacity due to dielectric polarization of the molecules; C1, Ct . Cn-l, C. are the capacities due t o the redistribution of adsorbed ions on the surface of the micelles or crystallites. Rl, R1 R.-J-~,R. are the series resistances equivalent to the frictional resistances which impede the process of forming a polarized distribution of adsorbed ions. Rd.c. is the direct current resistance. Both capacities and resistances decrease as the distance from the interface of the layers of ions to which they refer increases.

..

.. . .

resistance, both the capacities and the resistances being smaller the greater the distance from the interface. The essential thing here is that the time constants of each of the condensers with t’heir series resistances are different, and increase the closer the corresponding layer of adsorbed ions is to the interface; that is, the polarized distribution of the adsorbed ions on the surface of each structural unit has a different relaxation time for each layer of adsorbed ions. Dielectric Absorption The interstitial conduction system described, and particularly the adsorption of ions which is its most essential property for the present purpose, appears t o be capable of adequately explaining the characteristics of dielectric absorption. This phenomena may be described as follows: When an e.m.f. is applied to a dielectric the current decreases with time beyond the


605

time required for charging the geometric capacity of the condenser, and when the voltage is removed and the geometric capacity discharged, a charge still remains in the material, This remaining charge is called the absorbed or residual charge, and the decreasing current is usually called the absorption, or anomalous charging current. Any satisfactory mechanism of dielectric absorption must be able to explain the following important properties: (a) The form of the absorption current-time curve; (b) the superposition principle; (c) the change in the distribution of potential which accompanies the formation of a residual charge in some cases but not in others. Form o j the absorption current-time curve: One characteristic of the anomalous charging and discharging currents is that they do not become reduced to zero following an exponential curve, but are usually best represented by an expression of the form i = A t - n , where i is the anomalous charging or discharging current, t the time of charging or discharging, and A and n constants; n is of the order of 0.8.~~This equation is probably not valid, however, when t is very small. Theories of dielectric absorption based on a simple mechanism, such as those of Maxwell or Pellat, all lead to an exponential law of decrease of the absorption current with time. To reconcile the Pellat theory'g with experiment, von Schweidler proposed a mechanism in which each element contributes t o the anomalous current according to an expression of the form i = const. e-t/T, where T is a time constant, each element however having a different time constant. The summation of the currents due to a sufficient number of elements of this kind can represent the observed results when the constants are properly chosen, and in particular can represent data which would be satisfactorily expressed by i = At-". The preceding discussion of the times of relaxation characteristic of changes in the distribution of adsorbed ions showed that, where there are several layers of them, each layer may have a different relaxation time (cf. Fig. 2-B). The presence in dielectrics of ions adsorbed with varying degrees of intensity therefore provides a new physical interpretation of the Pellat-v.Schweidler'8 theory of dielectric absorption. The charging currents due t o the redistribution of adsorbed ions on the surfaces of the micelles or crystallites in a dielectric may therefore be regarded as forming one component of the absorption current. This component may itself be composed of others corresponding to each layer of adsorbed ions. However, free ions, and possibly neutral molecules, can also contribute to the absorption current. The presence of inhomogeneities in the resistance of the dielectric would cause an absorption current due to free ions, as in the hfaxwell theory of absorption in dielectrics with layers of different dielectric constant and resistivity. Another way in which free ions may produce a component of the absorption current is through the formation of high resistance layers as a result of the electrode reactions. While all the other components of the absorption current should v. Schweldlw Ann. Phvsik, (4) 24, 711 (1907); E;. W.Wagner. Arch. Elektrotech , 3, 67 (1914); Whltehead and Xlarvin: J. Am. Inst. El Eng., 48, 187 (1928); Seumann: Z. Physik,45,717 (1927); Goldhammer: 47,671 (1928); 52,708 (1929); Salessky: 52,695 (1929). 19 Pellat: Ann. Chim. Phys., 18, 150 (1899); J. Phys., (3) 9, 3 1 3 (1900).

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decrease exponentially with time, this one would probably be a more complicated function of time because the resistance (or thickness) of the layers formed by the electrode products would be continuously changing as the electrolysis proceeded. I n some cases the absorption current may have fewer components, since some of those mentioned may be negligible. The initial and final stages of the absorption current have some characteristics which require further interpretation. The final stage of the decrease of the absorption current with time is sometimes extremely slow, and the anomalous discharge current may continue for several days or weeks. This may be explained by attributing t o the most strongly adsorbed ions a very large time of relaxation after a disturbance of their equilibrium distribution by the applied electric field, but in some cases, particularly w h m the conductivity of the dielectric is high, it is undoubtedly largely due to the difference between the chemical composition of the anodic and cathodic products of electrolysis; that is, the dielectric with its electrodes acts as an accumulator, and the energy is stored in chemical differences rather than by electrostatic charges or dielectric polarization.20 The initial part of the absorption current has been investigated by measuring the current for very short times after the application of the voltage.*l According to most investigators it does not approach a limiting value but continues to increase as the interval between the application of the voltage and the measurement of the current is shortened. Sinjelnikoff and Walther,Z1 however, consider that the initial current can be extrapolated to zero time, the value obtained being the true conduction current. They attribute the decrease in initial current to the back-e.m.f. caused by the formation of a space charge in the dielectric. Of the several components of the absorption current discussed the only one which would be expected to yield an initial wrrent which approaches a constant value corresponding to the true conduction current as the time between the application of the voltage and the measurement of the current is shortened is the one due to the formationof high resistance layers as a result of the electrode reactions accompanying the conduction current, This component of the absorption current would be practically zero until the electrolysis had continued long enough for the electrode reactions to produce an appreciable change in the resistance of some part of the dielectric. If all other components of the absorption current had sufficiently short relaxation times that they became reduced to zero before the conduction current had produced appreciable changes in the resistance of the dielectric, the initial current would remain sensibly constant until the effects of the electrode reactions on the resistance of the conduction paths became appreciable; this constant current is the true value of the conduction current. We have found that in cotton exposed to high humidities the Murphy: J. Phys. Chem., 33, 509 (1929). -‘Hopkinson: Phil. Trans., 166, Part 2, 489 (1876); 167, 599 (1877); 189A, I09 (1897); Tank: Ann. Physik, (4) 48, 307 (1915)’ Whitehead and Marvin: loc. cit., ref. 18; Goldhammer: loc. cit., ref. 18; Saleeaky: loc.’cit., ref. 18; Sinjelnikoff and U‘alther: loc. cit., ref. I ; Joff6: loc. cit., ref. I . 2o

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initial current in some cases remained sensibly constant for some time before commencing to decrease. Tank’s measurements on paper, which behaves similarly to cotton electrically, showed that the initial current does not reach a constant value even for very short times. Our measurements on cotton indicated that the initial current a t low humidities behaves differently from that a t high humidities, and probably similarly to the initial current in paper as observed by Tank. These results may be interpreted to mean that the components of absorption due to adsorbed ions and to molecules predominate when the conductivity of the dielectric is low and the current is measured after short times, while the electrolytically produced component predominates when the conductivity is high, particularly in the latter stages of the absorption current. This is in agreement with the views expressed by Goldhammer that the processes accompanying the passage of a current through quartz are to be divided into two types, a rapid and a slow, the latter being electrolytic in nature and resulting in the formation of a high resistance layer a t the anode, as previously observed by Warburg.22 The more rapid type could be identified with the process of displacing the adsorbed ions on the surface of the structural units to which they are attached, and in fact Goldhammer23 suggests a somewhat similar explanation. T h e Superposition Principle: HopkinsonZ4found that,, if a condenser which absorbs a residual charge is charged for some t,ime and then the sign of the applied e.m.f. reversed for a shorter time, the first part of the discharge current corresponds in direction to the last charge imposed on the condenser but the direction of the discharge current becomes reversed at a later stage of the discharge and corresponds in direction to the first charge. This phenomenon is included under Hopkinson’s law of the superposition of the effects of successively applied voltages. This behavior can be explained in terms of the mechanism proposed here by the difference in the relaxation times of different layers (or types) of adsorbed ions (cf. Fig. a-B); the first part of the discharge current is that due to the layers of adsorbed ions of small relaxation time, the second to the layers of larger relaxation time for which the ionic distribution corresponding to the first charge was not completely effaced by the second charging. The discharge current in the external circuit would then be given by i = Ale-t/Tl A2e--t!Tx . . . , . , , , , . , . , , A,-1 e-tITn-1 A, e--tpTn. The sign of the charge on those elementary condensers whose first charge was not completely discharged because of their large time constant-those designated by the subscripts n, n-I, --would be opposite to that on those of small time constant-those desi ted by subscripts I , 2 , . . ., that is, A,, A,,-, . . . would be negative when A1, Aq Another aspect of the superposition pri basis of measurements on many dielectrics, is that the constant final value

+

+

** JVarburg and Tegetmaver: M-ied. Ann. 41,

+

18 (1890). Goldhammer: loc. cit. &f. 18, p 719, Hopkinson: loc. cit., ref. 21. 25 Curis: Ann. Chim. Phys., (6) 18, 203 (1889).

*3

g4

+

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of the charging current when added to the discharge current-time curve gives the charging current-time curve with sign reversed. This may be regarded as a superposition of the absorption current due to adsorbed ions and to molecules on the conduction current. Potential Distribution: It has been experimentally shown that in some cases the absorption current changes the distribution of potential in a dielectric and in others not. For instance, J o f f P found that in calcite the absorption current is accompanied by the formation of a non-uniform potential gradient, almost the whole of the potential drop being concentrated in a very thin layer a t one of the electrodes after the voltage had been applied for some hours. Yon SeelenZ7and also Gingold29have found that for natural rock salt single crystals the same quantity of electricity was returned on discharging as went into the crystal on charging. I n order to determine whether the absorption current was accompanied in this case by a back-e.m.f. concentrated in a thin layer a t the electrodes, such as Joff4 found for calcite, Gingold split the crystal into many sections after long charging and found that the polarization back-e.m.f. was uniformly d i ~ t r i b u t e d . ~Gingold’s ~ interpretation of this is based upon Smekal’s theory that conduction in crystals is confined to the lattice faults. The absence of any measurable conduction current would indicate that natural single crystals of rock salt a t room temperature do not contain any faults which go the whole way through the crystal. He therefore attributes the absorption current to the movement of ions in short conducting paths and their accumulation a t the ends of these paths. On the present hypothesis the absorption current in natural S a C l crystals may be explained as due to the displacement of ions on the surfaces of the crystallites of which the crystal is composed. This explanation is in agreement with Gingold’s except that we substitute the adsorptive forces of the crystallites, which are presumably bounded by the lattice faults, for the “ends“ of the short conducting paths. In cotton, which is a dielectric whose conductivity is due to the water which it contains, and therefore conducte quite differently from rock salt or calcite, we have found that a t high humidities the absorption current is accompanied by the production of a non-uniform potential gradient, the greater part of the potential drop being concentrated a t one of the electrodes.* The change in potential distribution was found to depend on the electrode material and was shown to be due to a localized increase in the resistance of the dielectric because of electrolytically produced chemical changes. As the humidity was reduced this process became slower, and over a wide range of humidity (40-7076.) the absorption current was negligibly small in comparison with the conduction current and the potential distribution was uniform after 0.5 minutes. At still lower humidities, however, the absorption curJoffB: Ann. Physik, (4)72, 495 (1923). v. Seelen: 2. Physik, 29, 125 (1924). ** Gingold : Z. Physik, 50, 633 (1928). 29 v. Seelen, working a t a higher temperature, found that the potential distribution in XaCl crystals is independent of the time and direction of current flow. 26

27


639

rent again became prominent. Here the absorption current differed from that a t high humidities in that, whereas a t high humidities the resistance of the dielectric was practically unchanged by a reversal in the direction of the applied voltage, a t low humidities the apparent resistance was changed by large amounts on reversal, and the decrease of the current with time a t low humidities appeared to be entirely due to the back-e.m.f. due to the absorbed charge. Further, the increased apparent resistance a t high humidities persisted long after the residual e.m.f. was negligible, while a t low humidities it returned practically to the original resistance when the residual e.m.f. disappeared. On the present hypothesis this behavior indicates that a t low humidities the free ions are present in such relatively small amounts that the displacement current due to the adsorbed ions predominates over the conduction current, while a t high humidities the conductivity is so high that the displacement current due to adsorbed ions is negligible and the apparent absorption current is due to the resistance changes produced by the products of electrolysis, and the discharge current to an electro-chemically produced e.m.f. as mentioned above. Other Characteristics of Dielectric Absorption: I n addition to the properties which have been considered the most important in the discussion of dielectric absorption, namely, the form of the anomalous current-time curve, the superposition principle and the effect of the absorption current on potential gradient, the effects of voltage, temperature and exposure to ionizing radiations have been considered and are found to be not inconsistent with the mechanisms proposed to explain the other properties. It has been found that the conductivity of most solid dielectrics increases with increasing applied voltage.30 As mentioned previously this appears t o be readily explained by the desorption of adsorbed ions. It would therefore be expected that the final value of the absorbed charge would increase less rapidly than the applied voltage. The results of Whitehead and Marvin,’ showing that the absorbed charge falls off more rapidly on discharge the higher the charging voltage, may therefore probably be regarded as in agreement with the adsorbed ion mechanism. It is possible also that a quantitative relationship may exist between the change of conductivity with voltage and the change of absorbed charge with voltage. Increase of temperature would have three effects; it would increase the total concentration of ions, but at the same time it would tend to cause the desorption of ions and therefore would result in an increase in the ratio of free to adsorbed ions but might either increase or decrease the total number of adsorbed ions; it would also increase the mobility of the ions. These effects permit consistent explanations of the data in the literature,31 if assumptions are made on general grounds as to which effects predominate under different conditions. 90Evershed: J. Inst. El. Eng.,52, 51 (1914)’ Poole: Phil. Mag., 42,488 (1921); Schiller: Ann. Physik, 81, 32 (1926); Smekal: Z. t e c h . bhyaik, 8, 561 (1927). aLHopkinson:loc. cit., ref. 21; Wagner; loc. cit., ref. 18;Whitehead and Marvin: loc. cit., ref. I ; Salesaky: loc. cit., ref. 18.

610


Irradiation in general causes an increase in the conductivity of a dielectric but apparently does not affect the absorbed charge,32 Since there is evidence that the recombination of ions in solid dielectrics is a very slow process,33 it would not be expected that irradiation would greatly affect a polarized distribution of adsorbed ions, particularly since the mobility of the adsorbed ions should be much less than that of free ions. The conclusions from the above discussion of absorption may be summarized as follows:- It seems advantageous to recognize that dielectric absorption may have several components due to different mechanisms :AI, the absorption due to free ions.-The discharge of the ions at the electrodes results in chemical changes which, in some cases, produce high resistances in the conduction paths and therefore space charges in the dielectric. Space charges would also result from inhomogeneities already existing in the dielectric. Azl the absorption due to adsorbed ions.-Elastic displacement or reversible changes in the distribution of ions adsorbed on inner surfaces under the influence of an applied electric field affords an explanation of many of the experimentally observed facts of dielectric absorption. A3, absorption due to moLecuZes.-If the dielectric contains some molecules with long relaxation times for the displacement of the charges within them or the orientation of the molecule as a whole in the electric field, a residual charge due to the molecules would result (cf. v. Schweidler); but the relaxation times connected with such processes would usually be expected t o be very short. The main characteristics of these several components of the absorption current are as follows: (I) With the exception of the free ion absorption due to electrolytically produced changes in the resistance of the dielectric, all of the components of the absorption current would probably decrease exponentially with time, but the values of the relaxation times would in general be different for each component. I n the case of the component due to adsorbed ions each layer of ions may have a different relaxation time. The total absorption current is therefore in general the sum of several components which decrease exponentially with time and also one which probably does not. (2) Unless the inhomogeneities are uniformly distributed, the absorption current due to free ions is accompanied by the formation of a non-uniform potential gradient in the dielectric, indicating the presence of a space charge, while the absorption currents due to adsorbed ions and molecules are not accompanied by the formation of a space charge. (3) Where there is a component due to the electrolytically produced changes in the resistance of the dielectric the apparent absorption current would not in general obey the superposition principle quantitatively on account of the change in the resistance of the dielectric with time of application of the voltage. The relative importance of the different components of the absorption current should depend on the nature of the material and the conditions. The JPThornton: Proc. Phys. SOC., 22, 186 (1910);Neumann: loc. cit., ref. 18. SJ Goldhammer: Z.Physik, 47,671 (1928).

DIELECTRIC ABSORPTION A S D DIELECTRIC LOSS

611

component due to electrolytically produced changes in the resistance of the dielectric is likely to predominate where the conductivity of the dielectric is high, either because of its high temperature, because of being exposed t o a high humidity in moisture-absorbing materials, or because of the presence of many interstitial conduction paths in crystals. Further, the adsorbed ion type of dielectric absorption is likely to predominate in a given dielectric in the initial stage of the absorption current while the electrolytically produced type of absorption may be the effect predominating after the current has flowed for many minutes or

Dielectric Loss In the most .general terms dielectric loss is the electrical energy converted into heat when an alternating voltage is applied to a material classified as a dielectric. It is given by E2G or IzR, where E is the r.m.s. value of the applied alternating voltage, G is the equivalent parallel conductance, I the r.m.s. value of the current, and R the equivalent series resistance. Part of this loss is due to the Joule heat corresponding to the direct current conductance but this part of the loss is usually negligible. That there is a component of dielectric loss not directly due to the direct current conductance has been inferred from the fact that the equivalent parallel conductance of a dielectric for alternating current is considerably greater than the direct current conductance. Some uncertainty is connected with the magnitude of the difference between these two conductances since the d.c. conductance in general depends on the time of application of the measuring voltage. It has been shown t h e ~ r e t i c a l l ythat ~ ~ dielectrics which show absorption, Le., a residual charge, in constant electric fields must also dissipabe electrical energy as heat when an alternating voltage is applied. I n some cases, moreover, it has been demonstrated experimentally that practically the whole dielectric loss is due to absorptio~Pand in other cases to d.c. conduction. Dielectric loss would therefore be expected to be a t least as complex as dielectric absorption if not more so. On the basis of the interstitial mechanism of conduction and absorption which has been described, dielectric loss would be expected to be divisible into the following main components: Li, that due to free ions; Lp,that due to adsorbed ions; LB,that due to the dielectric polarization of the molecules; this would exist even if there were no ions in the dielectric. Free Ion Dielectric Loss: This includes, of course, the Joule heat due t o direct current conduction. I n fact, Sinjelnikoff and Walther3’ and Joff 15~’ 34 The interpretation given by Goldhammer (ref. 18)of his experiments on the conductivitv of quartz IS similar to this in indicating that there are two processes, one rapid and the otKer slow, and that the back e.m.f. of polarization is not due t o space charges in the initial stages. a Schweidler: loc. cit., ref. 18. 36 Tank: loc. cit., ref. 21. 37 Sinjelnikoff and Walther: loc. cit., ref. I; JoffB: Ann. Physik, 48, 288 (1928).

612

E. J. MURPHY‘ AND H. H. LOWRY

state that they have found that if the direct current conductance is properly measured it explains all the dielectric loss, except that obviously due to inhomogeneity of the dielectric according to the Maxwell-Wagner theory. This conclusion has been adversely criticized by Schiller3*and by Smekal.39 The results of Sinjelnikoff and Walther may well be a special case and not of such general applicability as they suggest. For instance, we have found that in cotton a t low frequencies and high moisture contents the dielectric loss is completely accounted for by the d.c. conductivity when the latter is so measured that the error due to changes in resistance produced by the electrode reactions is avoided; but we find that a t humidities below 7 5 % the dielectric loss cannot be accounted for in this way.40 I n addition to providing a constant conduction current with its attendant I*R heat loss, free ions are able to produce dielectric loss in other ways. For instance, if the resistance of the conduction path is non-uniform, as when there is a high resistance a t one or both of the electrodes, the conduction path instead of being a pure resistance becomes equivalent to a resistance in series with a condenser, and the a.c. conductance is therefore greater than the d.c. conductance. The non-uniformity in the resistance of the conduction paths may be due to high contact resistances a t the electrodes or to the chemical products of the electrolysis associated with ionic conduction. I n dielectrics, such as textiles, paper, etc., whose conductivity is due practically entirely to the moisture which they contain, the free ions may contribute to dielectric loss also through losses associated with the electrolytic polarization capacity of the conduction paths. This is a quantity which has been studied independently in conducting solutions and is very large in some cases. It appears to be largely due to concentration differences and relatively high resistances a t the electrode^.^^ The Debye-Falkenhagen theory of the dispersion of conductivity and dielectric constant of electrolytic solutions42 also indicates that free ions such as exist in the conducting paths in moisture absorbing dielectrics should behave to some extent like a dielectric, owing to the “ionic atmosphere” which surrounds each ion. That is, the free ions carry not only a non-condensive conduction current but also to a small extent a complex current with a displacement current component and a conduction current component, both dependent on frequency, because of the formation of these ionic atmospheres. It is to be concluded therefore that, particularly in dielectrics whose conductivity is due mainly t o moisture, free ions can contribute to dielectric loss in several ways: by the constant direct current conductance which they produce; by the interactions between free ions (Debye-Falkenhagen effect) ; by the polarization capacity generally involved in electrolytic conduction, 8s 89

Schiller: loc. cit., ref. I. Smekal: Z.techn. Physik, 6,561 (1927).

Murphy: J. Phys. Chem., 33, 200 (1929). See Fig. 4. “Banerji: Trans. Faraday SOC., 22, 1 1 1 (1926). Debye and Fakenhagen: Physik. Z., 29, IZI (1928);Sack: 29,627 (1928);Zahn:Z. Physik, 51, 351 (1928). (0

DIELECTRIC ABSORPTIOK AND DIELECTRIC LOSS

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at least in solutions; and by the prior existence, or production by the current, of non-uniformity in the resistance of the conduction paths. All of these factors except the first produce an equivalent parallel conductance and capacity which varies with frequency in a somewhat similar general manner to the variations in equivalent parallel conductance and capacity observed in dielectrics. Dielectric Loss due to Adsorbed Ions: The way in which adsorbed ions could contribute to dielectric loss is readily evident from Fig. I-B, and from the circuit of Fig. 2-B, which was shown in connection with dielectric absorption to represent the electrical effect of the redistribution of ions on the surface of the structural unit by which they are adsorbed. When an alternating voltage is applied to such a system, the adsorbed ions will move back and forth on the surface of the structural unit t o which they are attached; the motion of these ions contributes to the alternating current conductance and capacity but not to the direct current conductance. It would be expected that the dielectric loss associated with this polarization of the ions adsorbed on the surface of a micelle or a crystallite would be greater than that associated with the polarization of a molecule because adsorbed ions probably share in the thermal motion as individuals, whereas the opposite charges of a molecule move as a whole in regard to thermal motion. The electrical effects of the adsorbed ions can most readily be seen from the equivalent circuit of Fig. 2-B. As pointed out in the discussion of dielectric absorption, the elements of this circuit are equivalent to the molecules having different time constants in von Schweidler’s theory, which can therefore be applied without modification to adsorbed ion dielectric loss in accordance with the mechanism proposed here. Molecular Dielectric Loss: The types of dielectric loss so far discussed depend upon the existence of ions, either free or adsorbed, in the dielectric, But electrical energy can be transmitted through a dielectric as a displacement current even if it contains no ions, the energy being transmitted from molecule to molecule through the dielectric by means of the forces due to the electric polarization of the molecules. These electrical forces would tend to produce mechanical displacements of the molecules which would in general be accompanied by some loss of energy as heat due to damping. The outstanding theory which involves what may be called molecular dielectric loss is deb ye'^^^ dipole theory, which has proved to be a valuable means of investigating the structure of molecules. According to this theory the molecules of some dielectrics have permanent electric moments and the orientation of these dipoles in the gaseous or dissolved state by an electric field contributes to the dielectric polarization and is also accompanied by the absorption of electrical energy as heat. Debye has shown that with certain simplifying assumptions the frequency at which the absorption is a maximum may be calculated from the physical constants of dielectrics with qualitative agreement with experiment. u Debye: Verh. deutsch. physik. Ges., 15, 777 (1913).

614

E. J. MURPHY A S D H. H. LOWRY

Discussion: The main facts regarding dielectric loss which must be explained by any proposed mechanism are the form of the dielectric loss-frequency curve, the apparent capacity-frequency curve, the loss angle-frequency curve, and the effect of temperature and voltage on these curves. With the exception of the Joule heat loss, all of the mechanisms involved in the components of dielectric loss discussed in the preceding pargraphs can be approximately represented by somewhat similar systems of resistances in series and parallel with capacities, and they should therefore all be characterized by approximately the same general type of variation of capacity, dielectric loss and loss angle with frequency. The existence of these several components of dielectric loss described above provides an alternative physical interpretation of the several characteristic time constants introduced in the Maxwell-Wagner theory of dielectric absorption and loss to account for the experimental facts and attributed by Wagner4' to the presence of several different types of impurities in the dielectric. The application of the ideas developed above to the behavior of typical commercial dielectrics will serve to illustrate the advantages of recognizing the complex nature of dielectric loss and particularly the contribution of the adsorbed ions. It has been fou'nd that dielectric loss in cotton is greater the greater the salt content of the cotton.45 This was found to be true not only of the range of humidities where the dielectric loss was shown to be almost entirely due to d.c. conduction but also in the range where it was demonstrated not t o be due to d.c. conduction. I n the latter range of humidity the potential gradient was also unchanged even by an application of a direct voltage for some minutes. These observations can readily be interpreted in terms of the adsorbed ion hypothesis, since the adsorption of the ions by the cellulose micelles would increase with the total number of ions available and the dielectric loss due to adsorbedions would therefore be greater the greater the salt content of the cotton. As another example we may consider the behavior of such substances as rubber and beeswax. TTagner46found for these substances that the loss angle when platted as a function of temperature has a maximum, and that this maximum is displaced toward higher temperatures by increasing the frequency. Curtis and collaborators47 have also found that on increasing the sulphur content in rubber both the power factor and the capacity at first increase, reach a maximum and then decrease while at the same time the hardness, density, and d.c. resistivity increase continuously. Kitchenh8 found that the maxima are displaced to lower sulphur contents the higher the frequency. Since both a decrease in sulphur content and an increase in temperature cause an increase in softness in rubber, this is analogous to the behavior found by TTagner with respect to the variation of power factor with

'' K. W

Wagner: Arch. Elektrotech., 2, 371 (1914); 3, 67 (1914). Murphy: loc. cit., ref. 40. Fig. 4. 45K. W.Wagner: loc. cit., refs. I and 44. '7 Curtis, McPherson and Scott: Sci. Papers, Bur. of Standards, 22, S o . 560 (1927). 48 Kitchen: loc. cit., ref. I. 46

D I E L E C T R I C A B S O R P T I O S A S D D I E L E C T R I C LOSS

6Tj

temperature. Kitchen proposed an explanation of this in terms of the Debye dipole theory; but, since rubber, owing to its colloidal structure, is a material in which the effects of adsorbed ions ought to be particularly prominent, it appears worth while to attempt an alternative explanation of this phenomenon in terms of the adsorbed ion hypothesis. The fact that for the first increments of sulphur the capacity increases while the d.c. conductivity decreases, suggests that the ions which take part in d.c. conduction a t lower sulphur contents become adsorbed as the sulphur content is increased because of an increase in the strength of the adsorptive forces-which may perhaps be inferred from the increase in hardness. This would have three effects. It would tend t o increase the component of capacity due to adsorbed ions because of the increase in their number, but at the same time it would tend to decrease it by reducing Lhe polarizability of the adsorbed ions, because the amount of displacement of the adsorbed ions produced by a given electric field would decrease as the strength of the adsorption forces increases. Further, in accordance with previous assumptions, it would tend to increase the frictional resistance to displacement of the adsorbed ions by the electric field. In accordance with previous considerations it will be assumed that the unit of the physical mechanism of conduction in rubber, i.e., the elements of structure (micelles) with their adsorbed ions, is equivalent electrically to the circuit of Fig. 2-B. The equivalent parallel capacity of this circuit is

the equivalent, parallel conductance

and the power factor,

w = Z H x frequency; j = d?; C1, . . . C, and R 1 . . . R, have the same significance as in Fig. 2-B. I n the remainder of the discussion only one layer of adsorbed ions will be considered for convenience. As the sulphur content increases R1 and Ci increase, and the relaxation time RICl therefore also increases. Equation ( I ) shows that while (RIClw)? is less than I , increasing the sulphur content causes C t o increase but when (RIClw)*becomes larger than I , C decreases with increasing sulphur content, thus explaining the maximum in the capacity-composition curve. A further influence tending to cause this maximum is the decrease in the polarizability of the adsorbed ions with increasing strength of the adsorptive forces. Equation ( I ) also shows that the maximum will occur a t a smaller relaxation time (i.e,, sulphur content) the higher the frequency.

616


The effect of changes in sulphur content on the power factor is evident from equation ( 3 ) . I n this equation, since rubber is a good insulator, I/Rd.c. is negligible in comparison with the second term in the numerator except where the conductivity is high, as a t high temperatures. The imaginary term is the larger of the two terms in brackets in the denominator since the observed power factors are only a few percent. The power factor is therefore approximately RiC1'W

I

Since RlCl increases with increasing sulphur content, the power factor increases with increasing sulphur content when ( R 1 C 1 ~ )is2 less than I , but decreases with increasing sulphur content when (RIC1u)2 is greater than I . As in the case of the capacity the maximum is displaced toward lower sulphur contents by an increase in frequency. The variation of power factor with frequency is also evident from equations ( 3 ) or (4). Where ( R I C 1 ~ )isz less than I the power factor increases approximately in direct proportion to the frequency, but passes through a maximum, and for very high frequencies is approximately inversely proportional to the frequency. The variation of equivalent parallel capacity with frequency is given by equation ( I ) . For low frequencies the capacity is C, C1, but it decreases with increasing frequency, becoming C, for large values of o. That is, a t high frequencies the capacity term due to adsorbed ions, or similar processes involving long relaxation times, becomes zero and only the capacity due to the polarization of the charges within the molecules is left. The main characteristics of the variation of power factor and capacity with frequency, temperature and sulphur content (in rubber) appear to be consistently explained by a mechanism electrically equivalent to the circuit of Fig. 2-B. However, the Debye dipole theory and also the MaxwellWagner theory of dielectric absorption lead to equations which yield types of Variation of capacity and power factor with frequency which are very similar to those derived above. Results similar to the above could therefore probably also be obtained by assuming that adsorbed ions are equivalent in some of their electrical effects to the dipoles of the Debye theory.* An advantage of the adsorbed ion explanation is in explaining the increase of capacity with increasing sulphur content. This was explained by Kitchen as due to an increase in the average dipole moment by the formation of unsymmetrical sulphur-rubber compounds. A distinction between this mechanism and the adsorbed ion mechanism could perhaps be made by investigation of the effects

+

* I n the theory of dielectric polarization three types of polarization are recognized (L. Ebert: Z. hysik Chem., 113, I (1924)), Pa the displacement of the electrons within the molecule, the dlsplacement of the atoms within the molecule, P, the orientation of the molecule 88 a whole where it has a n electric moment. The present suggestion essentially amounts to adding a fourth type of polarization Pi, the polarization due to adsorbed, or simdarly bound ions.

DIELECTRIC ABSORPTIOS AND DIELECTRIC LOSS

617

of voltage, for the adsorbed ions should be desorbed with increasing voltage with a consequent increase in d.c. conductivity and possibly also other measurable effects. While the mechanisms developed for explaining dielectric loss in solid dielectrics are not directly applicable to liquid dielectrics, there appear to be reasons for expecting an analogous mechanism whereby the ions in a liquid dielectric can contribute to the a.c. conductivity but not to the d.c. conductivity. The process in liquids which is most nearly analogous t o the adsorption of ions in solids is the association of ions with neutral molecules (e.g., solvation). Both in liquids and in gases49studies of ionic mobilities indicate that it is probable that the ions condense neutral molecules around them and become fairly large aggregates. The effect of this is only to reduce the mobility of the ion and hence reduce the d.c. conductivity, for unlike the similar process in solids, the neutral particles to which the ions are attached are free to move under the influence of an electric field. But if both positive and negative ions have neutral molecules condensed around them, and if the concentration of ions in the liquid is determined by a kinetic equilibrium between the processes of ionization and recombination, it appears probable that oppositely charged aggregates would tend to become associated and thus form a dipole; for the oppositely charged ions mould exert an attraction upon each other but would be prevented from combining by the neutral molecules of the aggregates of which they form the nuclei. Such aggregates might be fairly stable because their formation would probably involve a decrease of potential energy. They would form “ionic dipoles” of molecular dimensions or larger, and would differ from molecular dipoles in that their number would depend on the concentration of ions in the liquid. It is possible that the effects of this type of dipole could explain some of the electrical properties of liquid dielectrics. Dipoles of this kind might contribute to the explanation of the relationships between d.c. conductivity and dielectric loss, and would also be expected to be readily separated into their constituent ions by an increase in voltage. Consequently, the conductivity would increase with increasing voltage because of the transformation of some of the dipoles into free ions which would accompany the increase in voltage. W e n found such an increase of conductivity with voltage in electrolyte^.^^ Gyemantso has observed a further effect in high-resistance liquid dielectrics which lends itself t o ready explanation in these terms. He found that while the conductivity of certain high resistance liquid dielectrics increases with increasing field strength in the direction of the field, it is unaffected in the direction normal to the field. This observation may be readily explained in accordance with the above mechanism and may be regarded as contributory evidence in favor of the role of adsorbed or associated ions in conduction phenomena in liquids. As already stated, there is evidence that 4g

Loeb: Phys. Rev., (2) 32, 81 (1928). X e n : Ann. Physik, (A) 83, 327 (1927);J0o.s and Blumentritt: Physik. Z., 28, 836 Gyemant: 29, 289 (1928);Joos; 29,570 (1928).

(1927);

618


in some cases liquids may be associated into aggregates which may be regarded as ionic dipoles and which could adsorb ions. These ionic dipoles with their adsorbed ions would differ from the free ions in that they would not give the medium an isotropic conductivity for two fields of different strengths, applied a t right angles to each other, but would become oriented in the field and the adsorbed or associated ions would be liberated in larger numbers in the direction of the larger field than in the direction of the smaller field. This is very similar to the explanation of the phenomenon proposed by Gyemant who assumed the presence of pairs of associated ions which are neither chemically united nor free. Since it is generally recognized that association is present in liquids and that ions form effective centers for association and that aggregates containing as many as 1 0 5 molecules are of frequent occurrence it is probable that the dipoles resulting from the association of ionic aggregates of opposite sign may frequently be factors in determining the dielectric behavior of liquids. The above discussion of dielectric loss may be summarized as follows: I t has been shown that dielectric loss may involve in some cases three independent mechanisms. Debye has shown that there is a certain dielectric loss associated with molecular polarization. It is evident that the molecular dielectric loss is not dependent upon the presence of ions of any kind and therefore this theory could not be applied to a material unless correction were first made for the ionic dielectric loss. A correction based on the d.c. conductivity may be insufficient since this takes account only of the free ions. Whether the molecular dielectric loss or the ionic dielectric loss predominates in any material will depend not only on the material itself but also on the temperature, voltage and frequency of the measurement. If it proves feasible to separate dielectric loss into its components they may each in turn be correlated with other physical properties which can be independently measured. Molecular dielectric loss may be correlated with viscosity in liquids, as has been done for example in Kitchen’ss1 work on rosin oil and castor oil, and in solids perhaps with such properties as the cohesion and thermal conductivity, so that in this way the dielectric loss may perhaps become as useful an indication of the structure of solids and liquids as the dielectric constant is of molecular structure. The adsorbed-ion dielectric loss, on the other hand, may be associated with the dimensions of structural aggregates containing many molecules, with the influences tending to cause ionization, and with the phenomena of adsorption. The free-ion dielectric loss may in some cases be related to the properties of electrolytic solutions, such as polarization capacity and direct current conduction. It seems necessary to relate didectric loss to other independently measurable physical properties in order to distinguish between the possible physical mechanisms which yield a similar type of variation of power factor and capacity with frequency, temperature, etc. This division indicates that the apparent successes of both molecular and ionic theories of dielectric loss may not be contradictory, but due to 61

Kitchen: loc. cit., ref. I.

DIELECTRIC ABSORPTIOS AND DIELECTRIC LOSS

619

experimental conditions being such that molecular dielectric loss is being studied in the one case and ionic dielectric loss in the other; low conductivities, low temperatures, low humidities, and high frequencies would favor the first mentioned condition and the opposite the second condition.

Summary I n most solid dielectrics direct-current conduction appears to take place not uniformly through the material, but through a system of conduction paths of sub-microscopic dimensions dispersed in the insulating medium in a manner related fundamentally to the structure of the material. This conclusion IS chiefly based upon Smekal’s investigations of crystalline dielectrics and our own results for textiles. Smekal shows that crystalline dielectrics are composed of ideally-formed structural units, between which they are imperfectly formed regions which have a higher conductivity than the ideal parts of the lattice. In materials such as cotton, conduction takes place through water which is probably condensed in the interstices between the cellulose micelles, An important property of such “interstitial conduction” systems is that ions would undoubtedly be adsorbed by the interface between the insulating units and the relatively conducting interstitial medium, and since the interfacial area would be large as compared with the volume of such conduction paths, the influence of these adsorbed ions on the electrical properties of the dielectric would be expected to be very important in some cases. The ions may be regarded as free to move over the surface of the particular structural unit by which they are adsorbed but not to migrate to adjacent structural units. The application of an electric field produces a polarized distribution of the ions adsorbed on the surface of each structural unit and the ions return to their normal distribution after the removal of the electric field. The electrical effect of the adsorbed ions is therefore similar to that of a dipole, and they produce a kind of “dielectric” polarization. According to this picture of the structure of a dielectric, free ions, adsorbed ions, and neutral molecules may each contribute to the total dielectric absorption (residual charge) and dielectric loss, and the relative prominence of each of these components should depend on the type of dielectric, the temperature and other factors. The characteristics of dielectric absorption and loss are discussed from the point of view of this division. The form of the absorption current-time curve can be explained by the following considerations: (a) If the structural units of the dielectric are surrounded by an atmosphere of adsorbed ions which diminishes in density with distance from the interface, each layer of ions can be regarded as having a different time of relaxation for the polarized distribution produced by an electric field. The sum of the absorption currents due to several layers of ions, as well as those due to inhomogeneity in the resistance of the dielectric, could give the observed curves. (b) The latter stages of the absorption current are probably due to the electrode reactions which accompany free ion conduction.

620


The superposition principle can readily be given a physical interpretation if it is assumed that dielectrics contain ions adsorbed with degrees of intensity ranging over wide limits, the relaxation time of the ions increasing with the strength of the adsorption. The important fact that in some cases dielectric absorption is accompanied by the formation of a space charge and non-uniform potential distribution and in others not can be explained if the absorption in the first case is due to free ions and in the second to adsorbed ions. For the residual charge due to adsorbed ions, according to the present mechanism, does not produce a space charge or non-uniform potential gradient, while that due to free ions does. Several different ways in which free ions may produce dielectric losses are discussed. The ways in which adsorbed ions and neutral molecules contribute to dielectric loss are also discussed. The existence of layers of adsorbed ions with different relaxation times provides a new physical interpretation of von Schweidler’s theory of dielectric absorption and loss wherein he attributes to the molecules a wide range of relaxation times. The presence of components of dielectric loss due to free ions, to adsorbed ions and to molecules, each component varying with frequency in a somewhat different way, provides an alternative physical interpretation of the characteristic time constants which Wagner attributed to different types of impurities. The observation that dielectric loss in cotton is very sensitive to changes in the amount of water-soluble salts in the material even a t humidities where the dielectric loss was shown not to be due to direct current conduction may be interpreted as a strong evidence of the existence of dielectric loss due to adsorbed ions. An attempt is made to explain variations in power factor and dielectric constant in rubber with changes in sulphur content on the adsorbed ion hypothesis. I n liquid dielectrics ion of opposite sign which have neutral molecules condensed around them may become associated to form “ionic dipoles,” whose electrical effects may be somewhat similar to those of adsorbed ions in solids. An important property of adsorbed ions in solids or ionic dipoles in liquids is that as the strength of the applied field is increased adsorbed ions should become “desorbed” and ionic dipoles separated into their constituent ions. This affords the possibility of relating the changes in the conductivity of dielectrics with voltage to other electrical properties such as absorption. Bell Telephone Laboratories, New York, N . Y .

The Complex Nature of Dielectric Absorption and Dielectric Loss

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