Dielectric Losses in Polar
Liquids and Solids 8.0.MORGAN Bell Telephone Laboratories, New York, N. Y.
D
IELECTRIC loss is the energy dissipated as heat i n a dielectric when it is in an electric field. Losses due to dipoles represent only one of a number of possible means by which energy may be dissipated in a dielectric; there may be losses due to free ions and also due to dielectric polarisations other than dipole polarizations. However, in many inat,erials dipoles are an important source of loss; it is tho purpose of this p p e r t.o consider some of the typical cases of dipole loss and to point out some of the rclaLions bctvecn cheniical conipsition and dipole loss which follov from the recent experimental and theoret.ics1 study of dielectric brhavior.
Equations The power loss in a dielectric-- -forexample, in a condenser is given by tlie equation: or where
~~
W = A'I sin 6 W = EzG = cffectivc voltage = offeetivc current 6 = loss angle of the dieleetrio G = t,otal conductance
E I
If the energy dissipation is regarded as occurring uniformly throughout the dielectric, the power loss per cubic centimeter may he expressed in terms of the dielectric constant, e, and loss angle of the material, 6, for the alternating current case by tlie equation: W = 55.5 e' tan 6 / V 2 X lo-$ na!ts (3)
Equations of the same form as those given by the Debye dipole theory can be used to express the frequency variation of dielectric constant and loss factor for any dielectric polarization of long relaxation time-i. e., corresponding t o power or radio frequencies. Some of the consequences of these equations are discussed. The Debye theory provides a more simple interpretation of the constants expressing the values of e., e m . and T than is possible at present for other polarizations. Curves are given showing the dielectric loss factor for pure polar liquids and solids, as well as for commercial insulating liquids known to contain dipoles. These illustrate the effect of chemical structure upon dielectric properties and also the behavior of the loss factor for different types of transition from the liquid to the solid state.
when:
1
= frequency 1' = voltage gradient, kv. per mm.
The rlerivation of these equations i s clearly presented in a review by Hartshorn (5). The description of dielectric properties in terms familiar to engineers, who arc perhaps the ones most concern& about dielectric loss, is facilitatetl by tlie use of an equivalent circuit such as shown in Figure 1, in which C represents the equiva-
lent parallel capacitance of the dielectric and 0 its equivalent parallel conductance. The admittance or reciprocal impedance of such an equivalent circuit is given in terms of the complex quantities customarily used in circuit analysis (4, 8)by Equation 4. 273
VOL. 30, NO. 3
INDUSTRIAL AND ENGINEERING CHEMISTRY
274
Y
where i = w
=
G
=
+ iwC
(4)
fl
2~frequency
If e is considered as a complex quantity given by e
€1
- is”
(5)
then the admittance may also be expressed as Y = iwcoe
= i,C,(El
- id’) = w c o (e”
+ id)
(6)
From the equivalence of Equations 4 and 6, e’ or the real part of the complex dielectric constant is: €I
c/co
=
capacity of condenser containing dielectric Co = capacity of same geometric arrangement of electrodes in a vacuum (or, for practical purposes, in air)
where C
acts as a restoring force tending to keep the dipoles randomly oriented. Dipole polarizations are therefore temperature dependent, being greater a t low temperatures where the thermal motion of the molecules interferesless withorientation. The dipole polarization also depends upon the frequency, if the electric field is alternating, because a finite time is required for the dipoles to orient and they contribute t o the dielectric polarization only when the frequency is low enoughi. e., the period long enough-to permit orientation before the field reverses sign. The Debye theory expresses the relation between these quantities by the equation :
=
e”, the imaginary or dissipative part of the complex dielectric constant, is defined as: e“ = G/oCo
(If the conductance G is in mhos, the capacitance Co must be expressed in farads.) From the circuit analogy we obtain the familiar relation: (7)
Equation 7 is perhaps more familiar in the form E“
=
E )
tan 6
From Equation 3 it can be seen that e“ is proportional to the loss per cycle, and it is usually called the “loss factor.” The product E” f is proportional to the conductivity in Equation 2. It is in terms of the conductivity defined in this way-i. e., as a dissipation factor or in terms of the loss factor-that the dielectric loss due to dipoles will be described. The loss in a dielectric is, in general, made up of two parts: one is the energy dissipated by the motion of free ions and the other is that dissipated by the displacement of bound ions, the orientation of dipoles, or other absorptive types of dielectric polarizations. The equivalent parallel conductance of the dielectric is, then, the sum of two terms, Gr, the conductance due to free ions, and G p , the conductance due to dipoles or other dielectric polarizations. Although dielectric losses due to free ions and to other than dipole polarisations are often of considerable importance, it is the purpose of this paper to consider only those losses due to dipoles. The loss factor used for the remainder of the paper will be defined as: €11
G, = G - G/ ~
wco
wco
(8)
The dielectric loss factor is thus given in terms of quantities which can be measured directly on a bridge or other measuring e circuit. The Debye theory ( 2 , IO) is too familiar to need description; it has become so well established by the vast amount of study of the dielectric properties of materials of known chemical composition that it is now regarded as one of the most useful tools for the study of chemical structure. According to this theory a dielectric polarization results when an electric field is applied to any material containing dipoles that are able to orient. This is in addition to the dielectric polarization due to the displacement of electrons or atoms. The formation of this dipole polarization is due to the tendency of the dipoles to align themselves with the field, and its formation is opposed by the thermal motion of the molecules which
P , the molar polarization (the electric moment per unit field strength per mole of dielectric), is related to the dielectric constant by the Clausius-Mosotti equation and is the sum of two terms. The first is the part of the polarization due to electronic and atomic motions within the molecule. Such a polarization is present in all dielectrics whether polar or nonpolar. The second term, 4n-N
3 x - 3kT xp2 -
1
+1ior’
is the part of the polarization due to orientation of dipoles. N is Avogadro’s number, p is the electric moment of the molecule, k is the Boltzmann constant, T the absolute temperature, and T’ the time of relaxation of the dipoles. This term is complex and so the polarization must have a dissipative component. The real and imaginary (or dissipative) parts of the complex dielectric constant are given by the equations :
These equations express the variations of dielectric constant and loss factor with frequency in terms of three constants of the material: e., the static or low frequency dielectric constant; E , , the infinite or high-frequency dielectric constant; and r , the time of relaxation of the dielectric. Although these equations are similar to those derived by Debye for dipole polarizations (S), it should be pointed out that Equations 10 and 11 are not uniquely characteristic of dipole polarizations but are common to other types of absorptive polarizations (7) as well. It is theinterpretation of the quantities ea, e,, and r and of the temperature variation of re in terms of a particular molecular hypothesis that is the distinctive feature of the dipole theory. From Equation 10 it is apparent that the real part or ordinary dielectric constant varies with frequency between the limits-e, a t low frequencies where w l/.r-that have time to orient and so do not contribute to the dielectric constant. The change from the high to the low value of dielectric constant is a continuous decrease, as shown in Figure 2 which is the experimental curve for a glycol. For this particular material and temperature the dipoles are contributing a large and essentially constant amount to the dielectric constant (es = 38) a t frequencies below 100 cycles and practically nothing above 10 kilocycles, where the dielectric constant has decreased to the low value ( e , = 3) due to electronic and atomic polarizations. The difference (e8 - e m =
MARCH, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
35) is the part of the dielectric constant due to dipoles for this glycol. The dielectrics of most practical importance are organic materials such as oils, waxes, resins, textiles, and rubber, and for these materials the value of e m , which is determined almost entirely by electronic polarizations, is usually about 3. The electronic polarization is measured by the refractive index, n, which is related to the dielectric constant by the familar relation known as Maxwell's rule: c = n2
The fact that the refractive index for organic materials is usually between 1.4 and 1.8 sets the limits for e m in this type of material as being roughly between 2 and 3. 4
3
€
2
I
0 FREQUENCY IN K C
FIGURE2. CURVES OF DIELECTRIC CONSTANT, E',
AND
DI-
ELECTRIC LOSS FACTOR, e", VS. FREQUEI~CYFOR 2-METHYL-2,4-
275
case of a gas or dilute solution where the polar molecules exert no influence upon one another. For the liquids and solids with which we are concerned, it is the value of r , the time required for the polarization to form in the dielectric, in which we are interested.
Dielectric Loss and Chemical Composition One of the principal objects of this paper is to bring out the relations between dielectric loss and chemical composition which have been established by the measurement of the static and infinite frequency values of the dielectric constant. e m is, for all practical purposes, equal to the square of the refractive index. es is the sum of ern and a component due to dipoles. The study of the relation between electric moment and chemical composition is a familiar story ( I O ) . The results may be conveniently described by regarding each bond between two atoms or between groups of atoms as having a dipole moment associated with it. If these "bond moments" are regarded as vectors directed along the bond, then the polarity of the molecule is given by the vector sum of the bond moments for the molecule. Nonpolar molecules are then described as those in which the sum of these vector or group moments is zero, and polar molecules are all others in which the resultant moment is different from zero. Methane and carbon tetrachloride are nonpolar because they each contain four equal vectors directed a t tetrahedral angles, the
PENTANDIOL AT -60" C .
Dashed curve calculated from Equation 10
The dielectric loss factor according to Equation 11 should approach zero a t both high and low frequencies and have a maximum a t the frequency where w = 1/r. The value of the loss factor a t the maximum should be 6''
mnx.
= '/z
(€8
- Em)
(12)
The E " curve of Figure 2 shows the variation with frequency of the loss factor for the same glycol. I n this and the other examples given in this paper the loss factor is that due to dielectric absorption alone; the contribution of free ions to the conductivity, which is independent of frequency, has been subtracted as in Equation 8. From Equation 12 and the above statement that e m is usually about 3, it is apparent that the maximum value which the loss factor can have is large for materials with a high static or low-frequency dielectric constant. For materials with a low static dielectric constant the maximum value of the loss factor must be small, and e m becomes important in determining its exact value. The loss due to dipoles is large only in a certain range of frequencies-i. e., where the frequency of the applied field has a value not very different from f = - The relaxation 2nr.
time r in Equations 10 and 11 is related to the r' of Equation 9 b y the relation:
where T = time of relaxation of dielectric T' = time of relaxation of polar molecule The latter is expressed by Debye in terms of molecular constants by the equation 7'
where
= {/2kT = 4 r p a a / k T
(14)
internal friction coefficient p = coefficient of viscosity a = radius of molecule =
The use of the ordinary coefficient of visoscity for expressing the internal friction coefficient is permissible only for the
APPARATUS FOR IMPREGNATING PAPERIN VACUUM,USED IN CONNECTION WITH DIELECTRIC STUDIES
INDUSTRIAL AND ENGINEERING CHEMISTRY
276
resultant moment in each case being zero. Chloromethane, on the other hand, is polar because the carbon-chlorine moment is considerably greater than the resultant of the three carbon-hydrogen moments, On this view certain groups, such as nitro or cyano, must be assigned large vector moments since the substitution of one such group for hydrogen in a nonpolar hydrocarbon such as methane or benzene results in a polar material with a large dipole moment and dielectric constant. Other groups, such as methyl, have only small vector moments, and their substitution for hydrogen produces a relatively small increase in dielectric constant. Table I gives the values of the group or vector moment which experiment has shown should be assigned to each of the more important atoms or groups for their substitution in benzene and ethane.
with the highest dielectric constants, although nitrobenzene with the highest moment of the group does not have the highest dielectric constant. For the hydroxy compounds there is a large progressive decrease of dielectric constant from methyl alcohol to phenol, although in each case the electric moment is practically the same. The moments of the methyl, ethyl, and cyclohexyl chlorides are higher than those of the corresponding hydroxy compounds but the dielectric constants are lower. Only in the phenyl compounds is there an approximate relation between the value of the group moment and the dielectric constant of the liquids containing these groups. Even in the favorable cases the observed dielectric constant of the pure liquid is much lower than that calculated from Equation 9. For room temperature and for the static case this equation may be written in the form:
CeHs
C,Hs
NO: CN CHO COOCHa OH
3.9 3.85 2.75 1.8 1.7 1.2
3.2 3.4 2.4 1.7 1.7 1.2
M o m e n t of:
OCHa
Atom or Group
M o m e n t of: ClHs
CaHs
NHa
F
c1
Br
1.5 1.4 1.55 1.50 1.25
1.3 2:o 1.85 1.65
d
e - 1
TABLEI. COMPARISON OF MOMENTS ( X 1OI8) OF ATOMS AND GROUPS IN PHENYL AND ETHYL COMPOUNDS Atom or Group
VOL. 30, NO. 3
e-=-
+
(P2 20.7p2>
Calculating the dielectric constant of nitrobenzene from its electric moment by substituting in the right-hand side of this equation the appropriate values for density, molecular weight, electronic polarization, and electric moment gives for nitrobenzene, for example, (e - l)/(e - 2) = 3.4. This is an impossible result, since for positive values of E the quantity (E - l)/(r 2) never has a value greater than 1, which it approaches as E approaches 0 3 . A similar calculation for chlorobenzene gives (E - 1 ) / ( ~ 2) = 0.74,from which E =E 9.5 as compared to the observed value of 5.6. The lack of agreement between observed values of the dielectric constant of liquids and those calculated by the Debye theory from the electric moment has led to some question as to whether or not dipoles are the cause of the high dielectric constant and the losses in many complex commercial insulating materials. The difficulty arises from the use of the simple equation, which is rigidly applicable only t o gases, for the case of condensed liquids where molecular interactions obviously cannot be neglected. There appears to be little doubt that the high dielectric constants of nitrobenzene or
+
The values of group moments in Table I are somewhat different for the different hydrocarbons in which they are substituted. These values represent only the simple case of a single substituted polar group; the substitution of more than one polar group in the 'same hydrocarbon radical often results in moments which depart from the calculated values by large amounts. Thus in o-dichlorobenzene the observed electric moment is considerably smaller than that calculated for two carbon-chlorine vectors acting a t an angle of 60" from each other in the plane of the ring, either because the effective angle between the groups is widened by their mutual repulsion or because of induction effects.
+
Dielectric Constants In considering the dielectric loss, we are interested in the way in which the dipole moments of polar molecules are reflected in the static dielectric constants of liquids and solids. Table I1 presents data, taken for the most part from the literature, for typical polar groups substituted in methyl, ethyl, cyclohexyl, and phenyl radicals. TABLE11. COMPARISON OF MOMENTS AND DIELECTRIC CONSTANTS FOR TYPICAL GROUPS AT ROOM TEMPERATURE Group
---NOzP
*
CIHS
3.1 3.2
39 30
CeHi
3.9
34 l8
CHI
can
...
-OHP
1.7 1.7 1.7 1.7
-GI#
34 24
P
*
1.85 2.0
12.6"
16
2.1
8:4
10.3"
1.65
6.6
a Values at melting point.
1.0
0.8
0.2
0-6
-5
-4
-2
-I
I
0
LOG
2
3
4
5
6
WTO
FIGURE 3. TYPECURVES FOR VARIATION OF DIELECTRIC Loss FACTOR WITH FREQUENCY FOR DIFFERENT DISTRIBUTIONS OF RELAXATION TIME T~
The values of electric moment are those determined from measurements on gases or dilute solutions, and the values of dielectric constant are for the pure liquids at low frequency and a t room temperature except as noted. It is apparent that there is no simple relation between eIectric moment of the gaseous molecules and dielectric conatant of the liquid. No value of electric moment is available for nitrocyclohexane, but the methyl, ethyl, and phenyl nitro compounds which are among the organic compounds with the highest electric moments are also among those compounds
-3
is most prominent relaxation time.
chlorobenzene, for example, are due to the orientation and alignment with the field of dipoles in the liquids. This, however, is not free orientation as postulated by the original Debye theory for gases but is very much restricted orientstion because of the interaction between dipoles in the liquid; the restriction, however, is much greater for nitrobenzene than for chlorobenzene. This restraint upon the dipoles in the pure liquids is qualitatively similar to that obtained in many polar liquids on solidification. I n the solid state the polar molecules are, so to speak, frozen out; and where they
MARCH, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
277
dilute solutions for which the theory was proposed, is probably not justifiable for many liquids and certainly not for the materials in Table IIIC which are polymerized and contain particles of more than one size. If instead of a single value a distribution of relaxation times about some probable value is assumed, a modified theory (11) results which predicts that the maximum of E” should be less than ’/% (E* - e m ) by an amount which depends upon the density of the distribution. Figure 3 from Yager’s paper (11) shows that for a distribution constant b = a , corresponding to a single relaxation time, the maximum of has the value ‘/z (a em). For b = 1, which corresponds to a narrow distribution-i. e., to relaxation times which are not very different from one another-the ratio of the value of E ” mm., assuming a distribution of relaxation times to that for a single relaxation time, is only slightly less than 1. However, for b = 0.15, which corresponds to a large number of relaxation times having values very different 100 KC. E” from one another, the ratio of values of e”msr. is much lower than 1, and the curve is spread TEMPERATURE IN DEGREES C E N T I G R A D E out over a wide range of frequencies. CONSTANT AND Loss FACTOR us. TEMFIGURE 4. CURVESOF DIELECTRIC Surprisingly enough, the closest agreement PERATURE FOR CY-TERPINEOL AT 1 AND 100 KILOCYCLES between observed and calculated values of Erfmas. 0 100 kilocycles, 0 1 kilocycle is found in the alcohol, glycol, and glycerol group - - of compounds in Table IIIA, w h i c h cannot rotate, their dipoles cannot contribute to the dielecare polar because of the presence in the molecule of one tric constant. The theory has been modified by Debye (1) to or more hydroxyl groups. The experimentally observed valtake account of the dipole interactions, and he has concluded ues are from 80 to 90 per cent of the values calculated for a from several considerations that, as regards molecular orientasingle relaxation time. A similar result was reported for ice tion, the liquids behave as quasi crystals; i. e., the orientation by Murphy (6). This class of compounds is generally reand coupling of molecules in liquids are very similar to the garded as highly associated and might have beenexpected binding in solid crystals. to have aggregates of different sizes and hence a distribution of relaxation times. The data in Table IIIA do not refute the idea that these compounds are associated but they do Dielectric Loss Factor
-
The dielectric loss factor varies with frequency in the manner given by Equation 11. The magnitude of the loss factor of a material can no more be predicted from the value of the dipole moment than can the dielectric constant. This equation predicts, however, that the magnitude of the loss will depend upon the values of the static and infinite frequency dielectric constants. The experimental data bearing on this point are not numerous, but some representative values for pure materials and commercial insulating liquids have been compiled in Table 111. This table gives values of e,, e m , and E”,-., both observed and calculated. For most of the materials the data are given for the temperature a t which the maximum of eN was observed for a frequency of 100 kilocycles. Since it is seldom possible to secure data over a sufficiently wide range of frequencies to determine both ea and Em directly, extrapolation was necessary in the determination of some of the values in Table 111. I n no case is the probable error due to this cause large enough to change the calculated values of 6”msx. by large amounts. However, these and the values of e m are to be regarded as approximations. Agreement between observed and calculated values of exmar. is not evidence in support of the Debye theory but only of Equation 11, which applies equally well for any type of absorptive polarization. This equation, however, involves the assumption that the polarization has a single relaxation time-i. e., in the case of polar molecules that they all require the same time for orientation in an applied electric field or, conversely, to return to a random orientation upon removal of the field. This assumption, which suffices for gases or
~~~
TABLE 111.
~~
COMPARISON OF OBSERVED AND CALCULATED
VALUESOF
Substance
to
c.
E
”
~
~
~
. max..
--€‘I
ea
em
Obsvd.
Calcd.
A.
Alcohols, Glycols, Glycerol 59.5 3.5 24 Propylene glycol -75 3.2 Trimethylene glycol -90 66.5 28 2.7 -60 2-Methyl-2,4-pentandi 01 39 17 -32 3.0 Glycerol 58 20 9 2.5 4-Methylcyclohexanol 23 -35 50 2.5 3-Methylcyolohexanol 25.5 > 9 10 -30 2.5 2-Methylcyclohexanol 25 -10 3 27 > 10 ~. n-Propanol -10 21 3 5-7 Amyl alcohol B. Chlorinated ComDounds 2.7 2.1 -90 9.7 2.7 1.5 -15 6.6 0.97 2.7 5.2 +15
-
4.67 2.8 2.75 4.05 2.75 3.37 Rosin-Type Materials +45 17 2.8 +95 8.5 2.8 -10 4.28 2.54 +26 +40
C. Petrex Petrex resin 5 Ethyl abietate Abietic acid Dipolymer 1 Dipolymer 2 Rosin oil 1
+80
2% -17
+10
D.
+
Sucrose octaiicetate (glass) +75 Sucrose octabenzoate (glass) 85 -30 Terpineol glass) -50 Terpineol !solid) -70 Anethole (solid) -112 Mesityl oxide solid) -110 10 d,l-Camphor,($1 Bornyl chloride (SI 11) -120 -55 Cyclopentanol (8x14 III)
3 . 79 2.85 2.89 Solids 5.9 5.85 3.8 2.83 3.0 4.5 4.8 3.5 42
2 . 75 2.4 2.46 3.0 3.0 2.4 2.4 2.6 2.5 2.6 2.5 2.5
28 33 18 27.5 10.3 11.5 10.5 12 9 3.5 1.95 1.25
0.79 0.48 0.22
0.94 0.65 0.31
3.5 0.7 3 87
7.1 2 . 89 8 0
0.22 0.26 0.08 0.11
0.60 0.70 0.22 0.21
0.71 0.67 0.30 0.10 0.07
1.45 1.4 0.70 0.21 0.20 1.0 1.1 0.50 19.5
0.4
0.34 0.30 16.0
INDUSTRIAL AND ENGINEERING CHEMISTRY
278
VOL. 30, NO. 3
is about half the calculated value. The first value for terpineol was obtained on a sample which was somewhat impure and supercooled 10 to a glass instead of freezing. The second value is for a sample which had been purified 8 until i t crystallized, apparently completely, at E.' its freezing point. However, the dielectric con6 stant of the crystalline solid did not decrease to 2.4 (the low value for the glass) a t the freezing point but to 2.83, and a t a lower tempera4 ture a second decrease to 2.4 took place. This behavior, which has been observed in many 2 compounds, is shown in Figure 4. The values of eNmaX.are for the region of anomalous dispersion in the crystalline solid. Among the other materials showing this region of anoma6'(0.2 l o u s d i s p e r s i o n below t h e f r e e z i n g point are anethole and mesityl oxide (Table IIID). The observed values of for these com0 -180 -160 -140 -120 -100 -a0 -60 -40 -20 o 20 40 pounds are from one-third to one-half of those T E M P E R A T U R E IN DEGREES C E N T I G R A D E calculated. FIGURE5 . DIELECTRIC CONSTANT 9 N D DIELECTRIC LOSS F a C T O R O F dlT a b l e I I I D a l s o gives the data for dlCAMPHOR US. T E M P E R a T U R E AT 1, 10, AND 100 KILOCYCLES camphor and bornyl chloride, crystalline solids 0 Ascending, 0 descending temperature in which loss factor maxima are observed. Figure 5 shows the curves for d.Z-camohor which is typical of many of these solids in which polar molecules are indicate that the aggregates of molecules formed by such able to rotate (13). The last values in Table I I I D are for association must be limited to few sizes-for example, cyclopentanol in the solid state. The observed value is much dimers or trimers having relaxation times close to that of the more nearly equal to the calculated than are those of the monomer. These data are not consistent with the view other solids. Similarly, good agreement has been found for that the association results in aggregates of all sizes from solid cyclohexanol ( I S ) . It is of interest to note that the single molecules up to large aggregates. If large aggregates cyclohexyl alcohols give good agreement between observed of molecules are formed, it must be assumed that the rotating polar entity is not the entire aggregate but single or a t least small molecules rotating within the aggregate. 7.0 For the chlorinated aromatic compounds (Table IIIB) the 6.0 observed values of enmax. are roughly 70 to 80 per cent of 5.0 the calculated. These compounds are commercial mixtures E' and may contain both isomers and compounds of different 4.0 chlorine content so that a considerable spread of relaxation 3.0 times is not unexpected. For the rosin type of materials 2.0 (Table IIIC) the agreement is poorest; the observed values of e"max. are from one-third to one-half of those calculated. 150 n I 1 ; It is well known that these materials polymerize readily, and ' 1 1 , 1 25 they probably contain a large number of particle sizes. The 100 distribution of molecular sizes represents only one possible I E " 0.75 ! 1 , , ( explanation of the difference between experimentally ob1 1 ' served and calculated values of loss factor. The distribution of relaxation times may, as has been pointed out by Yager, result from a distribution of any of a number of factors which affect the relaxation time, such as particle size, particle t' shape, or internal friction. I n order for dipoles to contribute to the dielectric constant FIGURE 6. CURVES OF DIELECTRIC CONSTANT AND Loss FACTOR us. TEMPERATURE FOR FOURCHLORINATED DIand dielectric loss, it is necessary for them to be able to orient PHENYL COMPOUNDS with the field. Thus a difference between the magnitude of Values a t 1 kilocycle, except for sample 1 which has values f o r b o t h 1 dielectric constant and dielertric loss in liquids where orientaa n d 100 kilocycles. tion is easily poseible and solids where orientation is impossible is to be expected. I n most materials such a differand calculated values of enmax.,whether in the liquid or solid ence is observed ; the dielectric constant decreases from its state. The fact that for most of the solids the observed high value in the liquid state to a low value, equal to e m , values of enmax.are from one-third to one-half of the calculated a t or just below the freezing point. The high dielectric convalues suggests a distribution of relaxation times. This need stants observed in some solids give definite evidence, hownot necessarily imply a distribution of particle sizes but ever, that dipoles may also rotate in the solid. A review of may be due to differences in the internal frictional forces this behavior has been given by Smyth (9). which oppose the rotation of dipoles within the solid. I n Table IIID some values are given for certain solids I n every case the observed value of dielectric loss factor is typical of those whose molecules apparently rotate in the lower than that calculated from the theory which assumes a solid state with a degree of freedom comparable to that of the single relaxation time. I n many of the cases where this obliquid. These represent a variety of materials; sucrose served value is much lower than the calculated, the curve of octailcetate and octabenzoate are typical glasses formed by e " os. frequency is also spread out over a wide range of frethe melting of the crystalline solids. The observed eNmax 12
,,
I
,
AMARCH,1938
INDIISTHIAI, A I D EVGINEEHING CHEMISTRY
quencies, suggesting a wide distribution of relaxation times in these materials. In this paper attention has been centered on materials which have dipole mom e n t s and on frequencies and temperatures where these matcrials slioiv anomalous dispersion. The curve of Figure 2 may hc. regarded as typical of many OS these materials, except that tlie temperature and freqiicncy at which the cbxnge of dieiectrie constant from its high to its loa. valiie and the maxima of rlielcctric loss Eaetor o ~ c i i r will, i n general, be different Cor eaeli mat8crial; they arc determined l,? osity or iiiternal frictioii of the iliclectric. This is ilkstrsted in Figure F for foiiroliloriiiated diphenyls. Altlioiigli tliesr rnaterials are similar in ~ 0 1 1 1 position, they differ in viscos Yainple I, the least viscous, mobile liquid at room bempernturc; sample 2 is more viscoiis: sample 3 is so viscoos that it jiwt pours at rwrn ternperatwe; arid sample 4 is a brit,tle resin. Each has a region of anomalous dispersion at a different temperature; this region is higher, the more yiscous the material. One other Kioint brolig~ltollt in ~i~~~~(j is +,hat tilc of the maximum of the loss factor is greater, the greater tlie static or low-frequency dielectric constant of the material. Thus the magnitride of the dielectric loss, at least that part due to dipole absorption, is not iniiopeiiileiit of the dielectric constant hut is directly related to it; a high dielectric constant requires that at some frequency there he a large dielect,ric loss. The fact that in certain tvpes .. of materials the ohserved maxiinurn of e" is lower than the theoroticnl suggests thc application of the idea of a wide iIist~ri1~1t.iim of relaxation
27')
times to prorlucc lower values of power f a c t o r . H o w e v e r , the reduction of the maximum
valiie of loss factor by this means results in such a spreading out of the curve that the value at some lower or higher frequency may be made milch higher hy this means. The use of nonpolar materials would eliminate the possibility of m y d i e l e c t r i c loss from this source. Nonpolar materials, however, have low dielectric constants. The need for high capacitances in small voliimcs often requires the use of polar materials. This is possible w i t h o u t e n countering serious dielectric loss, if a proper choice of temperature ilnd frequencies is made so that ilie operating conditions are removed as far as possible from ttic regions of anomalous dispersion.
Literature Cited
(7)MurPtrs and Moraan, 8 e l l System Tech. d . , 16, 483-512 (1937). (8) Race, H. 15.. Phyr. Rev.,37,430-46 (1831). C , p., chern. Eev., 19, 329 (9) (io) Smgth. e. P., "Dieleotrie Constant, and M o l e d s r ~ t ~ ~ ~ ~ r , ~ ~ ~ . " h. C. S. Marrogrnph 55, N e w York. Chemical Catalog C o . , 111) W a1931. ~ ~ e rK, , ~,~,, i l ~Physili, ~ . 40, 817 (loin; YLIRpl,W,A,, Phy.*ics, 7, 434 (lYd6). (121 Whito and Morgan, .7. Am. C/,em. SOC.,57, 2078 ( 1 9 ~ ~ ) . (la1 Y a w and Morgan, I b d . 57. 2 O i l (1985). ~ i ~ , , ~ :u, ~ ~ ,~: .~ ~2 .~I'J:~,. , !
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