MICROWAVE ABSORPTION OF METALACETYLACETONATES IN BENZENE
3433
The Microwave Absorption of Several Metal Acetylacetonates in Benzene Solution’
by Ernest N. DiCarlo, Robert E. Stronski,2 and Charles E. Varga2 Department of Chemistry, Saint Joseph’s College, Philadelphia, Pennsylvania 19151 (ReceivedMarch 7, 1969)
Dielectric constants and losses have been measured at frequencies of 9133 and 25,680 MHz for benzene solutions of cobalt(II1) and aluminum acetylacetonates and at frequencies of 9133 and 24,560 MHz for benzene solutions of chromium(II1)and iron(II1) acetylacetonates. The microwave loss data have been used to calculate dielectric relaxation times and small apparent-moment values. The observed relaxation times, ca. 6 x 10-12 sec at 2 5 O , are much shorter than would be expected for orientation of a permanent dipole by rotation of molecules of this size and indicate an intramolecular relaxation mechanism. This fact, when considered together with other evidence which indicates zero permanent moments and very large atomic polarizationsfor these chelates, suggests that the small apparent-moment values, ca. 0.7 D, probably arise from atomic polarization. This is equivalent to saying that a considerable fraction of the total atomic polarization of each of these substancesappears to be associated with absorption in the microwave region while the remainder arises from the usual infrared absorption. In contrast, bis(acetylacetonato)mono(3-nitroacetylacetonato)chromium(III), Cr(acac)2(3-NOzacac),which has a relatively large permanent moment, was found to have a relaxation time about 20 times greater than those of the unsubstituted acetylacetonates investigated. The magnitude of the relaxation time, i.e., 115 )( 10-12 sec at 30°,indicates that the predominant relaxation mechanism of Cr(a~ac)~(3-NO~acac) is orientation of the permanent dipole in the applied field by molecular rotation. From the observed dispersion behavior of Cr(acac)2(3-NO~acac), a permanent molecular moment of 4.00 D has been determined which is in excellent agreement with the value, 3.99 D, obtained from a static dielectric constant study.
Introduction Recent s t u d i e ~have ~ , ~ shown that aluminum acetylacetonate in benzene solution exhibits considerable dielectric losses which are consistent with a very short dielectric relaxation time. This observation is quite significant in view of the large amount of evidence which favors a symmetrical structure for this chelate. X-Ray analysis has shown that the acetylacetone portion of the chelate ring is completely planar within the limits of accuracy of the data.6 Static dielectric constant investigations indicate a zero moment and a very large atomic polarization for this compound.6-1° Moreover, the previously observed microwave absorptions are much too large to be accounted for by the presence of polar impurities or dissociation of the aluminum chelate in s ~ l u t i o n . ~ Since the observed losses could not be readily explained as the relaxation losses of rotating permanent dipoles and the relatively short relaxation time indicates an intramolecular relaxation mechanism, it was suggested that the observed dielectric relaxation probably involves induced intramolecular polarizat i ~ n , i ~e . ,, ~atomic polarization. The present study was undertaken to obtain further evidence as to the possible relaxation mechanism. For this purpose, the microwave measurements have been extended not only to other probably symmetrical acetylacetonates but also to an acetylacetonate which is known to be polar so that a comparison of their respective relaxation behaviors could be made.
Experimental Section Apparatus. Dielectric constants and losses were measured at frequencies of 9133 and 25,680 (or 24,560) MHz employing the standing-wave method as developed by Heston, Franklin, Hennelly, and Smyth.” Figure 1 shows a block diagram of the experimental arrangement. The 9133-MHz apparatus and the 25,680-MHz apparatus12 have been set up in analogous manners. Monochromatic radiation is generated by a klystron (to which a square-wave reflector modulation of 1000 Hz is applied) and propagated along a rectangular guide (1) Research supported by the National Science Foundation under Grant GP-8464. (2) This paper represents part of the work submitted by R. E. Stronski and C. E. Varga to the Chemistry Department of Saint Joseph’s College in partial fulfillment of the requirements for the degree of Master of Science. (3) S. Dasgupta and C. P. Smyth, J . Amer. Chem. Soc., 89, 6632 (1967). (4) E.N.DiCarlo and R. E. Stronski, Nature, 216,679 (1967). ( 5 ) E. C. Lingafelter, Coord. Chem. Rev., 1,151 (1966). (6) E. N. DiCarlo, T. P. Logan, and R. E. Stronski, J. Phys. Chem., 72,1617 (1968). (7) I. E. Coop and L.E. Sutton, J. Chem. Soc., 1269 (1938). (8) A. E.Finn, G.C. Hampson, and L. E. Sutton, ibid., 1264 (1938). (9) J. McQueen and J. W. Smith, (bid., 1821 (1956). (10) J. W.Smith, “Electric Dipole Moments,” Butterworth and Co. Ltd., London, 1956,pp 262-263,276-279. (11) W. M. Heston, Jr., A. D. Franklin, E. J. Hennelly, and C. P. Smyth, J. Amer. Chem. Soc., 72,3443 (1960). (12) Measurements were also made with the latter apparatus a t a frequency of 24,560MHz. Hereafter, this experimental setrup will be referred to as the 25,680apparatus.
Volume 75, Number 10 October 1969
E. N. DICARLO,R. E. STRONSKI, AND C. E. VARGA
3434
-rl 3
Ill2
1 4
I 5
which sends a signal to a tuned amplifier and meter. A crystal detector mounted in the traveling probe samples the microwave energy in the primary arm of the setup and sends a signal to a highly tuned VSWR amplifier and meter. The dielectric cell (Figure 2a) consists of a standard section of solid coin silver (1/4 X l/z in. for the 25,680MHz apparatus and l/z X 1 in. for the 9133-RIHz apparatus) rectangular guide which is surrounded by a thermostatically controlled jacket which keeps the temperature constant to within 0.02” of the desired temperature. A mica window (0.0024 cm thick a t 25,680 MHz and 0.0050 cm thick at 9133 MHe) serves to separate the liquid dielectric from the remainder of the system. With the systems terminated in matched loads, the voltage standing-wave ratio, VSWR, was found to be 1.039 at 25,680 RIHz and 1.035 at 9133 MHz. (A VSWR of about 1.05 or lower indicates that the window is matched well enough to the system so that it will not introduce significant errors into the measurement. 11) A micrometer-driven open-circuit plunger, which is mounted in the cell, reflects the wave back into the guide and produces a standing wave. The plunger is constructed of brass with a quarterwave impedance transforming section filled with Teff on, a low-loss solid dielectric (see Figure 2b). In an effort to facilitate the discussion of errors, a brief description of the experimental procedure follows. In the standing-wave method for determining the dielectric constant, e’, of a low-loss liquid, the traveling probe is set to a minimum-power position with the The Journal of Physical Chemistry
liquid in the cell and the plunger at the cell window. The plunger is then moved upward, increasing the depth of the dielectric layer, until the first power minimum adjacent to the cell window is observed. The position of the plunger is recorded at identical power levels on each side of this minimum. The two readings are averaged to find the actual position of the plunger at this particular minimum. Similar readings are made at a higher position in the cell (the 14th minimum and the 10th minimum for the 25,680-MHa apparatus and the 9133-MHz apparatus, respectively), Ad, the wavelength in the dieIectric-filIed guide of the cell, is related to the measured distance, L, between the two respective minima by Ad
=e
2L m-1
___
where m is the ordinal number of the highest minimum from the dielectric-mica interface employed in the determination. It was found that by using relatively long cells and a micrometer-drive mechanism which enabled the position of the plunger to be known to 0.002 cm, Ad could be determined to an accuracy of 0.2% or better. For low-loss samples, e’ is given by €’
=
(ty+ (2J
where A, is the cutoff wavelength and A 0 is the freespace wavelength. Consideration of the possible sources of error involved in this technique has led to
MICROWAVE ABSORPTION OF METALACETYLACETONATES IN BENZENE estimated accuracies of k 0 . 3 and *0.2% at 25,680 (or 24,560) and 9133 MHz, respectively, for the E' determination. I n the standing-wave method for determining the dielectric loss, e", of a low-loss liquid, the power is minimized with the traveling probe with the liquid in the cell and the plunger at the cell window. The plunger is then brought up to the various successive minimum power positions and the 3-db width, Ax, of each minimum is measured (twice-minimum-power method). The reciprocal of the voltage standing-wave ratio, rAx/Xg, where A, is the wavelength in the airfilled cell, increases in value for successive minimum settings. For low-loss liquids, e" is given by (3) where n is the ordinal number of successive plunger settings starting from the window position and Axc are corrected (utilizing dissipation factors and attenuation constants) 3-db widths. It should be noted that the presence of the probe in the waveguide may be a serious source of error in low-loss measurements. l 3 If the probe penetrates too far into the guide (tight coupling between the probe and the wave), it will significantly disturb the waveguide mode resulting in measured standing-wave ratios which are low. (The latter is reflected in e" values which are too high.) If the penetration is not sufficiently deep, the amount of power sampled by the probe will be close to the noise level and again the determination of the 3-db widths will be incorrect. Between these two extremes there is a slight range of probe penetration which leads to the same results for e". A practical method for determining the probe penetration for which adequate microwave energy is sampled for the measurement with a minimum of coupling is to measure the variation of the loss of a sample with probe penetration. The probe depth should be set at some point between "a" and "b" (see Figure 3), where the slope of the curve of loss vs. probe penetration is very close to zero. This method is applicable to both sets of apparatus] but is only convenient to use at 25,680 MHz. With the 9133-MHz apparatus, a symmetrical wave pattern was used as the criterion of proper probe penetration. If the proper probe penetration is used, the accuracy of the measurement will depend, for the most part, on the accuracy to which the slope of nAx0/X, lis. n can be determined. The latter, of course, is greatly dependent on the number of 3-db widths which are measured. For the loss measurements reported in this study, 14 and 10 minima were employed at 25,680 and 9133-MHz1 respectively. All data were fitted by the method of least squares, employing the IBM 1620 computer. An error analysis of the present results has led to the following estimated accuracies in e": jzO.0001 or
3435
I I
I-
1
*2% (whichever is larger) at 25,680 (or 24,560) MHB and *0.00005 or 1 2 % (whichever is larger) at 9133 MHz. Materials. The substances investigated were obtained from (A) the J. T. Baker Chemical Co., (B) the Fisher Scientific Co., and (C) Professor M. Bursey, University of North Carolina. The source of each compound, the method of purification, and the melting point or the index of refraction are listed in Table I. Following purification, a carbon-hydrogen analysis (by Alfred Bernhardt Mikroanalytisches Laboratorium, Miillheim, West Germany) was performed on the following acetylacetonates. Anal. Calcd for Al(C5H,02)a: C, 55.55; H, 6.52. Found: C, 55.70; H, 6.86. Calcd for Cr(CgH70&: C, 51.57; H, 6.06. Found: C, 52.00; H, 5.96. Calcd for C O ( C ~ H , O ~ ) ~ : C, 50.57; H, 5.94. Found: C, 50.94; H, 6.05. Calcd for F ~ ( G H T O ~ C, ) ~ :51.01; H, 5.99. Found: C, 51.10; H, 6.12. Table I: Sources, Methods of Purification, and Melting Points or Refractive Index Compound
Aluminum acetylacetonate" Chromium(II1) acetylacetonatea Cobalt(II1) acetylacetonate" Iron(II1) acetylacetonate" Benzeneb Bis(acety1acetonato)mono(3-nitroacetylacetonato ) chromium(II1)'
Source
MP, 'C
A
193.4-193.8 214.2-214.6 213.0-213.8 181.2-181.4 (TL*~D 1.49786)
A A
A B
C
a Repeated crystallization from benzene-petroleum ether (bp 37-48') and drying under vacuum over phosphorus pentoxide. Reagent grade, thiophene-free benzene was fractionally distilled over sodium and stored over Drierite. ' Prepared and purified by Professor J. P. Collman, Stanford University. I t was dried under vacuum over phosphorus pentoxide immediately prior to measurement.
'
(13) Hewlett-Packard J . , 3 , no. 1,2. Volume 75, Number 10 October 1969
E. N. DICARLO,R. E. STRONSKI, AND C. E. VARGA
3436
Results and Discussion Unsubstituted Acetylacetonates. Cole-Cole arc plots14 could not be formulated with any degree of certainty due to the lack of significant frequency dependence of the dielectric constant, ca. 1% from 1 to 25,680 MHz for the most concentrated solutions studied and the fact that only two microwave frequencies were employed in the present investigation. Therefore, the absorption was examined solely in terms of the dielecto be aptric losses by assuming the Debye plicable. According to the theory of Debye, the slope a”, de“/dcz, where e‘‘ is the dielectric loss and cz is the mole fraction of solute, is given by
Table 11: Slopes, a’(, for the Dependence of the Dielectric Loss of Solutions on Mole Fraction of Solute, Relaxation Times, 7, and Effective Moments, 1.1 --a”Temp, ‘C
25,680 MHz
7 , 10-l2sec Aluminum Acetylacetonate (0-0.0425)
25 40 60 25 40 60
0.325 0.285 0.256
r = [
alttwz a21101022
- az”w1 ---]”a
-
Ull’W2W12
(5)
where all’ and az” refer to the measured values of a” at frequencies of o1 and w2, respectively. It should be noted that for a reliable estimate of T (assuming the dispersion does in fact follow the Debye form of the absorption curve) the two frequencies employed in the loss measurements must not be far removed from that corresponding to the maximum of absorption.l6 The unsubstituted acetylacetonates studied satisfied the latter condition. When a value for T has been determined in this way, the moment associated with the dispersion mechanism can be calculated from the a” value a t either frequency using eq 4. Table I1 contains the pertinent microwave data as a function of temperature for the unsubstituted acetylacetonates investigated. Also tabulated in parentheses immediately following the name of the chelate is the concentration range in mole fraction for each set of solutions examined. The error in the r results obtained at 2.5’ was estimated to be ca. f 20%. The values of r deduced from the parameters listed in Table I1 were checked by comparison with the values of r calculated from the dielectric loss data for each concentration. No significant variation of relaxation time with concentration was observed. Since at 2.5‘ the measuring frequencies are closest to the frequency corresponding to maximum a’’, the T values at this temperature are probably somewhat more reliable than those at the higher temperatures. For this reason only the p values a t 25” (found from eq 4) are tabulated.’’ The Journal of Physical Chemistry
0.206 0.168
0.131
6.2 5.7 4.5
Cobalt(II1) Acetylacetonate (0-0.0274) 0.248 0,147 5.7 0.224 0.123 5.1 0.176 0.093 4.8 24,580 MHz
where €1, dl, and M I , are the dielectric constant, density, and molecular weight, respectively, of the solvent, 1 is the effective moment associated with the observed loss, r is the time of relaxation of solute molecules, and o is the frequency in radians per second. It follows from eq 4 that r can be estimated at any given temperature from loss measurements at only two frequencies by employing the expression
9133 MNz
Iron(II1) Acetylacetonate (0-0.0429) 0 528 0 343 6.4 0.477 0.283 5.7 0.482 0.243 4.3 I
D
0.68
0.60
9133 MHz
Chromium(II1) Acetylacetonate (0-0.0395) 25 0.357 0.228 6.3 40 0.329 0.200 5.9 60 0.274 0.126 4.2 25 40 55
p,
I
0.72
0.87
As seen from the data in Table 11, all of the unsubstituted acetylacetonates investigated exhibit significant microwave absorption in benzene solution. Static dielectric constant studies indicate zero permanent moments and very large atomic polarixations for these compounds.6-10 X-Ray investigations aIso favor the assignment of symmetrical structures for these molecules, (X-Ray analysis has shown the six-membered rings in ferric acetylacetonate to be completely planar within experimental error. Therefore, in view of the preponderance of evidence which indicates symmetrical structures for these chelates, the fact that they show relatively strong dielectric absorption in benzene solution is quite significant. While the results of the present investigation do not, of themselves, exclude the possibility of small permanent dipole moments, they do favor the absence of permanent moments. In this connection, the first point to be made is that internal rotation, in the usual (14) K. S. Cole and R. H. Cole, J. Chem. Phys., 9,341 (1941). (16) P. Debye, “Polar Molecules,” Chemical Catalog Co., New York, N. Y.,1929, Chapter V. (16) For a critical discussion of this method of analysis, see D. H. Whiffen and H. W. Thompson, Trans. Faraday Soc., 42, 114 (1946). (17).With the exception of iron(II1) acetylacetonate, the largest deviation between the moment values calculated at the different temperatures for the unsubstituted chelates is 0.04D. I n the case of the iron complex, the largest difference is 0.07 D (the derived I.L a t 6 6 O is 0.94 D). Considering the magnitude of the experimental error involved in these low-loss measurements, no significance can be attached to the apparent variation exhibited by the iron chelate, (18) R.€3. Roof, Jr., Acta Crystallogr., 9,781 (1956). (19) J. Iball and C. H. Morgan, ibid., 23,239 (1967).
MICROWAVE ABSORPTION OF
RIETAL
ACETYLACETONATES I N BENZENE
sense, can be excluded as a possible relaxation mechanism since these chelate molecules, even if they were permanently polar, do not possess the type of polar group capable of orienting in the applied field by an internal rotation. Also, the observed relaxation times in solution are much smaller than would be expected for the orientation of a permanent dipole by molecular rotation of molecules of this size. For example, Cr(acac)z(3-NOzacac), which has a relatively large permanent moment, was found to have a relaxation time about 20 times greater than those of the unsubstituted chelates investigated. (See Table IV.) Secondly, the losses are much too large to be accounted for by the presence of polar impurities in the starting material^,^ complex formation between the solvent and the chelates, or dissociation of the acetylacetonates in solution. With the exception of the Co(II1) complex, for which vapor-phase data are not available, the vapor total polarizations of the unsubstituted chelates' have been found to be in good agreement with their respective solution values6 (benzene solution measurements). The latter agreement is indicative of negligible complex formation between the solvent, benzene, and the chelate. Also, substantial dissociation in solution would have resulted in a measurable difference between the solution and vapor total polarization. Moreover, the infrared spectra of a number of metal acetylacetonates in solution show no evidence of absorption peaks due to dissociation products.20 Therefore, it appears clear that the observed dielectric losses cannot be explained as the relaxation losses of rotating permanent dipoles. Any interpretation of these losses must be in agreement with the decrease of loss with increase of temperature, with the frequency dependence of the loss, and with the fact that the solution total polarization of each of these chelates does not differ significantly from its vapor-phase value. The molecular distortion mechanism suggested by WhiffenZ1to account for the dielectric losses exhibited by benzene, carbon tetrachloride, and other nonpolar liquids cannot be invoked in the present case. The average effective-moment values, ca. 0.7 D, appear too large to be produced by molecular distortion in the dissolved state of these molecule^.^ Also, if the Whiffen mechanism, in which the dipole moment and the relaxation time arise from intermolecular effects, were actually operative, an appreciable difference between the solution and vapor total polarizations of each of these chelates would have been ~ b s e r v e d . ~For example, a t 2 5 O , a contribution of approximately 10 cm3to the solution static polarization of aluminum acetylacetonate, dispersing according to the Debye form of the loss curve with a relaxation time of 6.2 X 10-l2 sec, is calculated from the observed loss data. A solution total polarization 10 cm3 greater than that of the vapor certainly would have been detected. Actually, the vapor-phase value' is 130.8 cm3 at 240" and the solution
3437
valuee is 130.0 om3at 55". This same argument applies to the other unsubstituted chelates investigated. The measured losses cannot be reconciled with the fact that the long-wavelength tails of vibrational, infrared absorption bands are being observed. Two features conflict with such an assignment. First, the measured absorptions were found to decrease with increase in temperature (see Table 11),whereas an increase of the loss in the low-frequency tail would be expectedS2l (The line breadths of infrared bands, particularly low-frequency difference bands, increase with temperature.) Second, dielectric loss measurements up to 136 GHz on aluminum acetylacetonate in benzene solution a t 25" definitely show the maximum loss to be in the microwave regiona (at ca. 0.8 cm). Finally, it is evident that these absorptions are not related to the (Poley) far-infrared absorption,22the behavior of which seems to be characteristic of the structural features of the liquid ~ t a t e . ~ Very ~ - ~interesting ~ s t u d i e ~ ~ ~concerning -~8 the Poley-type absorption have conclusively shown that not only polar but also nonpolar molecules exhibit considerable absorptions centered between 30 and 80 cm-'. In view of the foregoing arguments, it seems reasonable to conclude that the apparent-moment values, derived from the observed losses (see Table 11), probably arise from induced intramolecular polarization, i e . , atomic polarization, PA. This is equivalent to saying that a considerable fraction of the total P A of each of these substances appears to be associated with absorption in the microwave region while the remainder arises from the usual infrared a b s o r p t i ~ n . ~ ~ Dasgupta and Smyth3 and DiCarlo and Stronski4 initially made the latter suggestion in microwave-loss studies bn the acetylacetonates of chromium(II1) and aluminum. The internal motion(s) responsible for the dielectric relaxation of these complexes cannot be specified since it is difficult to visualize an oscillation of a sufficiently low frequency. Therefore, while these results point to an intramolecular relaxation process, further discussion of the mechanism in terms of such an internal motion would be purely conjecture. It is to be (20) J. P. Dismukes, L. H. Jones, and J. C. Bailar, J.Phys. Chem., 65, 792 (1961). (21) D. H. Whiffen, Trans. Faraday Soc., 46,124 (1950). (22) J. Ph. Poley, J.Appl. Sci., B , 4,337 (1955). (23) H. A. Gebbie, N. W. B. Stone, F. D. Findlay, and E. C. Pyatt, Nature, 205,377 (1965). (24) G. W. Chantry and H. A. Gebbie, ibid., 208,378 (1965). (25) Y .Leroy and E. Constant, Cornpt. Rend., 262,1391 (1966). (26) G. W. Chantry, H. A. Gebbie, B. Lassier, and G. Wyllie, Nature, 214, 163 (1967). (27) J. E. Chamberlain, E. B. C. Werner, H. A. Gebbie, and W. Slough, Trans. Faraday SOC.,63,2605 (1967). (28) M. Davies, G. W. F. Pardoe, J. E. Chamberlain, and H. A. G e b bie, ;bid., 64, 847 (1968). (29) I n this regard, infrared refractive index measurements on these
substances would be very instructive. Volume 73, Number 10 October 1969
3438
E. N. DICARLO,R. E. STRONSKI, AND C. E. VARGA
noted, however, that the large amount of evidence showing that p-diketonates possess considerable flexibility a t the meta130-34suggests that some form of internal motion of the chelate rings about the metal atom as a center may be involved. This fact, together with the possible relation of intramolecular ligand exchange to the observed relaxation, will receive further consideration in a future publication. At present, microwaveloss measurements are being made on solutions of other supposedly symmetrical coordination compounds (for example, beryllium, thorium(IV), and zirconium(1V) acetylacetonates, and a number of trans-planar complexes of copper and nickel). The tetrahedral, cubic, and planar complexes are being studied in the hope of throwing additional light on the problem. C r ( a c ~ c ) ~ ( S - N O ~ a cBecause ~ c ) ~ of lack of sufficient material, only one benzene solution of bis(acety1acetonato)mono(3-nitroacetylacetonato)chromium(III), Cr(acac)z(3-NOzacac),was examined. For this system, the two measuring- frequencies were found to be far removed from the frequency of maximum absorption. As a result, the relaxation time could not be reliably determined as previously described. I n this instance, it was necessary to utilize both the dielectric constant and loss data in order to arrive at a realistic estimate of the relaxation time. According to the theory of Debye, e’ and e” are related to r by the expression 6’
=
€0
-
(6)
T(W€”)
where €0 is the static dielectric constant of the solution given by the value of e’ at the 1-MHz frequency in Table I11 : Dielectric Constants and Losses of Bis(acetylacetonato)mono( 3-nitroacetylacetonato)chromium(III)in Benzene (c2 = 0.001417) Temp, “C
Frequency,
30
26,680 9,133
MHz
e‘
1
4”
2.270 2,271 2.3000
0.0017 0 00431 I
Table IV : Relaxation Time, Dipole Moments, and InfiniteFrequency Dielectric Constant, e, of Bis( acety1acetonato)mono( 3-nitroacetylacetonato)ohromium(III) ( cz = 0.001417) Temp,
~(25,680
10-12 Beo
~(9133
O C
MHz)
MH5)
r(ed
30
115
3.89
4.05
4.00
7,
T h e Journal of Physical Chemistry
4,
2.269
Table 111. (Equation 6 is a combination of the Debye equations for dielectric dispersion and absorption.) Tables I11 and IV summarize the data. The loss data in Table I11 are incremental values, i.e., the loss of the solution minus the loss of the solvent. The apparatus employed in the determination of the static dielectric constant has been described elsewhere.6 Table IV lists the relaxation time (115 X 10-l2 sec f 30%) calculated from the parameters given in Table 111, using eq 6. Also included are the values of p found from eq 4, using the latter value of r and the data at each measuring frequency. (For example, EL (9133 R4Hz) designates the value of the dipole moment based on the 9133-MHz data and a relaxation time of 115 X 10-l2 sec.) The dipole moment was also found from the Debye equation modified for dilute solutions
where e, was estimated from the plot of e“ us. e‘. This value of the moment is designated in Table IV as p (E-). The value of e,, ie., 2.269, appears to be fairly accurate because of the favorable distribution of points along the arc plot. (Both the 9133- and the 25,680MHz points were on the extreme high-frequency side of the absorption maximum.) As seen from Table IV, the calculated diDole moments are internallv consistent and agree well with the value, 3.99 D, obtained from static dielectric constant measurements.as These results suggest that the Debye equations for dielectric dispersion and absorption give a reasonably satisfactory explanation of the data obtained for Cr(acac)z(3NOzacac). Also, the magnitude of the time of relaxation indicates that, as expected, the predominant relaxation mechanism of Cr(a~ac)~(3-N02acac) is orientation of the permanent dipole in the applied field by molecular rotation. Acknowledgment. We gratefully acknowledge financial assistance from the National Science Foundation (GP8464). (30) G. E. Glass and R. 6. Tobias, J . Amer. Chem. Xoc., 89, 6371 (1967). (31) G. E. Glass and R. 5. Tobias, J. OrganometaZ. Chem., 15, 481 (1968)* (32) J. P. Faokler, Progr. Inorg. Chem., 7,361 (1966). (33) L. Wolf, E. Butter, and H. Weinett, 2.Anorg. Allg. Chem., 306, 87 (1960). (34) G. Sohwarzenbaoh, Angew. Chem., 70,451 (1958). (35) R. H. Brook and H. Freiser, Inorg. Chem., 5, 2078 (1966).
