3456
J . Phys. Chem. 1987, 91, 3456-3462
point out the followings as an experimental result of our S P measurement: For alkali halide MX, the S P increases with increasing size of the cation M+ but for salts with a larger cation than anion, the observed SP leads to larger a V+O(M+) (smaller V-O(X-)) than predicted by several cm3/mol. Even for the TAA salt, the partial molar volumes of the halide ions C1-, Br-, and I- shown in Table 111 seem to be smaller than the generally accepted values, although an apparent self-consistency holds among V?(Br-) values within experimental precision. However, in case of the alkali hydroxide and TAA bromide, the correlations represented in Figure 7 are opposite to those for the alkali halide. Therefore, the observed deviation from the expected horizontal lines as shown in Figure 4 cannot simply be attributed to some sorts of incompleteness in the theoretical treatment of the S P nor to experimental errors inherent in our experimental procedure and apparatus. It may be probable that the observed deviation from theoretical prediction can shed light on the nature of the interaction around each ionic species. What is certain at present is that the origin of scattering among V+O and V? values determined from SP remains unsolved and that averaging a few of the smallest V+O and largest V-O values gives rather adequate self-consistent values. This averaging rule is applicable also for 1:2-, 2:l-, and 2:2-type electrolytes.
Tetraphenyl complexes Na[Ph4B], [Ph4P]C1, and [Ph4As]C1 have been used for the purpose of ionic division of such quantities as partial molar volume,'* molar condu~tivity,]~ and viscosity B coefficient14in aqueous as well as nonaqueous media. For [Ph4P]+ = 296.0 and 279.86 cm3/mol, and [Ph4B]- we have found respectively. As mentioned above, our S P values generally give larger V+O and smaller V? by several cm3/mol. Consequently, V+O([Ph4P]+)is slightly larger than V-O([Ph4B]-) and the crude approximation to set V+'( [Ph4P]+)= V ? ([Ph4B]-) can hold. For ease of measurement, more widespread use of tetraphenyl complexes will be made as references for ionic division in nonaqueous media. With suitable attention, our oscillating cell method will take the place of UVP in many cases where the ionic partial molar volume on the absolute scale is eagerly required. Acknowledgment. The author is pleased to thank Professors H. Nomura and F. Kawaizumi of Nagoya University for their valuable suggestions and for a critical reading of the manuscript. (12) Millero, F. J. J . Phys. Chem. 1971, 75, 280. (13) Gill, D. S.; Sekhri, M. B. J . Chem. Soc., Faraday Trans. I 1982, 78, 119. (14) Domenech, J.; Rivera, S . J . Chem. Soc., Faraday Trans. I 1984.80, 1249.
A Study of the Dielectric Relaxation Behavior of Photoinduced Transient Species Richard W. Fessenden* and A. Hitachit Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: May 16, 1986; I n Final Form: February 20, 1987) Microwave absorption methods have been extended to measure changes in both components of the complex dielectric constant which occur following photoexcitation of the sample. For a number of systems, the ratio of the change in dielectric constant (dispersion) to that in dielectric loss (absorption) is very similar to the corresponding ratio for the ground state of the molecule under consideration. Thus, the triplet states of such molecules as 9-fluorenone or 4-(dimethy1amino)benzaldehyde have orientational relaxation rates similar to those of their ground state. The charge-transfer triplet state of 4,4'-bis(dimethy1amino)benzophenone is shown to have an anomalously short relaxation time, possibly related to an intramolecular charge-transfer process. The ratio of dispersion to absorption can be used to determine the relaxation time for short-lived species which cannot be studied by conventional methods, if an appropriate model for the relaxation (for example, Debye type) can be assumed. This approach is used in determining the dipole moment of the anthracene/dimethylanilineexciplex. Introduction
A previous paper reported1 time-resolved measurements of the changes in microwave dielectric absorption which accompanied excitation of various molecules to their lowest triplet states. These changes in absorption were then quantitatively related to the changes in dipole moment between the ground state and the triplet. Calculation of the dipole moment required knowing the dielectric relaxation behavior for the molecule under consideration. In many cases (as for rigid molecules) it was appropriate to assume that the ground and excited states would reorient at the same rates. Static experiments with the ground states could then be used to calibrate the amount of loss produced by a given concentration and dipole moment. Some systems such as exciplexes have significant charge-transfer character and are obvious candidates for study by this method. However, the lack of a suitable model compound with which to determine the relaxation behavior has prevented reduction of the observed changes in microwave absorption to values of dipole moment. The present work represents a somewhat different approach to this latter problem by measuring transient changes in both dielectric loss and dielectric constant. Together these two measurements provide more information on the orientational relaxation of the transient. If a particular model of relaxation (such as Debye-type relaxation) can be assumed then the dielectric relaxation time and dipole moment can be deter+ Present address: Science and Engineering Research Laboratory, Waseda University, 17 Kikui-cho, Shinjuku-ku, Tokyo 162, Japan
0022-3654/87/2091-3456$01 S O / O
mined. We note that some recent microwave studies of excited-state dipole have used orientational relaxation times determined from fluorescence measurements in a Debye-type model for calculating their result. The method reported here could be used to provide more information on the accuracy of that assumption. The capability of measuring dielectric relaxation times also provides for new applications. For example, measurement of local viscosity is possible through measurement of the relaxation times for suitable probe molecules. While this method cannot be applied to inhomogeneous systems involving water as a major constituent it should work well for small molecules in polymer solutions or liquid crystals. Conduction by charge carriers in solids has an associated correlation time which is derivable from the ratio of dielectric loss to dielectric constant and this value provides a second parameter after mobility to characterize the conduction. Such a measurement for photolytically produced charge carriers in TiO, particles has already been made.4 Experimental Section
Static measurements of loss and dispersion were made with the (1) Fessenden, R. W.; Carton, P. M.; Shimamori, H.; Scaiano, J. C. J . Phys. Chem. 1982, 86, 3803. (2) Visser. R. J.; Wiesenborn, P. C. M.; Varma, C. A. G. 0.;DeHaas, M. P.; Warman, J. M. Chem. Phys. Lett. 1986, 104, 38. (3) Warman, J. M.; DeHaas, M. P.; Oevering, H.; Verhoeven, J. W.; Paddon-Row, M. N.; Oliver, A. M. Chem. Phys. Letr. 1986, 128, 95. (4) Fessenden, R. W.; Kamat, P. V. Chem. Phys. Lett. 1986, 123, 233.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3451
Dielectric Relaxation Behavior apparatus described previously' which consisted of a klystron, a precision 3-dB coupler for measurement of incident power, a circulator, the cavity and adjustable coupling device, and a power meter. A Hewlett-Packard 5246L frequency counter with 5255A plug-in (connected to a suitable power take-off) was used to monitor the microwave frequency in order that it could be kept constant where desired. Because the cavity frequency is a sensitive function of temperature through thermal expansion, particularly with the relatively large solvent sample in place, the cavity was thermostatted at room temperature (23 "C) by flswing coolant through a copper coil in contact with the cavity. A typical frequency shift of the cavity resonance using the standard sample size (3 X 7 mm fused silica tube) from pure benzene to a 10 mM solution of fluorenone in benzene was 1.5 MHz. The apparatus for the transient experiment was similar to that described previously' with the detector changed to a doublebalanced mixer to aid in measurements with varying phase relationships between signal and detector reference signal. The signal path after the cavity and circulator passed through a waveguide to S M A coaxial adapter, a directional coupler (which takes off a signal at -10 dB to an auxiliary detector to aid in setup adjustments), an isolator, a low-noise microwave amplifier (Narda N62448-65), and the double-balanced mixer (Lorch Electronics Inc., FC-325G). The mixer output went to an amplifier constructed from Avantek GPD-460 series modules with a total gain of 100 into a 50-ohm load with a rise time of 1.5 ns (IO-90%). The reference signal to the mixer passed through a phase shifter consisting of a circulator and micrometer screw adjustable short. Approximately 460 dial units corresponded to a 180" phase shift a t the frequency usually used (9180 MHz). The position corresponding to 0 or 180" phase between reference signal and an absorptive signal from the cavity could generally be repeated to about 1 unit. In practice, some deviations from the travel for 180" were found depending on the position of the short in its 1-in. total travel. The size of the deviations does not affect phase measurements to more than about 2". It was verified that the mixer sensitivity did not change as the reference phase setting was varied. The chemicals used in this study were mostly obtained from Aldrich Chemical Co., Inc., and in many cases were the same as were used in the previous work.' The anthracene was Aldrich Gold Label. Aldrich dimethylaniline was distilled. The phenanthrenequinone and 9-fluorenone had been recrystallized and the Michler's ketone (from Fluka) sublimed. The ethyl bromide was from Matheson Coleman and Bell and was reagent grade. The solvents were Aldrich Gold Label benzene, and Fisher benzene and cyclohexane of Spectranalysed grade. Some care was necessary with benzene solutions in particular to keep the solvent dry and to use glassware and cells which had been baked to remove water from the surfaces. Water in benzene produces mainly a frequency shift (dispersion) rather than a loss. The transient experiments were done at about 22 "C. Photolysis was with pulses ( 6 4 s width at half-height) of 355 nm light from a Quanta Ray DCR-1 YAG laser. The samples were contained in silica cells made from 3 X 7 mm tubing and were deoxygenated by bubbling with argon. The cavity was as described previously.' The transient electrical signals were digitized and processed by a Tektronix 7912 AD digitizer interfaced with a PDP 11/2 microcomputer. Normally, data from about 10 separate pulses were averaged together to improve the signal-to-noise ratio.
Results and Discussion The mathematical analysis given in the Appendix shows how the amplitude and power in the microwave signal reflected from the cavity change as the two components of the complex dielectric constant of the sample 6
= e' - jt"
(1)
vary. In particular, the measured quantities A and Bo A = trrQxv
(2)
(3) are defined where eo is the real dielectric constant of the sample
TABLE I: Dielectric Constant and Loss of Solutes in Benzene" BnIA
concn, this compd mM Ab Bob A / l S ] work ref 5c ref 5d fluorenone 10.7 0.736 0.750 68.8 1.02 1.14 1.23 phenanthrene- 5.23 0.917 0.697 175 0.76 0.88 0.99 quinone 9.73 0.804 0.805 82.6 1.00 1.01 1.08 anthrone OAt 23 OC. bThese values depend on the particular cell geometry and cavity Q. 'From the Cole-Cole arc plot parameters interpolated to 23 OC. dFrom the actual data at 3.22 cm interpolated to 23 O C .
before either addition of solute or photoinduced change, Q, is the cavity Q due to the external coupling, and 7 is a filling factor.' In the transient experiment, the microwave frequency is set at the center of the cavity resonance before any photoinduced changes and it does not change on the time scale of the measurements. The equation for the amplitude in the reflected wave from the cavity after the laser pulse is v, -- -A -jBo _ (4) vo 2 A + j B o
+
where j = (-l)'/*. The terms A and Bo are small so the denominator does not change. Thus the term A represents an amplitude which is in phase with a reflection from the cavity at its resonant frequency and Bo represents a signal at 90" to the former. The double-balanced mixer is phase sensitive and responds linearly to microwave amplitude so it will detect A or Bo or an appropriate vectorial sum depending on the phase of the reference signal to the mixer. The components of the dielectric constant of the solution can be expressed in the form used by Pitt and Smith5 t' = eo arcz (5)
+
e" = a'%, (6) where eo is the real dielectric constant of the solvent without the solute and C , is the solute concentration (mole fraction). The ratio B o / A will then be
B o / A = a'/a" (7) If Debye-type relaxation of the solute occurs then the value of 07, where w is the angular frequency of the microwave signal and T is the relaxation time, is given by (UT)-'
= Bo/A
(8)
The analysis in the Appendix shows how A and Bo are determined for a solution of a stable molecule from static microwave measurements. Static Measurements. Measurements of the reflected power were made with the apparatus described above and with data analysis as described in the Appendix. Typical data for solutions of fluorenone, phenanthrenequinone, and anthrone are given in Table I. The definitions of A and Bo are as given in eq 2 and 3 and the Appendix. It was shown earlier] that the A term is proportional to the concentration for a particular cavity and cell and measurements of Bo (not shown) confirm that Bo is as well. The ratio B o / A found by this method can be compared with that from earlier measurements by more conventional methods. Two values from Pitt and Smyth5 are listed in Table I for each compound. The first is determined for our exact frequency (9180 MHz) from their parameters describing the Cole-Cole arc plot (interpolated to 23 "C) used to fit the data at all frequencies. The second is from the coefficients, a'and a", for 3.22 cm (93 10 MHz) interpolated to 23 "C. This frequency is so close to our value that little error (- 1.5%) should come from the difference. It is seen that there is a systematic difference with the 3.22-cm data about 7% higher than the other. Nevertheless, there is reasonable agreement between our measurements and the previous data with the differences between compounds consistent in all cases. ( 5 ) Pitt, D. A.; Smyth, C. P. J . Am. Chem. SOC.1958, 72, 4097
3458 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
Fessenden and Hitachi
TABLE II: Ratios of Dielectric Constant to Loss for Ground-State Molecules”
compd ethyl bromide 2-adamantanone 2-adamantanone camphorquinone camphorquinone
solvent
BOIA
w,b D
cyclohexane
6.4 1.76 3.00 0.96 2.02 1.06
3.06 3.06 4.49 4.49
diphenylcyclopropenone
benzene cyclohexane benzene cyclohexane benzene benzene
4,4’-bis(dimethylamino)benzophenone
benzene
1-adamantanecarbonitrile
+ UT)^]' 0.152 0.430 0.300 0.499
0.387 0.300e 0.435 0,473
0.398
0.349 0.288
0.499 0.482 0.472 0.467
3.61 5.1 5.3
0.78 0.7 1
d
UT/[^
0.23 1
0.349 benzene 0.69 4.13 9-cyanoanthracene cyclohexane 0.7 1 4.13 0.472 9-cyanoanthracene 0.316 benzene 0.67 5.6 0.462 p-(CH3)2NC,H4CHO 0.289 benzene 0.58 6.60 0.434 p-(CH3)2NC6H4CN ‘Measured at 23 OC and about 9200 MHz. bValues taken from Tables of Experimental Dipole Moments, Vol. 11; Rahara Enterprises: El Cerrito, CA, 1974. ‘Taken from (UT) = A/Bo, eq 8. dValue obtained by use of eq 9 and a comparison with 9-fluorenone. e Assumed to be as given by B o / A and eq 10 TABLE 111: Dielectric Loss for Reference Compounds in Benzene
P/
&I/
compd A / [ S ] p,a D 9-fluorenone 74.3 3.38 phenanthrene- 183.5 5.36 quinone anthrone 87.6 3.63
A/[S]p2
(C~-’C~)‘
K
6.50 6.39
0.407 0.364
16.0
0.384
17.5
0.377
6.65
0.385
17.3
0.393
(tO-’ce)*
‘Value from ref 5. bRecalculated from eq 9 by using an average K of 16.93 and the values of A / [ S ] and w tabulated. To understand the meaning of the ratio Bo/A,it is convenient to think of the Cole-Cole semicircle plot of t” and e’. A solute will have values of E’’ and t’ at a given frequency depending on the viscosity. If the frequency or viscosity is lowered, the point on the Cole-Cole plot will move to the right along the semicircle corresponding to an increase in t’ or an increase in our Bo/A ratio. A decrease in rotational correlation time as for a smaller molecule would cause the same effect. Data from the current work for some other selected compounds are shown in Table I1 to illustrate the dependence of Bo/A upon the molecular size. As expected, ethyl bromide has a large ratio and the larger molecules a smaller ratio. Although the molecular weight of 2-adamantanone is comparable to that of the other compounds this molecule is quite compact and has a large ratio. The difference between benzene and cyclohexane solvent for the smaller molecules is surprising in that the viscosities are in the opposite sense Le. that of cyclohexane (0.977 CP at 20 oC)6 is larger than that of benzene (0.647 CP at 20 oC)6while the ratio B o / A is larger for cyclohexane solvent. Thus the rotational motion seems to be governed by both molecular interactions and viscosity. One purpose of this work is to use the observations of both dielectric constant and loss to calibrate the loss at a particular frequency in order to measure the dipole moment. If Debye-type relaxation is assumed, then the value of W T can be determined from Bo/A by eq 8. However, the results to follow show that few molecules of interest here follow such relaxation behavior. The absolute amount of loss can be determined from the earlier data for fluorenone, etc. given above. Our experiments measure the dielectric loss with a proportionality constant which depends on the cavity Q and sample geometry. Thus we can write (9) where 1.1 is the dipole moment of the molecule, [SI is its concentration, t” is the loss associated with the solute, to and are the low- and high-frequency dielectric constants associated with the solute, and K is a proportionality constant which depends on the cavity and sample geometry (which are kept constant for these measurements). The values of t”/(eO - em) from Pitt and SmythS as calculated for 9180 MHz and 23 OC are 0.407,0.364, and 0.385 for fluorenone, phenanthrenequinone, and anthrone, respectively. ( 6 ) Selected Values of Properties of Hydrocarbons and Related Compounds. American Petroleum Research Project 44.
I
1
1
I
I
I
I
, 0.
1
___--I
I
I .o
2.0 TIME
- p sec
I
I
3.0
1
1
Figure 1. The transient changes in microwave signals obtained upon photolysis of 10 mM 9-fluorenone in benzene at 355 nm. The upper portion shows an increase in dielectric loss associated with formation of the triplet state. The lower portion shows the dispersion signal at 90” electrical phase to the loss curve. This signal is decomposed into a portion
(dashed line) showing increased dielectric constant associated with the triplet state and a signal (----) like that in Figure 2 which is believed to represent heating of the sample and a decreased dielectric constant. These values were used to define K and an average value of K used with A / [ S ] p 2to recalculate e”/(eO - e m ) (see Table HI). The values from this recalculation are not very different from those taken from Pitt and S m ~ t h .Values ~ of this quantity for other compounds can then be determined by reference to one of these standard compounds (usually fluorenone). This evaluation of t”/(tO - em) is not much different than the earlier procedure’ except that the value is put on an absolute basis. The value of e”/(eO - e m ) together with the ratio B o / A goes quite far toward defining the relaxation behavior of the compound under study, However, the data show in most cases that the reorientation of the molecule does not follow Debye-type behavior. This fact can be seen by using the ratio B o / A to determine W T by eq 8 and ) the equation using this value to calculate ~ ( w T by
Dielectric Relaxation Behavior
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3459
DIAL
TIME - p sec
Figure 2. The transient changes in microwave signals obtained from 1 mM anthracene in benzene upon photolysis at 355 nm. Solid circles represent dielectric loss and open circles represent a decrease in dielectric
READING
Figure 3. The amplitude of microwave signal for 10 mM 9-fluorenone in benzene measured about 500 ns after photolysis with 355-nm light as a function of microwave phase at the detector. The points representing pure dielectric loss are marked by vertical bars. At that point an increase in loss is observed upon excitation. The phase angle between this point and that for maximum signal is 44”.
constant.
The value so calculated can be compared with the absolute value of E ” / ( E ~ - em) obtained from eq 9 and values of A , p, and K . Results of this latter calculation are given in Table 11. For example, the value of Bo/A = 0.71 for 4,4’-bis(dimethy1amino)benzophenone (Michler’s ketone) implies U T = 1.41 so t”/(tO E - ) should equal 0.47 whereas the comparison of the A / [ S ] p 2value with that for the calibration compounds (fluorenone, etc.) gives 0.27 for this same quantity. Thus the behavior is like that for fluorenone in that the value of d’/(tO - L) for a particular ratio Bo/A is less than the value corresponding to a point on a semicircle plot of E” vs. e’. The clear implication is that, as for fluorenone, a distribution of relaxation times is more appropriate so that the plot of E” vs. E’ is depressed (e.g., as the arc of a circle with the center below the e’ axis) so that the maximum value of t”/(t0 e m ) is considerably less than 0.50 for the function g ( w 7 ) . All of the compounds studied show this behavior to a considerable degree. Even the molecule 4-(dimethylamino)benzonitrile, which must turn end for end to reorient the dipole, shows this property. Measurement at other frequencies would help in further defining the behavior. It is of considerable value to be able to provide a compound of known t’’/(c0 - E - ) in other solvents than benzene. The most likely way to find a compound with predictable behavior is to look for a symmetrical molecule which should not show a distribution of relaxation times (at least from its own shape) and which could be assumed to follow Debye-type behavior. The molecules 2adamantanone and 1-adamantanecarbonitrile might be expected to fit this description. Of all the compounds studied, 2adamantanone best fits this picture. From Table I1 the value of g from the measurement of B o / A is 0.430 and the value obtained from a comparison with fluorenone is 0.387. Although these values do not agree exactly, they are closer than for any other compound in the table. Because Bo/A 2 it is clear that, at our frequency, the point on the plot oft” vs E’ is away from the maximum of AUT) so that the calculation of UT will be sensitive to the value of Bo/A. This compound, therefore, appears to obey Debye-type behavior so that a measurement of & / A in any solvent can be used to obtain a value of g which can in turn be used as a calibration for compounds to be studied photochemically. The values of g in Table I1 for cyclohexane solution were obtained this way. It should be noted that even 1-adamantanecarbonitrile departs somewhat from Debye-type behavior. Transient Measurements. Curves of microwave absorption against time are shown in Figure 1 for fluorenone in benzene, excited at 355 nm. The upper curve is at the phase setting for pure absorption and the lower one at that for dispersion, i.e. at
-
90’ to the former. The curve for dispersion is noisier than that for absorption because any small change in frequency by the klystron either as noise or because of electrical pickup in the power leads to the klystron (particularly the reflector) will appear as a change in reflected power. In addition, a long-term slow growth which continues for 10-20 p s is seen in the dispersion. Figure 2 shows the response for a solution of anthracene in benzene. There should be no polar products in this case and at the phase for absorption (solid points) none is seen. At the microwave phase for dispersion (open circles) a slow growth is seen as in the lower part of Figure 2. This growth corresponds to a decrease in the dielectric constant and is attributed to heating of the solution by the pulse. An increase in temperature lowers the density and the dielectric constant of the solvent. Because the corresponding expansion can only occur as fast as the velocity of sound in the solution, this signal takes some time to be produced. (Under some circumstances oscillations in the dispersion signal are seen with a period of several microseconds which corresponds to the time for an acoustic wave to traverse the sample.) Although an AFC circuit is used to hold the klystron at the cavity resonance, its response time is quite long so that the observed dispersion signal corresponds to a constant source frequency. At much longer times (milliseconds) the AFC circuit will act to reduce the observed dispersion signal. The signal in the lower part of Figure 1 was analyzed with the slowly growing response in mind. The dispersion caused by the formation of fluorenone triplet should follow the same time profile as the absorption signal and there also should be a response like that in Figure 2. The lower dashed curve represents a response like that for the fluorenone absorption and the upper dashed curve represents the difference between the lower curve and the data. This difference curve is very similar to the curve in Figure 2. If the amplitude of the transient corresponding to excitation of a triplet state, for example, is measured at relatively short times, such as within 500 ns of the laser pulse, then the dispersion signal will not be very important and will not seriously interfere. The signal due to thermal effects does not contribute at the phase corresponding to absorption. In addition to the thermal signal, a small signal representing increased absorption is seen when pure solvent is used. In samples of large absorbance this signal is reduced considerably. In most cases this spurious signal contributes less than 5% to the measured signals. Although the cavity interior is gold plated, there are a few joints in which surface oxides may exist. Production of charge carriers in these oxides could produce this small background signal. The amplitude of the signal from fluorenone triplet as a function of microwave phase setting at the detector is shown in Figure 3. The smooth curve through the points is a sine function chosen to fit the zero-crossing points and the amplitude. It is seen to fit well. The points corresponding to 0 and 180’ phase, that is pure
3460
The Journal of Physical Chemistry, Vol. 91, No.12, 1987
I
300F
0 #3 c -I -loot
44
I
I I
200
400
600
800
6 -200/J4 1
-=Of
DIAL
READING
Figure 4. Data like that in Figure 3 but for 1 mM 4-(dimethylamino)benzaldehyde in benzene.
W
n
3
t
0
200
d
2
DIAL
READING
Figure 5. Data like that in Figure 3 but for 1 mM 4,4’-bis(dimethy1amin0)benzophenone (Michler’s ketone) in benzene.
absorption, are marked by short vertical lines. The peak amplitude as determined by the midpoint between the axis-crossing points is at 44O to the 0” point. Similar data for 4-(dimethylamino)benzaldehyde and 4,4’-bis(dimethylamino)benzophenone(Michler’s ketone) are shown in Figures 4 and 5. The ratios of B o / A corresponding to the phase shift 4 between the maximum and the point for 0’ are given by & / A = tan q5
(11)
These values are given in Table IV for the triplet states of a number of ketones as well as for an exciplex. In cases where comparison with the ground state is possible, the values generally agree, with the exception of Michler’s ketone which will be discussed below. Diphenylcyclopropenone, which presents a system in which the polarity is permanently destroyed by the reaction 0
IIC
/\
Ph-C=C-Ph
hv
P h C E C P h f CO
also gives reasonable agreement with the static measurement in which the concentration is changed directly. A minor correction should be applied in comparing the two types of measurement and slightly different values should, in fact, be obtained. The static experiment measures changes in dielectric constant as a result of both the orientational polarization of the added solute as well as any changes in electronic polarization caused by addition of the solute and any consequent density changes. In the transient experiment, excitation of a triplet state, for example, changes the dipole moment and hence the orientational polarization while to a first approximation the electronic polarization is not changed since the same atoms are still present. For the fluorenone ground state, in benzene, the data of Pitt and SmythSshow that B o / A for a frequency of 9310 MHz (3.22 cm)
Fessenden and Hitachi should be 7.65/6.24 = 1.23 for changing the concentration of fluorenone but that the change in high-frequency dielectric constant contributes 0.87 to the numerator. As a result the value for changing only the dipole moment of the molecule should be B o / A = 6.78/6.24 = 1.08. This correction is relatively small, particularly for the molecules of larger dipole moment, and is not much larger than the experimental error. Nevertheless, the data in Table IV for fluorenone and phenanthrenequinone seem to show this trend. It appears that, with the one exception of Michler’s ketone noted, the excited states do exhibit the same relaxation behavior as the corresponding ground states. The preceeding discussion assumes that the only effect of the excitation of a triplet state, for example, is to change the dipole moment of the molecule and does not consider any possible changes in polarizability of the species. In a simple molecular orbital picture, the electron which was raised to a higher energy level will have a smaller binding energy and might be more polarizable. For most of the molecules this effect does not seem very important. An exciplex such as anthracene/dimethylaniline has roughly 50570 the character of an ion pair and could have a significant polarizability associated with changing the distance between the two partners. Although the measurement made here at one microwave frequency cannot distinguish such an effect, the possibility should be kept in mind. The ratio Bo/A for excitation of the triplet of Michler’s ketone corresponds to W T = 0.44 or a relaxation time of 8 ps. Such a value is completely impossible for a molecule of this size if it moves as a rigid unit. Internal rotation of the dimethylamino groups could shift some of the dielectric loss to higher frequencies but the size of the dipole associated with this group is quite small. In addition, no such effect is seen for the ground state or for the triplet states of 4-(dimethy1amino)benzaldehyde and 4-(dimethy1amino)benzophenone which behave quite normally. The only model which seems capable of accounting for the observation involves the suggestion that the excited state (which is of charge-transfer character) involves only one amino group at any one instant. Thus the dipole runs approximately from one amino nitrogen to the carbonyl oxygen as in Figure 6. A shift of positive charge from one nitrogen to the other reorients the dipole to a large extent without rotation of the whole molecule. The localization of charge on one nitrogen could result either from a different solvent configuration at that group which lowers the energy or to a twist of the N(CH& group as has been invoked A shift of positive charge for N,N-dimethylamin~benzonitrile.~ to the other N(CH& group would be induced by solvent fluctuations. Because of the high rate of such a transfer needed to produce the dispersion (7 8 ps), the energy difference between localizing the charge at the two sites cannot be large. A comment is appropriate here on the implications of the present work for the interpretation of similar experiments by Warman et al.2,3 In those experiments a detector which responds to changes in reflected microwave power was used. From eq A6 in the Appendix it is seen that the change in reflected power depends on both our terms A and Bo. Calibrations to evaluate the relaxation functions were done with ground-state molecules. As long as the ratio Bo/A for the excited state is like that for the ground state, no problem is encountered. However, in an extreme case such as that of Michler’s ketone the ratio B o / A changes by a large amount and the signal measured by a power detector would not be interpreted properly in terms of an excited-state dipole moment. As has been seen, the present method with a linear phase-sensitive detector can identify this type of problem and allows one to go somewhat further in calculating the excited-state moment. Measurements on the exciplex derived from quenching of anthracene singlet by dimethylaniline illustrate a case where the information from the dispersion component is of importance. In order to determine the dipole moment for this important species, as in all the other cases, one needs to know the value of the
-
(7) Grabowski, Z. R.; Rotkiewicz, K.; Siemiarczuk, A,; Cowley, D. J.; Baumann, W. NOUV.J . Chim.1979, 3, 443.
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3461
Dielectric Relaxation Behavior
TABLE I V Ratios of Dielectric Loss and Dielectric Constant Associated with Transient Species in Benzene”
compd fluorenone benzophenone phenanthrenequinone diphenylcyclopropenone 4-(dimethylamino)benzaldehyde 4-(dimethylamino)benzophenone 4,4’- bis(dimethy1amino)benzophenone 4-(dimethylamino)benzonitrile anthracene/dimethylaniline exciplex anthracene/dimethylaniline exciplex‘
transient phase shift, deg 42 34
transient
static
&/A
&/A 1.02
0.90 0.67 0.60 0.67
31 34 26 66
28 31
0.68
0.76 0.76 0.67
0.58 0.49 2.25 0.53
30
corrected* static B o / A 0.90
0.71
0.51
0.60 0.58
30
“Triplet states except for the exciplex. bCorrected for the change in refractive index using the data of ref 5 and applying the calculated correction factor to our data. C I n cyclohexane. 80
60
40
20
1
I
I
200
400
600
TIME
,-/ - - - - - - - \
L
Pl Figure 6. A representation of the two possible orientations for the dipole in an unsymmetrical charge transfer state for Michler’s ketone.
relaxation function t”/(tO - e-). In the case of a complex, there is no ground-state model to use for this purpose. Measurements were made on the anthracene/dimethylaniline exciplex in cyclohexane in order to be able to make use of the very detailed kinetic data of Hui and Ware.8 The exciplex was also studied in benzene. In order to assure that the measurement pertains to the complete conversion of excited anthracene to exciplex, experiments were carried out at a number of concentrations of dimethylaniline and a double reciprocal plot was used to extrapolate to infinite concentration. Several well-understood corrections had to be applied. The decay times of the exciplex are comparable to the apparatus response time determined by the cavity Q factor so that it was necessary to simulate the observed curves by a calculation which folded in this response time. In addition, as more aniline is added, the cavity Q decreases so that the response time changes. On top of that consideration, the fundamental sensitivity of the apparatus is also proportional to cavity Q. Static measurements of reflected power using the cavity and cell from the transient experiment were used to evaluate the Q and its decrease with dimethylaniline concentration.’ The apparatus time constants ranged from 40 ns for no lossy solute to 12 ns for 105 mM dimethylaniline. For solutions in cyclohexane, the kinetic simulation involved a computer program which integrated the kinetic equations by using the rate constants given by Hui and Ware,* including the timedependent rate constant for quenching, and the response of the apparatus as described above. It was found that the exciplex decay rate constant ( k , k , in ref 8) had to be increased from 0.9 X 107 to 1.3 x 107 M-1 s-1 t o fit the observed curves. This value remained the same for all samples. An example of data with a fitted curve is shown in Figure 7. The amplitudes used in the fitting were then corrected to give values for constant Q and then plotted in a double reciprocal plot as in the insert in Figure 7. The
+
(8) Hui, M.-H.; Ware, W. R.J . Am. Chem. SOC.1976, 98, 4718.
- nr
Figure 7. The microwave loss signal observed upon excitation of 1.4 mM anthracene in cyclohexane containing 3 1.5 mM dimethylaniline. The curve through the points was calculated as described in the text. The
insert shows the reciprocal of the corrected amplitude (see text) as a function of the reciprocal of the dimethylaniline concentration. The intercept of this plot was used in determining the dipole moment for the exciplex. intercept was compared with the signal seen for diphenylcyclopropenone and corrections made for absorbance of the samples and, in the exciplex case, for loss of the slightly polar dimethylaniline in forming the exciplex. If the observed ratio of B o / A (listed in Table IV) is used with the simple eq 10 to determine the relaxation behavior, a value of the relaxation function, g ( W T ) , of 0.43 is found. With this value, the dipole moment determined for the exciplex is 4.8D. If the relaxation is considered not to obey eq 10 then a smaller value of the relaxation function is possible for the B o / A found and a higher dipole moment would be calculated. Since the relaxation function only enters the calculation to the 0.5 power, a halving of the value of the relaxation function would only raise the dipole moment to 6.8 D. Similar measurements were carried out on this same exciplex in benzene. A simpler kinetic scheme was used for simulating the effect of apparatus time constant but the double reciprocal plot was still linear. In this case the dipole moment of the exciplex was calculated to be 6.3 D when the value g ( w ) was taken from the measured B o / A value. Although this value for the more polarizable solvent benzene is somewhat higher than that found for cyclohexane solution, both values are still much less than that of > 10 D calculated from solvent effects on emission wavelengthg or similar values from electrooptic emission studies.I0 It is not clear why our values differ from those from the two other types of experiment. The most obvious suggestion is that the relaxation function g ( W T ) for the exciplex has a much smaller value than used in the calculation. Based on the behavior observed for a number of molecules it is hard to see how the value can be small enough to allow a moment of 10-12 D. If that were the case, the relatively large dispersion would imply a large polarizability for the exciplex-an interesting point in itself. From our point of view it is clear that absorption/dispersion experiments at other microwave frequencies are needed to better
3462
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
Fessenden and Hitachi
define the relaxation behavior to improve the accuracy of the measurement of the relaxation function. (Each new frequency requires a whole new apparatus.) Experiments in other solvents are also needed to see whether a change in the dipole moment with solvent polarity as seen in the electrooptic is found in our type of experiment.
energy to the cavity. The reference state is taken as the cavity with cell filled with pure solvent and the dielectric constant and loss with solute are expressed as e' = eo a'C2 ('42)
Conclusions
where eo is the dielectric constant of the solvent and C2is the concentration of solute (mole fraction). The term L is given by L = a"Cza where 7 is the filling factor and the term B by
From the results reported here it is clear that measurements of both change in dielectric constant and dielectric loss can readily be made. This information is of considerable value for defining the orientational relaxation behavior of the transient. Such measurements can be used in low-viscosity media (short relaxation times 25 ps) much as fluorescence depolarization can be used to study the motion of probes at somewhat longer times. Measurement of the two components of the complex dielectric constant also helps in providing a value of the function t"/(tO - em) which is needed to convert measured microwave loss signals into changes in dipole moment for transient species whose relaxation behavior cannot be modeled by a stable molecule. However, the current measurements clearly show that most species of interest do not follow simple Debye-type relaxation. Consequently, it is desirable to follow up this work by measurements at other microwave frequencies in order to better define the actual relaxation behavior.
-
Acknowledgment. The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-2840 from the Notre Dame Radiation Laboratory. Appendix
Following the notation used earlier,] the microwave amplitude reflected from the cavity can be expressed as
where p1 = Qx/Qo represents the ratio of the Q factor due to the L is coupling to the cavity (Q,) to that for the cavity itself the loss, B = 2Q,((w - w o ) / w o ) with w the microwave frequency (angular units) and wo the cavity resonant frequency and j = (-l)'/z. The quantity Q, is adjusted by the device which couples
(eo),
(9) Beens, H.; Knibbe, H.; Weller, A. J . Chem. Phys. 1967, 47, 1183. (10) Baumann, W.; Bischof, H.; Frohling, J. C. J . Lumin. 1981, 2 4 / 2 5 , 555.
(1 1) Although a change in the dipole moment with solvent polarity has been suggested, we do not believe such an effect invalidates our extrapolation of the signal amplitude with concentration of amine. At the highest concentration the solution is only about 1% of the dimethylanilinewhich changes its dielectric constant only by a small amount.
+
e"
= a"C2
(A31
where wo is now the resonant frequency with the solvent present. If measurements are carried out at different concentrations of solute starting from a matched cavity (p' = 1) then eq A1 can be written V, -A - jB
_ -Vo
2+A+jB
('45)
with A = Q,L = Qxar'C2a. In the static measurement the reflected power is measured so
PI -_ Po
+ B2 ( 2 + A ) 2 +' B2 A'
('46)
Measurements at two frequencies on the sample with solute present allow both A and B to be determined. We have chosen the original cavity center frequency with pure solvent and the new cavity frequency with solvent and solute. At the new cavity frequency, B = 0 so A can be determined from the incident and reflected powers. Then the measurement at the original cavity frequency (w = w o ) corresponds to a particular value of B defined as Bo = Q,a'C2q. The term Bo can readily be determined now that A is known. The ratio B o / A comes out simply to be
B o / A = a'/arr
('47)
the ratio of dielectric constant to loss corresponding to a given concentration of solute. If that solute were created or destroyed in a photolytic process, the ratio of changes in the two dielectric quantities should be the same. Registry No. p-(CH,),NC6H4CH0, 100-10-7; p-(CH,),NC6H4CN, 1 197-19-9; 9-fluorenone, 486-25-9; phenanthrenequinone, 84-1 1-7; anthrone, 90-44-8; ethyl bromide, 74-96-4; 2-adamantanone, 700-58-3; camphorquinone, 465-29-2; 1-adamantanecarbonitrile,23074-42-2; diphenylcyclopropenone, 886-38-4; 4,4'-bis(dimethylamino)benzophe~one, 90-94-8; 9-cyanoanthracene, 1210-12-4; benzophenone, 119-61-9; 4(dimethylamino)benzophenone, 530-44-9; anthracene/dimethylaniline exciplex, 20371-01-1.
