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Fluorescence reabsorption in anthracene single crystals: Lifetime variations with emission wavelength and temperature
CHEMICAL PHYSICS 4 (1974) 402-408.4>
NORTH-HOLLAND PUBUSIIING COMPANY
FLUORESCENCE REABSORPTION IN ANTHRACENE SINGLE CRYSTALS: WITHEMISSIONWAVELENGTHANDTEMPER~TlJRE* LIFETIMEVARIATIONS Richard J. BATEhlAN *+, Ronald R CHANCE * and James F. HORNIG Lkrfmouth
College, Hanover, New Hampshire
03755,
USA
Received 17 December 1975 Revised manuscript received 27 February 1974
Fluorescence spectra and lifetimes of anthracene melt-grown single crystals and sublimation flakes have been examined at 298 and 77”K, using a mono-photon counting technique for the lifetime measurements. The observed emission decay times were nearly independent of the excitation wavelength, though a small dependence of the fluorescence specuum on the excitation wavelength was noted. By contrast. large variations of fluorescence lifetimes in thick crystals were found as a function of emission wavelength. For thick melt-grown single crystals at 298°K the lifetime was found lo increase from 9.8 nsec at 405 nm to 20.4 nsec a1 445 nm. For sublimation flakes at 77°K and at 298°K and for thick melt-grown crystals at 77OK. the lifetimes were less than 10 nsec and were nearly independent of emission wavelength. Despite these relatively large. variations in lifetimes, the decay rates at each separate wavelength remained exponential. within experimental error. Theoretical calculations were made of emission lifetimes based on a model with one reabsorbing state. The calculations ye in substantial agreement with the experimental IP sults.
1. introduction Previous investigations of fluorescence lifetimes of single anthracene crystals have been confined to the measurement of wavelength-averaged duration of fluorescence emission [ 1,2]. Logan et al. [2] observed an approximately threefold reduction in lifetime between 295 and 4.2%. and were able to account for this effect by a semi-empirical correction for reabsorption. The large temperature coefficient of this effect in anthracene is well known and stems from the absorption “hot band” which appears in antluacene at the band edge near 400 nm and which leads to sharply increased overlap of emission and absorption bands as the temperature is increased. Powell [3] has recently argued that while tie reduction in measured lifetime between 300 and 140°K may be attributed to reabl
7% work was supported in part by the National Science
Foundation. * Present addrus:
l
E.I. DuPont, Montague Works, Montague,
MichigvL * Author IO whom comspondence
should be addxesxd. Address after August 1.1974: Materials Research Center, Allied Chemical Corp., Morristown. NJ. 07960.
sorption, the decrease between 75 and 25°K must be accounted for on the basis of two emitting states in thermal equilibrium. Helftich and Lipsett [4] have further demonstrated the existence of a large, structureless background component to the anthracene emission spectrum of melt-grown crystals. They attribute this emission to traps caused by physical defects infroduced during.crystal growth and cite the supporting observation that their vapor-grown crystals exhibit substantially less background emission. McGhie et al. 151. on the other hand, observed shorter hole lifetimes in sublimation flakes than in meltgrown crystals and attribute the difference to impurity traps or structural defects in the sublimation flakes. Finally, Fielding and Jamagin [6] have carried out lifetime studies of anthracene fluorescence at low emission wavelength resolution. They suggest the possibility that formation of anthracene dimen is responsible for defect emission. The present paper reports a study of fluorescence lifetimes in single crystals of anthracene at moderately high wavelength resolution. Lifetimes and emission spectra are measured at room temperature and at 77°K for both thick melt grown crystals and for subli-
403
RI. Brenmn er al.. Fluorescence reabsorptionin anthracene singlecryslls
mation flakes. A front-surface geometry was used in all measurements. A theoretical model of the reabsorption process appears to represent adequately the observed lifetime measurements.
2. Experilnental All samples weregrepared from Eastman Organic Chemicals X480 anthracene which was chromatographed and then zone-refined in an argon atmosphere. Sublimation flakes were obtained either from the top of the zone-refining columns or from a sublimator similar to that described by GlBckner [I’]. Melt-grown crystals were prepared in a Bridgeman furnace and exhibited little hole or electron trapping. The meltgrown crystals were cleaved in a nitrogen atmosphere and mounted in a fluorescence cell which allowed front-surface excitation and collection of the fluorescznce emission, as well as temperature variation from 77 to 300°K. The cell was evacuated using a liquidnitrogen trapped high-vacuum pumping station. Emission spectra of all crystals were taken at 77°K and at’ room temperature both before and after temperature cycling. Illumination was provided by a high-pressure xenon lamp and Bausch and Lomb 250 mm grating monochromator set for a 17 nm band-pass. The fluorescence emission was collected from the front surface of the crystal with a parabolic mirror and imaged onto the input slits of a Bausch and Lomb high-intensity monochromator set for a band-pass of 3.7 nm. The fluorescence intensity was monitored with an EMI model 9601 B photomultiplier operated at -700 volt and recorded on an X-Y recorder. Spectra were collected by driving the wavelength selector of the analyzing monochrometer with a clock motor. Typical fluorescence spectra for sublimation flakes and thick crystals are shown in fig. 1, along with a composite absorption spectrum derived from work of Wolf [8], Clark and Philpott [9] and Nakada [IO]. The fluorescence spectra agree well with those obtained by other authors 14,111. The fluorescence of the sublimation flakes appears to be largely free of reabsorption effects, as indicated by the relative size of the vibronic bx:ds and by the fact that the emission spectrum is not affected by a IOO-fold change in the penetration depth of the exciting radiation. The thick
IO’-
350 WAVELENGTH
400
450
tnml
Fig. 1. Room temperature b-potied absorption spectra (solid curve) for anthracene single crystals from refs. (S-lo]. Also shown are our typical fluorescence spectra (dashed curves) obtained using front-surface collection and unpolarized excitation. The upper curve shows tbe results for a sublimation flake. at 77°K and for excitation rt either 300 nm or 360 nm. The lower curve shows the results for a chick crystal at room temperature ani for excitation at 360 nm. The O-O band in the thickcrystal results disappears completely for 300 nm excitation.
crystal, on the other hand, shows marked reabsorption effects. The O-O and O-l bands are greatly reduced in intensity relative to the O-2 band; in fact, the O-O band disappears completely for the deeply penetrating exciting radiation at 300 nm. Reduced temperature has the expected effect of reducing reabsorption effects in both types of crystal. The variable overlap of emission and absorption spectra is clearly evident in the temperature dependence of the absorption hot band as shown earlier by Nakada [IO]. The thick crystals show some reabsorption in the O-O band even at 77°K. For all crystals there is no perceptible change in the emission spectra after temperature cycling. Lifetime measurements of fluorescence emission were made by a single-photon counting technique [ 12). For these measurements a nanosecond flashlamp was substituted for the continuous Xe source in the emission apparatus described above. In addition an RCA 8575 timing photomultiplier operated at -2800 volt was used in place of the EM1 photomultiplier. To achieve adequate counting rates it was necessary to increase the bandpass of the excitation monochromator to 33 nm and the analyzing monochmmator to 14.8 nm.
404
RJ.
&reman
et al..
Fluorescence
reabsorption
in anthracene
single
crystals
r
Fig. 2. Block diagram of mono-photon counting appantus.
A block diagram of the apparatus is shown in fig. 2. The high-pressure hydrogen flash lamp was operated as a free-running relaxation oscillator at a repetition rate of about 2.5 -U-la. The delayed, attenuated (= 60 dB) voltage pulse, obtained by the use of a SOS2resistor in the flash lamp output circuit, provided the start signal for the EC&G Model TH 200A/N time to pulse amplitude converter (TAC). The TAC stop signal was derived from an EC&G model TDlO 1/N differential discriminator (single channel analyzer) operated in the differential mode. The more desirable lower level tuning mode of this discriminator could not be used due to the relatively small single-photon pulse amplitude available from the photomultiplier. Approximately one photon count was recorded for 100 lamp flashes. An EC&G model AN 109/N biased amplifier was used to interface the TAC and the 256 channel Northern Scientific Model 633 Minecoss pulse-height analyzer. A time resolution of approximately 0.19 nseclchannel was used for the collection of data. A model 33 ASR Teletvpe driven by the multichannel analyzer was used to provide a record of the data on paper tape; the data were subsequently transmitted to the Dartmouth time-sharing computer via an acoustic coupler for data processing and evaluation.
sublimation flake at 77OK and the thick melt-grown crystal at 298°K are shown in fig. 3 along with the signal recorded directly from the lamp. The lamp signal is sufficiently short so that no deconvolution of the data is required. The decay parameters are obtained by fitting the output of the multi-channel analyzer to a single exponential decay as shown in fig. 4. No significant discrepancy from the least-squares fit of the data for any wavelength examined is discernable indicating that the single-exponential function is an adequate description of the fluorescent emission. Standard deviations of all measurements are less than 0.2 nsec, and the estimated uncertainty is felt to be less than 0.5 nsec. The wavelength dependence of the fluorescence lifetime of the various classes of crystals studied is show< in fig. 5. The room-temperature fluorescence of the sublimation flake exhibits a decay with a lifetime weakly dependent on emission wavelength. The value:of this lifetime is found to increase from 8.1 nsec at 405 nm to 9.4 nsec at 445 run. At 77’K the lifetimes are decreased by approximately 2 nsec at each emission wavelength. At both temperatures the lifetime of tire sublimation flake is independent of excitation wavelength between 250 and 350 run. In contrast, the room-temperature fluorescence lifetime of the thick melt-grown crystal shows a strong dependence on the wavelength of tire observed emission. For such crystals an increase of approximately 10 nsec is observed between 405 and 445 run; the value of the lifetime at 405 nm is 9.8 nsec. at
3. Results 3.1. Experimental The typical time evolution of emission for the thin
Fig. 3. Typical fluorescence decay curves for a thick crystal and sublimation flake. The apparatus response function for the lamp alone is also shown.
405
R.J. Bafeman er aL. Fluorescence reabsorption in anfhmcenc singre crystals
of the lifetimes approach those obtained for the thin sublimation flake. 3.2. Theoretical It is well known that the effect of the imprisonment of luminescence is to lengthen the average duration of the emission. Corrections [ 13) have been proposed to account for the average increase in the lifetime due to fluorescence reabsorption in anthracene crystals. However, the differential .
1
Time Fig. 4. Fluorescence lifetime data for a thick crystal taken at several emission wavelengths.
I
,
I
1
dn (x. r)&f = -Kn(X, f) + F
1
l? t
I
I 400
YO
420
410
WAVELENGTH
440
450
Inml
Fig. 5. Summary of fluorescence lifetimes measured as a function of emission wavelength, temperature. and crystal
thickness.
425 nm it is 14.8 nsec and at 445 nm it increases to 20.4 nsec. No appreciable variation of the lifetime
with excitation wavelength is observed. The strong emission wavelength dependence of the fluorescence lifetime is sharply reduced at 77%. where the values
effect which ndia-
live migration and transfer exerts on various wavelengths of the emission spectrum has not to our knowledge been investigated. Qualitatively, of course. the first-order effect of reabsorption is an increase in lifetime at all emitted wavelengths. In a second-orde’r effect, however, it may be seen that lifetimes of the more weukly absorbed longer-wavelength radiation are increased more than the lifetimes of the short wavelengths. This result, somewhat surprising at fint, is easily seen to be a consequence of the fact that as time progresses the excitation density distribution moves farther into the crystal, from where the escape of the more weakly absorbed wavelength is favored. To account for the observed experimental results, a model for the reabsorption process has been examined theoretically. If one denotes the excitation density distribution as n(x. t), the first-order rate equation for a semi-infinite crystal with reabsorption included becomes Ri(X) )
(1)
where K is the usual first-order rate constant, Ri(X) is the rate of reabsorption of radiation in the wavelength region i, and x is measured along the C’ crystal direction. The exciton diffusion term , which would include effects of non-radiative energy transfer, has been neglected since it is found to have no significant effect on the lifetime as long as singlet quenching at
the surface is negligible (see append:bcx).To completely describe the physical situation the reabsorption terms Ri(X) must be three dimensional, must include the reflectivity of the surface, and must be properly weighted according to both the spectral distribution and the polarization ratio of the emitted light. This presents a rather complicated problem, but with a few very reasonable approximations we are able to
R J. Bateman et al. Fluorescence reabsorption in anthracene single crystals
406
calculate a useful comparison with our experiment.al
results. First, the polarization ratio (b to a) in anthracene is about 5.5 to 1 [14], so that the fluorescence radiation is emitted primarily in the plane defined by the C’ and 1 crystal axes. By assuming that the emitted light is all b polarized we reduce the problem to a two-dimensional calculation and R&z) may be written as * subject to the initial condition
4(x)
=F-
&j cl
dyn(,$,r)
0
d&O)
exp {-ki [(X1-X)2 + Y2 1‘12)
X
C
[(xl-x)2
f JJ] Ii2
+~ieXpI_ki[(X’+X)*
+Y’]“2}
[@‘+x)2 +y2] l/2
1’
(2)
for a semi-infinite crystal with surface at x=0 andy defmed as the II crystal direction. In this expression q is the fraction of the fluorescence in the wavelength range where the reabsorption is characterized by the absorption coefficient ki, and Qi is the reflectivity of the surface averaged over all angles of incidence for the emission wavelength region denoted by i. This averaged reflectivity would not be a sensitive function of wavelength since there would be substantial regions of essentially total internal reflection for each wavelength. We next simplify the calculation of n(x. t) by ap proximating the reabsorption by a single band containing a fraction Q of the fluorescence radiation and characterized by an effecthe absorption coefficient k. Simplified to the single reabsorption band and reduced to dimensionless form, eqs. (I) and (2) become dn (-2 @Ido =-n(-C,@+R(E)
(3)
and
l
of Beer’s law excita-
tion
A similar expression was originally derived by Agranovich and Faidish (IS] and letcr uwci by other authors Ill. 16 j in applications to steady-statekinetics. In each case only the radiative transfer of energy (fluorcscencc reabsorption) is considucd directly: non-radiative transfer may bc considered as a component of the dKTusionterm.
= exp(-U .
(3
Here k. is the absorption coefficient of the incident radiation, k is the absorption coefficient of the reabsorbed radiation, and 0, E, and 7 are equal to Kt, kOx, and k,,y, respectively. Eq. (3) is solved numerically for various combinations of the parameters OLand k/k, using Gauss’ formula to evaluate all integrals. A lower limit value of 0.8 is estimated for q3using the relevant optical data 191. The time dependence of the fluorescence at emission wavelength i is given by the following:
X
exp[-(k&M* +T~)“~I QZ t y*p
or, simplified to one-dimensional
fi(e)=
qki(l -@i) O” nk
0
I
(6)
geometry
J dSnQ,e) exp(-k&,1.
(7)
0
Eqs. (6) and (7) give essentially identical results for the cases of interest here. Numerical Integration of eq. (7) shows the intensity functions to be very nearly perfect single exponentials for the cases of interest. For comparison to the experimentally determined lifetimes, i.e., the roomtemperature thick-crystal results, we have chosen two cases: (1) ki/k, = 0 corresponding to the long-wavelength emission region and (2) ki/ko > 1 conespondingty roughly to the short-wavelength region. The results are shown in fig. 6 for various values of a, the fraction of the fluorescent photons characterized by
407
RJ. Ratemn et aL, Fluorescence reabsorption in anthmcene single crystals
the absorption coefficient k. First note that in agreement with experiment all lifetimes are lengthened, and long wavelengths are lengthened more than short. Secondly, the relative lifetimes depend only slightly on emission wavelength over a large range in k/kg. Finally, our experimental results would compare best to theory for a = 0.5 and k/k, == 1.O. The parameter k/k0 is probably best viewed as the ratio of the depth of the original excitation to the reabsorption length of the fluorescence in question. A value in the vi’cinity of unity is reasonable. ‘Ihe result a = 0.5 also appears quite consistent with our results: the O-O band is completely reabsorbed and the O-l band sharply attenuated; together these bands make up well over half of the emission.
4. Conclusion A two- to four-fold increase in the apparent fluorescence lifetime of anthracene is observed when the sample is in the form of single crystals thick compared to the absorption depth of the fluorescence radiation. The apparent increase in lifetime is greatest for the weakly reabsorbed (long-wavelength) components of the fluorescence radiation. This behavior is predicted qualitatively and semi-quantitatively by a model of the effects of multiple absorption and re-emission of the fluorescence radiation, including internal reflection from the crystal surface. The effects of exciton diffusion are found to be negligible.
46
I
-~-.mm___ H-C
-r
-075 30E Z -I
__---
__--
I
C--
1
a:05
____--___-_ ______J..OE I
40
w Fig. 6. Theoretid prediction of the r&tive ftuorescence tifetime increase due to reabsorption. Tlx pxamckr k/k. is the ratio of the penetration depth of the exciting radktion to the range of the reabsorbed fluorescence radiation; Q is a me-e of the fraction of the fluorescence radktion in the wavelength retion overlapping the absorption spectrum.
A solution suitable for numerical analysis is n&r)=
j
[K~R(x,x’)+P(x,x’)jn(x’.r-~)dr’,
where Af Q 1/K. The two probability distributions, R (x, x’) and P(x, x’), are needed to describe the time evolution of a delta-function distribution of singlet excitons. The term R (x, x’) is the probability that a photon, originating from a fluorescent event at x’, will be reabsorbed at a distance x from the surface.
Acknowledgement The authors wish to thank Professor C.L. Braun and Professor Alfred Prock for many helpful discussions and criticisms of this work and also Mr. David Homig for programming and carrying through the numerical calculations in the early stages of this work.
R(x,
mi
+ Appendix: Solution with diffusion included With the diffusion term included, eq. (1) becomes
an(x, o/at = D a*h.
tyax* -K~(x.
r) +R(x)
.(A11
x’) = -’Cqki
#i eXp{-ki[(X’
+X)* +y*]‘/*}
[(x’ t x)2 t yq ‘12
1
d_v-
WI
“Ihe quantity P(x, x’) is the probability distribution due to exciton diffusion and is simply the probability that an exciton originating at x’ will be found at x
R.J. Etaremanet aL. Fluorescence reabsorprion in anthracene sit&e crystals
408
after a time Art. Assuming no singlet quenching at the surface. P(x, x’) is given by
P(x, x’) =
1
,-KAt
2(DArn)‘~2
X {exp!-(x’-x)2/4Dat]
+ exp[-(x’+~)~/4DAt]
1. (A4)
Numerical results using this approach are found to be in good agreement with the results discussed earlier where diffusion is neglected. We therefore conclude that diffusion has no significant effect on the lifetime as long as surface quenching is negligible. References (I] J.B. BLks, T.A. King and I.H. hfUN0, Proc. PhyS. SOC. (London) 80 (1962) 355. :2] L.M. Logan, I.H. hfunro, D.F. Williams and F.R. Lipsett, in: Molecular luminescence, cd. EC. Lim (Benjamin, New York, 1969) p. 773.
[31 R.C. Powell, Phys. Rev. 82 (1970) 2090. 141 W. Helfrich and F.R. Lipsett, J. Chem. Phys. 43 (1965) 4368. (51 A.R. McGhie, A.M. Voshchenkov, P.J. Renaoft and MM. L&es, 1. Chem. whys. 48 (1968) 186. i6] P.E. Fielding and R.C. Jarnigan, J. Chem. Php. 47 (1967) 247. [7] E. Gl%kner. Diplomarbeit, Universidt Sluttgart (1969). 181 H.C. Wolf, Solid State Phys. 9 (1959) 1. 191 L.B. Clark and M.R. Phiipott, J.Chem. Phys. 53 (1970) 3790. [lo] 1. Nakada. J. phys. Sot. Japan 20 (1964) 346. [ 111 B_J. Mulder, Philips Res. Rept. Suppl. 4 (1968) 1. [ 121 C.D. Amata and P.K. Ludwig, J. Chem. Phys. 47 (1967) 3540. [ 131 J.B. Birks, in: Physics and chemistry of the organic solid state. eds. D. Fox, hf. Lakes and A. Weissberger (Interscience. New York, 1965) p. 434. [ 14) C.D. Akon and D.P. Craig, Trans. Faraday Sot. 62 (1966) 1673. 1151 V.M. Agranovich and A.N. Faidish, Opt. i Speklroskopiya 1 (1956) 885. [ 161 R.R. Chance and A. Rock. Phys. Stat. SOL b57 (1973) 597.
NORTH-HOLLAND PUBUSIIING COMPANY
FLUORESCENCE REABSORPTION IN ANTHRACENE SINGLE CRYSTALS: WITHEMISSIONWAVELENGTHANDTEMPER~TlJRE* LIFETIMEVARIATIONS Richard J. BATEhlAN *+, Ronald R CHANCE * and James F. HORNIG Lkrfmouth
College, Hanover, New Hampshire
03755,
USA
Received 17 December 1975 Revised manuscript received 27 February 1974
Fluorescence spectra and lifetimes of anthracene melt-grown single crystals and sublimation flakes have been examined at 298 and 77”K, using a mono-photon counting technique for the lifetime measurements. The observed emission decay times were nearly independent of the excitation wavelength, though a small dependence of the fluorescence specuum on the excitation wavelength was noted. By contrast. large variations of fluorescence lifetimes in thick crystals were found as a function of emission wavelength. For thick melt-grown single crystals at 298°K the lifetime was found lo increase from 9.8 nsec at 405 nm to 20.4 nsec a1 445 nm. For sublimation flakes at 77°K and at 298°K and for thick melt-grown crystals at 77OK. the lifetimes were less than 10 nsec and were nearly independent of emission wavelength. Despite these relatively large. variations in lifetimes, the decay rates at each separate wavelength remained exponential. within experimental error. Theoretical calculations were made of emission lifetimes based on a model with one reabsorbing state. The calculations ye in substantial agreement with the experimental IP sults.
1. introduction Previous investigations of fluorescence lifetimes of single anthracene crystals have been confined to the measurement of wavelength-averaged duration of fluorescence emission [ 1,2]. Logan et al. [2] observed an approximately threefold reduction in lifetime between 295 and 4.2%. and were able to account for this effect by a semi-empirical correction for reabsorption. The large temperature coefficient of this effect in anthracene is well known and stems from the absorption “hot band” which appears in antluacene at the band edge near 400 nm and which leads to sharply increased overlap of emission and absorption bands as the temperature is increased. Powell [3] has recently argued that while tie reduction in measured lifetime between 300 and 140°K may be attributed to reabl
7% work was supported in part by the National Science
Foundation. * Present addrus:
l
E.I. DuPont, Montague Works, Montague,
MichigvL * Author IO whom comspondence
should be addxesxd. Address after August 1.1974: Materials Research Center, Allied Chemical Corp., Morristown. NJ. 07960.
sorption, the decrease between 75 and 25°K must be accounted for on the basis of two emitting states in thermal equilibrium. Helftich and Lipsett [4] have further demonstrated the existence of a large, structureless background component to the anthracene emission spectrum of melt-grown crystals. They attribute this emission to traps caused by physical defects infroduced during.crystal growth and cite the supporting observation that their vapor-grown crystals exhibit substantially less background emission. McGhie et al. 151. on the other hand, observed shorter hole lifetimes in sublimation flakes than in meltgrown crystals and attribute the difference to impurity traps or structural defects in the sublimation flakes. Finally, Fielding and Jamagin [6] have carried out lifetime studies of anthracene fluorescence at low emission wavelength resolution. They suggest the possibility that formation of anthracene dimen is responsible for defect emission. The present paper reports a study of fluorescence lifetimes in single crystals of anthracene at moderately high wavelength resolution. Lifetimes and emission spectra are measured at room temperature and at 77°K for both thick melt grown crystals and for subli-
403
RI. Brenmn er al.. Fluorescence reabsorptionin anthracene singlecryslls
mation flakes. A front-surface geometry was used in all measurements. A theoretical model of the reabsorption process appears to represent adequately the observed lifetime measurements.
2. Experilnental All samples weregrepared from Eastman Organic Chemicals X480 anthracene which was chromatographed and then zone-refined in an argon atmosphere. Sublimation flakes were obtained either from the top of the zone-refining columns or from a sublimator similar to that described by GlBckner [I’]. Melt-grown crystals were prepared in a Bridgeman furnace and exhibited little hole or electron trapping. The meltgrown crystals were cleaved in a nitrogen atmosphere and mounted in a fluorescence cell which allowed front-surface excitation and collection of the fluorescznce emission, as well as temperature variation from 77 to 300°K. The cell was evacuated using a liquidnitrogen trapped high-vacuum pumping station. Emission spectra of all crystals were taken at 77°K and at’ room temperature both before and after temperature cycling. Illumination was provided by a high-pressure xenon lamp and Bausch and Lomb 250 mm grating monochromator set for a 17 nm band-pass. The fluorescence emission was collected from the front surface of the crystal with a parabolic mirror and imaged onto the input slits of a Bausch and Lomb high-intensity monochromator set for a band-pass of 3.7 nm. The fluorescence intensity was monitored with an EMI model 9601 B photomultiplier operated at -700 volt and recorded on an X-Y recorder. Spectra were collected by driving the wavelength selector of the analyzing monochrometer with a clock motor. Typical fluorescence spectra for sublimation flakes and thick crystals are shown in fig. 1, along with a composite absorption spectrum derived from work of Wolf [8], Clark and Philpott [9] and Nakada [IO]. The fluorescence spectra agree well with those obtained by other authors 14,111. The fluorescence of the sublimation flakes appears to be largely free of reabsorption effects, as indicated by the relative size of the vibronic bx:ds and by the fact that the emission spectrum is not affected by a IOO-fold change in the penetration depth of the exciting radiation. The thick
IO’-
350 WAVELENGTH
400
450
tnml
Fig. 1. Room temperature b-potied absorption spectra (solid curve) for anthracene single crystals from refs. (S-lo]. Also shown are our typical fluorescence spectra (dashed curves) obtained using front-surface collection and unpolarized excitation. The upper curve shows tbe results for a sublimation flake. at 77°K and for excitation rt either 300 nm or 360 nm. The lower curve shows the results for a chick crystal at room temperature ani for excitation at 360 nm. The O-O band in the thickcrystal results disappears completely for 300 nm excitation.
crystal, on the other hand, shows marked reabsorption effects. The O-O and O-l bands are greatly reduced in intensity relative to the O-2 band; in fact, the O-O band disappears completely for the deeply penetrating exciting radiation at 300 nm. Reduced temperature has the expected effect of reducing reabsorption effects in both types of crystal. The variable overlap of emission and absorption spectra is clearly evident in the temperature dependence of the absorption hot band as shown earlier by Nakada [IO]. The thick crystals show some reabsorption in the O-O band even at 77°K. For all crystals there is no perceptible change in the emission spectra after temperature cycling. Lifetime measurements of fluorescence emission were made by a single-photon counting technique [ 12). For these measurements a nanosecond flashlamp was substituted for the continuous Xe source in the emission apparatus described above. In addition an RCA 8575 timing photomultiplier operated at -2800 volt was used in place of the EM1 photomultiplier. To achieve adequate counting rates it was necessary to increase the bandpass of the excitation monochromator to 33 nm and the analyzing monochmmator to 14.8 nm.
404
RJ.
&reman
et al..
Fluorescence
reabsorption
in anthracene
single
crystals
r
Fig. 2. Block diagram of mono-photon counting appantus.
A block diagram of the apparatus is shown in fig. 2. The high-pressure hydrogen flash lamp was operated as a free-running relaxation oscillator at a repetition rate of about 2.5 -U-la. The delayed, attenuated (= 60 dB) voltage pulse, obtained by the use of a SOS2resistor in the flash lamp output circuit, provided the start signal for the EC&G Model TH 200A/N time to pulse amplitude converter (TAC). The TAC stop signal was derived from an EC&G model TDlO 1/N differential discriminator (single channel analyzer) operated in the differential mode. The more desirable lower level tuning mode of this discriminator could not be used due to the relatively small single-photon pulse amplitude available from the photomultiplier. Approximately one photon count was recorded for 100 lamp flashes. An EC&G model AN 109/N biased amplifier was used to interface the TAC and the 256 channel Northern Scientific Model 633 Minecoss pulse-height analyzer. A time resolution of approximately 0.19 nseclchannel was used for the collection of data. A model 33 ASR Teletvpe driven by the multichannel analyzer was used to provide a record of the data on paper tape; the data were subsequently transmitted to the Dartmouth time-sharing computer via an acoustic coupler for data processing and evaluation.
sublimation flake at 77OK and the thick melt-grown crystal at 298°K are shown in fig. 3 along with the signal recorded directly from the lamp. The lamp signal is sufficiently short so that no deconvolution of the data is required. The decay parameters are obtained by fitting the output of the multi-channel analyzer to a single exponential decay as shown in fig. 4. No significant discrepancy from the least-squares fit of the data for any wavelength examined is discernable indicating that the single-exponential function is an adequate description of the fluorescent emission. Standard deviations of all measurements are less than 0.2 nsec, and the estimated uncertainty is felt to be less than 0.5 nsec. The wavelength dependence of the fluorescence lifetime of the various classes of crystals studied is show< in fig. 5. The room-temperature fluorescence of the sublimation flake exhibits a decay with a lifetime weakly dependent on emission wavelength. The value:of this lifetime is found to increase from 8.1 nsec at 405 nm to 9.4 nsec at 445 run. At 77’K the lifetimes are decreased by approximately 2 nsec at each emission wavelength. At both temperatures the lifetime of tire sublimation flake is independent of excitation wavelength between 250 and 350 run. In contrast, the room-temperature fluorescence lifetime of the thick melt-grown crystal shows a strong dependence on the wavelength of tire observed emission. For such crystals an increase of approximately 10 nsec is observed between 405 and 445 run; the value of the lifetime at 405 nm is 9.8 nsec. at
3. Results 3.1. Experimental The typical time evolution of emission for the thin
Fig. 3. Typical fluorescence decay curves for a thick crystal and sublimation flake. The apparatus response function for the lamp alone is also shown.
405
R.J. Bafeman er aL. Fluorescence reabsorption in anfhmcenc singre crystals
of the lifetimes approach those obtained for the thin sublimation flake. 3.2. Theoretical It is well known that the effect of the imprisonment of luminescence is to lengthen the average duration of the emission. Corrections [ 13) have been proposed to account for the average increase in the lifetime due to fluorescence reabsorption in anthracene crystals. However, the differential .
1
Time Fig. 4. Fluorescence lifetime data for a thick crystal taken at several emission wavelengths.
I
,
I
1
dn (x. r)&f = -Kn(X, f) + F
1
l? t
I
I 400
YO
420
410
WAVELENGTH
440
450
Inml
Fig. 5. Summary of fluorescence lifetimes measured as a function of emission wavelength, temperature. and crystal
thickness.
425 nm it is 14.8 nsec and at 445 nm it increases to 20.4 nsec. No appreciable variation of the lifetime
with excitation wavelength is observed. The strong emission wavelength dependence of the fluorescence lifetime is sharply reduced at 77%. where the values
effect which ndia-
live migration and transfer exerts on various wavelengths of the emission spectrum has not to our knowledge been investigated. Qualitatively, of course. the first-order effect of reabsorption is an increase in lifetime at all emitted wavelengths. In a second-orde’r effect, however, it may be seen that lifetimes of the more weukly absorbed longer-wavelength radiation are increased more than the lifetimes of the short wavelengths. This result, somewhat surprising at fint, is easily seen to be a consequence of the fact that as time progresses the excitation density distribution moves farther into the crystal, from where the escape of the more weakly absorbed wavelength is favored. To account for the observed experimental results, a model for the reabsorption process has been examined theoretically. If one denotes the excitation density distribution as n(x. t), the first-order rate equation for a semi-infinite crystal with reabsorption included becomes Ri(X) )
(1)
where K is the usual first-order rate constant, Ri(X) is the rate of reabsorption of radiation in the wavelength region i, and x is measured along the C’ crystal direction. The exciton diffusion term , which would include effects of non-radiative energy transfer, has been neglected since it is found to have no significant effect on the lifetime as long as singlet quenching at
the surface is negligible (see append:bcx).To completely describe the physical situation the reabsorption terms Ri(X) must be three dimensional, must include the reflectivity of the surface, and must be properly weighted according to both the spectral distribution and the polarization ratio of the emitted light. This presents a rather complicated problem, but with a few very reasonable approximations we are able to
R J. Bateman et al. Fluorescence reabsorption in anthracene single crystals
406
calculate a useful comparison with our experiment.al
results. First, the polarization ratio (b to a) in anthracene is about 5.5 to 1 [14], so that the fluorescence radiation is emitted primarily in the plane defined by the C’ and 1 crystal axes. By assuming that the emitted light is all b polarized we reduce the problem to a two-dimensional calculation and R&z) may be written as * subject to the initial condition
4(x)
=F-
&j cl
dyn(,$,r)
0
d&O)
exp {-ki [(X1-X)2 + Y2 1‘12)
X
C
[(xl-x)2
f JJ] Ii2
+~ieXpI_ki[(X’+X)*
+Y’]“2}
[@‘+x)2 +y2] l/2
1’
(2)
for a semi-infinite crystal with surface at x=0 andy defmed as the II crystal direction. In this expression q is the fraction of the fluorescence in the wavelength range where the reabsorption is characterized by the absorption coefficient ki, and Qi is the reflectivity of the surface averaged over all angles of incidence for the emission wavelength region denoted by i. This averaged reflectivity would not be a sensitive function of wavelength since there would be substantial regions of essentially total internal reflection for each wavelength. We next simplify the calculation of n(x. t) by ap proximating the reabsorption by a single band containing a fraction Q of the fluorescence radiation and characterized by an effecthe absorption coefficient k. Simplified to the single reabsorption band and reduced to dimensionless form, eqs. (I) and (2) become dn (-2 @Ido =-n(-C,@+R(E)
(3)
and
l
of Beer’s law excita-
tion
A similar expression was originally derived by Agranovich and Faidish (IS] and letcr uwci by other authors Ill. 16 j in applications to steady-statekinetics. In each case only the radiative transfer of energy (fluorcscencc reabsorption) is considucd directly: non-radiative transfer may bc considered as a component of the dKTusionterm.
= exp(-U .
(3
Here k. is the absorption coefficient of the incident radiation, k is the absorption coefficient of the reabsorbed radiation, and 0, E, and 7 are equal to Kt, kOx, and k,,y, respectively. Eq. (3) is solved numerically for various combinations of the parameters OLand k/k, using Gauss’ formula to evaluate all integrals. A lower limit value of 0.8 is estimated for q3using the relevant optical data 191. The time dependence of the fluorescence at emission wavelength i is given by the following:
X
exp[-(k&M* +T~)“~I QZ t y*p
or, simplified to one-dimensional
fi(e)=
qki(l -@i) O” nk
0
I
(6)
geometry
J dSnQ,e) exp(-k&,1.
(7)
0
Eqs. (6) and (7) give essentially identical results for the cases of interest here. Numerical Integration of eq. (7) shows the intensity functions to be very nearly perfect single exponentials for the cases of interest. For comparison to the experimentally determined lifetimes, i.e., the roomtemperature thick-crystal results, we have chosen two cases: (1) ki/k, = 0 corresponding to the long-wavelength emission region and (2) ki/ko > 1 conespondingty roughly to the short-wavelength region. The results are shown in fig. 6 for various values of a, the fraction of the fluorescent photons characterized by
407
RJ. Ratemn et aL, Fluorescence reabsorption in anthmcene single crystals
the absorption coefficient k. First note that in agreement with experiment all lifetimes are lengthened, and long wavelengths are lengthened more than short. Secondly, the relative lifetimes depend only slightly on emission wavelength over a large range in k/kg. Finally, our experimental results would compare best to theory for a = 0.5 and k/k, == 1.O. The parameter k/k0 is probably best viewed as the ratio of the depth of the original excitation to the reabsorption length of the fluorescence in question. A value in the vi’cinity of unity is reasonable. ‘Ihe result a = 0.5 also appears quite consistent with our results: the O-O band is completely reabsorbed and the O-l band sharply attenuated; together these bands make up well over half of the emission.
4. Conclusion A two- to four-fold increase in the apparent fluorescence lifetime of anthracene is observed when the sample is in the form of single crystals thick compared to the absorption depth of the fluorescence radiation. The apparent increase in lifetime is greatest for the weakly reabsorbed (long-wavelength) components of the fluorescence radiation. This behavior is predicted qualitatively and semi-quantitatively by a model of the effects of multiple absorption and re-emission of the fluorescence radiation, including internal reflection from the crystal surface. The effects of exciton diffusion are found to be negligible.
46
I
-~-.mm___ H-C
-r
-075 30E Z -I
__---
__--
I
C--
1
a:05
____--___-_ ______J..OE I
40
w Fig. 6. Theoretid prediction of the r&tive ftuorescence tifetime increase due to reabsorption. Tlx pxamckr k/k. is the ratio of the penetration depth of the exciting radktion to the range of the reabsorbed fluorescence radiation; Q is a me-e of the fraction of the fluorescence radktion in the wavelength retion overlapping the absorption spectrum.
A solution suitable for numerical analysis is n&r)=
j
[K~R(x,x’)+P(x,x’)jn(x’.r-~)dr’,
where Af Q 1/K. The two probability distributions, R (x, x’) and P(x, x’), are needed to describe the time evolution of a delta-function distribution of singlet excitons. The term R (x, x’) is the probability that a photon, originating from a fluorescent event at x’, will be reabsorbed at a distance x from the surface.
Acknowledgement The authors wish to thank Professor C.L. Braun and Professor Alfred Prock for many helpful discussions and criticisms of this work and also Mr. David Homig for programming and carrying through the numerical calculations in the early stages of this work.
R(x,
mi
+ Appendix: Solution with diffusion included With the diffusion term included, eq. (1) becomes
an(x, o/at = D a*h.
tyax* -K~(x.
r) +R(x)
.(A11
x’) = -’Cqki
#i eXp{-ki[(X’
+X)* +y*]‘/*}
[(x’ t x)2 t yq ‘12
1
d_v-
WI
“Ihe quantity P(x, x’) is the probability distribution due to exciton diffusion and is simply the probability that an exciton originating at x’ will be found at x
R.J. Etaremanet aL. Fluorescence reabsorprion in anthracene sit&e crystals
408
after a time Art. Assuming no singlet quenching at the surface. P(x, x’) is given by
P(x, x’) =
1
,-KAt
2(DArn)‘~2
X {exp!-(x’-x)2/4Dat]
+ exp[-(x’+~)~/4DAt]
1. (A4)
Numerical results using this approach are found to be in good agreement with the results discussed earlier where diffusion is neglected. We therefore conclude that diffusion has no significant effect on the lifetime as long as surface quenching is negligible. References (I] J.B. BLks, T.A. King and I.H. hfUN0, Proc. PhyS. SOC. (London) 80 (1962) 355. :2] L.M. Logan, I.H. hfunro, D.F. Williams and F.R. Lipsett, in: Molecular luminescence, cd. EC. Lim (Benjamin, New York, 1969) p. 773.
[31 R.C. Powell, Phys. Rev. 82 (1970) 2090. 141 W. Helfrich and F.R. Lipsett, J. Chem. Phys. 43 (1965) 4368. (51 A.R. McGhie, A.M. Voshchenkov, P.J. Renaoft and MM. L&es, 1. Chem. whys. 48 (1968) 186. i6] P.E. Fielding and R.C. Jarnigan, J. Chem. Php. 47 (1967) 247. [7] E. Gl%kner. Diplomarbeit, Universidt Sluttgart (1969). 181 H.C. Wolf, Solid State Phys. 9 (1959) 1. 191 L.B. Clark and M.R. Phiipott, J.Chem. Phys. 53 (1970) 3790. [lo] 1. Nakada. J. phys. Sot. Japan 20 (1964) 346. [ 111 B_J. Mulder, Philips Res. Rept. Suppl. 4 (1968) 1. [ 121 C.D. Amata and P.K. Ludwig, J. Chem. Phys. 47 (1967) 3540. [ 131 J.B. Birks, in: Physics and chemistry of the organic solid state. eds. D. Fox, hf. Lakes and A. Weissberger (Interscience. New York, 1965) p. 434. [ 14) C.D. Akon and D.P. Craig, Trans. Faraday Sot. 62 (1966) 1673. 1151 V.M. Agranovich and A.N. Faidish, Opt. i Speklroskopiya 1 (1956) 885. [ 161 R.R. Chance and A. Rock. Phys. Stat. SOL b57 (1973) 597.