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Spectral diffusion of triplet excitation energy in molecular glasses and doped polymer solids
Chemical Physics 146 (1990) 303-314 North-Holland
Spectral diffusion of triplet excitation energy in molecular glasses and doped polymer solids Seong-Keun Kook and David M. Hanson Department of Chemistry, State University of New York, Stony Brook, NY I 1794-3400, US4 Received 12 January 1990
Steady state phosphorescence at 4.2 K is monitored for different concentrations of Cmethylbenzophenone (MBP) doped into polystyrene. At concentrations less than 20%. the spectra are characteristic of separated molecules embedded in a disordered matrix. As the concentration increases to 2O%,the vibronic bands shift to longr wavelengths and become slightly sharper. At concentrations above 30%,the spectra have additional features due to aggregates,which appear to be characteristic of a segregated phase of MBP. Triplet excitation energy transport in glassy MBP and MBP doped into a polystyrene matrix is monitored for different excitation energies and temperatures using time-resolved spectroscopy. These experiments reveal that spectral diffusion at liquid helium temperatures is not thermally activated, and that the spectral diffusion efftciency increases abruptly at a critical mole fraction of acceptors, 0.054, which corresponds to a critical distance of 9.8 A.Although low-dimensional energy transfer dynamics has been revealed in other studies of disordered systems, the results indicate that spectral diffusion in these systems is controlled by a three-dimensional exchange interaction and the emission of phonons and/or vibrons.
1. Introduction The phenomenon of excitation energy transport in condensed molecular systems has been of continuing research interest. Theories of energy transfer have been discussed in terms of different interaction mechanisms, e.g., exchange coupling, multipolar interaction, and superexchange tunneling [ l-31. Recent theoretical and experimental investigations have focused on this phenomenon in disordered systems. Inokuti and Hirayama [4] formulated a theory involving the isotropic exchange interaction for direct (single step) triplet state energy transfer from a donor to randomly distributed acceptors in three dimensions. This theory later was generalized to all dimensions, and a configuration average valid for all acceptor concentrations was introduced [ 5 1. The energy transfer problem in multicomponent systems has been associated with the concept of critical concentrations [ 6-91. Parson and Kopelman [lo] and Griinewald et al. [ 111 studied theoretically the migration of incoherent excitations in energetically disordered system using a self-consistent diagrammatic approximation. Spatial diffusion and energy relaxa0301-0104/90/$03.50
tion observables are related to the solution of a nonlinear integral equation. The dependence of spatial and spectral transport properties upon the spatial range and the energy dependence of the intermolecular hopping rate is examined. The intimate relationship between spatial transport and energy relaxation is discussed in detail. After Mandelbrot’s formulation of fractal geometry [ 121, the concept of a fmctal dimension has been used to describe complex geometric environments as well as processes that occur in these environments. Klafter, Blumen and Zumofen [ 13,141 suggested the application of energy transfer experiments to determine the fractal and spectral dimensions. The first experiment using energy transfer to obtain a fractal dimension was reported by Jortner and co-workers [ 15 1. Kopelman applied percolation theory [ 6 ] and fractal geometry [ 16 ] to the case of mutistep energy transfer, where the acceptor concentration is low. Lin and Hanson used the concept of a fractal dimension to analyze the kinetics of direct donor-acceptor energy transfer in a doped polymer glass [ 17 1. Spectral diffusion can be defined as the process of energy transfer between molecules that have differ-
0 1990 - Elsevier Science Publishers B.V. (North-Holland)
304
S.-K. Kook, D.M. Hanson 1 Triplet excitation energy in molecular glasses
ent transition energies in a single-component energy transfer system. The distribution of transition energies, which is called inhomogeneous broadening, results from the different local environments or disorder of the molecules in the sample. For the case where the inhomogeneous width is less than kT, spectral diffusion causes an initially sharp excitation line to broaden to the full inhomogeneous width. For the case where the inhomogeneous width is greater than kT, spectral diffusion causes relaxation to lower energy molecules or sites. Experimental studies of spectral diffusion generally have measured luminescence spectra as a function of excitation energy, temperature, concentration, and time. For molecular systems, time-resolved phosphorescence spectra have revealed the dynamics and demonstrated the excitation energy dependence of triplet state spectral diffusion in organic glasses [ 18-22 ] as well as in disordered organic crystals [ 23-29 1. Richert and B&sler [ 2 1,221 reported measurements of the decay of the 0,O phosphorescence band of organic glasses (benzophenone, anthraquinone, and phenanthrene) formed by vapor deposition on a cold substrate or in one case by quenching a molten drop on a liquid helium cold finger. The triplet state population was created indirectly with nitrogen laser excitation by intersystem crossing from the singlet manifold. Consequently, the initial distribution of triplet state excitation energies is not known. The data were analyzed in terms of multiple step hopping down the cascade of states that form the inhomogeneously broadened band. Jankowiak, Ries and Bgissler [ 191 observed spectral diffusion and triplet exciton localization in glassy 2-bromonaphthalene following direct triplet state excitation with a tunable, nitrogen laser pumped, dye laser. Both the origin of the phosphorescence and the Stokes shift between excitation and phosphorescence varied continuously with excitation energy. In all cases the phosphorescence was inhomogeneously broadened and the case of true resonance phosphorescence, characterized by sharp line emission, was not attained. The results were analyzed in terms of stochastic hopping down a Gaussian density of states. The relaxation rate decreases as the density of states decreases producing an excitation energy dependent phosphorescence origin and Stokes shift. El-Sayed and co-workers [ 23-261 studied energy
transfer and spectral diffusion in the orientationally disordered crystal I-bromo4chloronaphthalene. They observed the loss of resonance-like phosphorescence and the appearance of broad lower energy phosphorescence with time following direct triplet state excitation. The relaxation rate increased with temperature and with excitation energy. Unlike the case of glassy 2-bromonaphthalene [ 19 1, the Stokes shift of the relaxed phosphorescence appears to be independent of time, and the phosphorescence origin appears to be independent of the excitation energy. The spectral diffusion was attributed to rapid relaxation down the inhomogeneously broadened band of states until the density of acceptors is so low that the energy transfer rate becomes negligible. The relaxed phosphorescence thus appears at the same wavelength independent of excitation energy. The decay of the long wavelength portion of the 0, 0 phosphorescence band was described by energy transfer, occurring in a single step, to lower energy acceptors. It was found that the dominant mechanism for this energy transfer appears to switch from exchange to dipolar coupling as the density of acceptor decreases. Prasad and co-workers [ 26-291 observed spectral diffusion in orientationally disordered 4-bromo-4’chlorobenzophenone (BCBP) and in crystalline solutions of 1-bromo_4chloronaphthalene (BCN ) and 1+dibromonaphthalene (DBN). The latter system exhibits both orientational and substitutional disorder. For the case of BCBP, time-resolved studies revealed that the phosphorescence profile gradually shifts by a few wavenumbers toward the lower energy sites with increasing time following excitation. This observation implies that the density of acceptor states plays the dominant role in spectral diffusion and not coupling to phonons or vibrons. If the latter were dominant, the spectral profile should shift abruptly by much larger amounts, characteristic of the phonon or vibron frequencies. Spectral diffusion differs in the BCN/DBN solid solutions. For this system, the resonance phosphorescence decreases in intensity with increasing time after excitation, and a broad luminescence peak 20 cm-’ to the red increases in intensity, i.e. the resonance phosphorescence does not boraden and shift gradually with increasing delay time. The abrupt ( < 20 ps) appearance of a 20 cm-’ Stokes shift could be caused by emission of 20 cm-’ phonons or by rapid energy cascade through the in-
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular ghsses
tervening states. Since resonance-like phosphorescence is observed when these states are excited directly, the latter possibility can be eliminated, vide infra. To summerize, these previous studies of spectral diffusion of triplet excited states in molecular solids have revealed the existence of energy cascade relaxation involving both continuous and discrete energy losses. The relevance of various interaction mechanisms and theories of energy transfer have been examined. However, no studies of spectral diffusion following direct triplet excitation from the ground state in polymer glasses have been reported. Such experiments have been conducted only on disordered crystals or molecular glasses. Here we report observations of energy transfer and spectral diffusion in glassy Cmethylbenzophenone (MBP) and in MBP doped into a polystyrene glass. Time-resolved spectra were obtained for different excitation energies, acceptor concentrations, and temperatures. The data were analyzed in terms of direct donor-acceptor excitation transport by exchange coupling using the theoretical concepts presented by Blumen [ 51 and also used by Talpatra, Rao and Prasad [ 29 1.
305
fluid helium in an optical dewar to achieve temperatures of 4.2 and 1.8 K. A pulsed nitrogen laser (Molectron UV400) and a tunable dye laser (Molectron DL400) were used as excitation sources for the measurements. Pulse widths were 10 ns. Tram-diphenylstilbene (DPS ) dye (Exciton) was used. The phosphorescence was monitored with a double spectrometer (Spex 1302) and an EM1 9865 photomultiplier tube. Steady state measurements were made using a current amplifier. A boxcar integrator (PAR 162 with model 164 gated integrator modules) was used for time-resolved data acquisition. Light from the dye laser incident on a photodiode was used to trigger the boxcar. All the experiments were controlled by a Digital PDP 11/23 + computer system. The spectra, collected through an analog to digital converter, were stored on disc for further analysis. A schematic diagram of the instrumentation is shown in fig. 1. The time response of the electronics was tested with a pulse generator. It was found that the response time of the boxcar integrator, including a rc filter on the input, was faster than 2 us.
3. Results 2. Experimental techniques 4-methylbenzophenone, obtained from Aldrich, was recrystallized from ether, and zone refined for 100 passes at a velocity of 1.5 inch per hour. Glassy MBP was produced by quench freezing a molten droplet of the material on a cold quartz surface lying over a Pyrex evaporating dish containing liquid nitrogen. To prepare the doped polymer films, MBP was mixed with polystyrene, using toluene as a solvent, to obtain the desired concentrations ranging from 1 to 50 weight per cent. Polymer films were formed by placing 30 drops of the MBP/polystyrene solution onto a 1 cm x 1 cm quartz plate lying on a platform which was heated to 65 oC by a hot plate. The rate of solvent evaporation was controlled by covering the entire platform with a funnel. The films appeared optically clear for concentrations less than 20%, and milky for concentrations more than 30%. Concentrations between 20 and 30% were not prepared. The samples were immersed in liquid helium or super-
A set of steady state phosphorescence spectra, obtained at 4.2 K, for different concentrations of MBP doped into polystyrene, is shown in fig. 2. The vibronic bands shift to longer wavelengths and become slightly sharper as the concentration increases from 1 to 20%. See table 1 where the full width at half intensity (fwhi) of the O-l peak is listed. At higher concentrations, an additional band appears on the higher energy side of each of the original bands. These new bands match those of glassy MBP. Fig. 2 also shows the phosphorescence spectrum of glassy MBP. Fig. 3 shows time-sampled spectra in the region of the first vibronic band of the phosphorescence of glassy MBP at 4.2 K as a function of excitation energy. Excitation wavelengths are on and above the high energy edge of the O-O phosphorescence band. In each case the spectrum was sampled after a 10 us delay using a 5 us sampling time. In order to avoid interference with scattered light due to the laser, the first vibronic band of the emission was monitored. At the low excitation energy (4055 A), two relatively sharp ( fwhi z 35 cm- ’ ) resonant emission lines are
306
S.-K. Kook D.M. Hamon / Triplet excitation energy in mokcdar glasses 7
Grating :: /:
’ : : :
0
Photodiode
Fig. 1. A schematic diagram of the instrumentation.
Phosphorescence band positions (MBP/polystyrene) Cont. (96)
aom
ao% so%
1 5 10 20
(A) and bandwidth (cm-‘)
Phosphorescence band
Bandwidth O-l (cm-‘)
O-O
O-l
O-2
4145 4180 4186 4195
4452 4485 4488 4506
4769 4820 4828 4852
699 618 541 521
observed. As the excitation energy increases, a broad ( fwhi w 380 cm- ’ ) luminescence band of increasing intensity develops to lower energy, and the peak of this broad luminescence shifts to shorter wavelengths. The resonant emission lines shift with changes in the excitation energy as expected. See table 2 where the mean position of the doublet is listed, I,. Table 2 also gives the peak position and Stokes 4 Fig. 2. Steady state phosphorescence spectra obtained at 4.2 K for MBP/polystyrene at the specified weight per cent wncentrations. The lowermost spectrum is that of glassy MBP.
307
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
404lA
404sA
405oA
4055A
405sA
c
.
.
.
.
425
.
.
4
460 rinnm
Fig. 4. First vibronic band of glassy MBP phosphorescence at 1.8 K as a function of excitation energy. (Delay time: 10 ps, sampling time: 5 us.)
Fig. 3. First vibronic band of glassy MBP phosphorescence at 4.2 K as a function of excitation energy. (Delay time: 10 us, sampling time: 5 us. )
shift of the relaxed emission, A,,. At 1.8 K, similar features are observed, see fig. 4. The time delay of 10 ps between excitation and observation ensures that the sharp features are reso-
nance phosphorescence and are not caused by Raman scattering. In addition, the decreasing intensity of the sharp features with increasing excitation energy is not characteristic of Raman scattering. The Raman intensity should increase due to the v“ non-
Table 2 Correlation of excitation and phosphorescence wavelengths l) 1
(5
4041.0 4045.0 4050.0 4055.0
L(~l)
(A) 4322.7 4327.3 4333.3 4339.0
wit.
A-el(o-1)
boku
(cm-‘)
(A)
(cm-‘)
1613 1613 1614 1614
4377.0 4381.0 4386.0
287 283 277
*) &xc is the excitation wavelength, A, is the vibronic resonance phosphorescence shifted by an amount At&, Ati is the relaxed phosphorescence shifted by an amount A&+,
from A,
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
308
resonant frequency dependence and due to resonant contributions from the T, t So absorption. Time-resolved phosphorescence spectra of glassy MBP at 4.2 and 1.8 K for different delay times following excitation are shown in figs. 5 and 6, respectively. The excitation energy was 4055 A. At a short delay time, e.g., 10 us, as mentioned above, two sharp resonant emission lines on a broad background are observed. At longer delay times, a broad phosphorescence band develops to lower energy. The intensity of the broad band increases and the intensity of the sharp lines decreases as a function of increasing delay time. The position and width of the broad band appear to be independent of the delay time. At higher
b
.
425
.
,
460 Alnnm
Fig. 6. Time-resolved phosphorescence spectra of glassy MBP at 1.8 K for different delay times with excitation at 4055 A. The delay time is specified, the sampling time was 5 1s.
,
.
.
.
425
.
.
-
, 460
rinnm
Fig. 5. Time-resolved phosphorescence spectra of glassy MBP at 4.2 K for different delay times with excitation at 4055 A. The delay time is specified, the sampling time was 5 vs.
temperatures (77 K), no resonant phosphorescence is observed due to fast spectral diffusion. Only the broad peak was observed at all excitation energies, even at short times. Similar data were obtained at 4.2 K for MBP doped into polystyrene. Selected spectra obtained for 50% MBP are shown in fig. 7. The Stokes shift of the relaxed phosphorescence for the polymer glasses is about 760 cm-‘, which differs significantly from that observed for glassy MBP. A phosphorescence excitation spectrum obtained at 4.2 K for glassy MBP is shown in fig_ 8. The phosphorescence was monitored at 4396 A with a bandpass of 0.7 A, and the emission intensity was normalized to account for the variation in the laser intensity
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glosses
309
with wavelength. A photodiode was used to monitor the laser intensity. The peak in the excitation spectrum of glassy MBP is at 403 nm with a width of 197 cm-’ (fwhi).
4. Discussion 4.1. Concentration dependence
,
.
.
,
430
.
-1
46s
rinnm Fig. 7. First vibronic band of the phosphorescence of 50%MBP in polystyrene at 4.2 K as a function of excitation energy. (Delay time: 10 us, sampling time: 5 us.)
‘\
\ 1
&
400
401
402
403
l\,\ I
404
40B
452
A in nnr
Fig. 8. Excitation spectrum obtained by monitoring phosphorescence at 4.2 K for glassy MBP. The dotted curve is a Gaussian profile plotted in wavelength centered at 403 nm with a width of 197 cm-’ (fwhi). The arrows show the excitation wavelengths used in the phosphorescence studies.
The system of MBP in polystyrene is inhomogeneous. Molecules in different environments have different transition energies and produce different spectra. At low concentrations most MBP molecules are essentially isolated from each other and surrounded by polymer. The energy levels of these molecules are widely distributed due to the intrinsic disorder property of the polymer. This disorder produces the broad phosphorescence. As the concentration increases, the separation between MBP molecules decreases, the intermolecular interaction increases, and energy transfer becomes more efficient. As a result, the excitation energy can relax to a deeper and more homogeneous distribution of traps. Consequently as shown in fig. 2, the phosphorescence bands become narrower and shift to lower energy as the concentration increases. At and above 30% MBP, new peaks are present, and the samples appear milky. By inspecting the samples used in the experiments under a microscope ( 100 x ) , crystallites are observed that appear similar to crystals formed by recrystallization. The new peaks correspond in wavelength to those obtained from glassy MBP. These observations indicate that at concentration of 330% MBP aggregates form in the polymer films. Aggregation has been reported previously for 4bromo-4’-chlorobenzophenone (BCBP) in polystyrene by Lin and Hanson [ 17 1, but the characteristics of the aggregation differ for these two systems. For BCBP, the samples become translucent at a concentration of 12%, and by using a microscope ( 100 x ), the samples are seen to contain tree-like aggregates with numerous branches. These aggregates are different from crystals obtained by recrystallization. The aggregates are only present in samples at concentrations above about 10% and become increasingly dense as the concentration increases. Like MBP, the aggre-
S.-K. Kook, D.M. Hanson/ Tripletexcitationenergyin mokcu/arghsses
310
gates contribute additional bands to the phosphorescence spectrum. Unlike the case of MBP, in BCBP the aggregation occurs completely over a narrow concentration range. The phosphorescence spectrum of BCBP at 20% is entirely that of the aggregate. In contrast, the spectrum of MBP at 50% is still of mixed character, containing contributions from both aggregates and molecules. Since the conditions for the preparation of polystyrene films doped with MBP or with BCBP were different, it is not clear to what extent kinetic constraints affected the formation of the aggregates in these two systems. The morphology of the aggregates as seen with a microscope, however, seems to indicate that BCBP/polystyrene forms a mixed phase with a high BCBP concentration and that MBP forms a segregated phase.
The results shown in fgs. 3 and 4 reveal a strong dependence of the spectral diffusion rate on the excitation energy as was found for the disordered crystalline solutions of bromochloronaphthalene and dibromonaphthalene [ 29 1. We apply the analysis used for these crystals to the present case of a glass. The molecules are divided into three classifications: donors - molecules requiring an excitation energy equal to the initial excitation energy, acceptors - molecules requiring an excitation energy lower than the initial excitation energy, and barriers - molecules requiring an excitation energy greater than the initial excitation energy. The number of donors, acceptors, and barriers depends on the initial excitation energy used. As the excitation energy increases, the density of acceptor sites increases. This increase enhances the energy transfer rate from donors to acceptors. The mole fraction of acceptor concentration is given by 7 Z(v)dv/ --oD
7 Z(v)dv, --oo
x(Av)-‘]*}dv.
(1)
where Z( v) is the absorption profile for the system. If we assume a Gaussian distribution for the intensity profile,
(2)
Here Au is the half-width of the distribution (hwhi). The acceptor concentration then can be written in terms of an error function as [ 28 ]
Ca(vex)=t[l-erf(z)l,
(3)
vex) (ln2)‘/*/Av; v, is the abwhere z= (v,sorption maximum. In a similar way, if we assume that the laser profile is Gaussian with hwhi = A vL, centered at v,,, the donor concentration can be written as C,( v,,) = (Av,/Av)
4.2. Dynamics of spectral diji’kion
C,(v,,)=
C,( v,,)= (Av)-L(ln2/x)‘/2 “cr exp{-[(v-v,)(ln2)‘/* X I --oD
exp( -z*)
.
(4)
When the excitation energy is at 4055 A, using Au,= 0.5 cm-‘, we have the acceptor and the donor concentrations as c,=O.O34 and c,= 0.00168, expressed as mole fraction. Since the donor and acceptor are the same molecular species, we assume the same quantum yield and instrumental response for donor and acceptor emission. The spectral diffusion efficiency is given as the ratio of the integrated intensity of acceptor emission to the total integrated emission
43
a=la+ld*
(5)
Fig. 9 shows a plot of the ratio (Yversus the acceptor concentration c,, determined from eq. (3), for different excitation energies. This graph shows the dependence of the spectral diffusion efficiency on the density of the acceptor sites for a delay time of 10 ps and a sampling time of 5 ps with the sample temperature at 4.2 K. The ratio (Ychanges abruptly at a critical concentration. The critical concentration (where a = 0.5 ) is found to be 0.054, and the calculated critical distance is 9.8 A, see appendix A. These values compare with those found in other systems, e.g., the critical concentrations are 0.03,0.06-0.07, and 0.05 for benzene, naphthalene, and phenanzine respectively [ 9 1, and the critical distances are 1 l- 18 A for aromatic molecule systems [ 301. The abrupt change in (Yaround the critical concentration is characteris-
S.-K. Kook, D.M. Hanson / Tripletexcitationenergy in molecular glasses
0.0 -
O.O-
a
ca Fig. 9. Plot of the spectral difhsion ticiency concentration of glassy MBP at 4.2 K.
a wrsus acceptor
tic of a short range exchange interaction. Consequently the exchange mechanism is used to analyze the time evolution of the spectral diffusion. At 1.8 K., the phosphorescence spectra, including the position and width of the vibronic resonance peaks, are nearly identical to those observed at 4.2 K, compare figs. 3 and 4. This similarity indicates that spectral diffusion is not thermally activated. For a thermally activated process, as found in disordered crystals [ 27 1, the emission profile shifts to a lower energy and gets sharper as the temperature increases from 1.8 to 4.2 K. As the delay time increases, see figs. 5 and 6, the resonance phosphorescence does not broaden and shift gradually, rather a broad luminescence peak develops about 260 cm-’ to the red. This jump indicates that energy transfer from high to low energy sites in this system is controlled by emission of phonons or vibrons and not by the density of electronic accep tor states. When a donor transfers energy to a lower energy acceptor, the excess energy must be dissipated by phonons, which are intermolecular vibrations, or by vibrons, which are intramolecular vibrations. The rate of energy transfer depends upon the density of
311
electronic acceptor states and on the coupling with the phonons and vibrons, as well as on the electronic interaction. Here the term coupling includes the density of phonon and vibron states as well as the strength of the interaction. The density of electronic acceptor states decreases with increasing red shift from the donor. Consequently if this density of states controls the rate, the resonance line will gradually broaden and shift to lower energy. On the other hand, if the phonons and vibrons control the rate, the resonance line will lose intensity and a lower energy band will gain intensity following the time of excitation. The energy separation between the resonance line and the relaxed band is characteristic of the phonon and/or vibron fquencies that provide significant coupling and a high density of states. In some cases, discrete, as opposed to continuous, energy shifts between the resonant and relaxed emission could be caused by rapid relaxation through the intervening states. This possibility can be eliminated for glassy MBP because resonant phosphorescence from these states is observed when they are excited directly, e.g., see figs. 3 and 4. Similar data for the doped polymer were obtained (fig. 7 ) , but the results cannot be compared with the glass in detail because the absorption profile is not known. Because of the weak signal level for the polymer system, additional experiments on this system were not considered to be worthwhile. We now consider the time evolution of spectral diffusion shown in figs. 5 and 6. The excitation is generated at the donor sites, and the acceptor population results only from the energy transfer processes. At t=O, the number of donor sites Nd( 0) =N,, and the excitation density of the acceptor sites N,( 0) = 0. The decay of the excited state population of donor and acceptor molecules can be described by simple kinetics, dlv, -=-k.Nddt
1 W(ri)Nd, i
(6)
dN -A dt
1 W(ri)Nd , i
(7)
= -kN,+
where Nd is the number of donor molecules excited, k is the unimolecular decay rate, and W( ri) is the rate of energy transfer from the donors to the acceptors at a distance ri. N. represents the population of accep
312
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
tors due to excitation transfer. For the case of triplet energy transfer, the excitation transport generally is governed by the exchange interaction, taken as an approximation to be isotropic. The distance dependence of the energy transfer rate between a donor and an acceptor at distance r then is given as [ 21 Wr)=kew[dd--11
(8)
,
where d is the critical transfer distance, and .ycharacterizes the range of the exchange interaction and depends on the overlap of the donor phosphorescence and the acceptor absorption spectra as shown in refs. [ 2,4]. Under the condition of low donor concentration, donor-donor interactions are neglected. Also any possibility of back transfer can be excluded at low temperature. The donor depopulation function for energy transfer to the acceptors by exchange coupling is @p(t)= nexp{-ktexp[y(d-~j)]} i
(9)
for a particular configuration of acceptor molecules. What is measured in experiments is the decay function averaged over all configurations [ 53 11, o(t)=
l-l
j
[1-p(1--xp(-ktexp[y(d--r)l))l, (10)
where p is the probability of a site being occupied by an acceptor. By taking the logarithm and replacing the summation by an integral using the continuum approximation for a D-dimensional lattice [ 5 1, eq. ( 10 ) becomes In @(t) = - V,pymDpg,(
kt ed)
By solving eqs. ( 6 ) and ( 7 ) , using eq. ( 9 ) , we can write for the donor and the acceptor populations &(f) =No e-%(t)
,
l-@(t)]
Na(t)=Noe-ti[
(16) .
(17)
Because the intensity of luminescence is proportional to the population, the ratio of the donor intensity to total intensity at time t can be written, see appendix B, as P(l)=
Id(t) Id(f)
+1,(t)
c@(t).
(18)
Notethatcr+p=l.Fromeqs.(ll)and(18)wehave lnp(t)=
- VDpymDpgD(kte’“‘) .
(19)
Eqs. (19) and (13)-( 15) showthataplotofhtp(t) as a function of In twill produce a straight line, a quadratic, or a cubic function for one, two, and three dimensions respectively. In fig. 10 In p(t) versus In (1) is plotted for a sample of glassy MBP at 4.2 K. The points are from fig. 5 and additional data. The background was subtracted, andp( t) was determined from the integrated intensity of luminescence at each time. A least-squares technique was used to fit the data to a third-order polynomial, the solid curve in fig. 10, consistent with eqs. (15) and ( 19). From the agreement between the experimental points and the poly-
(11)
with Co g,(u)=D
I
[1-exp(-ue-l)]ya-‘dy,
(12)
0
where PO is the volume of a unit sphere in a space of D-dimension and p is the density of sites. The function of gD( u) is given by [ 5 ] g,(u)=lnu+0.57722,
(13)
g~(u)=(lnu)Z+1.154431nu+1.9871,
(14)
g,(u)=(lnU)3+1.73165(lnu)2 + 5.93434 In u+ 5.44487 .
(15)
Fig. 10. Plot of Inp( 1) versus In t for glassy MBP at 4.2 K.
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
nomial function, we conclude that an isotropic threedimensional exchange interaction topology is consistent with spectral diffusion in this system. The coefficients in the polynomial provide a value for yd of 1.7 + 0.2. This value is reasonable for aromatic systems, e.g., yd is 2.0 for the BCN/DBN system [28,29], and 5 for benzene and naphthalene [9]. Since d was found to equal 9.8 A, y=O. 17. The calculated value of constant V~py-~p is 2.3 x 10m3and is in good agreement with the coefficient from the lit.
5. Summary and conclusions Steady state phosphorescence at 4.2 K is monitored for different concentrations of 4-methylbenzophenone (MBP) doped into polystyrene. At concentrations ,<20%, the spectrum is characteristic of separated molecules. As the concentration increases to 2096, the vibronic bands shift to longer wavelengths and get slightly sharper. At concentrations above 30%, the spectrum has additional features due to aggregates. The aggregates formed by MBP differ from those formed by 4-bromo-4’-chlorobenzophenone (BCBP) in polystyrene. BCBP appears to form a mixed phase with the polymer, while MBP appears to form a segregated phase. The energy transfer dynamics in the doped polymer seems to be similar to those in the glass although a quantitative detailed analysis was not possible due to the low signal levels. Time-resolved phosphorescence of glassy MBP was observed as a function of excitation energy. This experiment reveals that the spectral diffusion efficiency is dependent on the number of acceptors and changes abruptly at a critical concentration of 0.054, corresponding to a critical distance of 9.8 A. As the delay time increases, the resonance phosphorescence does not broaden and shift gradually, as observed for some systems, rather a broad luminescence band develops 260 cm-’ to lower energy of the resonance phosphorescence. This observation implies that the emission of phonons or vibrons controls the energy transfer and not the density of electronic acceptor states. The observed spectra at 1.8 K are nearly identical to those at 4.2 K, indicating that spectral diffusion in this system is not thermally activated at these temperatures. The data were analyzed successfully in terms of a mechanism involving direct donor-acceptor excita-
313
tion transport by exchange coupling in these dimensions. The data therefore do not reveal evidence for superexchange coupling or correlations between excitation energy and spatial position.
Acknowledgement
Helpful and stimulating conversations with Paras Prasad were much appreciated, and support for this research from the National Science Foundation under Grant DMR-8305050 is gratefully acknowledged.
Appendix A
A characteristic half distance between neighboring acceptors has been taken to be written as [ 9,281 (QA=(PDpa)-“3
2
(A.11
where POis the volume of a unit sphere (4x/3), and p. is the number density of acceptors, which is found from the density of MBP ( 1.088 g/cm3) and the mole fraction of acceptors. The critical mole fraction concentration for glassy MBP (where (Y=0.5) is found to be 0.054 from fig. 9. The characteristic distance between a donor and an acceptor at the critical concentration then is 2 1.6 A. This characteristic distance is obtained from ( r3) through eq. (A. 1) . Since ( r3) is larger than ( r) 3and since eq. (A. 1) neglects the volume between spheres, the average distance between neighboring acceptors is smaller than this characteristic distance. A computer simulation was used to determine the average distance between a donor and an acceptor at the critical concentration. In the simulation, molecules were generated in the model space and assigned random coordinates xi, yip zi. To satisfy the condition that molecules do not overlap each other, any separation, [ (Xi-Xj)‘+ (Yi-JJj)2+ (z~-z,)~]"~, smaller than a 4 A molecular diameter was not allowed. The nearest-neighbor distance for each molecule was determined. Periodic boundary conditions were used. The average distance between neighbors was found to be 9.8 A.
S.-K. Kook, D.M. Hanson / Triplet excitation energy in mokcdar ghses
314
Appendix B
The decay of the excited state population of donor and acceptor molecules can be described as dlv, =-j& dt cw 2
dt
d-
=-ma+
c i
w(ri)Nd
c
W(Tj)Nd.
i
9
(B.1)
(B-2)
The donor depopulation function is O(t)=
nexp[-W(q)t].
(B.3)
i
Bysolvingeqs. (B.l) and (B.2),andusingeq. we have &(t)
=&
exp( -kt)ex p(-
=No exp( -kt)@(t)
(B.3),
7 wt) 0.4)
,
N,(t)=N,exp(-kt)[l-G(t)].
0.5)
The ratio of the donor intensity to total intensity at time t can be written as Id(t) p(t)=
Id(t)+za(t)
Nd(f)
= Nd(t)+Na(t)
=@(t).
(B.6)
Since p( t) is the ratio of the number of donors to total number of molecules excited at time t, p(t) is determined by integrating donor and acceptor intensities over the respective bandwidths.
References [ 1] T. Foster, Ann. Physik 2 ( 1948) 55. [2] D.L. Dexter, J. Chem. Phys. 21 (1953) 836. [ 31 G.W. Robinson and G.C. Nieman, J. Chem. Phys. 37 (1962) 2150. (41 M. Inokuti and F. Hirayama, J. Chem. Phys. 43 ( 1965) 1978. [ 51A. Blumen, J. Chem. Phys. 72 (1980) 2632.
[6] R. Kopehnan, in: Spectroscopy and Excitation Dynamics of Condensed Molecuiar Systems, eds. V.M. A8ranovicb and R.M. Hochstmsser (North-Holland, Amsterdam, 1983) p. 139. [ 71 J. Klafter and J. Jortner, Chem. Phys. Letters 49 (1977) 410. [8] E.H. Monberg and R. Kopelman, Chem. Phys. Letters 58 (1978) 492. [9] A. Blumen and R. Silbey, J. Chem. Phys. 70 (1979) 3707. [lo] R.P. Parson and R. Kopelman, J. Chem. Phys. 82 (1985) 3692. [ 111 M. Griinewald, B. Pohlmann, B. Movaghar and D. Wihtx, Phil. Ma8. B 49 (1984) 341. [ 121 B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1982). [ 131 J. Klafier, A. Blumen and G. Zumofen, J. Luminescence 31/32(1984)627. [ 141 J. Klafter and A. Blumen, J. Chem. Phys. 80 ( 1984) 875. [ 151 U. Even, K. Rademann, J. Jortner, N. Manor and R. Reisfeld, Phys. Rev. Letters 52 ( 1984) 2 164. [ 161 R. Kopelman, S. Parus and J. Prasad, Phys. Rev. Letters 56 (1986) 1742. [ 171 Y. Lin and D. Hanson, J. Phys. Chem. 91 (1987) 2279. [ 18 ] R. Jankowiak and H. Bilssler, Chem. Phys. Letters 108 ( 1984) 209. [ 191 R. Jankowiak, B. Ries and H. Biissler, Phys. Stat. Sol. 124b (1984) 363. [20] R. Richer& B. Ries and H. Biissler, Phil. Msg. B 49 ( 1984) [21]~6dichertandH.Biiss1er,Chem.Phys.Letters118(1985) 235. [22] R. Richert and H. Biissler, J. Chem. Phys. 84 ( 1986) 3567. [23] P.N.Prasad, J.R. Mor8anandM.A. El-Sayed, J. Phys.Cbem. 85 (1981) 3569. [ 241 J.R. Morgan and M.A. El-Sayed, J. Phys. Chem. 87 ( 1983) [25] %Mor8an and MA. El-Sayed, J. Phys. Chem. 87 (1983) 383. [26] J.R. Morgan and M.A. El-Sayed, J. Phys. Chem. 87 (1983) 2178. [ 271 G.B. Talapatra, D.N. Rao and P.N. Prasad, J. Phys. Chem. 88 (1984) 4636. [ 281 G.B. Talapatra, D.N. Rao and P.N. Prasad, J. Phys. Chem. 89 (1985) 3217. [29] G.B. Talapatra, D.N. Rao and P.N. Prasad, Chem. Phys. 101 (1986) 147. [30] G.B. Strambini and C. Galley, Chem. Phys. Letters 39 (1976) 257. [ 3 1 ] A. Blumen and J. Manx, J. Chem. Phys. 7 1 ( 1979) 4694.
Spectral diffusion of triplet excitation energy in molecular glasses and doped polymer solids Seong-Keun Kook and David M. Hanson Department of Chemistry, State University of New York, Stony Brook, NY I 1794-3400, US4 Received 12 January 1990
Steady state phosphorescence at 4.2 K is monitored for different concentrations of Cmethylbenzophenone (MBP) doped into polystyrene. At concentrations less than 20%. the spectra are characteristic of separated molecules embedded in a disordered matrix. As the concentration increases to 2O%,the vibronic bands shift to longr wavelengths and become slightly sharper. At concentrations above 30%,the spectra have additional features due to aggregates,which appear to be characteristic of a segregated phase of MBP. Triplet excitation energy transport in glassy MBP and MBP doped into a polystyrene matrix is monitored for different excitation energies and temperatures using time-resolved spectroscopy. These experiments reveal that spectral diffusion at liquid helium temperatures is not thermally activated, and that the spectral diffusion efftciency increases abruptly at a critical mole fraction of acceptors, 0.054, which corresponds to a critical distance of 9.8 A.Although low-dimensional energy transfer dynamics has been revealed in other studies of disordered systems, the results indicate that spectral diffusion in these systems is controlled by a three-dimensional exchange interaction and the emission of phonons and/or vibrons.
1. Introduction The phenomenon of excitation energy transport in condensed molecular systems has been of continuing research interest. Theories of energy transfer have been discussed in terms of different interaction mechanisms, e.g., exchange coupling, multipolar interaction, and superexchange tunneling [ l-31. Recent theoretical and experimental investigations have focused on this phenomenon in disordered systems. Inokuti and Hirayama [4] formulated a theory involving the isotropic exchange interaction for direct (single step) triplet state energy transfer from a donor to randomly distributed acceptors in three dimensions. This theory later was generalized to all dimensions, and a configuration average valid for all acceptor concentrations was introduced [ 5 1. The energy transfer problem in multicomponent systems has been associated with the concept of critical concentrations [ 6-91. Parson and Kopelman [lo] and Griinewald et al. [ 111 studied theoretically the migration of incoherent excitations in energetically disordered system using a self-consistent diagrammatic approximation. Spatial diffusion and energy relaxa0301-0104/90/$03.50
tion observables are related to the solution of a nonlinear integral equation. The dependence of spatial and spectral transport properties upon the spatial range and the energy dependence of the intermolecular hopping rate is examined. The intimate relationship between spatial transport and energy relaxation is discussed in detail. After Mandelbrot’s formulation of fractal geometry [ 121, the concept of a fmctal dimension has been used to describe complex geometric environments as well as processes that occur in these environments. Klafter, Blumen and Zumofen [ 13,141 suggested the application of energy transfer experiments to determine the fractal and spectral dimensions. The first experiment using energy transfer to obtain a fractal dimension was reported by Jortner and co-workers [ 15 1. Kopelman applied percolation theory [ 6 ] and fractal geometry [ 16 ] to the case of mutistep energy transfer, where the acceptor concentration is low. Lin and Hanson used the concept of a fractal dimension to analyze the kinetics of direct donor-acceptor energy transfer in a doped polymer glass [ 17 1. Spectral diffusion can be defined as the process of energy transfer between molecules that have differ-
0 1990 - Elsevier Science Publishers B.V. (North-Holland)
304
S.-K. Kook, D.M. Hanson 1 Triplet excitation energy in molecular glasses
ent transition energies in a single-component energy transfer system. The distribution of transition energies, which is called inhomogeneous broadening, results from the different local environments or disorder of the molecules in the sample. For the case where the inhomogeneous width is less than kT, spectral diffusion causes an initially sharp excitation line to broaden to the full inhomogeneous width. For the case where the inhomogeneous width is greater than kT, spectral diffusion causes relaxation to lower energy molecules or sites. Experimental studies of spectral diffusion generally have measured luminescence spectra as a function of excitation energy, temperature, concentration, and time. For molecular systems, time-resolved phosphorescence spectra have revealed the dynamics and demonstrated the excitation energy dependence of triplet state spectral diffusion in organic glasses [ 18-22 ] as well as in disordered organic crystals [ 23-29 1. Richert and B&sler [ 2 1,221 reported measurements of the decay of the 0,O phosphorescence band of organic glasses (benzophenone, anthraquinone, and phenanthrene) formed by vapor deposition on a cold substrate or in one case by quenching a molten drop on a liquid helium cold finger. The triplet state population was created indirectly with nitrogen laser excitation by intersystem crossing from the singlet manifold. Consequently, the initial distribution of triplet state excitation energies is not known. The data were analyzed in terms of multiple step hopping down the cascade of states that form the inhomogeneously broadened band. Jankowiak, Ries and Bgissler [ 191 observed spectral diffusion and triplet exciton localization in glassy 2-bromonaphthalene following direct triplet state excitation with a tunable, nitrogen laser pumped, dye laser. Both the origin of the phosphorescence and the Stokes shift between excitation and phosphorescence varied continuously with excitation energy. In all cases the phosphorescence was inhomogeneously broadened and the case of true resonance phosphorescence, characterized by sharp line emission, was not attained. The results were analyzed in terms of stochastic hopping down a Gaussian density of states. The relaxation rate decreases as the density of states decreases producing an excitation energy dependent phosphorescence origin and Stokes shift. El-Sayed and co-workers [ 23-261 studied energy
transfer and spectral diffusion in the orientationally disordered crystal I-bromo4chloronaphthalene. They observed the loss of resonance-like phosphorescence and the appearance of broad lower energy phosphorescence with time following direct triplet state excitation. The relaxation rate increased with temperature and with excitation energy. Unlike the case of glassy 2-bromonaphthalene [ 19 1, the Stokes shift of the relaxed phosphorescence appears to be independent of time, and the phosphorescence origin appears to be independent of the excitation energy. The spectral diffusion was attributed to rapid relaxation down the inhomogeneously broadened band of states until the density of acceptors is so low that the energy transfer rate becomes negligible. The relaxed phosphorescence thus appears at the same wavelength independent of excitation energy. The decay of the long wavelength portion of the 0, 0 phosphorescence band was described by energy transfer, occurring in a single step, to lower energy acceptors. It was found that the dominant mechanism for this energy transfer appears to switch from exchange to dipolar coupling as the density of acceptor decreases. Prasad and co-workers [ 26-291 observed spectral diffusion in orientationally disordered 4-bromo-4’chlorobenzophenone (BCBP) and in crystalline solutions of 1-bromo_4chloronaphthalene (BCN ) and 1+dibromonaphthalene (DBN). The latter system exhibits both orientational and substitutional disorder. For the case of BCBP, time-resolved studies revealed that the phosphorescence profile gradually shifts by a few wavenumbers toward the lower energy sites with increasing time following excitation. This observation implies that the density of acceptor states plays the dominant role in spectral diffusion and not coupling to phonons or vibrons. If the latter were dominant, the spectral profile should shift abruptly by much larger amounts, characteristic of the phonon or vibron frequencies. Spectral diffusion differs in the BCN/DBN solid solutions. For this system, the resonance phosphorescence decreases in intensity with increasing time after excitation, and a broad luminescence peak 20 cm-’ to the red increases in intensity, i.e. the resonance phosphorescence does not boraden and shift gradually with increasing delay time. The abrupt ( < 20 ps) appearance of a 20 cm-’ Stokes shift could be caused by emission of 20 cm-’ phonons or by rapid energy cascade through the in-
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular ghsses
tervening states. Since resonance-like phosphorescence is observed when these states are excited directly, the latter possibility can be eliminated, vide infra. To summerize, these previous studies of spectral diffusion of triplet excited states in molecular solids have revealed the existence of energy cascade relaxation involving both continuous and discrete energy losses. The relevance of various interaction mechanisms and theories of energy transfer have been examined. However, no studies of spectral diffusion following direct triplet excitation from the ground state in polymer glasses have been reported. Such experiments have been conducted only on disordered crystals or molecular glasses. Here we report observations of energy transfer and spectral diffusion in glassy Cmethylbenzophenone (MBP) and in MBP doped into a polystyrene glass. Time-resolved spectra were obtained for different excitation energies, acceptor concentrations, and temperatures. The data were analyzed in terms of direct donor-acceptor excitation transport by exchange coupling using the theoretical concepts presented by Blumen [ 51 and also used by Talpatra, Rao and Prasad [ 29 1.
305
fluid helium in an optical dewar to achieve temperatures of 4.2 and 1.8 K. A pulsed nitrogen laser (Molectron UV400) and a tunable dye laser (Molectron DL400) were used as excitation sources for the measurements. Pulse widths were 10 ns. Tram-diphenylstilbene (DPS ) dye (Exciton) was used. The phosphorescence was monitored with a double spectrometer (Spex 1302) and an EM1 9865 photomultiplier tube. Steady state measurements were made using a current amplifier. A boxcar integrator (PAR 162 with model 164 gated integrator modules) was used for time-resolved data acquisition. Light from the dye laser incident on a photodiode was used to trigger the boxcar. All the experiments were controlled by a Digital PDP 11/23 + computer system. The spectra, collected through an analog to digital converter, were stored on disc for further analysis. A schematic diagram of the instrumentation is shown in fig. 1. The time response of the electronics was tested with a pulse generator. It was found that the response time of the boxcar integrator, including a rc filter on the input, was faster than 2 us.
3. Results 2. Experimental techniques 4-methylbenzophenone, obtained from Aldrich, was recrystallized from ether, and zone refined for 100 passes at a velocity of 1.5 inch per hour. Glassy MBP was produced by quench freezing a molten droplet of the material on a cold quartz surface lying over a Pyrex evaporating dish containing liquid nitrogen. To prepare the doped polymer films, MBP was mixed with polystyrene, using toluene as a solvent, to obtain the desired concentrations ranging from 1 to 50 weight per cent. Polymer films were formed by placing 30 drops of the MBP/polystyrene solution onto a 1 cm x 1 cm quartz plate lying on a platform which was heated to 65 oC by a hot plate. The rate of solvent evaporation was controlled by covering the entire platform with a funnel. The films appeared optically clear for concentrations less than 20%, and milky for concentrations more than 30%. Concentrations between 20 and 30% were not prepared. The samples were immersed in liquid helium or super-
A set of steady state phosphorescence spectra, obtained at 4.2 K, for different concentrations of MBP doped into polystyrene, is shown in fig. 2. The vibronic bands shift to longer wavelengths and become slightly sharper as the concentration increases from 1 to 20%. See table 1 where the full width at half intensity (fwhi) of the O-l peak is listed. At higher concentrations, an additional band appears on the higher energy side of each of the original bands. These new bands match those of glassy MBP. Fig. 2 also shows the phosphorescence spectrum of glassy MBP. Fig. 3 shows time-sampled spectra in the region of the first vibronic band of the phosphorescence of glassy MBP at 4.2 K as a function of excitation energy. Excitation wavelengths are on and above the high energy edge of the O-O phosphorescence band. In each case the spectrum was sampled after a 10 us delay using a 5 us sampling time. In order to avoid interference with scattered light due to the laser, the first vibronic band of the emission was monitored. At the low excitation energy (4055 A), two relatively sharp ( fwhi z 35 cm- ’ ) resonant emission lines are
306
S.-K. Kook D.M. Hamon / Triplet excitation energy in mokcdar glasses 7
Grating :: /:
’ : : :
0
Photodiode
Fig. 1. A schematic diagram of the instrumentation.
Phosphorescence band positions (MBP/polystyrene) Cont. (96)
aom
ao% so%
1 5 10 20
(A) and bandwidth (cm-‘)
Phosphorescence band
Bandwidth O-l (cm-‘)
O-O
O-l
O-2
4145 4180 4186 4195
4452 4485 4488 4506
4769 4820 4828 4852
699 618 541 521
observed. As the excitation energy increases, a broad ( fwhi w 380 cm- ’ ) luminescence band of increasing intensity develops to lower energy, and the peak of this broad luminescence shifts to shorter wavelengths. The resonant emission lines shift with changes in the excitation energy as expected. See table 2 where the mean position of the doublet is listed, I,. Table 2 also gives the peak position and Stokes 4 Fig. 2. Steady state phosphorescence spectra obtained at 4.2 K for MBP/polystyrene at the specified weight per cent wncentrations. The lowermost spectrum is that of glassy MBP.
307
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
404lA
404sA
405oA
4055A
405sA
c
.
.
.
.
425
.
.
4
460 rinnm
Fig. 4. First vibronic band of glassy MBP phosphorescence at 1.8 K as a function of excitation energy. (Delay time: 10 ps, sampling time: 5 us.)
Fig. 3. First vibronic band of glassy MBP phosphorescence at 4.2 K as a function of excitation energy. (Delay time: 10 us, sampling time: 5 us. )
shift of the relaxed emission, A,,. At 1.8 K, similar features are observed, see fig. 4. The time delay of 10 ps between excitation and observation ensures that the sharp features are reso-
nance phosphorescence and are not caused by Raman scattering. In addition, the decreasing intensity of the sharp features with increasing excitation energy is not characteristic of Raman scattering. The Raman intensity should increase due to the v“ non-
Table 2 Correlation of excitation and phosphorescence wavelengths l) 1
(5
4041.0 4045.0 4050.0 4055.0
L(~l)
(A) 4322.7 4327.3 4333.3 4339.0
wit.
A-el(o-1)
boku
(cm-‘)
(A)
(cm-‘)
1613 1613 1614 1614
4377.0 4381.0 4386.0
287 283 277
*) &xc is the excitation wavelength, A, is the vibronic resonance phosphorescence shifted by an amount At&, Ati is the relaxed phosphorescence shifted by an amount A&+,
from A,
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
308
resonant frequency dependence and due to resonant contributions from the T, t So absorption. Time-resolved phosphorescence spectra of glassy MBP at 4.2 and 1.8 K for different delay times following excitation are shown in figs. 5 and 6, respectively. The excitation energy was 4055 A. At a short delay time, e.g., 10 us, as mentioned above, two sharp resonant emission lines on a broad background are observed. At longer delay times, a broad phosphorescence band develops to lower energy. The intensity of the broad band increases and the intensity of the sharp lines decreases as a function of increasing delay time. The position and width of the broad band appear to be independent of the delay time. At higher
b
.
425
.
,
460 Alnnm
Fig. 6. Time-resolved phosphorescence spectra of glassy MBP at 1.8 K for different delay times with excitation at 4055 A. The delay time is specified, the sampling time was 5 1s.
,
.
.
.
425
.
.
-
, 460
rinnm
Fig. 5. Time-resolved phosphorescence spectra of glassy MBP at 4.2 K for different delay times with excitation at 4055 A. The delay time is specified, the sampling time was 5 vs.
temperatures (77 K), no resonant phosphorescence is observed due to fast spectral diffusion. Only the broad peak was observed at all excitation energies, even at short times. Similar data were obtained at 4.2 K for MBP doped into polystyrene. Selected spectra obtained for 50% MBP are shown in fig. 7. The Stokes shift of the relaxed phosphorescence for the polymer glasses is about 760 cm-‘, which differs significantly from that observed for glassy MBP. A phosphorescence excitation spectrum obtained at 4.2 K for glassy MBP is shown in fig_ 8. The phosphorescence was monitored at 4396 A with a bandpass of 0.7 A, and the emission intensity was normalized to account for the variation in the laser intensity
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glosses
309
with wavelength. A photodiode was used to monitor the laser intensity. The peak in the excitation spectrum of glassy MBP is at 403 nm with a width of 197 cm-’ (fwhi).
4. Discussion 4.1. Concentration dependence
,
.
.
,
430
.
-1
46s
rinnm Fig. 7. First vibronic band of the phosphorescence of 50%MBP in polystyrene at 4.2 K as a function of excitation energy. (Delay time: 10 us, sampling time: 5 us.)
‘\
\ 1
&
400
401
402
403
l\,\ I
404
40B
452
A in nnr
Fig. 8. Excitation spectrum obtained by monitoring phosphorescence at 4.2 K for glassy MBP. The dotted curve is a Gaussian profile plotted in wavelength centered at 403 nm with a width of 197 cm-’ (fwhi). The arrows show the excitation wavelengths used in the phosphorescence studies.
The system of MBP in polystyrene is inhomogeneous. Molecules in different environments have different transition energies and produce different spectra. At low concentrations most MBP molecules are essentially isolated from each other and surrounded by polymer. The energy levels of these molecules are widely distributed due to the intrinsic disorder property of the polymer. This disorder produces the broad phosphorescence. As the concentration increases, the separation between MBP molecules decreases, the intermolecular interaction increases, and energy transfer becomes more efficient. As a result, the excitation energy can relax to a deeper and more homogeneous distribution of traps. Consequently as shown in fig. 2, the phosphorescence bands become narrower and shift to lower energy as the concentration increases. At and above 30% MBP, new peaks are present, and the samples appear milky. By inspecting the samples used in the experiments under a microscope ( 100 x ) , crystallites are observed that appear similar to crystals formed by recrystallization. The new peaks correspond in wavelength to those obtained from glassy MBP. These observations indicate that at concentration of 330% MBP aggregates form in the polymer films. Aggregation has been reported previously for 4bromo-4’-chlorobenzophenone (BCBP) in polystyrene by Lin and Hanson [ 17 1, but the characteristics of the aggregation differ for these two systems. For BCBP, the samples become translucent at a concentration of 12%, and by using a microscope ( 100 x ), the samples are seen to contain tree-like aggregates with numerous branches. These aggregates are different from crystals obtained by recrystallization. The aggregates are only present in samples at concentrations above about 10% and become increasingly dense as the concentration increases. Like MBP, the aggre-
S.-K. Kook, D.M. Hanson/ Tripletexcitationenergyin mokcu/arghsses
310
gates contribute additional bands to the phosphorescence spectrum. Unlike the case of MBP, in BCBP the aggregation occurs completely over a narrow concentration range. The phosphorescence spectrum of BCBP at 20% is entirely that of the aggregate. In contrast, the spectrum of MBP at 50% is still of mixed character, containing contributions from both aggregates and molecules. Since the conditions for the preparation of polystyrene films doped with MBP or with BCBP were different, it is not clear to what extent kinetic constraints affected the formation of the aggregates in these two systems. The morphology of the aggregates as seen with a microscope, however, seems to indicate that BCBP/polystyrene forms a mixed phase with a high BCBP concentration and that MBP forms a segregated phase.
The results shown in fgs. 3 and 4 reveal a strong dependence of the spectral diffusion rate on the excitation energy as was found for the disordered crystalline solutions of bromochloronaphthalene and dibromonaphthalene [ 29 1. We apply the analysis used for these crystals to the present case of a glass. The molecules are divided into three classifications: donors - molecules requiring an excitation energy equal to the initial excitation energy, acceptors - molecules requiring an excitation energy lower than the initial excitation energy, and barriers - molecules requiring an excitation energy greater than the initial excitation energy. The number of donors, acceptors, and barriers depends on the initial excitation energy used. As the excitation energy increases, the density of acceptor sites increases. This increase enhances the energy transfer rate from donors to acceptors. The mole fraction of acceptor concentration is given by 7 Z(v)dv/ --oD
7 Z(v)dv, --oo
x(Av)-‘]*}dv.
(1)
where Z( v) is the absorption profile for the system. If we assume a Gaussian distribution for the intensity profile,
(2)
Here Au is the half-width of the distribution (hwhi). The acceptor concentration then can be written in terms of an error function as [ 28 ]
Ca(vex)=t[l-erf(z)l,
(3)
vex) (ln2)‘/*/Av; v, is the abwhere z= (v,sorption maximum. In a similar way, if we assume that the laser profile is Gaussian with hwhi = A vL, centered at v,,, the donor concentration can be written as C,( v,,) = (Av,/Av)
4.2. Dynamics of spectral diji’kion
C,(v,,)=
C,( v,,)= (Av)-L(ln2/x)‘/2 “cr exp{-[(v-v,)(ln2)‘/* X I --oD
exp( -z*)
.
(4)
When the excitation energy is at 4055 A, using Au,= 0.5 cm-‘, we have the acceptor and the donor concentrations as c,=O.O34 and c,= 0.00168, expressed as mole fraction. Since the donor and acceptor are the same molecular species, we assume the same quantum yield and instrumental response for donor and acceptor emission. The spectral diffusion efficiency is given as the ratio of the integrated intensity of acceptor emission to the total integrated emission
43
a=la+ld*
(5)
Fig. 9 shows a plot of the ratio (Yversus the acceptor concentration c,, determined from eq. (3), for different excitation energies. This graph shows the dependence of the spectral diffusion efficiency on the density of the acceptor sites for a delay time of 10 ps and a sampling time of 5 ps with the sample temperature at 4.2 K. The ratio (Ychanges abruptly at a critical concentration. The critical concentration (where a = 0.5 ) is found to be 0.054, and the calculated critical distance is 9.8 A, see appendix A. These values compare with those found in other systems, e.g., the critical concentrations are 0.03,0.06-0.07, and 0.05 for benzene, naphthalene, and phenanzine respectively [ 9 1, and the critical distances are 1 l- 18 A for aromatic molecule systems [ 301. The abrupt change in (Yaround the critical concentration is characteris-
S.-K. Kook, D.M. Hanson / Tripletexcitationenergy in molecular glasses
0.0 -
O.O-
a
ca Fig. 9. Plot of the spectral difhsion ticiency concentration of glassy MBP at 4.2 K.
a wrsus acceptor
tic of a short range exchange interaction. Consequently the exchange mechanism is used to analyze the time evolution of the spectral diffusion. At 1.8 K., the phosphorescence spectra, including the position and width of the vibronic resonance peaks, are nearly identical to those observed at 4.2 K, compare figs. 3 and 4. This similarity indicates that spectral diffusion is not thermally activated. For a thermally activated process, as found in disordered crystals [ 27 1, the emission profile shifts to a lower energy and gets sharper as the temperature increases from 1.8 to 4.2 K. As the delay time increases, see figs. 5 and 6, the resonance phosphorescence does not broaden and shift gradually, rather a broad luminescence peak develops about 260 cm-’ to the red. This jump indicates that energy transfer from high to low energy sites in this system is controlled by emission of phonons or vibrons and not by the density of electronic accep tor states. When a donor transfers energy to a lower energy acceptor, the excess energy must be dissipated by phonons, which are intermolecular vibrations, or by vibrons, which are intramolecular vibrations. The rate of energy transfer depends upon the density of
311
electronic acceptor states and on the coupling with the phonons and vibrons, as well as on the electronic interaction. Here the term coupling includes the density of phonon and vibron states as well as the strength of the interaction. The density of electronic acceptor states decreases with increasing red shift from the donor. Consequently if this density of states controls the rate, the resonance line will gradually broaden and shift to lower energy. On the other hand, if the phonons and vibrons control the rate, the resonance line will lose intensity and a lower energy band will gain intensity following the time of excitation. The energy separation between the resonance line and the relaxed band is characteristic of the phonon and/or vibron fquencies that provide significant coupling and a high density of states. In some cases, discrete, as opposed to continuous, energy shifts between the resonant and relaxed emission could be caused by rapid relaxation through the intervening states. This possibility can be eliminated for glassy MBP because resonant phosphorescence from these states is observed when they are excited directly, e.g., see figs. 3 and 4. Similar data for the doped polymer were obtained (fig. 7 ) , but the results cannot be compared with the glass in detail because the absorption profile is not known. Because of the weak signal level for the polymer system, additional experiments on this system were not considered to be worthwhile. We now consider the time evolution of spectral diffusion shown in figs. 5 and 6. The excitation is generated at the donor sites, and the acceptor population results only from the energy transfer processes. At t=O, the number of donor sites Nd( 0) =N,, and the excitation density of the acceptor sites N,( 0) = 0. The decay of the excited state population of donor and acceptor molecules can be described by simple kinetics, dlv, -=-k.Nddt
1 W(ri)Nd, i
(6)
dN -A dt
1 W(ri)Nd , i
(7)
= -kN,+
where Nd is the number of donor molecules excited, k is the unimolecular decay rate, and W( ri) is the rate of energy transfer from the donors to the acceptors at a distance ri. N. represents the population of accep
312
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
tors due to excitation transfer. For the case of triplet energy transfer, the excitation transport generally is governed by the exchange interaction, taken as an approximation to be isotropic. The distance dependence of the energy transfer rate between a donor and an acceptor at distance r then is given as [ 21 Wr)=kew[dd--11
(8)
,
where d is the critical transfer distance, and .ycharacterizes the range of the exchange interaction and depends on the overlap of the donor phosphorescence and the acceptor absorption spectra as shown in refs. [ 2,4]. Under the condition of low donor concentration, donor-donor interactions are neglected. Also any possibility of back transfer can be excluded at low temperature. The donor depopulation function for energy transfer to the acceptors by exchange coupling is @p(t)= nexp{-ktexp[y(d-~j)]} i
(9)
for a particular configuration of acceptor molecules. What is measured in experiments is the decay function averaged over all configurations [ 53 11, o(t)=
l-l
j
[1-p(1--xp(-ktexp[y(d--r)l))l, (10)
where p is the probability of a site being occupied by an acceptor. By taking the logarithm and replacing the summation by an integral using the continuum approximation for a D-dimensional lattice [ 5 1, eq. ( 10 ) becomes In @(t) = - V,pymDpg,(
kt ed)
By solving eqs. ( 6 ) and ( 7 ) , using eq. ( 9 ) , we can write for the donor and the acceptor populations &(f) =No e-%(t)
,
l-@(t)]
Na(t)=Noe-ti[
(16) .
(17)
Because the intensity of luminescence is proportional to the population, the ratio of the donor intensity to total intensity at time t can be written, see appendix B, as P(l)=
Id(t) Id(f)
+1,(t)
c@(t).
(18)
Notethatcr+p=l.Fromeqs.(ll)and(18)wehave lnp(t)=
- VDpymDpgD(kte’“‘) .
(19)
Eqs. (19) and (13)-( 15) showthataplotofhtp(t) as a function of In twill produce a straight line, a quadratic, or a cubic function for one, two, and three dimensions respectively. In fig. 10 In p(t) versus In (1) is plotted for a sample of glassy MBP at 4.2 K. The points are from fig. 5 and additional data. The background was subtracted, andp( t) was determined from the integrated intensity of luminescence at each time. A least-squares technique was used to fit the data to a third-order polynomial, the solid curve in fig. 10, consistent with eqs. (15) and ( 19). From the agreement between the experimental points and the poly-
(11)
with Co g,(u)=D
I
[1-exp(-ue-l)]ya-‘dy,
(12)
0
where PO is the volume of a unit sphere in a space of D-dimension and p is the density of sites. The function of gD( u) is given by [ 5 ] g,(u)=lnu+0.57722,
(13)
g~(u)=(lnu)Z+1.154431nu+1.9871,
(14)
g,(u)=(lnU)3+1.73165(lnu)2 + 5.93434 In u+ 5.44487 .
(15)
Fig. 10. Plot of Inp( 1) versus In t for glassy MBP at 4.2 K.
S.-K. Kook, D.M. Hanson / Triplet excitation energy in molecular glasses
nomial function, we conclude that an isotropic threedimensional exchange interaction topology is consistent with spectral diffusion in this system. The coefficients in the polynomial provide a value for yd of 1.7 + 0.2. This value is reasonable for aromatic systems, e.g., yd is 2.0 for the BCN/DBN system [28,29], and 5 for benzene and naphthalene [9]. Since d was found to equal 9.8 A, y=O. 17. The calculated value of constant V~py-~p is 2.3 x 10m3and is in good agreement with the coefficient from the lit.
5. Summary and conclusions Steady state phosphorescence at 4.2 K is monitored for different concentrations of 4-methylbenzophenone (MBP) doped into polystyrene. At concentrations ,<20%, the spectrum is characteristic of separated molecules. As the concentration increases to 2096, the vibronic bands shift to longer wavelengths and get slightly sharper. At concentrations above 30%, the spectrum has additional features due to aggregates. The aggregates formed by MBP differ from those formed by 4-bromo-4’-chlorobenzophenone (BCBP) in polystyrene. BCBP appears to form a mixed phase with the polymer, while MBP appears to form a segregated phase. The energy transfer dynamics in the doped polymer seems to be similar to those in the glass although a quantitative detailed analysis was not possible due to the low signal levels. Time-resolved phosphorescence of glassy MBP was observed as a function of excitation energy. This experiment reveals that the spectral diffusion efficiency is dependent on the number of acceptors and changes abruptly at a critical concentration of 0.054, corresponding to a critical distance of 9.8 A. As the delay time increases, the resonance phosphorescence does not broaden and shift gradually, as observed for some systems, rather a broad luminescence band develops 260 cm-’ to lower energy of the resonance phosphorescence. This observation implies that the emission of phonons or vibrons controls the energy transfer and not the density of electronic acceptor states. The observed spectra at 1.8 K are nearly identical to those at 4.2 K, indicating that spectral diffusion in this system is not thermally activated at these temperatures. The data were analyzed successfully in terms of a mechanism involving direct donor-acceptor excita-
313
tion transport by exchange coupling in these dimensions. The data therefore do not reveal evidence for superexchange coupling or correlations between excitation energy and spatial position.
Acknowledgement
Helpful and stimulating conversations with Paras Prasad were much appreciated, and support for this research from the National Science Foundation under Grant DMR-8305050 is gratefully acknowledged.
Appendix A
A characteristic half distance between neighboring acceptors has been taken to be written as [ 9,281 (QA=(PDpa)-“3
2
(A.11
where POis the volume of a unit sphere (4x/3), and p. is the number density of acceptors, which is found from the density of MBP ( 1.088 g/cm3) and the mole fraction of acceptors. The critical mole fraction concentration for glassy MBP (where (Y=0.5) is found to be 0.054 from fig. 9. The characteristic distance between a donor and an acceptor at the critical concentration then is 2 1.6 A. This characteristic distance is obtained from ( r3) through eq. (A. 1) . Since ( r3) is larger than ( r) 3and since eq. (A. 1) neglects the volume between spheres, the average distance between neighboring acceptors is smaller than this characteristic distance. A computer simulation was used to determine the average distance between a donor and an acceptor at the critical concentration. In the simulation, molecules were generated in the model space and assigned random coordinates xi, yip zi. To satisfy the condition that molecules do not overlap each other, any separation, [ (Xi-Xj)‘+ (Yi-JJj)2+ (z~-z,)~]"~, smaller than a 4 A molecular diameter was not allowed. The nearest-neighbor distance for each molecule was determined. Periodic boundary conditions were used. The average distance between neighbors was found to be 9.8 A.
S.-K. Kook, D.M. Hanson / Triplet excitation energy in mokcdar ghses
314
Appendix B
The decay of the excited state population of donor and acceptor molecules can be described as dlv, =-j& dt cw 2
dt
d-
=-ma+
c i
w(ri)Nd
c
W(Tj)Nd.
i
9
(B.1)
(B-2)
The donor depopulation function is O(t)=
nexp[-W(q)t].
(B.3)
i
Bysolvingeqs. (B.l) and (B.2),andusingeq. we have &(t)
=&
exp( -kt)ex p(-
=No exp( -kt)@(t)
(B.3),
7 wt) 0.4)
,
N,(t)=N,exp(-kt)[l-G(t)].
0.5)
The ratio of the donor intensity to total intensity at time t can be written as Id(t) p(t)=
Id(t)+za(t)
Nd(f)
= Nd(t)+Na(t)
=@(t).
(B.6)
Since p( t) is the ratio of the number of donors to total number of molecules excited at time t, p(t) is determined by integrating donor and acceptor intensities over the respective bandwidths.
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