Formation of Excited Singlet States parison. The yield of methanol, 0.72, corresponds closely with that of G(H202). Although quantitative agreement has not yet been achieved, the following mechanism accounts for the general features of our results in saturated CH4 solutions. Under these conditions all OW radicals may besassumed to react ‘with CH4.
In the absence of N 2 0 , the main sequence of reactions is 1 and 3-13. Reactions 4-6 and 13 raise G(H2) yields above
3867
0.45; reactions 7-9, 11, and 12 lower G(-CHd); reaction 10 forms CzHs, whereas reactions 12 and 13 consume it. Methanol forms via reaction 11although its yield is lowered by reaction 3. In the presence of NzO all eaq- reactions are eliminated and the simplified mechanism consisting of reactions 1, 2, 5,7, and 9-13 dominate. The low C2Hs yield, as well as the rapid establishment of a low steady-state CzHs concentration, indicates an efficient reaction of C2Hs with free radicals present during irradiation. Because h(CH4 + OH) = 1.2 X lo8 M - I sec-l and CH4 is present a t the m M level there must be an efficient C2Hs scavenging reaction. ‘Therefore we propose reaction 12 although reaction 13 may also contribute to the low steady-state level of C2Hs. These reactions also account for the low G(-CH4) yields found in all CH4 solutions. Support for these reactions has recently been obtained by the observation that extensive methylation readily occurs in these aqueous CH4 solutions. For example, ethane, propane, isobutane, n-butane, neopentane, isopentane, and n-pentane have been detected in a 5-krad irradiation1&which corresponds to less than 3% CH4 reacted. Methyl radicals continuously generated by reaction 6 interact with C2 cals from reactions 12 and 13. The higher alkanes then form uia similar reactions of CH3 and possibly H with C&Is, CqHlo, and so forth. (18) W G Brown and E J Hart, unpublished results
xcited Singlet States in Irradiated Aromatic Liquids
I
Fuchs, F. Heisel, and R. Voltz*
iaboratoire de Physique des Ravonnements et d’Eiecbonique Nucleaire, Centre de Recherches Nucleaires, 67. Strasbourg 3, France (Received May 9, 1972) Pubkation costs assisted by lnstitut National de Physique Nucieaire et de Physique des Particuies
Vacuum ultraviolet excited fluorescence and fast electron excited radioluminescence are used to study the mechanisms of formation of the lowest excited singlet states in liquid benzene and alkylbenzenes. From the measurements of fluorescence excitation spectra, it is concluded that the upper singlet levels in these liquids essentially decay by autoionization when their excitation energy is larger than a characteristic critical value, equal to 7 eV in the case of benzene. Efficient recombination fluorescence indicates that charge separation is followed by geminate recombination, without spin relaxation, from the lowest charge-transfer state to the first excited singlet state of the molecules. The scintillation decay laws and absolute yields, measured under electron irradiation, allow one to distinguish the promptly formed singlet states from those resulting from triplet-triplet annihilation in blobs and short tracks. The “prompt” singlet states are found to be produced with G values near unity; the data are interpreted using the general results obtained with vacuum ultraviolet excitation and taking into account the possible track effects.
Introduction
primary highly activated states to the lower excited levels
ago1 and has since been actively studied, using in particular scintillation and pulse-radiolysis technique^.^*^ However, the sequence of the radiationless processes, leading from the
(1) M. Burton, Actions Chim. Bioi. Radiat., 3, 1 (1958). (2) R, voltz, ~ ~Chim, Bio/, t Radjat,, j 13, ~ 1 (1969). ~ ~ (3) J. K. Thomas, Ann. Rev. Pbys. Chem., 2 1 , 1 7 (3970). The Journal of Physical Chemistry, Voi. 76, No. 25, 1972
C. Fuchs, F. Heisel, and R. Voltz
3868
and of charge-separated states as intermediates in the initial stages of radiation action, for example, is not yet clearly established. The object of the present study was to get more precise information on the early processes responsible for the production of the lowest excited singlet states (ILb, denoted by SI)in liquid benzene and derivatives, under high-energy irradiation. As a first part of this investigation, it appeared to be useful to reexamine some of the electronic relaxation processes from the highly excited molecular states in the liquids. The experimental method was to measure the variation of fluorescence quantum yield with excitation energies up to the vacuum ultraviolet range. In previous work, the same technique was used to study mainly the behavior of the second (ILar 32) arid third (I&,, $3) excited states in In this report, attention will be more conthe centrated on higher vibronic levels, which are those mainly formed after initial activation of the condensed medium by charged particles. The production of singlet excited molecules in the aromatic liquids under fast electron irradiation is discussed in the second part of this work. The experimental information to be used comes essentially from radioluminescence studies; useful indications on modes and yields of SIstate formation can indeed be obtained by analyzing the scintillation decay curves and by measuring absolute scintillation yields.2
Excitation by ~ ~ c Ultraviolet ~ ~ r Light n Valuable information on the radiationless transitions from upper electronic levels of organic molecules in liquids and crystals is obtained from measurements of the fluorescence efficiency as a function of excitation wavelength.4-6 Since, for the neat aromatic liquids, the fluorescence quantum yield is very low, it is found convenient to introduce small concentzations of a suitable solute, accepting the electronic energy from the aromatic host material and emitting light with a high efficiency. In addition to the electronic relaxation phenomena operative in the pure liquids, the analysis of the results must therefore also consider the solvent-solute energy transfer processes. e
The equipment is iliustrated in Figure 1. The exciting system consists of a hydrogen-discharge lamp and a McPherson Model 218 monochromator. The incident light, focused by an LiF lens, enters an irradiation cell where the mirrors Ns and N M are placed so that a constant intensity ratio is ensured for the beams exciting the sample (CS) and a sodium salicylate layer ( C M ) in identical LiF cells. Two photomultipliers measure the fluorescence intensities Is and IM from the sample and from the sodium salicylate monitor preparation (wavelength invariant quantum yield). The setup allowed selective excitation of molecular levels with wavelengths down to 150 nm. The ratio Is\h)/IM, obtained for the excitation wavelength A, provides a relative measurement of the fluorescence quantum yield q(X). In the following, we present and discuss the results on the fluorescence excitation spectra, considering the relative fluorescence efficiency R( A) = q(A)/v(Al), where XI) corresponds to an excitation of the SI state. The experiments were carried out at room temperature with the following degassed and purified liquids containing aNPO ( ~ - n a p h t y ~ ~ 2 - p h e n yoxazole-1,3) l”5 as the fluoresThe Journal of Physics/ Chemistry, Vol. 76,
No. 25, 1972
Figure 1.
Experimental arrangement.
cent solute: benzene, perdeuterated benzene, toluene, perdeuterated toluene, p-xylene, and mesitylene. The results on the variations of the relative fluorescence efficiency R with excitation wavelength and solute concentration, in the case of benzene solutions, are represented in Figure 2.8 Similar curves were also determined for the other liquid^.^ The action spectra (Figure 2a) have the same general form as those reported by Braun, et al.,4 and by Birks, et ~ 1 . ; ~ excitation to the S Z state leads to a decrease of R with a value approximately constant over the whole second absorption band. A further decrease to a value characteristic for the third excitation band is observed for higher excitation energies E,,,. We note, however, that when the latter exceed a critical value WO( = 7 eV, for benzene), the efficiency R increases with E,,,. In accord with the data of Figure 2b, Laor and WeinreblO also observed that E( A) increases with increasing solute concentrations. ‘Fhe data reported in Figure 3 show that chloroform and oxygen act as efficient fluorescence quenchers for excitation energies larger than WO,but they have a negligible influence if E,,,
< Wo. Analysis of the Results The experimental results indicate a drastic change in the behavior of the upper vibronic levels when the excitation energy exceeds the critical quantity WO;the values characteristic for the various aromatic liquids are reported in Table I. For the reasons to be developed later, energy WO is interpreted as a threshold for molecular autoionization in the liquid. We will therefore distinguish between “excited” states (Eexc < WO)and “superexcited” states (E,,, 2 Wo).of the molecules in the condensed phase. (4) 6. L. Braun, S. Kato, and S. Lipsky, J. Chem. Phys., 39, 1645 (1963). (5) J. B. Birks, J. C. Conte, and G. Walker, Proc. Phys. Soc, London, Sect. 5, 1, 934 ( 1968), (6) N. Geacintov, M. Pope, and H. Kailmann, J. Chem. Phys., 45, 2639 (1966). (7) R . Voltz, Radiat. Res. Rev., 1, 301 (1968). (8) By exciting aNPO in aliphatic solutions, we have verified that this solute has a quantum yield constant in the wavelength range used in the present exp’eriments. (9) C. Fuchs, Thesis, Strasbourg, 1972. (10) U. Laor and A. Weinreb, J. Chem. Phys., 43, 1565 (1965); 50, 94 (1969).
Formation of Excited Singlet States
3869
TABLE I: Autoionizetion and Recombination. Experimentally Determined Parameters
wo
Solvent
a(N 3
Limits of
eV
Benzene Perdeuterated benzene Toluene Perdeuterated toluene p-Xylene Mesitylene
Te
a 1 5 0 I)M
a150
a160
01170
PM
KF,
M-’
7.0
0.42-0.58
0.7
0.5
0.2
0.7
9
7.0 6.9
0.22-0.48 0.35-0.65
0.6 0.7
0.4 0.5
0.15 0.4
0.6 0.7
7 20
6.9
0.35-0.65 0.75-0.92 0.82-0.95
0.7 0.9 0.9
0.5 0.7 0.7
0.35 0.4 0.4
0.7 0.95 0.95
20
6.8
6.8 Degassed benzene solutions
Degassed
bunzeno solutians
NA 1 9
-106
Q3
a)
.lo3 0.5 .lo2
5
L
1
3 2
Figure 2. (a) Absorption spectrum of t h e solvent (1).Fluorescence excitation spectra of the solutions: [aNPO], 10-1 M (2); 3 X 1W2M (3);1.5 X lo-* M (4);5 X M (5). ( b ) Variation of R ( X ) with t h e solute (aNPO) concentration: X 205 nm (1);X 180 nm (2); 170 nm (3);h 160 nm (4);h 150 n m (5). 1. Excited States (E,,,
< W O )In . this energy range, the
fluorescence excitation spectra (Figure 2a) illustrate the characteristic deviations from Vavilov’s law, already reported for benzene and its derivatives and explained by the existence of photochemical processes in the La and Bb states, which reduce the internal conversion efficiency.li It is interesting to note that since the relative fluorescence efficiency R(X) is constant over each absorption band, it only depends on the efficiency of the transitions between electronic states (Le., vibrational relaxation is faster than electronic relaxation). The processes we expect to be of importance for the Sz and S 3 levels of benzene and its derivatives are indicated in Figure 4 together with the corresponding rate constants. In addition to the well established internal conversion and photochemical processes, we also consider energy transfer from the upper levels of the solvent to the solute, which should not be ignored a priori.7 Denoting by 7-3 = ( K30 + k 3 2 ) - 1 , 7-2 and 71, the lifetimes of the SS, SZ,and SI levels in the absence of the solute, we can
Figure 3. (a) Fluorescence excitation spectra of benzene-aNPO (1.8 X lo-’ M ) solutions containing chloroform or oxygen: [CHCIs] = 0 (1);5 X lo-’ M (2);lo-’ M (3);2 X lo-’ M (4); 5 X l o - ’ M (5); solution under 1 atm of O2 (6). (b) Variation of R ( h ) with the chloroform concentration: X 205 n m (1); X 180 nm (2); 170 nm (3);X 160 nm (4);X 150 nm (5).
define the following efficiencies: for internal conversion P32
=
73k32, P21
for energy transfer e3
= k t 3 ~ 1 [ F l / ( 1+ k t ~ n [ F I ) 62, ,
€1
for light emission from SI @
kri
The fluorescence quantum yield of the solute will be represented by @’. In cases like aNPO, where internal conversion of the solute molecule has an efficiency of one (8’32 = P’21 = l ) , we easily obtain the fluorescence quantum (11) J B Birks, “Photophysics of Aromatlc Molecules,’ Wiley-lnterscience, New York, N Y , 1970
The Journal of Physical Chernistry, Vol. 76, No. 25, 1972
C. Fuchs, F. Heisel, and R. Voltz
387
Superoxcited
:-Q
states
2
, = ,
I-a
/
\.
10
20
Fo Figure 4.
Energy levels and transitions.
yields 71, 72, 7 3 for excitation in the SI, Sz, Sa bands of the solvent. The relative quantities measured in the present study are given by
Rz = ‘)2/71 R3
=
03/lji
=
IO
e2(+’/d + (1 - 6 Z ) p z l
= d+’/~ + (1 i )- d P 3 z R 2
with 71 = e l + ’ + (1 - e l ) @ . In the limiting cases where [F] = 0, we have RZ = PZI and R3 = f i 3 2 R 2 = P3&. We can evaluate the internal conversion efficiencies from the values obtained by extrapolation to [F] T= 0 of the experimental curves giving Ra and R3 as functions of [F] (cf. Figure 2b). The values thus determined are listed in Table 11; they agree with the previously published data.4 For concentrations IF] high enough so that €I@’ >> (1 e l ) @ , the transfer efficiencies can be written as € 2 = ( R z 8zdi(tl-i - B Z I ~and t3 = (R3 - @32R2)/(€1-’ - P 3 2 R Z ) . The experimental values of Rz, f i z l , P 3 2 , and el9 thus allow determination of t 2 and t3 for the various solute concentrations. If the proposed kinetic scheme is correct, these quantities must agree with Stern-Volmer relations, i.e., 6 - l 1 = (7kt[F])-1. This is indeed the case, as illustrated in Figure 5 , where the results for the benzene solutions are presented. These Stern-Volmer plots allow determination of the constants htZ7Z and ht373 given in Table 11; the values, which may be justified by theoretical argument^,^ are about three orders of magnitude lower than those of ktl 71 characteristic of solvent-solute energy transfer from the SI states.7sll Similar evidence for energy transfer from the highly excited singlet states in the aromatic liquids was also presented by Laor and WeinreblO and by Horrocks.lZ Following the data in Figure 3, the influence of chloroform and oxygen on the kinetics of the Sz and S3 states appears as negligible. This is in accord with the results of Laor and Weinreb,lo but in disagreement with an analysis of Lawson, et al.13 At variance with our discussion, these authors also ignored solvent-solute energy transfer uia higher states. They further assumed the direct S3 ---* S1 transitions to be important; in the present work, we have verified that our results could not be reconciled with a kinetic scheme including such a process. This agrees with the well established “energy gap law”11 according to which the succession of transitions between neighboring electronic SI ralevels should indeed be more probable than a Sa diationless transition. 2. Superexcited States (E,,, > Wo). The increase of fluorescence efficiency R with the excitation energy, observed in this energy range (Figure Ba), indicates that the fluorescing lowest singlet states in the liquids have prelevels that are subcursors different from the iL, and
-
The Journal of Physical Chemistry, Voi. 76, No. 25, 1972
Variations of zene solutions).
Figure 5.
tp-I
- 1 and 63-l
-
1 with I F ] - ’ (ben-
TABLE 11: Internal Conversion and Energy Transfer from the S2 and S3 States. Experimentally Determined Parameters
Benzene Perdeuterated benzene Toluene Perdeuterated toluene p-Xylene Mesitylene
0.44
0.61
5.2
1
0.55 0.71
0.62 0.64
4.5 8.5
I 1
0.73
0.66 0.82
8.8
1 1.2 1.2
0.83 0.89
0.82
e25 =25
mitted to the photochemical processes which strongly reduce the internal conversion efficiencies. The data in Figure 3 further show that, in contrast to the iL, and states, these precursors are severely quenched by chloroform and oxygen known as efficient electron ~cavengers.1~ These results, together with the evidence from similar studies in crystalline materials,6 lead to identify the precursors as charge-separated states, and Wo as a threshold energy where autoionization begins to compete with the fast vibrational relaxation processes from upper vibrational levels of the electronic state.15 In the gas phase, superexcited levels have excitation energies larger t,han the first ionization limit. In the condensed phase, the role of autoionization is not confined to such high activation energies; it must also be considered for lower activated molecular levels. (12) D. L. Horrocks, J . Chem. Phys., 52, 519 (1961). (13) C. W. Lawson, F. Hirayama, and S. Lipsky, “Molecuiar Luminescence,“ E. C. Lim. Ed., Benjamin, New York, N. Y., 1969, p 837. (14) L. G. Christophorou, “Atomic and Molecular Radiation Physics,” Wiley. London, 1971. (15) Direct transitions from the upper molecular states to t h e Sj state could in principle be invoked to interpret the increase of R with excitation energy, but such a possibility does not account for the observed influence of chloroform; also, it is difficult to reconcile with the energy gap law for radiationless transitions.”
Formation of Excited Singlet States
'53 EC
E52 E CT E51
Z T
Figure 6. Schematic representation of bound and charge-separated states in liquid benzene. The numerical data used are I , = 9.2 eV and A, = 0 for the solvent, A, = 0.6 eV and 1.75 e V 2.5 eV.9,16 for aNPO and chioroform, respectively, and Pi
Information on these charge-separated states essentially comes from the studies with aromatic crystals.16 A broad conduction band, in which electrons are quasi-free to move and are little localized at any particular molecule, has the bottom edge a t an energy E , = I , - P+ - P-, where I , is the gas-phase ionization energy and P+, P- are the polarization energies associated with the holes and electrons, respectively. For liquid aromatics, the onset of these ionization continua may be roughly estimated at E , 2 I , - 3 eV, assuming ?+ = P- 5, 1.5 eV.16 The charge-separated states below the conducting levels are the charge-transfer (CT) states, in which the positive hole and the electron are located at molecular sites and are correlated by the Coulomb attraction; the excitation energy of these nonconducting states is given by ECT = I, - A, - P , - C ( r ) , where I , and A, denote the ionization energy and the electron affinity of the gas, P, is the polarization energy associated with the ion pair in the condensed medium, and C is the Coulomb energy dependent on the hole-electron separation distance r. In benzene, the lowest of these CT states, in which the ion pair is situated on neighboring sites ( r = 5 A), is estimated to be at ECT = 5.2 eV9 (cf. Figure 6). The expected sequence of processes initiated by excitation to a molecular superexcited level in the aromatic liquids is schematically pictured in Figure 6. Autoionization is characterized by its efficiency a( A) which should increase with increasing excitation energies E,*,. The hot electron in the conduction band is moderated by the mechanisms generally postulated for the subexcitation and subvibrationa1 ranges (excitation of intra- and intermolecular vibrations) and enters the manifold of charge-transfer states before the ion separation reaches the Onsager critical dist a n ~ e . 9The ~ subsequent ion recombination may be regarded as a succession of radiationless transitions between the charge-transfer states [M+, M - ] along the energy sur, finally to the lowest CT level. U1face . E c ~ ( r ) leading tirnate neutralization involves a transition from this state to an isoenergetic neutral molecular state which, following rough numerical estimates like those presented above, should be the SI sta.te in all the liquids. From the experimental action spectra it i s directly apparent that we cannot
3871
invoke recombination in the So or S3 state, a necessary consequence being that R(X) 5 RB < Rz, which disagrees with the experimental observations. We denote by pnz the efficiency of recombination, in the S I state. In the presence of the fluorescent solute F (aNPQ) and of the quencher Q (chloroform), electron scavenging by these compounds interferes with the recombination processes. Electron trapping by F is characterized by an efficiency YF and leads F-] to one of the localized charge-transfer states [Mf, which may be subsequently neutralized, yielding an excited solute molecule. Similarly, the efficiencies of formation of the [M +, Q -1 and the [M+, M - J-CT states are denoted by y~ and yll, as indicated in Figcire 4. We note that a production of SIstates from the low [M *, Q-1 levels is excluded on energetic grounds, which explains the quenching action of chloroform. Following this analysis, the efficiency of fluorescence upon excitation to superexcited states, in solutions without chloroform, can be expressed as
[I - 4 X ) 1 ? / 3 f a(N[(I - Y F ) P M ? I ~+ Y F P F @ ' ' ~ where the first term represents the production of S1 states by internal conversion, while the second describes the formation through autoionization followed by recombination; pF denotes the efficiency of the reaction [M+, F-] IF* (lowest excited singlet state of the emitting solute). For the neat liquids, where [F] = 0, the relative fluorescence efficiency is of the form
-
Experimentally, these values can be determined from the curves representing R( A) for various solute concentrations, extrapolated to the axis [F] = 0 (Figure 2b). In order t o get ? proceed by estimates for the quantities a(X) and p ~ we noting that since a(X) 5 1 and PM 2 1, we have
which leads to upper and lower limits for a( h ) p ~In. the case of benzene solutions, for example, 0.42 5 a ( h ) p ~5 0.58, a t 150 nm. The limits thus obtained, indicated in Table I, allow us to choose a "mean" value (e.g., a p = 0.50 for benzene) which, inserted in the equation for RIA), allow us to determine PM and a(X), assuming that only the latter quantity depends on the excitation wavelength. For benzene, pM = 0.7 and a(X) = 0.7, 0.5, and 0 2 at X = 150, 160, and 170 nm. All the results are listed in Table I. In the other limiting case of solutions with high solute concentrations [F], so that t l = 1, the expression of R(X) becomes
R ( N = [I - LY(X)]RB + ~ X ) P Mf
-
~ ~ ) Y F ( P FPM)
where R3 and y~ depend on [F]; since a(X), and p l 1 are known, the experimental curves for R ( h ) (Figure 2b) allow us to evaluate the quantities yF(pF - pM). i n all the cases, even for the mesitylene solutions where pJa = 0.95, positive values were obtained, which means that PF > p ~ In. order to estimate YF, we have put pF = 1 and found that this electron trapping efficiency increases with the concentration [F]as expected. Figure 7 shows that yp can be described (16) F. Gutmann and L. E. Lyons, "Organic Semiconductors," Wiiey, New York, N. Y . , 1967. (17) R. Voltz, "International Discussion on Progress and Problems in Contemporary Radiation Chemistry," Vol. 1, Prague, 1971, p 139. The Journai o i Physical Chemistry Vol 76. No 25, 1972
C. Fuchs, F. Heisel, and R. Voltz
387
energies of the SI and Sz states. We note that all these conclusions should be considered in the discussion of the early effects of ionizing particles, which mainly excite molecular levels with Eexc > WOin the aromatic liquids.
11. Excitation by High-Energy Electrons Among the observable effects of high-energy radiation in aromatic media, luminescence is an experimental tool of particular interest in the present study. The information it provides on the produced singlet states is indeed very direct, rapid (in the nanosecond range), and corresponds to the action of the single incident particles. Studies of the time dependence of radioluminescence in organic materials led us to distinguish between two different emission components, qualified as “prompt” and “delayed,” which have different physical origins.2 The prompt emission decays as fluorescence and is due to singlet excited molecules produced rapidly, Le., in a time period notably less than 1 nsec, after the passage of the incident particle. In the case of the liquid solutions with solute concentrations so that €1 = 1, as used in the following experiments, the intensity is of the form
Zp(t) = k’tlNs(0) exp( - t / n ’ ) Figure 7.
Variation of
YF-’
- 1 with [F]-’ (benzene solutions).
by a Stern-Volmer form, the characteristic constant being hFre = 9 M-1 for the benzene solutions; hF must be regarded as the rate constant of electron attachment by a N P 0 , and as the mean lifetime of the charge-separated :states in the neat solvents. The values derived for the other solutions are indicated in Table I. In the present context, it does not seem necessary to discuss in detail the data obtained with the solutions containing chloroform ( c f Figure 3). As mentioned before, these results are clear evidence for the role of charge. separated precursors of the S1 states in the liquids excited a t energies higher than WO.
Conclusions The characteristic increase of fluorescence efficiency with excitation energies exceeding the critical values WOindicates that the experimentally observed SI states in the aromatic liquids have precursors different from the S Z and SI states which are submitted to the “photochemical” processes that strongly reduce the internal conversion efficiencies. These precursors are identified as chargeseparated states which result from autoionization of the singlet excited molecules in the condensed phase. The energy Wo is found, for all the liquids, to be approximately equal to I , - 2 eV. It must be considered as the activation energy where autoionization in the broad conduction band begins to compete with the intramolecular vibrational and electronic relaxation processes. In the explored wavelength range, the ionization efficiency CY rapidly increases with excitation energy. This agrees with similar observations on gaseous or crystalline systems.18 The high values observed for the efficiency PM of final production of the SI state, after excitation in an upper singlet state, imply that geminate recombination without spin relaxation I s essentially involved. Also the energy of the lowest C T state must be intermediate between the The Journal of Physical Chemistry, Vol. 76, No. 25, 1972
where Ns(0) is the initial number of SI states, h’ is the fluorescence emission rate constant, and 71’ (= 2.2 nsec for aNPO) is the mean lifetime of the solute lowest excited singlet state. Integrating I p ( t ) , we obtain the number of photons emitted, per absorbed particle, in the prompt component
L, = @’€1NS(O) The singlet excited states responsible for the delayed scintillation component are formed through bimolecular reactions of molecules in triplet excited states. In the liquid solutions, the latter were identified as the long-lived solute states, formed by triplet excitation transfer from the solvent.9J9.20 Denoting the correspondent transfer effi, intensity of the delayed component is, ciency by t ~ the if t~ = 1 Z d t ) = k’aFtrNT(0)x
NT(O) represents the number of excited triplet states initially produced in the zones of high activation density (blobs, short tracks) where the triplet-triplet annihilation processes take place; CYFis defined as the mean number of singlet states produced per triplet state disappearing in such reactions; t , and t b are time constants related to the decrease of local triplet-state concentration due, respectively, to the diffusion out of the blobs and short tracks and to the bimolecular annihilation processes.2 The integrated intensity, i e . , the total number of delayed photons, per incident particle, is Ld
= @’oIFCT”l’(o)
(18) F. I . Vilesov and M. F. Akopyan, “Elementary Photoprocesses in Molecules,” B. S. Neporent, Ed., Consultants Bureau, New York,
N. Y., 1968,p 2 2 . (19) F. Spurny, Collect. Czech. Chem. Commun., 35, 565 (1970) (20)J. E. Birks. Chem. Phys. Lett., 7,293 (1970).
Formation of Excited Singlet States
3873
scintillation intensity I( t ) with the impulse response function R ( t ) of the apparatus: J ( t ) = I ( t ) * R ( t ) .R ( t ) was determined using pulses from Cerenkov emission.S,21 Knowing the form of Ip(t) from fluorescence decay measurements, we evaluated J p ( t ) = I p ( t ) * R ( t ) which was then substracted. from J ( t ) to obtain the shape J d ( t ) of the delayed pulse (cf. Figure 8). Having thus separated the two scintillation components, we could determine the ratio L p / L d by integrating the curves: the values are listed in Table HI. The principle of the method used to measure absolute radioluminescence yield has been described elsewhere.24 The aromatic solutions are first irradiated by the electrons. The scintillations are observed by a p h o t o m u l t ~ p ~which i~r delivers pulses with B height Hsuch as 1
t:o
10
20
30
H = Uke’Nhi’p
time (ns)
Figure 8. Radioluminescence decay curves (1.8 X IO-‘ M aNPO in benzene): (1) total luminescence J ( f ) = Jp(f) J d ( f ) (experimental curve): (2) theoretical prompt luminescence /,,(f); (3) prompt luminescence Jp(f) = /,(f) * R ( f ) ; (4) theoretical delayed luminescence / d ( f ) ; (5) delayed luminescence J d ( t ) = /d(f)* N ( f ) = J ( I ) - J p ( f ) .
+
where a is a constant and iz is the photon collection efficiency of the photomultiplier; Np is the total number of solute molecules excited in the lowest singlet state per incident electron
NF
TABLE Ill: S, Slates Formation under Fast Electron Irradiation. Experimentally Determined Parameters
tiNs(O)f ~ F ~ T N T ( O )
In a second step of the experiments, the same solutions are irradiated, by short monochromatic pulses, only absorbed by the solute molecules, which are thus excited in their first singlet state. The observed pulse height is here given by
H’ = ak’e’n enzene Perdeuterated benzene Toluene Perdeuterated toluene p-Xylene Mesitylene
3.5
0.9
0.7
2.8
1 1.1
0.8
0.6
0.34
0.9
0.7
0.45
1.15 1.2 1.15
0.9 0.95 0.9
0.7 0.95 0.95
0.48 0.68 0.73
4
3 3.5
3.5
0.7
0.27
While the analysis of the delayed component gives indications on the formation and behavior of triplet states in the blobs and tracks, the prompt component informs us on the direct formation of the SI states by the incident particle and its secondaries. For the present purpose, we therefore present, and discuss in some detail, the results on the prompt light emission component, obtained in a systematic study of radioluminescence decay laws and absolute efficiencies in the liquid aromatic solutions.9~21 Experimental Results
A first step of the experimental study was to analyze the time dependence of the scintillation intensity I ( t ) = r,(t) 4- r d ( t ) , and to separate the two components. This allows relative measurements of the quantities L , and Ld by integrating the intensities and thus determines the ratio I R, the probability of quenching is taken as negligible. Considering a n electron of energy T , and differential energy loss dTjdx, in the degradation spectrum, we assume that the quenching species are distributed along the particle path, according to a Poisson law, with a mean free distance given by X(T) = W(dT/dx)-l
where W is the mean energy required to form a quenching center. The probability of survival of a singlet state in the electron track is then identified with the probability that no quenching center exists within a distance R, i . e . P(T)
where N denotes the number of molecules per unit volume. In this expression, y ( T ) characterizes the degradation spectrum for incident electrons of energy TO.It may be regarded as the number of electrons with energy T crossing per units of time and energy, a spherical volume presenting a unit cross-sectional area.29 The lowest integration limit E1 is the excitation energy of SI states. u n ( T ) is the excitation cross section of the primary state of energy E , by an electron of energy T , 2 , represents the summation over the whole excitation spectrum. The efficiency of formation of an SI state from the primary level E , in the track of an electron with energy Tis denoted by an( T ) . From work on the characteristic energy losses of fast electrons in liquids and solids,30,31 it is known that a large pari of the primary collisions excite collective oscillations of the valence electrons (plasmons). In the case of aromatic compounds, the excitation spectra in the condensed phase generally present two major maxima: the first, located around 7 eV in b e n ~ e n e , 3is~attributed to the molecular P electrons; the second, at about 20 eV, is characteristic of all the organic materials and corresponds to an oscillation of the total number of molecular valence electrons. These initially activated plasmons promptly decay to excite isoenergetic states of individual molecules, which thence have excitation energies E,,, 2 7 eV.17 According to the results of the first section of this study, the molecular states formed after plasmon decay in the aromatic liquids are typically “superexcited.” The following stage of radiation action involves the set of processes converting these highly excited molecular states to the lower $1 states. Useful information hereupon comes from part I of the present work, but in addition, we must take into account 1he consequences of spatial correlation for the excited states along the particle tracks in condensed matter. The significance vf bimolecular reactions between excited molecules in condensed aromatic materials under particle irradiation has often been discussed.2~33~34 According to the secent studies of exciton interaction mechanisms in molecular crystals, the singlet states are submitted to very efficient quenching processes, which appear to be of paramount importance in the present context; the reactions SI SI S , iSo (Snz upper singlet states) and Si TI -TT, So (TI and T,: triplet states), in particular, have high rate constants (y = 10-8 cmJ sec-I), meaning that long-range
+
The Journal of Physical Chemistry, Vol. 76,
No. 25, 7972
+
+
4
=
exp[- ~ R / X ( T = ) ] exp[-- B
dT
(.I.)]
with B = 2RjW. Under these conditions, the efficiency qn( 2‘) for the formation, in the electron track, of an SI state which can be observed, can be written as
where q, is the conversion efficiency in the absence of track effects, as observed under light irradiation ( c f . part I). Inserted in the theoretical expression of Gs, we get the obvious simplified form
with T such as d T ( T )Jdx = B - I . Taking R = 10 A, W = 50 eV, we obtain B-1 = WJ2R = 2.5 eVJA or T’ = 1 keV as reasonable orders of magnitude. The integration is then restricted to the high-energy part of the degradation spectrum and yields simply36
where 2 is the number of valence electrons per molecule and denotes the oscillator strength for the transition to the primary level of energy En. As noted before, most of the primary levels have energies higher than 7 eV in benzene, which is precisely the onset Wo of superexcitation, as defined in the first part of this study. The efficiencies qn should then be considered as 7, = P M ( Y n , with the autoionization efficiencies an increasing rapidly to unity as E , increases, and with the values determined in
fn
(26) R. Cooper.and J. K. Thomas, J. Chem. Phys., 48, 5097 (1968). These authors do not discriminate between the prompt and delayed singlet states, which explains, at least partiaily, their higher Gs values. (27) J. 8. Birks. “The Theory and Practice of .Scintillation Counting,’’ Pergamon Press, Oxford, 1964. (28) R. L. Piatzman, Radiat. Res., 30, 20 (1967). (29) L. V. Spencer and U. Fano, Phys. Rev., 93,1172 (1954). (30) D. Pines, “Elementary Excitations in Solids,” Benjamin, New York, N. YI, 1964. (31) C. J. Powell, HealthPhys., 13, 1265 (1967). (32) 6. L. Sowers, E. T. Arakawa, and R. D. Birkhoff, J. Chem. Phys., 54, 2319 (1971). (33) W. G. Burns and R. Earker, Progr. React. Kinef., 3, 303 (1965). (34) M. Schott, Proceedings of the 4th Conference on Radiation Research, Evian, 1970, to be published. (35) V. Ern, J. L. Saint-Clair, M. Schott, and G. Delacote, Chem. Phys. Lett., 10, 287 (1971). (36) See, for example, I. Santar and J. Bedna?, Collect. Czech. Chem. Commun., 33, 1 (1968).
F‘ormation of Excited Singlet States Section I for the efficiency p~ of recombination in the SI state. For relatively higher excitation energies ( e . g . , En 1 15 eV), geminate neutralization without spin relaxation is expected to become less probable. The kinetic energy of the quasi-free electrons may indeed become sufficient to excite triplet states with concomitant relaxation of initial spin; also C-H and C-C bonding electrons are known to be mainly excited in this energy range for benzene and derivative^.^' In this case, the excited positive ions do not necessarily convert to their bound ground state, which again might prevent the formation of SImolecular states. This suggests that the summation Z;n(fnjEn) should be restricted to an energy range limited by an upper value. Introducing an effective number neff of electrons taking part in transitions to such energy levels, and a corresponding mean excitation energy E e f f , we then get the expression
which may be conveniently compared to the experimental data in Table IIB. An inspection of the experimental results on Gs and PM listed together in Table 111 first allows verification of the expected relationship between these two quantities. This suggests that, in accord with our analysis, the observed relative variations of Gs are related to variations of the recombination efficiency p ~ In, previous work,21,25 it has been assumed that the SIstates mainly result from internal conversion from primary S3 states; for the sake of comparison, the efficiencies of these processes have also been listed in Table 1x1. St is seen that while Gs follows approximately the same ordering as the p3zp21 values, the correla-
3875
tion with p~ is notably better. The absolute Gs values lead to (iOO/Z)(nefr/Eeff)= 1. For benzene (2 = 30), we may take E e f f = 10 eV and neff = 3, restricting the summation 2 , over primary states with En 5 15 eV, in accord with our preceding arguments.
Conclusions The description of the very early processes leading to the SI states in the aromatic liquids under fast electron irradiation, which has been suggested in part I of this study, does interpret our data on the scintillation yields. Further evidence for the mechanism involving autoionization of the upper primary singlet levels and subsequent geminate ion recombination comes from the observed decrease of G s with increasing concentrations of chloroform.3 Similar conclusions have also been drawn from the pulse-radiolysis studies of Cooper and Thomas.26 The primary states leading ultimately to the lowest excited singlet levels are mainly activated by the fast electrons of the degradation spectrum, in optical collisions with a relatively small energy transfer I( 15 or 20 eV); they thus correspond to only a minor fraction of the “isolated spurs,” as defined in ref 38. This, together with the efficient bimolecular quenching reactions of excited molecules in the blobs and short tracks, is considered to account for the low yields of SI formation in the condensed aromatic materials under high-energy radiati0n.3~ (37) B. 0. Jonsson and E. Lindholm, Ark. Fys., 39,65 (1969). (38) I . Santar and J. Bednay, Int. J. Radiat. Phys. Chem., 1, 133 (1969). (39) Typical L.E.T. effects in the aromatic materials have been interpreted using similar arguments; cf. ref 2.
The Journal of Physical Chemistry, Vol. 76, No. 25. 1972
