Concentration quenching of pyrene 1B1u in the vapour phase

Chemical Physics 63 (1981) 209-218 North-HoIIand Publishing Company

CONCENTRATION Andrew

DAVIS,

QUENCHING Michael

J. PILLING

OF PYRENE and Margaret

*RI, IN THE

VAPOUR

PHASE

J. WESTSYt

Physical Chemisrry Lnborutory, Oxford. OX1 3QZ, UK

Received

20 July 1981

The lifztime of pyrene ‘B,, has been observed in the vapour phase under conditions of vibrational equilibrium, over the temperature range 480-560 K. The lifetime was found to depend on the concentration of pyrene in the vapour phase and a rate constant for concentration quenching of 1.4 x 1U” dm” mol-’ s-l at 500 K was found. The rate constant including Landaudecreases with temperature with an activation energy of -36k6 kJ mol-*. Models for the quenching Zener type curve crossing and excimer formation are discussed in detail.

I. Introduction

stant similar to those of Williams and Stevens and assumed a single step quenching mechanism

The interaction between ground state and electronically excited aromatic molecules has both kinetic and spectroscopic consequences [l]. The observation of red shifted fluorescence led to the proposal of bound excimer states and, subsequently, to the accumulation of kinetic and thermodynamic data on these states. Concentration quenching without the associated excimer emission has been invoked for some systems and has been the subject of intensive study, particularly with regard to models for photosynthetic processes in green plants 121. No excimer emission has been observed in the gas phase although Stevens and McCartin [3] found concentration quenching of anthracene fluorescence using Stern-Volmer methods and discussed a model involving excimer formation. A long lived emission, originally attributed to the excimer, was later assigned to triplet-triplet annihilation [4]. Ware and Cunningham [S], using lifetime measurements, also observed concentration quenching in anthracene vapour. They found values for the quenching rate con+ Present

address: The Royal Institution, Street, London, WlX 4BS, UK.

0301-0104/81/0000-0000/$02.75

21. Albemarle

A*iALAAA, thus obviating the requirement of a stabilised excimer intermediate, for which there is no direct evidence. Recently, several examples of vapour phase exciplexes have been reported in the literature [6]. These exciplexes have, in many cases, been sufficiently long lived for exciplex emission to be observed, accompanied by quenching of the monomer fluorescence. This opens up once again the possibility that anthracene concentration quenching occurs via an excimer. It is important that the nature of the quenching process be elucidated, and also, if possible, the effect extended to other systems before any conclusions can be drawn about the relationship between excimer formation and fluorescence quenching in the vapour phase. Pyrene has been extensively investigated in solution [l], its long fluorescence lifetime and large fluorescence quantum yield making it ideal for study by both Stem-Volmer and time correlated single photon counting methods. The vapour has been studied by Werkhoven et al. at both high pressure [7]

Q 1981 North-Holland

and isolated molecule [S] limits, and some narrow band excitation studies have been performed. Thus pyrene provides a well characterised system for this study. We report here the temperature dependence of pyrene concentration quenching in the vapour phase.

2. Esperimentai Samples were prepared by evacuating a 1 cm square Pyrex cell containing pyrene (Oxford Grganic Chemicals, zone refined, recrzystallised from methanol and sublimed) to lo-’ Torr overnight, ?hen admitting argon (BGC research grade, 300 Torr) and sealing. Lifetime measurements were performed on an Grtec time correlated single photon counting apparatus in an arrangement similar to that described by Ware and co-workers [9]. The Pyrex cell was housed in a copper block, maintained at temperatures between 480 and 560 K to -~0.2 K with a purpose built temperature controlIer. temperature measurements being made with a calibrated platinum resistance thermometer. SampIes were irradiated at 318 nm through a monochramator with a 20 nm bandpass, corresponding to excitation of pyrene S2, and the resulting fluorescence observed at 385 nm through a similar monochromator. Care was taken to ensure that no fluorescence was observed from solid pyrene condensing on the walls of the cell. The fluorescence spectrum of solid pyrene has been measured by Birks [lo] and by US at temperatures similar to those used in this experiment_ The emission peak is at 420 nm and virtually no emission is seen at 3SS nm, the emission wavelength used here. In addition, the lifetime of the solid fluorescence is found to be an order of magnitude shorter than that of vapour phase pyrene, and no such emission was detected. Data collected over 500 channels for lo20 min at count rates of up to 5% were output from the multichannel analyser to a Research Machines 3802 microcomputer which was used to perform analyses including pile-up correction by the method of Coates [11] and deconvoi-

ution. Following a temperature dependent kinetic study, the celIs were heated at one end to drive any pyrene to the bottom of the cell, opened, and 3 cm’ of spectroscopic grade cyclohexane added. Absorbance was then determined on a Unicam SP800 ultraviolet spectrophotometer at 350 and 328 nm to give the concentration of pyrene in the cell. The method used for deconvolution was that of iterative reconvolution, using a lamp profile determined immediately after data collection. We have found deconvolution to be necessary even on a long timescale (2 )IS) because cur free-running, air filled lamp has a small but significant tail which extends well over 1 +s, the effect of which is to modify lifetimes by up to 2% _ The validity of the procedure was examined by the analysis of simutated decays, and found to be more precise and accurate than any method not including pile-up correction and deconvoIution. The rate constant obtained is relatively insensitive to the offset of the lamp peak relative to that of the start of the decay (since the tail, and not the peak, is the major source of error) SO no wavelength corrections were made when coliecring the flash profile [12]. Analysis was inset slightly from the start of the decay to minimise errors due to scattered tight.

3. Results The pyrene fluorescence decay rate was determined over the temperature range 480560 K and over a wide range of pyrene concentrations (10-‘-10-3 mol dmd3). Plots of the first-order decay constant (kobs) versus temperature are shown in fig. 1 for typical concentrations. Fig. 2 describes the variation of rate constant (/cobs)with concentration of pyrene for some typical temperatures_ The plots in fig. 2 show a non-linear dependence on the pyrene concentration with a linear rise followed by a horizontal section. The position of the break occurs at higher pyrene concentrations as the temperature increases. This effect may be ascribed to the attainment of the pyrene

480

5co

I 520

560 540 T/K

Fig. 1. Temperature dependence of the observed first order decay constant (Robs)_Concentrations of pyrene (mol dm-‘) are L! 4.26x IO-“, A 3.45x lOma, 0 1.03x IO-’ and @ excess pyrene.

saturated vapour pressure at a given temperature. Thus further increases in the amount of pyrene added to the cell do not increase the concentration in the gas phase. Points in the horizontal region may therefore be determined accurately by using an excess of pyrene in the cell. As the temperature rises the saturated

Fig. 2. Observed first order decay constant (!q,,,J as a function of pyrex concentration at temperatures 8 507 K, 0 526 K, A 546 K and 0 566 K. The positions of the broken lines are given by the average of several experiments with different atmxmts of excess pyrene in the sample cell.

vapour pressure, and thus the limiting gas phase concentration, increases. This proposed explanation of the observed behaviour may be tested, since the concentration of pyrene at which the measured rate deviates from the limiting rate at each temperature enables a crude estimate to be made of the vapour pressure of pyrene at that temperature. No data are available on pyrene vapour pressure in this temperature range, but the vapour pressure at the triple point (424 K, 6.848 X lo-’ atm [13]) and at the boiling point (666 K, 1 atm [?4]) are known. The values obtained from this work are plotted in fig. 3 as well as the extrapolation from triple to boiling points. It may be seen that there is good agreement between the two data sets. From plots of rate versus concentration the spontaneous (intercept) and self-quenching (slope) rate constants were determined at each temperature. There are fewer useful determinations of rate constants at low temperatures, since the range of concentrations for which all the pyrene would be in the vapour phase is smaller. Thus spontaneous and quenching rate constants are determined with lower precision at low temperatures. Fig. 4 shows plots of the logarithm of the spontaneous decay rate constant (k,) versus reciprocal temperature. Thii plot appears linear over the temperature range suggesting that all processes affecting this rate have a similar energy dependence, or that one is dominant. Werkhoven et al. [7] measured spontaneous rates over a wider temperature range and observed some curvature. Determination of fluorescence quantum yields as well as decay

l@ODK/T Fig. 3. Experimentally determined pyrene vapour pressures. The poinis ar the extremes are given by vapour pressures at the boiling and triple points.

Iso

1

I 1

,

I8

19

20 2.1 lOOOK/i

Fig. 1. Spontaneous decay rate constant versus temperature. Vertical error bars represent 5 1 standard deviation.

rates following narrow band excitation enabled him to assign non-radiative processes such as intersystem crossing as the dominant factor in pyrene spontaneous decay. The concentration quenching rate constant, k2, may be determined from the slopes of the plots in fig. 2 at pyrene concentrations below the break. k, exhibits a strong negative temperature dependence, the Arrhenius plot of fig. 5 yielding, on a least-squares fit, weighting with the inverse square of the experimental standard deviations, an activation energy of -36* 6 kJ mol-’ and a pre-exponential factor of

i / ,’

!/

Fig. 5. Temperature dependence of the concentration quenching rate cofistant. Vertical error bars represent *I standard deviation and the connecting tine is given by a weighted least-squares bes: fit procedure.

(2.4kO.6) x lo5 dm3 mol-* s-l, where the quoted error represents one standard deviation. The value of the negative activation energy for kz is remarkably close to the binding energy of the excimer in so!ution [l], and it is interesting to note that anthracene concentration quenching also shows this equivalence between vapour and solution phases (20 kJ molK’ in this case cl, 51). Although this equivalence may be fortuitous, and does not in itself prove the involvement of the excimer in the quenching process, any mode1 which is proposed must account for the strong negative temperature dependence. Ware and Cunningham [S] suggested that it could be accounted for by the reduction in the lifetime of the collision complex with temperature and the subsequent reduction in the probability of crossing to a lower, non-emitting potential surface. In the following discussion, we examine this and other reaction mechanisms in an attempt to account for the temperature dependence of the observed concentration quenching.

The most general method used to account for curve crossing in collisions between atoms is based on the Landau-Zener model. Such a model could be applicable to the present problem if the lifetime of the complex were sufficiently short that delocalisation of the relative translational energy of the collision partners among their vibrational modes did not occur. The atom-atom model may be extended to poiyatomic systems and the crossing may then be thought of as occurring from a family of approximately parallel potential energy curves for the various reactant quantum states to a similar family for the product states (fig. 6). For a particular reactant state, the reaction probability is optimised around a range of product states whose identity is determined by the interplay between the curve crossing probability and the Franck-Condon factors for the transitions between the reactant and product quantum states. Thus, for each reactant state, the problem efiectively reduces to a quasi-diatomic

where K, contains the Landau-Zener crossing probability and is related to the nature of the crossing point by KP= Z;iV’(R,)[h

Fig. 6. Parallel curve theory.

crossings

in

Distance extended Landau-Zenrr

curve crossing problem. Child [15] has discussed the extension of Landau-Zener theory to triatomic systems. The model is most appropriate if the geometries of the initial and final states are similar because the range of final vibrational states for a particular initial state is then small. This is likely to be true for the transitions involved in the present case. The rate constant from an initial state i to a set of final states {f} is k,n,, where
(1)

/d(V, - V#dR[&,

(2)

where R, is the separation at the locaiised crossing point, V(R,) is the coupling matrix element between the diabatic potential curves at R,, Id( VI - VZ)/dRjR, is the difference in slopes of the potential curves at the transition radius, and p is the probability of approaching along a curve of the correct symmetry for crossing to occur. A-* contains the essence of the temperature dependence of the model, .and has been evaluated by Faist and Bernstein in terms of a reduced temperature parameter, T*‘, and a dimensionless parameter i*_ The high temperature Iirnit of ii -* is unity, and at suf?icientIy low temperatures an inverse square root temperature dependence is obtained. The physical interpretation of such a model is that at low temperatures the partners approach and pass through the transition region slowly, thereby facilitating crossing. As the temperature rises the mean velocity increases and the transition probability fails. This is essentially the argument advanced by Ware and Cunningham [5] to explain the temperature dependence of anthracene concentration quenching. However, eq. (1) suggests that the maximum temperature dependence to be expected from such a mode1 is T-I”, which would correspond, over our temperature range, to an activation energy of only -2 kJ moI-‘. This vaIue is far too small for the model to be considered realistic, even allowing for the obvious limitations and approximations involved. Only if the curve crossing probability decreased markedly as the vibrational energy of the reactants increased would such a model account for the observed temperature dependence. The energy dependence of the rates of radiationless transitions in isolated aromatic molecules suggest that the net rate increases with the vibrational energy of the initial state. contrary to the required behaviour. The Faist and Bernstein treatment calculates rate constants from Landau-Zener cross sections

for head on cohisions. Thus angular momentum and the effects of centrifugal maxima are disregarded. Simple treatments of atom recombination reactions show that inclusion of such effects leads to a decrease in the rate constant with temperature [IS], but, once again, the dependence is small (typically, k a T-“3) and, even when combined with the temperature dependence obtained from the Faist and Bernstein treatment, does not Iead to the large negative temperature dependence observed experimentally. Negative temperature dependences have aIs. been observed experimentally and rationalised theoretically for near resonant energy transfer [19]_ The dependence is, however, weak and typicahy of the form T-I”. Thus we conclude that a model which precludes energy delocalisation and uses two dimensional Landau-Zener analysis, modulated by FranckCondon factors, is unable to account for the observed temperature dependence. If energy delocaIisation does indeed occur and a bound complex is involved, then models based on unimolecular rate theory may be employed. These may be represented by the scheme shown in fig. 7 where P and P* are ground and excited state pyrene molecules respectively, and (PP*)r is a vibrationally unrelaxed complex, isoenergetic with the coIliding molecules, whilst (PP*)u represents a complex drawn from a Boltzmann distribution following vibrational relaxation induced by collision with the bath gas, M. l3oth (PP’): and (PP*)n may undergo spontaneous decay, with a rate constant X-r which is determined by the energy, E, of the complex. In fig. 7, .?c: refers to an average of k: over a BoItzmann distribution. The full solution of this kinetic scheme is complex, and, as we shall see, unnecessary in the

lP+P*),

5

CPP’);

k:

Products

UMI

Fig. 7. Reaction analysis.

scheme for unimolecular

rate theory

present case. We may proceed, instead, by examining the behaviour at the extremes of zero and infinite bath gas pressures. In the latter case, k,[M] % (k,’ + ICI) and collisions induce a Boltzmann distribution amongst the states of the complex. Provided kfr s k:, the complex and separated molecules are in equilibrium. We shall assume for the present that this is so and justify it a posteriori. Thus the rate of formation of the products is given by d[products]/dr

= kJP][P*]

= [ k:n 2 dE,

(3)

I, where n& is the number of complex molecules per unit volume at energy E under Boltzmann conditions and k2 is the overall bimolecular rate constant for quenching. Thus kz = C(Q~Y),.JQ~QYI 22

exp (eJk7’)

kL’V*(&) exp (-s/k37

X

dE,

(4)

0

where (Qpp-)i.r is the rotational/translational partition function for the complex, QP and Qr. are the total partition functions for the reactants, and N*(E) is the density of vibrational states for the complex at energy E. The energy zero has been taken as the zero point level of the complex, and e. is the dissociation energy of the complex at zero K. The partition functions are referred to the zero point energies of the molecules concerned. It has been assumed in eq. (4) that kr is independent of rotational energy. If k: is independent of E, eq. (4) reduces to Kz = Kk,,

(5)

where K is the equilibrium constant for complex formation. Provided that k, is temperature independent, kz shows a negative activation energy equal to the mean energy difference between reactants and complex. If, on the other hand, the complex is too short lived to undergo collisional stabilisation, then: nE = [k?f(~)

d&/k’i][P][P*].

(6)

kfs is the total rate constant for formation of PP” from P* +P, and kTCf(.s) de is the fractional rate constant into the energy range E to E + ds ; it has been assumed, once again, that k’_, s kz. The evaluation of f(c) d.s and kct is well known in unimolecular rate theory [Xl], and using the RRKM model, they are given by ={Wie)

f(E)d&

x exp C--b - edlkT1

dEVkT(QkL,

(7)

and = C~~E~I~~*~E~IC~Q~~-~~.~/~QPP~~~.~I,

kf,

(8)

where (Q&v) is the partition function of the transition state, which lies between the reactants and the complex, and W(F) is the sum of vibrational states at the transition state up to energy E. ky is the total rate constant at infinite pressure and is given by k;” = (kT/h)(Q,-)/Q,Q,-. Thus, combining

(9)

eqs. (6)-(9),

ne = [(Q,,*),.,/Q~Q~-~[PI[P*IM*(E) x exp [-(E -c,)/kT]

dc.

(10)

Substituting into eq. (3) and integrating over the range of accessible energies, co to ~0, gives finally kZ = [(QPP-L/QPQP=I

exp

CEO/~T)

co

k:N*(&) exp (-&/kT)

X I

de.

(11)

to be unchanged on electronic excitation or complex formation Rough estimates were made of the remaining six vibrational frequencies of the complex. The P-P” stretching frequency was taken as 180 cm-’ since this is twice the zero point energy of the crystal excimer [tO] and the remaining vibrational frequencies were all initially assumed to be 50 cm-‘. These vibrations are expected to be very anharmonic, but do not seriously affect the immediate result. Fig. 8 shows the variation of N*(,E) exp (-&/kT) with E for three different temperatures. Also shown is the approximate position of co which was assumed to be 40 kJ mol-‘. It is easily seen that the integral of N*(E) exp (-c/kT) is, to a very good approximation, independent of the lower limit of the integration between 0 and co, at the temperature range over which this experiment was carried out. Thus, provided k, does not increase dramatically with energy, there will be no detectable difference between the high and low pressure limits for k2. Because of its size, the PP* complex effectively acts as its own heat bath and equilibrium between reactants and complex is effected even in the absence of thermalising collisions. The temperature dependence is governed by the binding energy of the complex, modulaied by any energy dependence of k,. It is interesting to note that the shorter lifetimes of the higher energy states of the complex have no effect on the temperature dependence. Eq. (7) is derived using the principle of detailed balancing and so the

E” Comparison of eqs. (4) and (ll), for the high and low pressure limiting rate constants respectively, reveals that the two differ only in the range of integration of the weighted densities of states. We have compared the two limits by evaluating the integrand over wide energy and temperature ranges. Densities of states were evaIuated with the Beyer-Swinehart algorithm with a grain size of 5 cm-‘. Vibrational frequencies for both the pyrene and singlet excited pyrene were taken from assignments for the ground state [21] and, for the purposes of the present crude model, frequencies were assumed

Fig. 8. Evaluation of integrand of qs. (41 and (11). Points are nonnzlised to the total vibrational partirion function. Temperatures @ :OO K, I 100 K, A 500 K.

increase in k’-r with e is exactly balanced by the increase in dki. We now return to the problem of justifying our initial assumption that k?l S= kz. If we consider the classical reaction scheme in fig. 9, then the rate constant for quenching of electronically excited pyrene via an excimer intermediate is given by (12)

kl=kik,f(k_,tk,~.

Here, the classical rate constants kel and k, are averages of ki, and k: over all possible reacting states, and may be expected to reflect the relative magnitudes of k?, and k: over the most important contributing energies. Assuming k I > k,, eq. (121 reduces to eq. (5), which is the classical equivalent of the high pressure rate constant given by eq. (4), and, as we have discussed, will lead to a negative activation energy for kl. If, on the other hand, k, * k-1, eq. (12) suggests that the quenching rate constant will be governed by the rate of formation of the excimer, kl, which is expected to be relatively independent of temperature, and cannot explain the observed temperature dependence. In addition, kr is likely to be of the order of the collision frequency, 2, whilst the experimental value of kZ is =1-O-” 2. The effect of reducing k~ I relative to k, and switching between the two cases has been illustrated by Hirayama 1221. Here, exciplexes formed from X,&I-dimethylaniline and a series of cyano-substituted anthracenes were examined in the vapour phase. Both 9-cyano-IO-ethyl anthracene and 9-cyano-?O-phenyl anthracene produced exciplexes with lifetimes that decreased with temperature, corresponding to the relationship k_l > k,, whereas 9,10-dicyano anthracene gave a more strongly bound exciplex in which kc> k-1 and little temperature dependence of the exciplex characteristics was observed.

The magnitude of the rate constants for pyrene can be estimated using eq. (5) and the measured quenching rate constant. The equilibrium constant K is Qpp* exp (.cO/kT)/QpQp and values are given in table 1 for several different sets of interfragment frequencies, including, in some cases, free internal rotation, over a range of temperatures. In these calculations, E,, was taken as 36 kJ mol-‘. $, and I,., the moments of inertia of the pyrene molecule about the x and y axes, were calculated to be 901.76 and 492.21 amu A’, respectively, and the other moments of inertia were evaluated using the perpendicular and parallel axis theorems with ro, the equilibrium interfragment separation, as shown in the table. Table 1 also shows the values of k, required to reproduce the experimental values for X-2. If k, is to be close to the solution phase value of 2 x 10’s_i Cl] for the spontaneous decay of the excimer, then K must be greater than ten and the interfragment frequencies very low indeed. This suggests that the complex may be much looser in the gas phase than in solution. Alternatively, k, may be higher at the typical excimer energies applicable in the present work than at the lower energies which apply in solution. Ottolenghi [23] suggested that radiationless transitions may occur more rapidly from unrelaxed excimers. One further consequence of the excimer kinetic scheme is the presence of excimer emission and of biexponential decay of the emission intensity. These phenomena are observed in solution but neither was found in the present study, despite an extensive search. In a biexponential decay, the monomer fluorescence response function [l] is given by iM(t) =e-*“+A

e-A2’,

(13)

where A*.2=&[X+

Ys{(Y-X)2+4klk-*[P]}‘/‘1,

A=(X-A#(&-X),

X=k,+kl[P]

and P Fig. 9.

Classical

Products reaction

scheme.

Y=k,+k_l, and the dimer fluorescence

response

function is

Table 1 Equilibrium

180

constants

calculated

50 6

I

100 100

10

180 180 100 100

50 6 10 IO

I I 50 6 10 10

180

10

=’ Number in parentheses

given

I

from inter-fragment

3.26 3.26 326 5.00 3.26 3.26 3.26 SO0

frequencies.

9.5(-3)“’ 3.511) 7.5 1.2(l) 9.3(-j) 3.5(-l! 7.3k2) 1.21-l)

S.6(-3) 2.111) 4.5 7.3 52-5) X0(-1) 3.31-2) 6.9(-2)

3.61-3) I.-Ill) 3.0 4.8 3.21-5) 1.2(-l) 2.7(-71 1.3(-21

indicates the power of ten to which each value is to be multiplied

by

j,(r) = e-V-e-%*_

(14)

The intensity of dimer fluorescence and the deviation from single exponential behaviour for the monomer decay thus depends on the concentration of excited dimer relative to that of excited monomer, and the rate constants k,, k,, k_, and k,. An estimate of the ratio of excited dimer to monomer may be obtained from the equilibrium constant for dimer formation, K, since K = k,/k-;

I denotes full internal rotation

= [PP*]/[P][P*J.

(1.5)

We have calculated this ratio of concentrations, and also the coefficients for the biexponential monomer decay, using these equations. k, and [P] were determined experimentally as described above, K was assigned ttie range of values shown in table 2, k, was chosen so as to reproduce the experimental value of kz, and kl was varied from 1O’Oto 5 x 10” dm’ mol-’ s-l. The results show that the ratio of excimer to monomer concentrations is always small; it is unlikely that we would observe excimer emission under these circumstances on our apparatus even if the excimer fluorescence quantum yield was unity. Also, the expected monomer decay is almost entirely single exponential in character with the addition of a very low intensity, short lifetime, component which again would not be observable. The measured rate constant kobs thus correspcnds to Al from the long lived component of

the monomer emission, but the experimental relation k&s = k, + &z[P] is not a general relationship for A,. However, under conditions where k,, k_l s- k,, k,, as applicable here, the “high temperature limit” pertains and A1 is given by (16) Since, from tabie 2, [PP*]/[P*] is small, A~, may be seen to give the same dependence on [PI as does kobs. The major conclusion that can be drawn from the present work is the occurrence OI concentration quenching in pyrene vapour. The rate constant decreases rapidIy with temperature, and has an activation energy of a magnitude which suggests that quenching occurs via the excimer. A kinetic model, based on unimolecular rate theory, supports this conclusion although the excimer characteristics are such that it was not possible to observe excimer emission or decay kinetics, characteristic of excimer formation, directly. Further studies with much more sensitive apparatus would be required to prove beyond doubt the intermediacy of stabilised excimers in the quenching process.

Acknowledgement We thank the Science Research Council for a research studentship to A.D.

Table

2

Encimer model characteristics” X-l rdm’ mol-’

5-l)

T tK,

k,

Is-‘1

2.9(11, 4.71 IO 2.3111) 4.5( 101 2.9(091 5.7(OS) Z.3iO91 -!._i(OS) 2.9toW 5.3;.07 1

Z.3OSl 5.1f.07) _I’ Xumbsr

in parentheses

indicates

A,

(S-I)

4.2t6) 6.-t(6) 4.2(6’) 6.4(6) 1.2(6) 6.4~6) 4.2(6) 6.4(6) 4.2(6) 6.-1(6) 4.2(6) 6.4(6)

A:

!s-‘)

1.3(12) 1.0(12) 5.0(13) 5.0(13) 1.3(10) l.O(lO) 5.0(11) j.O(ll) l-3(9) l-1(9) 5.0(101 5.l(lOI

A

l.l(-6) l&-3) 1X(-6) 2.0(-5) l.l(-4) l-8(-3) l.S(-4) 2.0(-3) l.l(-3) 1.8(-2) l&-3) 2.0(-2)

l.S(-6) 2.0(-j) 1X(-6) X0(-5) l&-4) X0(-3) 1.8(-4) 2.0(-3) l-8(-3) X0(-2) 1.&u-3) 2.0(-2)

the power of ten to which each value is fo be multiplied.

References [l] J.B. Birks. Photophysics of aromatic molecules (Wiley, Nea York. 1970). [2] G.S. Blddard and G. Porier, Xature 260 (1976) 366. [3] B. Stevens and P.J. XfcCartin, Mol. Phys. 3 (1960) 425. [s] 6. Stevens, W.S. Walker and E. Hutton, Proc. Chem. sot. (1963) 62. [5] W.R. Ware and P.T. Cunningham, J. Chem. Phys. 43 !1965) 3826. [6] S. Hirayama, Chem. Phys. Letters 79 (1981) 174; S. Hirayama and D. Phillips, J. Phys. Chem. 85 i.1981) 643; S. Okajima and E.C. Lim, Chem. Phys. Letters 70 (1980) 283. [71 C.J. Werkhoven, P.A. Geldof, M.F.M. Post, J. Langelaar. R.P.H. Rettschnick and J.D.W. van Voorst, Chem. Phys. Letters 9 (1971) 6. J. Langelaar, R.P.H. WI C.J. Werkhoven, T. D&urn, Rettschnick and J.D.W. van Voorst, Chem. Phys. Letters 32 (1975) 325. 191 C. Lewis, W.R. Ware, LJ. Doemeny and J.L. Nemzek, Rev. Sci. Instrum. 34 i19731 107. [lOI J.B. Birks and A.A. Kauaz. Proc. Roy. Sot. A304 (1968) 291.

[ll] P.B. Coates, J. Sci. Instrum. 1 (1968) 875. [12] Ph.Wahl. J.C. Auchet and B. Donzel, Rev. Sci. 1nsrrum. 45 (1974) 2s. [13] W.K. Wang and E.F. Westrum, J. Chem. Therntodyn. 3 (1971) 5; L. Malaspina, G. Bardi and R. Gigli, J. Chem. Thermodyn. 6 (1974) 1053. [14] C.R.C. handbook of chemistry and physics (C.R.C. Press, Cleveland, 1974). [15] MS. Child, Disc. Faraday Sot. 55 (1973) 30. [16] P. Avouris, WM. GeIbart and M.A. EI-Sayed, Chem. Rev. 77 (1977) 793. [17] M.B. Faist and R.B. Bernstein, J. Chem. Phys. 64 (1976) 3924. [IS] I.W.M. Smith, Kinetics and dynamics of elementary gas reactions (Butterworths. London, 1980). [19] J.D. Sterrler and N.M. Witriol, Chem. Phys. Letters 23 (1973) 95. [20] P.J. Robinson and K.A. Holbrook, Unimolecular reactions (Wiley, New York, 1972). [21] A. Bree, R.A. Kydd. T.N. Misra and V.V.B. Vilkes, Spectrochim. Acta. 27A (1971) 2315. [22] S. Hirayama, Chem. Phys. Letters 63 (1979) 596. [23] M. Ottolenghi. Act. Chem. Res. 6 (1973) 153.