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The electronic relaxation of methylglyoxal in the vapor phase
Chcmica1 0 Nor
l’hysics
16 (1976)
tlr-llolhnd Publishir+!
15 l--15Y Company
THE ELECTRONIC RELAXATION OF METHYLGLYOXAL IN THE VAPOR PHASE
Reccivcd
Tbc
6 April
rime-rcstrlvcd
c~~msrancus LriplsL
1976
LI du;ll
cwpling,
111cprcsrurc
the tlissipativc
induction
As found the former
flwrcsccncc l~~c~rcsccncc
previously bcinr
111osc afglyoxal
more
of
obscwcrl.
Icol;
rllcs
the Ihcrm:dizcd in biacctyl,
ustcnsivc
and biaccryl.
basis or Lhc diffcrcnces
o1’nwthylglyosal ws
in their
(rum
was studied
l:rom sinplct
2nd rriplcl
phospborcsccncc
rhc cscilcd
manifuld
in ~netl~yI~lyos;~l.Tl~c The
diffcrcnccs
Icvcl dcnsilics.
as ;I function
111csc mc~~remcn~s
in bclnvior
NX
Very recently Coveleskie et a!. [l-4] reported detailed studies of the photophysical behavior of methylglyoxal (CH,COCOH). According to the theory for “intermcdiate.c3se” molecules of klhrnani, Trumer and Tric [5] they obsenfcd. among other things, a biexponential fluorescence decay. As could be cspected. the behavior of methylglyoxal appeared to be intermediate between that of its analogues: glyoxal [6] and biacetyl [7-IO]. In our recent paper [IO] we pointed out the important difference between the low energy range where the singlet widths do not overlap (“black hole region”) and the “overl;lp region” at higher energies. IL also ap. peared that the energy range studied by Coveleskie et al. (up to I1 15 cm-l excess energy) FJIIs in Ihe “black hole” region. In this paper, therefore, data for a more extensive energy range (up to 3000 cm-l) are reported. At low energies we find the same results and come to the same conclusions as Coveleskie et al. As expected from our earlier work at higher energies, where the singlet widths do overlap. we find interesting changes in the decay behavior, which are reported here. In addition we studied the pressure induction of the :hermalized phosphorescence. * PrescnI address: Koninklijkc/Sbell Laboratorium, Bndhuiswee 3, Amsterdam, The Netherlands.
bu divided
characteristics
bctwecn
due to the different
1. Introduction
and tllc
cncrgy
and prcssurc~
IIIC p;lramcrcrs
duscribin;
tlu~lrcsucncc
qucnchinc
il black
region
In all cirrhc sinylct-
cwwI211Is.
Also.
studied.
sl~ould decay
51aW
of oscilation
WI: obraincd
rbc three number
into
hole
ofn~cthyl~lyosal molcculcr
and nn ovcrlnp
arc inrcrmsdiarc
can bc readily
rlf ;LtomLs in lhcsc
undcrstoud
qiun.
bctwccn on the
molcc~lss.
The theoretical background of our inlerpretation has been extensively given in our previous paper [IO]. After a discussion or the experiments and their interpretation we make il comparison of the relaxation patterns of the three I ,?-dicarbonyls ttnder consideration.
2. Experimental From a 40% solution of polymeric methylglyoxal (Aldrich) the major amount of water was distilled off. The residue was depolymerizcd at about 90°C in the presence of P205 as described in ref. [I]. The tnonomerit methylglyoxal was degassed each time before ust until Lhc vapor pressure 31 --2!?.9”C was constwt. A mass spectrum showed no impurities. In some esperiments high quality cyclohcxanc (hlerck) was used. The experimental arrangement (consisting bf a pulsed tunable dye laser, a large spherical Fluorescence cell and single photon counting equipment), the experimental conditions. the measuring techniques and data analysis methods have been fully described in our previous paper [ !O]. 2.1. The /Iuorexerrce
decay
The fluorescence was studied in the excitation range 4X5-3975 A. At each excitation wavelength
the fluorescence decay was recorded on two time ~calcs. one at 100 or 200 ns and one on a longer time scale (40~~500 I-IS)&pending on the Lifetime of the slow fluorescence component. The short-lived component was studied at mcthylglyoxul pressures ranging rrorn 10 mtorr (low energy excitation) to 25Omtorr (,at 3975 8, excitation). The long-lived component was sludied in a pressure domain ranging from 0.25-10
mtorr (4.555A) to IO-500 mtorr (3975 a). At 4010 A excitation the pressure dependence of the long-lived component was also studied as a functiorl of cyclohcxane pressure The ratios of yields of fast and slow tluorcscencc were measured at pressures ranging from 0.25 mtorr (4555 I!) to 80 mtorr (3975 A).
2.2. Pressuredeper&ence pliosp/rorc,sccrrce yield
of file themalized
It was shown previously [I] that in methylglyoxal, triplet self-quenching occurs with a rate of I.57 s-l mtorr-t. In order to avoid complications due to this effect the methylglyoxal pressure should be kept small. However, at such pressures the phosphorescence induction is not yet complete. We therefore used a mixture of methylglyoxal (7.5%) in cyclohexane. The thcrrnalizcd phosphorcscencc yield was studied as a function of the pressure of this mixture in the range of 8-4OOnitorr at 4OlOA excitation Then the errors due to self-quenching were below 3%. The signal was measured with the “delay-add&r” method [IO]. The delay time, used to prcvcnt detection of lluorescencc and Lo assure complctt thermaltiation in the triplet manifold was 150~s. both add and sub-timeswere 4.8 ms.
lutions OF the laser curve and emission curves titted
best on the measured decay curve. We assumed exponential decay behavior. The rates. measured at IO2SOmtorr rnethylelyoxal were considered as zeropressure rates. ThE time between collisions for 5 17
diameter hard-sphere collisions always exceeded the fast fluorescence lifetime by a factor of 30 or more. The energy dependence OFthe zero-pressure hst fluorescence rates (k+) is given in table 1 and tig. I. We see a smooth increase of X-+with energy. Note that the energy dependence of kf is very similar to that of biacctyl 17.101 and glyoxal [6].
The slow fluorescence decay was mildly non-exponential for all excitation wavelengths and all pressures. At most escitation wavelengths the pressure (P) dependence of the observed lifetime (T) satisfied the Stern-Vobiier relation: r-t = x_-+ ,$p.
(‘1
Table I and ties. 2 and 3 show the energy dependence of Lhe zero-pressure slow fluorescence rates (k-) and lhe tluorescencc quenching constant cLI Around 24000 cnl-I he Stern-Volmer slraight line, but consisted
one
This is due to the Boltzrnann
plots did not yield OF two
linear
distribution
branches.
of
the vapor and the consequent optical excitation of energies cncornpassiny, higher and lower 4 values. Data given here are from
the low pressure
branches. yielding the
higher mu values. The.low energy value of cn is larger than the 5 A hard-sphere collision rate by a factor of 8. It remains constant up to 23600 cm-l. then sharply
3. Results The Fluorescence decay appeared to be roughly biexponential at all excitation wavelengths and pressures
studied. The ktst component has a lifetime of the order of IO ns, the slow component
of some micro-
seconds.
I
1
3.1. T?le fastJImresceme The fast fluorescence rates were determined by establishing which of the computer simulated convo-
kST
05.d L
1 22000
-
Eacitatlon 23000
energylcm-‘I ZLOOO
]
I 25000
Fig. I. Obscrvcd fxt fluoresmncc rntc versus excitation cncrgy separation ork+into k$!T and ks is discusxd in Ihc text.
The
153 Tnblc 1 Obxrvcd quantities -___._
--.-..-.
LxcitaLion wavelcn~rh
Waxnumber
(4) ~-
(cm-‘)
4555 4527 4492 4440 4416 4355 4320 4280 4240 4200 4160 4125 4090 4050 4010 3975
21954 22090 22262 22482 22645 22962 23148 23364 23585 23810 24038 24242 24450 2469 1 24938 25157
Typkli
errors:
._---
. ..-___
----..-.-._.
..-.
Zero-pressure r;ltc of f;lsr fluorcsccn@2
Zero-prCSSUrC ril1c of slow nuorcsccncc
k+(10’5-1) _-.-_ _ . ..__ _.
Ji- (IO” s-1) __. ._..-__--._.-
8.7 8.7 8.5 a.7 9.1 8.7 9.5 12.1 _
1.95 2.1 1.25
I .0.5 1.00 0.80 0.70 0.85
I so
14.3
2.4 3.6 6.6 11.3 18.1 21.2
2 10%
512%
12,5 13.8 -
drops off to a value, which is only 40% of the hardsphere collision rate. At 4010 a excitation the
- ...---
-..-
._ .___
_._-
-
Ratio of zcroRatioof preprcssurc yields esponential of fast and slow fxlors fluorcsccncc Y+/YA+lA___.--_ --_ _____-.---.--
Fluoresczncz quenching consmn t
-
-
c’l(1045-‘) mtorr-‘)
3.8
4.8 4.2 10.5 13 28 51 101 120 130 185 240 260 280 370 520
0.037 0.043 0.071 0.095 0. I70 0.37 0.69
I.26 2.3 4.6 7.6
8.7 8.2 8.4 7.9 9.0 8.6 8.1 7.4 4.2 3.6 2.0 0.57 0.39 0.35 0.48
515% quenching constant due to cyclohexane collisions was equal to 4.8 X IO3 5-l mtorr-’ (within 20%).
k-isec-‘1
i
Fig. 2. (e) Observed zero-pressure slow Fluorcscencc rate vcrsus excitation energy. (0) Rale ol thcrmalizcd phosptores. CCILT.The solid section ol‘rhc upper curve indicates the region whcrc kT can bc calculated with surkicnt accuracy-The dotted curve is a (fairly arbitwy) interpolation bcrwcen the Solid curve and the thcrmalizcd triplet value. For comparison the analogous kT curve of biacetyl has also been drawn.
hard
sphere-
-
-
_
_
A\-
-
_
-
-
Fig. 3. Fluorcsccncc quenching rate versus excitation cncrgy. The collision rate for hard-sphcrc collisions (5 A diamerer) is indicated (1.06 X lo4 s-l mrorr-‘).
3.3. The ratio o/pm-cxporwtltiai
factors of’fast and
slow J7uorcscenrc In the exci!3tion
4555-4355 A the ratio of prcexponcntial factors of fast and slow fluorcscencc (.4+/A-) was delermincd from Ihe area under the fast emission curve, the decay rate of the f;lst fluorescence range
and the prc-exponential factor of the slow fluorcscence. At hipher energies th-_ prc-esponential factor or the slow fluorcscencc could not bc determined di-
rcctly because of its rapidly decreasing magnitude. We then mcasurcd the ratio of the yields or fast and slow fluorcsccncc (Y+/Y-) at low pressures. Knowing the values of k+, k- and cq. the zero-pressure ratio A+/Acan be calculated [lo]. A+/A- 3s a function of energy has been given in table I In general our results arc in very good agreement with those of Coveleskic ct al. [3,4]. However. they lind somewhat higher values lor Rf. Since we used lower prcssurcs and single photon counting we feel that our results arc somewhat more reliable. They also differ with us on the values of k- which mjgh~ be due to a difference in taking the average charactcrislic time of a non-exponential decay curve.
first established that at 4OlOii excitation quenching of the phosphorescence due to cyclohexane did not take place even at high (up to 7-Otorr) cyclohexane pressbrcs. At lower pressures and 4010 A excitation the phosphorescence signal (SPll) as a function of the pressure of the mixture metbylglyoxalcyclohexane satisfied the relation: It
pling matrix elements are t!ST and the singlet and triplet level densities are pS and pT, respectively. The total dissipative decay rates from singlet and triplet states are called kS and k,. Both channels arc, or may be, a combination of radiative (kc;), non-radiative (I+,,, kTSo j and photodissociative (k P, k ,,) channels. lfN% 1 or evenif hr 2 1 761, &e tinwresolved fluores-
[%W1
cence signal can roughly be written as: A+ esp (- k+t) +A- exp (,- k-r),
where k+= kSTtkS,
(4)
k- = h-T + (ksTfk+) (x-,/IV),
(5)
A+/A- = (k+/k&
(6)
(2)
where fl= 220? 30 mtorr and r/b = 0.7 + 0.2 mtorr.
4. Analysis of the dab Expressions, describing the fluorescence decay behavior of molecules in the intermediate strongcoupling case, have been derived in our previous paper [lo] for several limiting situations. We conside:ed a zero-order state IS ), eflectively coupled to N zero-order triplet states of a manifold IT ). The cou-
IV,
and X-ST= 2ilIJ;TpT.
(7)
The expression to be used for N depends cm the ratio of the zero.order singlet widths and the mean single1 energy separation [lo]. If the singlet widths (k+) are much smaller than the mean level separation (pil), the sir&t levels may be considered as isolated. This will occur at low energies. In that case N is connected with the number of triplet states within the width kST: N = 2i+&
was
P/L$,=cr(l+/_l/Pty/P~),
(3)
(8)
At higher energies, however, the singlet widths may overlap (k+ >piIj. Then N becomes the ratio of densities: N=PT/PS-
(9)
The discrimination between the two regions has also been shown to be of importance for the pressure dependence of the slow fluorescence. If the singlet levels are isolated, the cross section for slow fluorescence quenching is expected to be large, because a collision capable of removing a very small amount of energy (exceeding the width k+ = 5 X 10m4cm-l) is sufficient to transfer the molecule to a state without resonantly coupled singlet character. Therefore, long-range collisions play an important role in the quenching process. The regions between the zero-order singlet states containing these non-fluorescent states are called “black holes” [lo]. In the region where the singlet widths overlap, a much larger energy removai is needed to
Tnblc 2 Culculaled quantilics Txcifation cncrgy (cm-‘)
N
(10m4cm-‘) 1.62
3.8 4.8 4.2 10.4 13 27 45 a2 88 06 110 136 132 140 175 250
-
p~i~+600 cm-‘) (calcnlatcd (IO3 cm) ’3 (lo3 cm) -_.--~.._---_-___-__._._________ 2.1 0.27 PT (CXP)
w ._-,-
21954 22090 22262 224.92 22645 22962 23148 23364 23585 23810 24038 24242 24450 24691 24938 25157
__.___.
---.-----_--._.
1.44 1.56 1.00 0.92 0.64 0.50 0.38 0.37 0.38 0.34
3.4 3.0 7.3 8.7 18.4 30 54 57 55 70 _ _ _ --_.-_.._
-
0.31 0.46 0.64 0.87 1.51 2.1 3.0 4.2 6.0 8.5
_.__-_
--
k~
%
10s s-1)
(106 s-1)
-
_
_
0.92 0.86 1.23 1.21 2.4 5.5
-
-
-
_____
_-__
1.84 4.6 9.2 16.4 20
-
‘) Assumed O--O 22180 cm-‘. transfer the molecule
to il “black hole”. Only head-on collisions can then be effective in the quenching process and much smaller cross sections are expected. We now wish to solve eqs. (4)--(G) fork,,, k,, k, and N as a function of energy. However, we only have three known quantities nt each energy: k+. /c- and
102-
A+/K In our biacetyl experiments [IO] we succeeded in also determining the contributions of kST and FrSin X-+as a function of energy. This, however, was so time consuming that we did not repeat this proccdue for methylglyoxal. Because, however, the energy dependence of k+ in biacetyl [7,10], methylglyoxnl and glyoxal [6] are very similar we assume that the energy dependence of ksT is also very similar. In biacetyl at the lowest energy kST is almost equa: to I?, while X-n increases by only about 30% in going from 22500 cm-l to 27500 M-I-~. The assumed similar energy dependence of kST for methylglyoxal is indicated in fig. 1. 4.1. Black hole and overlap regions
I’ I ,
22000
-
Excltallon energy 1
23000
,
2LOOO
lcm-‘I ,
25000
Fig. 4. Energy dependence ofN. The doltcd ct~rvegtics the best fit of km(fp~)/?c (cf. eq. 10) to the data, withpT from the cornput& alculations and I= 11.5. The solid curve gives the computer ~Iculated valuesoT~~/~~_
With the known quantities A+/A- and k+ and the estimated values for ksr we can calculate the energy dependence of N by using N= @+/A-) (kCST/k+)2 from eq. (6). The values are given in table 2 and fig. 4. We see that N first increases exponehtially until 23500 cm-‘. Above this energy a plateau roughly ap pears. Unfortunately we were not able to show a decrease of N at higher energies, as for biacetyl, because A+/A- could not be determined accurately above 25000 an-‘.
In our previocs paper about the biacetyl emissions [IO], the separation of 111~energy range into a black hole region (isolated singlets) 2nd an overlap rc$on was based on two arguments. First, in the black hole should increase with energy, region N(=ZG&pS) while in the overlap region A’(= pT/+) should dccrease again. Second. in the black hole region large fluorcscencc quenching cross sections are expected, while thcsc will be small in the overlap region. Both features were actually present in the biacetyl case. For methylglyoxal both the large magnitude of cq and the rapid increase of N with energy in the low energy region were observed and thcrcfore establish that the black hole region estcnds to about 24400 cm-‘. At this energy cq drops to below the hard-sphere collision rate (I .06 X IO4 s-t mlorr-I). while N rcachcs a plateau. Although we were unable to show a decrease of/V at higher energies we still believe that lhc singlet widths overlap at energies above 24400 CIII-~-
lo-
TL
$1 1
10: IO'
glyonol
/
lo-:,
lo-+ 1
0
’ -
u~brolfan
2o'co
energy
Icm”l
LOO0
--
6COO
hp. 5. Vibrarion lcvcl dcnsitics ol’ thc threel,l-dicarbonyl molcculcsversusvibralinn cncrgy.
Knowing Ihe energy dependence of kST and N it is possible to calculate coupling matrix elements (usT) and level densities. At all energies we have k,, = ~TRJ,$,-~~eq. (7). In the black hole region (k’piLjIv=pT/pseq. (9). In’thc lransilion region we expect k’= pi’. Using eqs. (7) and (8) we can calculate uST and pT in Ihe black hole region: pT (in cm) = ?chr[kST,
(10)
and uST (in cm-‘) = (+ Iv)liZ/(irpT).
(II)
The values are given in table 2. Note ihe decrcasc of usT and the increase of pT with energy. At the energy where the singlet widths start to over!ap (presumably -24400 cm-‘) the level density in the singlet manifold can be calculated by using: ps (in cm) z= ?irc/k+.
(13
:We find ps (24400 cm-’ ) C=1.35 X 1O3 cm. In the appendix we describe the calculation of the vihrurim level densities in the S,, S and T manifolds. The energy dependence of the vibration level densities of. {S} and {T} is given in fig. 5. Disregarding ro. tations, the total level density in [T) is obtained by
multiplying the vibration level density by three due to the presence of three magnetic sublevels. When comparing these densities with those from experiment, we should take into account that the average Boltzmann ground state energy of about 600 cm-l is transferred to the excited state as an excess to the energy (E) of the exciting light [lo]. Therefore. the computer calculated quantities pT (table 7-)andpT/PS (fig. 4) are given for energies (E+ 600) cm-‘. The computer calculated value of ps (24400 +600) is 8.5 X lo1 cm. In fig. 4 th? dotted line gives the best lit of X-,,(fr~~)/?c (cf. eq. (IO)), With pT from the computer calculutions, to the experimentally determined values of N. Very good agreement is ubtained for f= 11.5. A comparison of the calculated and the experimental densities shows the following noteworthy features: (a) At low energies flT (from experiment) is larger than pT (calculated) by a factor off= 1 I .5 + 4 (fig. 4). (b) The experimental value for ps (24400 cm-l) is also about an order of magnitude larger than the one calculated. (c) In the overlap region the calculated quantities pT /ps agree reasonably well with the experimental values for N (fig. 4). It is clear that as in biacetyl the rotational sfates Izuve ta be ir&lded in both ps and pT; be it that the enhancement (f= 11.5) is somewhat larger in this case.
R. rat1 dcr Wcrf cr al./Ekcrrorlic
4.3. ,bergy arid kT)
deperzderrce of tile zero-order rates (kS
With the known values of C;-,X-+and N and the estimated energy dependences of kST and kS. we can in principle clllculate kT as a function of energy by using k-= k, + (liST/k+) (X-,/N) eq. (5). For energies above 24240 cm-1 the energy dependence of k, is given in cable 2 and fig. 2. We see ;I rapid increase of X-Twith energy. For energies above 24600 cm-l we find L+ 2: k-. Note that at these energies the calculated values of/+ are not very sensitive to the values of k and k,, assumed. For energies below 24240
cm- s, the relative uncertainty in k, is too large to permit a reliable calculation of ksT. Again, as we did for biacetyl [lo], we assume a smooth inlerpolation between the value of x-T 31 the energy of the thermalized triplet (- 19800 cm-l [l] ) and the value at 24240 cm-l. From the observed thermalized phosohorescencc rate we have kT(19800 cm-l) = 5.05 x1o?s-’ [l]. With the assumed energy dependence of L+ (fig. 2) we can calculate .$ in the low energy region by using, eq. (5). Note thal for energies below 23000 cm-’ the
calculated values of k, arc not very sensitive for the choice of the $- curve. At the lowest energies X-- is practically completely determined by the term (kST/kf) ($/N) or (because kST is about equal to k+ at these energies) by ks/hr: the diluted singlet leak rate, a conclusion which was recently also reached by Coveleskie et al. [4]. The values of kS in the low energy region are given in table 2. Note the significant in-
crease of kS with energy.
rclmariorl ofrrrcrh~~l@oxal
157
where P(E) = k-(+hO,
04)
~(E)@(E)= k+Ac)/~‘~‘~.
(15)
Because y is non-zero we can conclude that for 24940 cm -I at least two effective head-on collisions are needed in order to reach the thermalized triplet. In our experiment the value of cl’” 1smainly determined by collisions with cyclohexane. From the fluorescence’ quenching with cyclohcxane we obtained the value for cho, because in the overlap region we have cho = cq =4.8 X lo3 s-l mtorr-I. At 24940 cm-’ we also calculate fl from k-/P (cyclohexane) = 380 mtorr, which compares reasonably well with 0 = 220 mtorr. We can also estimate k, (E--E). the mean decay rate of black hole slates reached after the first effective head-on collision. Using eq. (15) we find kT (24940Ae) = 3.5 X IO3 s-l. By comparing this value with the interpolated curve ofk, values (fig.?) we eslimate the energy rcmovcd per effective head-on collision to be a few thousand wavenumbers. which is in the same order of magnilude as & for biucetyl(2200 cm-I [IO] ).
As could be expected, the decay behavior of methylglyoxal is intermediate between that of its analagues, glyoxal [G] and biacetyl [7-lo]. As in the latter case we can distinguish ;I black hole region and an overlap region, with a large cross section for the fluorescence quenching in the former. The fact, that at low energies the slow tluorescence rate is mainly due to the dilution of the singlet decay rate, could be
very nicely demonstrated in this compound, even though at higher energies the radiationless decay out Simple models describing the phosphorescence in. duction are discussed in [IO]. The analysis in the black hole region is somewhat complicated. We, however, studied the phosphorescence induction at 24940 cm-l:
in the overlap region. Assuming a simple ladder model, in which effective head-on collision remove equal amounts of vibrational cnerEy (AE) with a rate chyoP, it wn be derived [IO] that the phosphorescence yield (Y ) as a function of pressure, under conditions simph ilar to those prevailing here, satisfies the relation:
I Yph=U(I+fl/P+ylP*
+_..),
(13)
of the triplet state dominates.
5. Comparison between glyoxal, methylglyoxal and bincetyl
In this section we will show that the apparent differences in the relaxation behavior of lhe ?hree molecules can be completely understood on the basis of the differences in the level densities. For glyoxal at low energies the excited singlets are not effectively
coupled to the triplet manifold:
tional states have to be included in the density of the accepting [T} manifold. Fig. 6 gives a plot of the numbcr of interacting states (N) versus energy. The cornputcr calculated curves ofPT are fitled to these points. The enhancement factors arc 8.7. I I .5 and 6.3 for glyosal. rnethylglyoxal and biacctyl. respectively. The larger value for methylglyoxal mcy well be due to the lower symmetry of this molecule. making symrnctry restrictions less severe. Also in fig. 6 for methylglyosal and biacelyt lhe overlap region can be clearly distinguished. The sjngleltriplet rnising is Ihen governed byPT/pS. which quantity has also been calculated and gives a decenl fil Lo the data.
I
i t
.
I’. ,. ,
-
zzboo
Ercllatlon
energy (cm-‘] 1
ZLbciO
26000
Us~p-j4 1 [G] ~ at higher energies A’2 1. In methylglyosal and biacetyl we have N > 1 for all energies. In this discussion we will limit oursclvcs to the situalion IV > I. For each molecule at low encrgics the single1 widths do not overlap because of the small singlet level density. The widths start to overiap when ps = (k+)-t This means that the size of the black hole region decreases in going from glyosal to biacelyl. This effect is clearly demonstrated in fig:6. We have shown that the values of fi+ as a function of energy arc quite similar for the three molecules discused. Also kST(= k&@) appears to be the same. niis implies that uST goes asPT-t/1 which in its turn implies that the amplitudes of the interacting IT) states OFa harmonic basis are distributed “dernocratiwlly” across the {T) manifold. The numerical values OFoT in the black hole region showed that rota.
The black hole region is characterized by very high fluorescence quenching constants; we find in mcihylglyoxal and biucetyl values up to about 7 molecular diameters. In all three molecules tile decay is mainly radiationless: @ < ks and X-F”< kT. For methylglyosal and biacetyl it was observed that both kS and kT increase rapidly with energy. A comment should be made here about our previous glyoxal paper 161.The observed rapid increase of k- with energy was altributed to k,. Knowing now that kS can also increase rapidly wilh energy, this conclusion cannot after all be drown. Therefore. it can only be concluded that either ,Q. or k, or both rates increase rapidly with energy in that molecule. Frcm our csperimunts no separation of the nonradiilive channels into unimolecular photodissociation ($,1. /$p) or conversion to {S,) (kS&, k-&) can be made. Theoretically it is known (I I] that for large energy gaps (here S-S, and T-S,) the radiationless rate increases with energy. However. froln urlimolecular rate theories such as the RRKM theory [II] : it f01lows that photochemical rates also increase rapidly with energy. The photochemistry of glyoxal [13-151 and biacetyl [IS-191 has been studied for a few decades. however, mainly at excitations above 27000 cm-l. From these studies it can be qualitatively concluded that the primary quantum yieIds increase with excitation energy and temperature and decrease with pressure. Recently Porter et al. [ZO] studied the photodecomposition of another analogous compound: hexafluorobiacetyl. It was shown there that photochemis_ try occurred from both the excited singlet and triplei
states. Here also the zero-pressure photochemiczd yields increase with energy and decrease with pressure. It should be noted, however, that the values for the
pholochemical rales, given by these authors, are based on the complete neglect of both k,, and kTSO, which may be in error. From thcsc consid&tions WCconclude that, especially at higher energies, both kS and kT are at least partially photochemical rates. This, finally, is also in agreement with the observation Illal at higher energies kT.(rnrthylglyoxal) > kf (biacetyl). which can be seen I’rom fig. ?. RRKM models predict [ 121 that a photochemical rate will decrease with increasing size of Ihe molecule. Simply, when the vibrational phase space volume increases, it takes longer for a molecule to reach the critical configuration for dissociation.
of the methyl torsional mode. The densities SO obtained are given in fig. 5.
References
[ 11 R.A. Covclcskic and J.T. Yardley, J. Am. Chem. SOC. 97 (1975) 1667. 121 R.L. Opilx. R.A. Covclrskic and J.T. Yardlcy, J. Chcm. Phys. 63 (1975) 593. 131 R.A. Covclcskic and J .T. Yardlcy, Chem. Phys. 9 (197.5) 275. 141 R.A. Covclcskic and J.T. Yardlcy,Chcm. I’hys. 13 (1976) 441. [S] F. Lahmani, A. Tramcr and C. Tric, J. Chcm. Phys. 60 (1974) 4431. [6] R. VUI dcr Wcrf, II. Schutlcn and J. Kommandcur, Chcm. Phys. 11 (1975) 281. 171 C.M. h!cClcllnnd and J.T. Yardlcy, J.Chem. Phys. 58 (1973) 4368. IS] R. wn dcr \Verr, D. Zevcnhuijzcn
Acknowledgement The invesligalions were supported by the Netherlands Foundation for Chemical Research @Oh’) with financial aid from the Dutch Organization for the Advnnccment
of Pure Research (ZWO).
Appendix: Calculation of the vibration level densities in the So, S and T manifolds The vibration level densities were calculated with the Haarhoff formula [21]. The groundstate frequencies are obtained from [22] or estimated from the vibration frequencies of glyoxal [23] and biacetyl [IO]. We used (in cm-l);2975 (3 CH-strelch); 1400 (3 CH3.deformations); 1 I60 (2 CH3-rocking); 100 (CHj-torsion); 1320.260,478 and 530 (in-plane skeletal bend); 1730, 1730.980.930 and 2850 (inplane skeletal stretch), 780 and 595 (out-of-plane skeletal deformations) and 105 (central C-C torsion). For both esciteci states we took the same frequencies except for the OC-CO torsional mode. In analogy to glyoxal [23] it was assumed that this frequency increases by a factor of 1.8 upon electronic excitation. The calculated densities are multiplied by a factor of three Lo account for the threefold quasi-degeneracy
and J. Kommnndcur, Chem. Phys. Let;. 27 (1974) 325. [9] A.Z. hlossund J.T. Yardlcy.1. Chem. Phys 61 (1974) 2883. 1lo] R. van dcr Wcrr and J. Kummandcur, Chcm. Ph!-s. 16 (1976) 125. [II] S.1’. I:ischcr, A..L. Stanl’ord and EC. Lim, J. Chcm. Phys. 61 (1974) 581. [I21 See lor inslancc: (a) B.S. Rabinovilch and D.W. Sctsr. Advan. Phorochemistry 3 (1964) I; (b) D.J. Robinson and LA. Holbruok, Unimolcculnr reactions (Wiley-lntcrscicnce, 1977); (c)W. Forsl, Theory of unimolccular reactions (An dcmic Press. (1973). [ 131J.G. CalvcTI and G.S. Layne, 1. Am. Chcm. Sot. 75 (1953) 856. [14] C.S. Parmentcr, J. Chcm. Phys. 41 (1964) 658. [ 151 R.D. Cund;lll and A.S. Davies. Progr. React. Kinct. 4 (1967) 149. 1161 W.A. Noy*cs Jr., C.B. Porlcr and I.E. Jolley, Chcm. Rev. 56 (1956) 49.
[ 171 J.C. Roof und F.E. Blzccl, 1. Am. [ 18 ] [ 191 (201 1211 [22] [23]
Chcm.
Sot.
63 (1941)
1126. H-U’. Anderson and G.K. RollcTson, J. Am. Chem. Sot. 63 (1941) 816. G.F. Shuts and W.A. h’oycs Jr., J. Am. Chcm. Sot. 77 (1955) i421. G.B. Porter and W-J. Reid, J. Photoch. 3 (1974) 27. P.C. HaarhofI, Mol. Phys. 7 (1963) 101. R.K. Harris and R.E. Witkowski, Spcctrochim. Acta 20 (1964) 1651. W. Holzcr and D.A. Ramuy, Can. J. Phys. 48 (1970) 1759.
l’hysics
16 (1976)
tlr-llolhnd Publishir+!
15 l--15Y Company
THE ELECTRONIC RELAXATION OF METHYLGLYOXAL IN THE VAPOR PHASE
Reccivcd
Tbc
6 April
rime-rcstrlvcd
c~~msrancus LriplsL
1976
LI du;ll
cwpling,
111cprcsrurc
the tlissipativc
induction
As found the former
flwrcsccncc l~~c~rcsccncc
previously bcinr
111osc afglyoxal
more
of
obscwcrl.
Icol;
rllcs
the Ihcrm:dizcd in biacctyl,
ustcnsivc
and biaccryl.
basis or Lhc diffcrcnces
o1’nwthylglyosal ws
in their
(rum
was studied
l:rom sinplct
2nd rriplcl
phospborcsccncc
rhc cscilcd
manifuld
in ~netl~yI~lyos;~l.Tl~c The
diffcrcnccs
Icvcl dcnsilics.
as ;I function
111csc mc~~remcn~s
in bclnvior
NX
Very recently Coveleskie et a!. [l-4] reported detailed studies of the photophysical behavior of methylglyoxal (CH,COCOH). According to the theory for “intermcdiate.c3se” molecules of klhrnani, Trumer and Tric [5] they obsenfcd. among other things, a biexponential fluorescence decay. As could be cspected. the behavior of methylglyoxal appeared to be intermediate between that of its analogues: glyoxal [6] and biacetyl [7-IO]. In our recent paper [IO] we pointed out the important difference between the low energy range where the singlet widths do not overlap (“black hole region”) and the “overl;lp region” at higher energies. IL also ap. peared that the energy range studied by Coveleskie et al. (up to I1 15 cm-l excess energy) FJIIs in Ihe “black hole” region. In this paper, therefore, data for a more extensive energy range (up to 3000 cm-l) are reported. At low energies we find the same results and come to the same conclusions as Coveleskie et al. As expected from our earlier work at higher energies, where the singlet widths do overlap. we find interesting changes in the decay behavior, which are reported here. In addition we studied the pressure induction of the :hermalized phosphorescence. * PrescnI address: Koninklijkc/Sbell Laboratorium, Bndhuiswee 3, Amsterdam, The Netherlands.
bu divided
characteristics
bctwecn
due to the different
1. Introduction
and tllc
cncrgy
and prcssurc~
IIIC p;lramcrcrs
duscribin;
tlu~lrcsucncc
qucnchinc
il black
region
In all cirrhc sinylct-
cwwI211Is.
Also.
studied.
sl~ould decay
51aW
of oscilation
WI: obraincd
rbc three number
into
hole
ofn~cthyl~lyosal molcculcr
and nn ovcrlnp
arc inrcrmsdiarc
can bc readily
rlf ;LtomLs in lhcsc
undcrstoud
qiun.
bctwccn on the
molcc~lss.
The theoretical background of our inlerpretation has been extensively given in our previous paper [IO]. After a discussion or the experiments and their interpretation we make il comparison of the relaxation patterns of the three I ,?-dicarbonyls ttnder consideration.
2. Experimental From a 40% solution of polymeric methylglyoxal (Aldrich) the major amount of water was distilled off. The residue was depolymerizcd at about 90°C in the presence of P205 as described in ref. [I]. The tnonomerit methylglyoxal was degassed each time before ust until Lhc vapor pressure 31 --2!?.9”C was constwt. A mass spectrum showed no impurities. In some esperiments high quality cyclohcxanc (hlerck) was used. The experimental arrangement (consisting bf a pulsed tunable dye laser, a large spherical Fluorescence cell and single photon counting equipment), the experimental conditions. the measuring techniques and data analysis methods have been fully described in our previous paper [ !O]. 2.1. The /Iuorexerrce
decay
The fluorescence was studied in the excitation range 4X5-3975 A. At each excitation wavelength
the fluorescence decay was recorded on two time ~calcs. one at 100 or 200 ns and one on a longer time scale (40~~500 I-IS)&pending on the Lifetime of the slow fluorescence component. The short-lived component was studied at mcthylglyoxul pressures ranging rrorn 10 mtorr (low energy excitation) to 25Omtorr (,at 3975 8, excitation). The long-lived component was sludied in a pressure domain ranging from 0.25-10
mtorr (4.555A) to IO-500 mtorr (3975 a). At 4010 A excitation the pressure dependence of the long-lived component was also studied as a functiorl of cyclohcxane pressure The ratios of yields of fast and slow tluorcscencc were measured at pressures ranging from 0.25 mtorr (4555 I!) to 80 mtorr (3975 A).
2.2. Pressuredeper&ence pliosp/rorc,sccrrce yield
of file themalized
It was shown previously [I] that in methylglyoxal, triplet self-quenching occurs with a rate of I.57 s-l mtorr-t. In order to avoid complications due to this effect the methylglyoxal pressure should be kept small. However, at such pressures the phosphorescence induction is not yet complete. We therefore used a mixture of methylglyoxal (7.5%) in cyclohexane. The thcrrnalizcd phosphorcscencc yield was studied as a function of the pressure of this mixture in the range of 8-4OOnitorr at 4OlOA excitation Then the errors due to self-quenching were below 3%. The signal was measured with the “delay-add&r” method [IO]. The delay time, used to prcvcnt detection of lluorescencc and Lo assure complctt thermaltiation in the triplet manifold was 150~s. both add and sub-timeswere 4.8 ms.
lutions OF the laser curve and emission curves titted
best on the measured decay curve. We assumed exponential decay behavior. The rates. measured at IO2SOmtorr rnethylelyoxal were considered as zeropressure rates. ThE time between collisions for 5 17
diameter hard-sphere collisions always exceeded the fast fluorescence lifetime by a factor of 30 or more. The energy dependence OFthe zero-pressure hst fluorescence rates (k+) is given in table 1 and tig. I. We see a smooth increase of X-+with energy. Note that the energy dependence of kf is very similar to that of biacctyl 17.101 and glyoxal [6].
The slow fluorescence decay was mildly non-exponential for all excitation wavelengths and all pressures. At most escitation wavelengths the pressure (P) dependence of the observed lifetime (T) satisfied the Stern-Vobiier relation: r-t = x_-+ ,$p.
(‘1
Table I and ties. 2 and 3 show the energy dependence of Lhe zero-pressure slow fluorescence rates (k-) and lhe tluorescencc quenching constant cLI Around 24000 cnl-I he Stern-Volmer slraight line, but consisted
one
This is due to the Boltzrnann
plots did not yield OF two
linear
distribution
branches.
of
the vapor and the consequent optical excitation of energies cncornpassiny, higher and lower 4 values. Data given here are from
the low pressure
branches. yielding the
higher mu values. The.low energy value of cn is larger than the 5 A hard-sphere collision rate by a factor of 8. It remains constant up to 23600 cm-l. then sharply
3. Results The Fluorescence decay appeared to be roughly biexponential at all excitation wavelengths and pressures
studied. The ktst component has a lifetime of the order of IO ns, the slow component
of some micro-
seconds.
I
1
3.1. T?le fastJImresceme The fast fluorescence rates were determined by establishing which of the computer simulated convo-
kST
05.d L
1 22000
-
Eacitatlon 23000
energylcm-‘I ZLOOO
]
I 25000
Fig. I. Obscrvcd fxt fluoresmncc rntc versus excitation cncrgy separation ork+into k$!T and ks is discusxd in Ihc text.
The
153 Tnblc 1 Obxrvcd quantities -___._
--.-..-.
LxcitaLion wavelcn~rh
Waxnumber
(4) ~-
(cm-‘)
4555 4527 4492 4440 4416 4355 4320 4280 4240 4200 4160 4125 4090 4050 4010 3975
21954 22090 22262 22482 22645 22962 23148 23364 23585 23810 24038 24242 24450 2469 1 24938 25157
Typkli
errors:
._---
. ..-___
----..-.-._.
..-.
Zero-pressure r;ltc of f;lsr fluorcsccn@2
Zero-prCSSUrC ril1c of slow nuorcsccncc
k+(10’5-1) _-.-_ _ . ..__ _.
Ji- (IO” s-1) __. ._..-__--._.-
8.7 8.7 8.5 a.7 9.1 8.7 9.5 12.1 _
1.95 2.1 1.25
I .0.5 1.00 0.80 0.70 0.85
I so
14.3
2.4 3.6 6.6 11.3 18.1 21.2
2 10%
512%
12,5 13.8 -
drops off to a value, which is only 40% of the hardsphere collision rate. At 4010 a excitation the
- ...---
-..-
._ .___
_._-
-
Ratio of zcroRatioof preprcssurc yields esponential of fast and slow fxlors fluorcsccncc Y+/YA+lA___.--_ --_ _____-.---.--
Fluoresczncz quenching consmn t
-
-
c’l(1045-‘) mtorr-‘)
3.8
4.8 4.2 10.5 13 28 51 101 120 130 185 240 260 280 370 520
0.037 0.043 0.071 0.095 0. I70 0.37 0.69
I.26 2.3 4.6 7.6
8.7 8.2 8.4 7.9 9.0 8.6 8.1 7.4 4.2 3.6 2.0 0.57 0.39 0.35 0.48
515% quenching constant due to cyclohexane collisions was equal to 4.8 X IO3 5-l mtorr-’ (within 20%).
k-isec-‘1
i
Fig. 2. (e) Observed zero-pressure slow Fluorcscencc rate vcrsus excitation energy. (0) Rale ol thcrmalizcd phosptores. CCILT.The solid section ol‘rhc upper curve indicates the region whcrc kT can bc calculated with surkicnt accuracy-The dotted curve is a (fairly arbitwy) interpolation bcrwcen the Solid curve and the thcrmalizcd triplet value. For comparison the analogous kT curve of biacetyl has also been drawn.
hard
sphere-
-
-
_
_
A\-
-
_
-
-
Fig. 3. Fluorcsccncc quenching rate versus excitation cncrgy. The collision rate for hard-sphcrc collisions (5 A diamerer) is indicated (1.06 X lo4 s-l mrorr-‘).
3.3. The ratio o/pm-cxporwtltiai
factors of’fast and
slow J7uorcscenrc In the exci!3tion
4555-4355 A the ratio of prcexponcntial factors of fast and slow fluorcscencc (.4+/A-) was delermincd from Ihe area under the fast emission curve, the decay rate of the f;lst fluorescence range
and the prc-exponential factor of the slow fluorcscence. At hipher energies th-_ prc-esponential factor or the slow fluorcscencc could not bc determined di-
rcctly because of its rapidly decreasing magnitude. We then mcasurcd the ratio of the yields or fast and slow fluorcsccncc (Y+/Y-) at low pressures. Knowing the values of k+, k- and cq. the zero-pressure ratio A+/Acan be calculated [lo]. A+/A- 3s a function of energy has been given in table I In general our results arc in very good agreement with those of Coveleskic ct al. [3,4]. However. they lind somewhat higher values lor Rf. Since we used lower prcssurcs and single photon counting we feel that our results arc somewhat more reliable. They also differ with us on the values of k- which mjgh~ be due to a difference in taking the average charactcrislic time of a non-exponential decay curve.
first established that at 4OlOii excitation quenching of the phosphorescence due to cyclohexane did not take place even at high (up to 7-Otorr) cyclohexane pressbrcs. At lower pressures and 4010 A excitation the phosphorescence signal (SPll) as a function of the pressure of the mixture metbylglyoxalcyclohexane satisfied the relation: It
pling matrix elements are t!ST and the singlet and triplet level densities are pS and pT, respectively. The total dissipative decay rates from singlet and triplet states are called kS and k,. Both channels arc, or may be, a combination of radiative (kc;), non-radiative (I+,,, kTSo j and photodissociative (k P, k ,,) channels. lfN% 1 or evenif hr 2 1 761, &e tinwresolved fluores-
[%W1
cence signal can roughly be written as: A+ esp (- k+t) +A- exp (,- k-r),
where k+= kSTtkS,
(4)
k- = h-T + (ksTfk+) (x-,/IV),
(5)
A+/A- = (k+/k&
(6)
(2)
where fl= 220? 30 mtorr and r/b = 0.7 + 0.2 mtorr.
4. Analysis of the dab Expressions, describing the fluorescence decay behavior of molecules in the intermediate strongcoupling case, have been derived in our previous paper [lo] for several limiting situations. We conside:ed a zero-order state IS ), eflectively coupled to N zero-order triplet states of a manifold IT ). The cou-
IV,
and X-ST= 2ilIJ;TpT.
(7)
The expression to be used for N depends cm the ratio of the zero.order singlet widths and the mean single1 energy separation [lo]. If the singlet widths (k+) are much smaller than the mean level separation (pil), the sir&t levels may be considered as isolated. This will occur at low energies. In that case N is connected with the number of triplet states within the width kST: N = 2i+&
was
P/L$,=cr(l+/_l/Pty/P~),
(3)
(8)
At higher energies, however, the singlet widths may overlap (k+ >piIj. Then N becomes the ratio of densities: N=PT/PS-
(9)
The discrimination between the two regions has also been shown to be of importance for the pressure dependence of the slow fluorescence. If the singlet levels are isolated, the cross section for slow fluorescence quenching is expected to be large, because a collision capable of removing a very small amount of energy (exceeding the width k+ = 5 X 10m4cm-l) is sufficient to transfer the molecule to a state without resonantly coupled singlet character. Therefore, long-range collisions play an important role in the quenching process. The regions between the zero-order singlet states containing these non-fluorescent states are called “black holes” [lo]. In the region where the singlet widths overlap, a much larger energy removai is needed to
Tnblc 2 Culculaled quantilics Txcifation cncrgy (cm-‘)
N
(10m4cm-‘) 1.62
3.8 4.8 4.2 10.4 13 27 45 a2 88 06 110 136 132 140 175 250
-
p~i~+600 cm-‘) (calcnlatcd (IO3 cm) ’3 (lo3 cm) -_.--~.._---_-___-__._._________ 2.1 0.27 PT (CXP)
w ._-,-
21954 22090 22262 224.92 22645 22962 23148 23364 23585 23810 24038 24242 24450 24691 24938 25157
__.___.
---.-----_--._.
1.44 1.56 1.00 0.92 0.64 0.50 0.38 0.37 0.38 0.34
3.4 3.0 7.3 8.7 18.4 30 54 57 55 70 _ _ _ --_.-_.._
-
0.31 0.46 0.64 0.87 1.51 2.1 3.0 4.2 6.0 8.5
_.__-_
--
k~
%
10s s-1)
(106 s-1)
-
_
_
0.92 0.86 1.23 1.21 2.4 5.5
-
-
-
_____
_-__
1.84 4.6 9.2 16.4 20
-
‘) Assumed O--O 22180 cm-‘. transfer the molecule
to il “black hole”. Only head-on collisions can then be effective in the quenching process and much smaller cross sections are expected. We now wish to solve eqs. (4)--(G) fork,,, k,, k, and N as a function of energy. However, we only have three known quantities nt each energy: k+. /c- and
102-
A+/K In our biacetyl experiments [IO] we succeeded in also determining the contributions of kST and FrSin X-+as a function of energy. This, however, was so time consuming that we did not repeat this proccdue for methylglyoxal. Because, however, the energy dependence of k+ in biacetyl [7,10], methylglyoxnl and glyoxal [6] are very similar we assume that the energy dependence of ksT is also very similar. In biacetyl at the lowest energy kST is almost equa: to I?, while X-n increases by only about 30% in going from 22500 cm-l to 27500 M-I-~. The assumed similar energy dependence of kST for methylglyoxal is indicated in fig. 1. 4.1. Black hole and overlap regions
I’ I ,
22000
-
Excltallon energy 1
23000
,
2LOOO
lcm-‘I ,
25000
Fig. 4. Energy dependence ofN. The doltcd ct~rvegtics the best fit of km(fp~)/?c (cf. eq. 10) to the data, withpT from the cornput& alculations and I= 11.5. The solid curve gives the computer ~Iculated valuesoT~~/~~_
With the known quantities A+/A- and k+ and the estimated values for ksr we can calculate the energy dependence of N by using N= @+/A-) (kCST/k+)2 from eq. (6). The values are given in table 2 and fig. 4. We see that N first increases exponehtially until 23500 cm-‘. Above this energy a plateau roughly ap pears. Unfortunately we were not able to show a decrease of N at higher energies, as for biacetyl, because A+/A- could not be determined accurately above 25000 an-‘.
In our previocs paper about the biacetyl emissions [IO], the separation of 111~energy range into a black hole region (isolated singlets) 2nd an overlap rc$on was based on two arguments. First, in the black hole should increase with energy, region N(=ZG&pS) while in the overlap region A’(= pT/+) should dccrease again. Second. in the black hole region large fluorcscencc quenching cross sections are expected, while thcsc will be small in the overlap region. Both features were actually present in the biacetyl case. For methylglyoxal both the large magnitude of cq and the rapid increase of N with energy in the low energy region were observed and thcrcfore establish that the black hole region estcnds to about 24400 cm-‘. At this energy cq drops to below the hard-sphere collision rate (I .06 X IO4 s-t mlorr-I). while N rcachcs a plateau. Although we were unable to show a decrease of/V at higher energies we still believe that lhc singlet widths overlap at energies above 24400 CIII-~-
lo-
TL
$1 1
10: IO'
glyonol
/
lo-:,
lo-+ 1
0
’ -
u~brolfan
2o'co
energy
Icm”l
LOO0
--
6COO
hp. 5. Vibrarion lcvcl dcnsitics ol’ thc threel,l-dicarbonyl molcculcsversusvibralinn cncrgy.
Knowing Ihe energy dependence of kST and N it is possible to calculate coupling matrix elements (usT) and level densities. At all energies we have k,, = ~TRJ,$,-~~eq. (7). In the black hole region (k’
(10)
and uST (in cm-‘) = (+ Iv)liZ/(irpT).
(II)
The values are given in table 2. Note ihe decrcasc of usT and the increase of pT with energy. At the energy where the singlet widths start to over!ap (presumably -24400 cm-‘) the level density in the singlet manifold can be calculated by using: ps (in cm) z= ?irc/k+.
(13
:We find ps (24400 cm-’ ) C=1.35 X 1O3 cm. In the appendix we describe the calculation of the vihrurim level densities in the S,, S and T manifolds. The energy dependence of the vibration level densities of. {S} and {T} is given in fig. 5. Disregarding ro. tations, the total level density in [T) is obtained by
multiplying the vibration level density by three due to the presence of three magnetic sublevels. When comparing these densities with those from experiment, we should take into account that the average Boltzmann ground state energy of about 600 cm-l is transferred to the excited state as an excess to the energy (E) of the exciting light [lo]. Therefore. the computer calculated quantities pT (table 7-)andpT/PS (fig. 4) are given for energies (E+ 600) cm-‘. The computer calculated value of ps (24400 +600) is 8.5 X lo1 cm. In fig. 4 th? dotted line gives the best lit of X-,,(fr~~)/?c (cf. eq. (IO)), With pT from the computer calculutions, to the experimentally determined values of N. Very good agreement is ubtained for f= 11.5. A comparison of the calculated and the experimental densities shows the following noteworthy features: (a) At low energies flT (from experiment) is larger than pT (calculated) by a factor off= 1 I .5 + 4 (fig. 4). (b) The experimental value for ps (24400 cm-l) is also about an order of magnitude larger than the one calculated. (c) In the overlap region the calculated quantities pT /ps agree reasonably well with the experimental values for N (fig. 4). It is clear that as in biacetyl the rotational sfates Izuve ta be ir&lded in both ps and pT; be it that the enhancement (f= 11.5) is somewhat larger in this case.
R. rat1 dcr Wcrf cr al./Ekcrrorlic
4.3. ,bergy arid kT)
deperzderrce of tile zero-order rates (kS
With the known values of C;-,X-+and N and the estimated energy dependences of kST and kS. we can in principle clllculate kT as a function of energy by using k-= k, + (liST/k+) (X-,/N) eq. (5). For energies above 24240 cm-1 the energy dependence of k, is given in cable 2 and fig. 2. We see ;I rapid increase of X-Twith energy. For energies above 24600 cm-l we find L+ 2: k-. Note that at these energies the calculated values of/+ are not very sensitive to the values of k and k,, assumed. For energies below 24240
cm- s, the relative uncertainty in k, is too large to permit a reliable calculation of ksT. Again, as we did for biacetyl [lo], we assume a smooth inlerpolation between the value of x-T 31 the energy of the thermalized triplet (- 19800 cm-l [l] ) and the value at 24240 cm-l. From the observed thermalized phosohorescencc rate we have kT(19800 cm-l) = 5.05 x1o?s-’ [l]. With the assumed energy dependence of L+ (fig. 2) we can calculate .$ in the low energy region by using, eq. (5). Note thal for energies below 23000 cm-’ the
calculated values of k, arc not very sensitive for the choice of the $- curve. At the lowest energies X-- is practically completely determined by the term (kST/kf) ($/N) or (because kST is about equal to k+ at these energies) by ks/hr: the diluted singlet leak rate, a conclusion which was recently also reached by Coveleskie et al. [4]. The values of kS in the low energy region are given in table 2. Note the significant in-
crease of kS with energy.
rclmariorl ofrrrcrh~~l@oxal
157
where P(E) = k-(+hO,
04)
~(E)@(E)= k+Ac)/~‘~‘~.
(15)
Because y is non-zero we can conclude that for 24940 cm -I at least two effective head-on collisions are needed in order to reach the thermalized triplet. In our experiment the value of cl’” 1smainly determined by collisions with cyclohexane. From the fluorescence’ quenching with cyclohcxane we obtained the value for cho, because in the overlap region we have cho = cq =4.8 X lo3 s-l mtorr-I. At 24940 cm-’ we also calculate fl from k-/P (cyclohexane) = 380 mtorr, which compares reasonably well with 0 = 220 mtorr. We can also estimate k, (E--E). the mean decay rate of black hole slates reached after the first effective head-on collision. Using eq. (15) we find kT (24940Ae) = 3.5 X IO3 s-l. By comparing this value with the interpolated curve ofk, values (fig.?) we eslimate the energy rcmovcd per effective head-on collision to be a few thousand wavenumbers. which is in the same order of magnilude as & for biucetyl(2200 cm-I [IO] ).
As could be expected, the decay behavior of methylglyoxal is intermediate between that of its analagues, glyoxal [G] and biacetyl [7-lo]. As in the latter case we can distinguish ;I black hole region and an overlap region, with a large cross section for the fluorescence quenching in the former. The fact, that at low energies the slow tluorescence rate is mainly due to the dilution of the singlet decay rate, could be
very nicely demonstrated in this compound, even though at higher energies the radiationless decay out Simple models describing the phosphorescence in. duction are discussed in [IO]. The analysis in the black hole region is somewhat complicated. We, however, studied the phosphorescence induction at 24940 cm-l:
in the overlap region. Assuming a simple ladder model, in which effective head-on collision remove equal amounts of vibrational cnerEy (AE) with a rate chyoP, it wn be derived [IO] that the phosphorescence yield (Y ) as a function of pressure, under conditions simph ilar to those prevailing here, satisfies the relation:
I Yph=U(I+fl/P+ylP*
+_..),
(13)
of the triplet state dominates.
5. Comparison between glyoxal, methylglyoxal and bincetyl
In this section we will show that the apparent differences in the relaxation behavior of lhe ?hree molecules can be completely understood on the basis of the differences in the level densities. For glyoxal at low energies the excited singlets are not effectively
coupled to the triplet manifold:
tional states have to be included in the density of the accepting [T} manifold. Fig. 6 gives a plot of the numbcr of interacting states (N) versus energy. The cornputcr calculated curves ofPT are fitled to these points. The enhancement factors arc 8.7. I I .5 and 6.3 for glyosal. rnethylglyoxal and biacctyl. respectively. The larger value for methylglyoxal mcy well be due to the lower symmetry of this molecule. making symrnctry restrictions less severe. Also in fig. 6 for methylglyosal and biacelyt lhe overlap region can be clearly distinguished. The sjngleltriplet rnising is Ihen governed byPT/pS. which quantity has also been calculated and gives a decenl fil Lo the data.
I
i t
.
I’. ,. ,
-
zzboo
Ercllatlon
energy (cm-‘] 1
ZLbciO
26000
Us~p-j4 1 [G] ~ at higher energies A’2 1. In methylglyosal and biacetyl we have N > 1 for all energies. In this discussion we will limit oursclvcs to the situalion IV > I. For each molecule at low encrgics the single1 widths do not overlap because of the small singlet level density. The widths start to overiap when ps = (k+)-t This means that the size of the black hole region decreases in going from glyosal to biacelyl. This effect is clearly demonstrated in fig:6. We have shown that the values of fi+ as a function of energy arc quite similar for the three molecules discused. Also kST(= k&@) appears to be the same. niis implies that uST goes asPT-t/1 which in its turn implies that the amplitudes of the interacting IT) states OFa harmonic basis are distributed “dernocratiwlly” across the {T) manifold. The numerical values OFoT in the black hole region showed that rota.
The black hole region is characterized by very high fluorescence quenching constants; we find in mcihylglyoxal and biucetyl values up to about 7 molecular diameters. In all three molecules tile decay is mainly radiationless: @ < ks and X-F”< kT. For methylglyosal and biacetyl it was observed that both kS and kT increase rapidly with energy. A comment should be made here about our previous glyoxal paper 161.The observed rapid increase of k- with energy was altributed to k,. Knowing now that kS can also increase rapidly wilh energy, this conclusion cannot after all be drown. Therefore. it can only be concluded that either ,Q. or k, or both rates increase rapidly with energy in that molecule. Frcm our csperimunts no separation of the nonradiilive channels into unimolecular photodissociation ($,1. /$p) or conversion to {S,) (kS&, k-&) can be made. Theoretically it is known (I I] that for large energy gaps (here S-S, and T-S,) the radiationless rate increases with energy. However. froln urlimolecular rate theories such as the RRKM theory [II] : it f01lows that photochemical rates also increase rapidly with energy. The photochemistry of glyoxal [13-151 and biacetyl [IS-191 has been studied for a few decades. however, mainly at excitations above 27000 cm-l. From these studies it can be qualitatively concluded that the primary quantum yieIds increase with excitation energy and temperature and decrease with pressure. Recently Porter et al. [ZO] studied the photodecomposition of another analogous compound: hexafluorobiacetyl. It was shown there that photochemis_ try occurred from both the excited singlet and triplei
states. Here also the zero-pressure photochemiczd yields increase with energy and decrease with pressure. It should be noted, however, that the values for the
pholochemical rales, given by these authors, are based on the complete neglect of both k,, and kTSO, which may be in error. From thcsc consid&tions WCconclude that, especially at higher energies, both kS and kT are at least partially photochemical rates. This, finally, is also in agreement with the observation Illal at higher energies kT.(rnrthylglyoxal) > kf (biacetyl). which can be seen I’rom fig. ?. RRKM models predict [ 121 that a photochemical rate will decrease with increasing size of Ihe molecule. Simply, when the vibrational phase space volume increases, it takes longer for a molecule to reach the critical configuration for dissociation.
of the methyl torsional mode. The densities SO obtained are given in fig. 5.
References
[ 11 R.A. Covclcskic and J.T. Yardley, J. Am. Chem. SOC. 97 (1975) 1667. 121 R.L. Opilx. R.A. Covclrskic and J.T. Yardlcy, J. Chcm. Phys. 63 (1975) 593. 131 R.A. Covclcskic and J .T. Yardlcy, Chem. Phys. 9 (197.5) 275. 141 R.A. Covclcskic and J.T. Yardlcy,Chcm. I’hys. 13 (1976) 441. [S] F. Lahmani, A. Tramcr and C. Tric, J. Chcm. Phys. 60 (1974) 4431. [6] R. VUI dcr Wcrf, II. Schutlcn and J. Kommandcur, Chcm. Phys. 11 (1975) 281. 171 C.M. h!cClcllnnd and J.T. Yardlcy, J.Chem. Phys. 58 (1973) 4368. IS] R. wn dcr \Verr, D. Zevcnhuijzcn
Acknowledgement The invesligalions were supported by the Netherlands Foundation for Chemical Research @Oh’) with financial aid from the Dutch Organization for the Advnnccment
of Pure Research (ZWO).
Appendix: Calculation of the vibration level densities in the So, S and T manifolds The vibration level densities were calculated with the Haarhoff formula [21]. The groundstate frequencies are obtained from [22] or estimated from the vibration frequencies of glyoxal [23] and biacetyl [IO]. We used (in cm-l);2975 (3 CH-strelch); 1400 (3 CH3.deformations); 1 I60 (2 CH3-rocking); 100 (CHj-torsion); 1320.260,478 and 530 (in-plane skeletal bend); 1730, 1730.980.930 and 2850 (inplane skeletal stretch), 780 and 595 (out-of-plane skeletal deformations) and 105 (central C-C torsion). For both esciteci states we took the same frequencies except for the OC-CO torsional mode. In analogy to glyoxal [23] it was assumed that this frequency increases by a factor of 1.8 upon electronic excitation. The calculated densities are multiplied by a factor of three Lo account for the threefold quasi-degeneracy
and J. Kommnndcur, Chem. Phys. Let;. 27 (1974) 325. [9] A.Z. hlossund J.T. Yardlcy.1. Chem. Phys 61 (1974) 2883. 1lo] R. van dcr Wcrr and J. Kummandcur, Chcm. Ph!-s. 16 (1976) 125. [II] S.1’. I:ischcr, A..L. Stanl’ord and EC. Lim, J. Chcm. Phys. 61 (1974) 581. [I21 See lor inslancc: (a) B.S. Rabinovilch and D.W. Sctsr. Advan. Phorochemistry 3 (1964) I; (b) D.J. Robinson and LA. Holbruok, Unimolcculnr reactions (Wiley-lntcrscicnce, 1977); (c)W. Forsl, Theory of unimolccular reactions (An dcmic Press. (1973). [ 131J.G. CalvcTI and G.S. Layne, 1. Am. Chcm. Sot. 75 (1953) 856. [14] C.S. Parmentcr, J. Chcm. Phys. 41 (1964) 658. [ 151 R.D. Cund;lll and A.S. Davies. Progr. React. Kinct. 4 (1967) 149. 1161 W.A. Noy*cs Jr., C.B. Porlcr and I.E. Jolley, Chcm. Rev. 56 (1956) 49.
[ 171 J.C. Roof und F.E. Blzccl, 1. Am. [ 18 ] [ 191 (201 1211 [22] [23]
Chcm.
Sot.
63 (1941)
1126. H-U’. Anderson and G.K. RollcTson, J. Am. Chem. Sot. 63 (1941) 816. G.F. Shuts and W.A. h’oycs Jr., J. Am. Chcm. Sot. 77 (1955) i421. G.B. Porter and W-J. Reid, J. Photoch. 3 (1974) 27. P.C. HaarhofI, Mol. Phys. 7 (1963) 101. R.K. Harris and R.E. Witkowski, Spcctrochim. Acta 20 (1964) 1651. W. Holzcr and D.A. Ramuy, Can. J. Phys. 48 (1970) 1759.