2240
J . Phys. Chem. 1988, 92, 2240-2248
ScintHlatlon Process in Three-Component Systems: Mechanism of the Luminescence Minimum Yoichi Yoshida and Sanford Lipsky* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: September 29, 1987)
Three-component systems consisting of a saturated hydrocarbon solvent, C, an aromatic solvent, B, and a fluorescent solute, T, are excited either optically (in the absorption band of C and below its ionization potential) or with 0.67-MeV particles. The luminescence of T is detected and studied as a function of the B/C concentration ratio. Systems studied are C = cyclohexane, rrans-decalin, methylcyclohexane, bicyclohexyl, n-heptane, or 2,3-dimethylbutane; B = benzene or toluene; and T = N,N,N’,N’-tetramethylphenylenediamine(TMPD), p-terphenyl, or 2,5-diphenyloxazole (PPO). The luminescence behavior is observed under both aerated and nitrogenated conditions. For B = benzene, the luminescence of T is depressed by the replacement of C with B, at low B/C concentration ratios. This occurs for both modes of excitation for all C except bicyclohexyl and 2,3-dimethylbutane. At higher B/C concentration ratios, the luminescence of T recovers and ultimately exceeds its intensity in pure C + T. Thus there is observed a ‘luminescence minimum”. At low T concentrations the position and depth of the minimum are very sensitive to the presence of 02,but at higher concentrations this sensitivity is lost. For B = toluene, the “luminescence minimum” is only observed under @- particle excitation conditions. A mechanism is developed to accommodate these observations. Its analysis indicates that production of SI states of B (Le., B*) via either energy transfer from C* or via charge transfer from C+ followed by the geminate recombination B+ + e- B* is intrinsically inefficient in dilute cyclohexane solutions. For B = benzene this inefficiency resides mainly in the electronic energy transfer process and for toluene in the ion-recombination process. Also, the analysis indicates that there must be two states of C that can transfer energy to B and/or T. One of these is the SI state of C, and the other is a much longer lived state of C that derives from C* and is tentatively identified as the lowest triplet state of C.
-
Introduction In general, aromatic liquids tend to be better scintillation solvents than are their saturated derivatives.’ For example, the emission from millimolar solutions of p-terphenyl irradiated with high-energy electrons is about 3-4 times larger in benzene than in cyclohexane. In these systems, the primary energy absorption is by the solvent which then transfers energy either through neutral or through ionic channels to the fluorescent solute. The mechanism of this transport can be quite complex. This is best illustrated by an intriguing observation made many years ago on threecomponent system^.^-^ In aerated mixtures of cyclohexane and benzene containing a fixed concentration of p-terphenyl, it was observed that, as the mole fraction of benzene was increased, the intensity of p-terphenyl emission first declined, reached a minimum intensity at -2% mole fraction of benzene, and thereafter monotonically increased to a maximum intensity in pure benzene. In the absence of air, this “luminescence minimum” seemed essentially to disappear and, instead, the p-terphenyl intensity was reported to increase monotonically as the benzene mole fraction increased. The minimum was only reliably observed with b e n ~ e n e .If~ present at all with toluene or p-xylene, it was certainly much less pronounced. However, replacement of cyclohexane with saturated hydrocarbons that were “equally good” or ”better” scintillation solvents (such as methylcyclohexane, bicyclohexyl, and decalin) gave results qualitatively similar to those for cyclohexane, but replacement by “poorer” scintillation solvents (such as cyclopentane and isooctane) led to a disappearance of the m i n i m ~ m .Replacement ~ of O2 with N 2 0 removed the m i n i m ~ m but , ~ with some other quenchers (such as phenyl bromide and methyl iodide) the minimum appeared to be retained.3 (1) Kallman, H.; Furst, M. Phys. Rev. 1951, 81, 833. Furst, M.; Kallmann, H. Phys. Reu. 1952, 85, 816. Ibid. 1954, 94, 503. (2) Burton, M.; Berry, P. J.; Lipsky, S . J . Chim. Phys. 1955, 52, 657. Berry, P. J.; Burton, M. J . Chem. Phys. 1955, 22, 1969. Burton, M.; Dreeskamp, H. Discuss. Faraday SOC.1959, 27, 64. (3) Nosworthy, J. M.; Magee, J. L.; Burton, M. J . Chem. Phys. 1961, 34, 83. (4) Sato, S.; Satoh, S . Organic Scintillators and Liquid Scintillation Counting; Horrocks, D. L.. Peng, C. T., Eds.; Academic: New York, 1971; p 371.
0022-3654/88/2092-2240$01.50/0
Clearly, to explain the minimum it was necessary to invoke some form of energy transfer between cyclohexane and benzene, but the nature of this transfer was controversial. Burton and cow o r k e r ~favored ~ ~ ~ a mechanism involving electronic energy transfer between cyclohexane and benzene and postulated that, in dilute solutions of benzene in cyclohexane, the excited benzene was less efficient than excited cyclohexane in transferring energy to pterphenyl but at higher benzene concentrations this difference in efficiency was reversed due to some form of energy migration within the benzene. On the other hand, Sato and Satoh4 took the alternative point of view that the mechanism of the transfer involved ionic channels requiring electron capture by p-terphenyl, charge transfer from cyclohexane positive ion to benzene, and radiative recombinations of cyclohexane and benzene positive ions with p-terphenyl anions. The precise nature of the ionic mechanism was, however, not fully developed. Also, the role of 0, and the uniqueness of benzene in these phenomena were never clearly established by either group of investigators. In a recent paper6 we reexamined the problem of the luminescence minimum and derived rather general conditions for its observation. New experimental results were also reported for cyclohexane-benzene and cyclohexane-toluene with M, N,N,N’,N’-tetramethylphenylenediamine(TMPD) as scintillation solute. These systems were excited both with /3 particles and optically (in the cyclohexane absorption band) at energies above and below the cyclohexane ionization threshold. The TMPD was chosen as the fluorescent solute since its cross section for capture of thermal electrons is sufficiently small as to preclude any significant electronic activation via neutralization of its anions with the solvent positive ions. For the cyclohexane-benzene systems, deep minima were observed under all excitation conditions, whereas for cyclohexanetoluene systems, minima (and very shallow ones) were only obtained for optical excitation above the cyclohexane ionization threshold and for irradiation with particles. The presence or absence of air had very little effect on these results. ( 5 ) Burton, M.; Dillon, M. A,; Mullin, C. R.; Rein, R. J . Chem. Phys. 1964, 41, 2236. Dillon, M. A.; Burton, M. Pulse Radiolysis; Ebere, M.,
Keene, J. P., Swallow, A. J., Baxendale, J. H., Eds.; Academic: New York, 1965; 259. (6) Yoshida, Y.; Walter, L.; Lipsky, S . Radiat. Phys. Chem. in press.
0 1988 American Chemical Society
Scintillation Process in Three-Component Systems By use of the derived conditions for observation of the minimum, it was shown that, for cyclohexane-benzene systems, the initial decline of the TMPD emission intensity with increasing benzene concentration was due almost exclusively to inefficiency in the internal conversion to the SIstate of benzene from its more highly excited states that are generated via electronic energy transfer from cyclohexane.6 The eventual increase of this internal conversion efficiency at higher benzene concentrations also appeared capable of partially explaining the subsequent upswing in the scintillation yield. Since the internal-conversion efficiency of toluene is significantly larger than that of benzene, the above mechanism was also shown to predict properly that no minimum would be observed in cyclohexane-toluene systems, at least for excitation energies below the ionization threshold of cyclohexane. To explain the appearance of weak minima at higher excitation energies and for 8-particle irradiation, ionic mechanisms were now invoked in which inefficiency was postulated to reside in the production of SI states of toluene via geminate recombination of electrons and toluene radical cations. In the present investigation, we extend our measurements to saturated hydrocarbons other than cyclohexane and to scintillation solutes other than TMPD. Benzene and toluene, however, remain as the aromatic solvents. By changing the saturated hydrocarbon solvent, we are able to verify a predicted effect on the efficiency of generating benzene SI states. By replacement of TMPD with 2,5-diphenyloxazole (PPO) (which has a higher cross section for capture of thermal electrons than does TMPD), we are able to examine the validity of our mechanism under much more complex conditions. Also, since PPO has a significantly higher fluorescence quantum yield than TMPD, it becomes possible to work reliably at lower solute concentrations. This has revealed some new features of the scintillation process.
Experimental Section All high-energy irradiations employed the @--particle spectrum from 250 mCi of *%r (E- = 0.67 MeV) contained in a standard source capsule fitted with a 0.005-cm-thick stainless steel window. The source was placed about 5 cm away from a sample cell, the front window of which was made of 0.017-cm-thick Suprasil quartz attached to the cell body via an indium wire gasket. The emission was collected from this front window at 45O to the optical axis by two Suprasil quartz lenses and focused onto the entrance slit of a 0.3-m McPherson Model 218 monochromator usually set to the maximum of the solute emission spectrum. The dispersed fluorescence was detected with a cooled Hamamatsu R943-02 photomultiplier. Single photon pulses from this were amplified, discriminated, and counted. For optical experiments, light from a Hamamatsu L879 D2 lamp was passed through a 0.5-m vacuum monochromator and then focused with a LiF lens onto the front face of the sample cell, the window of which was now replaced with 1-“-thick LiF. The collecting and analyzing systems were as described above. Benzene (Omnisolv), toluene (Mallinckrodt), p-terphenyl (Eastman), and PPO (Aldrich) were purchased as spectrophotometric or scintillation grade and used without additional purification. Cyclohexane (Mallinckrodt, Spectrophotometric Grade), trans-decalin (Wiley, 99.9%), bicyclohexyl (Aldrich, 99%), methylcyclohexane (Matheson, Coleman and Bell, Spectroquality Reagent), n-heptane (Wiley, 99.9%), and 2,3-dimethylbutane (Wiley, 99.9%) were purified by percolation through activated silica gel. TMPD (Aldrich) was purified by vacuum sublimation. When necessary, air was removed from the solvents by purging with nitrogen, and solutions were then prepared under a nitrogen atmosphere in a dry box. Results In all of the systems studied here, we will refer to the saturated hydrocarbon solvent as C, the aromatic solvent (either benzene or toluene) as B, and the scintillation solute (either TMPD or PPO) as T. The fluorescence we observe is exclusively the fluorescence from SI states of T (Le., T*). The yield of these states
The Journal of Physical Chemistry, VOI.92, No. 8, 1988 2241 1.0
*
0
0.6 0.5
1 I Volume % Benzene
0
2
+ +
Figure 1. Scintillation efficiency, x, of the system C B T relative to scintillation efficiency, xc, of the system C T vs volume percent B, VB, for C = aerated cyclohexane (e) or aerated trans-decalin (O), B = benzene, and T = lo-* M TMPD.Results are shown for both F-particle and E = 7.9-eV-photon excitation.
+
+
we will refer to as the scintillation yield. In pure C T, in pure B T, and in C B T solutions, the scintillation yield will be referred to as xc, xB,and x, respectively and the ratio of XB/XC will be referred to as R.’3 In Figure 1, x/xc is shown plotted as a function of the volume fraction, VB, of component B for the air-equilibrated systems C = cyclohexane or trans-decalin, B = benzene, and T = lo-’ M TMPD. The cyclohexane results have been presented previously6 and are shown here for comparison purposes. For both systems, x/xC is reduced below unity by the addition of benzene. This is true both for optical excitation at 7.9 eV and for 8-particle excitation. Although minima are not shown in Figure 1 for the optical excitation, it is clear from the values of R that they must exist at higher VB. At photon energies greater than 4 . 5 eV, the optical absorption cross sections of the saturated hydrocarbons become sufficiently high as to reduce the penetration depth of light into the liquid to such low values (=lOOO %.)that any photochemical products that are generated even in low yield will build up in steady state to substantial concentrations within the illuminated volume. If these products act as quenchers of C* and B*, then clearly, since B* is longer lived than C*, the net effect will be generally to depress x. This so called “photochemical artifact” has been discussed p r e v i o ~ s l y .In ~ ~view ~ ~ of ~ ~the uncertainty in many of the parameters required to correct for this effect, we limit ourselves in this investigation to studies using 7.9-eV and 8-particle excitation. At 7.9 eV, the effect appears to be minor as judged by O2 saturation experiments6 and by the results of studies to be presented later on the dependence of R on excitation energy E . For 8-particle irradiation, the source is sufficiently weak and the average pFnetration depth of the particles sufficiently large as to also make the effect unimportant. In addition to the optical studies on cyclohexane and transdecalin shown in Figure 1, measurements were also made on a variety of other C solvents. This data is collected in Table I, which contains values of (x - xC)/xc at low benzene concentrations” for air-equilibrated solutions containing M TMPD excited
+
+ +
(7) The values for R reported for TMPD solutions have been corrected for the difference in TMPD fluorescence quantum yield, 4, in benzene and in cyclohexane. The quantum yield ratio 4B/$c = 1.2 was determined simply from the product of the intensity ratio for excitation of TMPD at 325 nm (1.33) with the square of the ratio of the refractive indices in cyclohexane and benzene (0.88). For PPO solutions @B/q6CN 1 (see ref 8). The ratios were assumed to be the same when cyclohexane was replaced by other C solvents and benzene replaced by toluene. (8) Choi, H. T.; Hirayama, F.; Lipsky, S. J . Phys. Chem. 1984,88, 4246. (9) Lawson, C. W.; Hirayama, F.; Lipsky, S . Molecular Luminescence; Lim, E. C., Ed.; Benjamin; New York, 1969; p 837. (10) (a) Lawson, C. W.; Hirayama, F.; Lipsky, S. J . Chem. Phys. 1969, 51, 1590. (b) Lawson, C. W. Ph.D. Dissertation, University of Minnesota, 1973. See also ref 6, footnote 20. (1 1) It will often be convenient to express benzene concentration in moles per liter, Cg.The connection with volume percent at low concentrations is simply CB= 0.1 1 VB.
Yoshida and Lipsky
t
12 I I
Toluene
D:
(air)
IO IO
;0 9
Benzene Lair)
*
\
5
08 1 11
I
8 07
06
1
O5 0
IOmM.alrLR;1.4)/,
I
1
10
Figure 4. Ratio of
XB/XC R vs photon energy, E , for the systems C = cyclohexane, T = lo-’ M PPO, and B = benzene (nitrogenated), toluene (aerated), or benzene (aerated).
2
F
Volume % Benzene
Figure 2. x / x c vs VB (see caption Figure 1) for the system C = cyclohexane (aerated and nitrogenated), B = benzene, and T = lo-’ M PPO M PPO (-) for E = 7.9-eV-photonexcitation. (- - -) or T = 18
9 Energy ( e v )
I
p
I
a)R=98
1.1
I u 1.0 K
’
\
3 3
0.9
14
0.8
17
??
* \
~
O70
05
IO
10 Volume % Benzene
15
X / X C vs VB(see caption Figure 1) for the aerated systems B = benzene, T = M TMPD, and C = 2,3-dimethylbutane (a), nheptane (b), bicyclohexyl (c), methylcyclohexane (d), cyclohexane (e), and trans-decalin (f) for 8-particle excitation.
Figure 5.
06
0
01
0 2
Volume % Toluene
Figure 3. X / X C vs VB (see caption Figure 1) for the system C = aerated cyclohexane, B = toluene, and T = lo-’ M PPO for both 8-particle and E = 7.9-eV-photon excitation.
at 7.9 eV. Other entries in this table will be discussed later in analyzing these results. All measurements with TMPD were performed at a concenM. The significantly more intense emission from tration of PPO, however, permitted reliable measurements to be made on M. Figure 2 this solute also at lower concentrations of contrasts the effect of changing PPO concentration from to M on x/xc for both air-equilibrated and nitrogenated solutions of cyclohexane-benzene excited at E = 7.9 eV. Qualitatively similar results were obtained with p-terphenyl as solute except that the minima were shallower (Le., for 8-particle excitation, x/xc at the minimum was 0.98 ( V , = 0.1%) and 0.80 (V, = 1%) for nitrogenated and aerated solutions respectively containing M p-terphenyl and, for 7.9-eV excitation, x / x c at the minimum was 0.96 (V, = 0.1%) for nitrogenated solutions and 0.78 (V, = 2%) for the aerated solution). The effect of replacing benzene with toluene is illustrated in Figure 3 for M PPO solutions of aerated cyclohexane. As has been previously reported6 for lo-* M TMPD solutions of cyclohexane-toluene, x/xc remains greater than 1.0 at all V, for E = 7.9 eV but exhibits a shallow minimum for @--particle excitation. The variation of R with photon energy E is displayed in Figure 4 for M solutions of PPO in cydohexane-benzene (aerated and nitrogenated) and in cyclohexane-toluene (air equilibrated).’,* An entirely similar dependence of R on E was observed for all M PPO other solutions studied here (Le., those containing or TMPD).
I .2 1.1 1.0 u
K K
\
0.9
0.8 0.7
0.6
0.5
1
1 0
I
2
Volume % Benzene
x/xc vs VB (see caption Figure 1) for the system C = cyclohexane (aerated and nitrogenated), B = benzene, and T = lo-’ M PPO M PPO (-) for 8-particle excitation. ( - - - ) or T =
Figure 6.
In Figure 5 we contrast the scintillation behavior of a series of aerated solutions containing M TMPD, all excited with 8 particles, but utilizing different C solvents. Although it is not shown in Figure 5 , we have found that nitrogenation has only a small effect on the results under these conditions. Thus, for example, for nitrogenated cyclohexane, x/xc at V, = 0.125,0.25, 0.5 0.75, 1 , and 2% are respectively 0.89, 0.85, 0.82, 0.83, 0.85, and 0.96, with an R of 3.8.
Scintillation Process in Three-Component Systems
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2243
TABLE I: Effect of the C Solvent on the Value of fi Calculated via Eq 5 Utilizing Data from the Scintillation Efficiency of C M T M P D Aerated Solutions Excited at E = 7.9 eV and Utilizing Stem-Volmer Constants Scaled to Those of Cyclohexane
h,,'
C
7/7cycb
DIDcycc
Kce
(dd" CB, M
+ Benzene + 10-2
(xc - x ) / x ~
P
KBT (PBT)~,'
KCT (PCT)~,'
cyclohexane
201
1.o
1.o
273 (0.73)
43 (0.30)
39 (0.60) (0.75)
0.056 0.11
-0.33 -0.38
0.18 0.20
n-heptane
206
1.o
2.1
573 (0.85)
90 (0.47)
82 (0.23) (0.32)
0.007 0.011
-0.115 -0.164
0.28 0.27
methylcyclohexane
21 3
1.o
1.2
328 (0.77)
52 (0.34)
47 (0.25) (0.77)
0.011 0.11
-0.07, -0.20
0.31 0.33
trans-decalin
217
2.3
0.43
117 (0.54)
43 (0.30)
39 (0.60) (0.75)
0.056 0.11
-0.23 -0.29
0.34 0.34
bicyclohexyl
226
1.6
0.27
74 (0.43)
19 (0.16)
17 (0.07) (0.34)
0.005 0.036
0.00 0.00
0.37 0.37
2,3-dimethylbutane
242
0.83
2.3
628 (0.86)
82 (0.45)
74 (0.31) (0.82)
0.011 0.11
0.03 0.125
0.57 0.60
Wavelength maximum in nm of emission spectral distribution of C (see ref 19). bRatio of C* lifetime to that of cyclohexane utilizing data in ref 25. cRatio of self-diffusion constants as estimated by the empirical equation of ref 23 and critical data taken or estimated from ref 24. dSternVolmer constants K have units of M-l and are scaled to those of cyclohexane by using the procedure outlined in the text. The values of pBT,pCT, and ~ C (at B two benzene concentrations, CB),are calculated via the Stern-Volmer equation. 'For cyclohexane KBT, KcT, and K c B are obtained from data in ref 6, 21, and 22, respectively.
In Figure 6 are presented results analogous to those displayed in Figure 2 but for 8-particle excitation rather than E = 7.9eV-photon excitation. Discussion A . Optical Excitation. We first consider the results obtained for optical excitation at 7.9 eV. This energy is well below the ionization threshold of each of the C solvents studied here.12 Under these conditions, the scintillation efficiency, x, can be expressed as
x = f C X I C [ ( l - 'PCB)PCT + 'PCBPPBTI + f B X I B P B T (1) where fc and fB are the fractions of light absorbed by C and B, respectively, X,C and XIB are the probabilities that absorption by C and B ultimately generates the lowest excited singlet states of C and B (hereafter referred to as C*and B*), is the probability that C*is quenched by B, /3 is the probability that B* is a product of this quenching reaction, pBTis the probability that B* transfers electronic energy to T to generate T*, and pcT is the probability that C* transfers energy to T to generate T* but conditional on there being no B present. Recognizing that xc = X;,p& and xB = X i B P i T (where the superscripts imply values of these parameters in pure C and B, respectively) it is simple to derive from eq 1 that for solutions of B in C, sufficiently dilute for Xlc = A;, and pCT = PtT
-
x - xc
-
xc where
and R = -X=BXC
XiBPiT
(4)
XICPCT
For M solutions of TMPD in air-equilibrated cyclohexane, the second term on the rhs (right-hand side) of eq 2 is small and can be ignored for benzene concentrations not exceeding =2% by volume. This can be verified with substitutions into eq 3 and 4 of pBT/pCT 2.4,6 pcB 'v 0.86 (at VB = 2%),6/3 = 0.19; and X I B 0.213914and Xlc at E = 7.9 eV to give F 0.4.
- - -
-
(12) Casanovas, J.; Grob, R.; Delacroix, D.; Guelfucci, J. P.; Blanc, D. J . Chem. Phys. 1981, 75,4661. (13) This value is corrected slightly upward from the value 0.14 at E = 7.1 eV reported in ref 14 due both to the estimated energy dependence of X I B and to corrections for photochemical artifacts (see ref 9 and 10).
-
Since fB 0.02 (as estimated from vapor-phase absorptions at 7.9 eV),l6>l7it follows that FfB cannot exceed -2% of the first term in eq 2 so long as VB 5 2%. For our purposes, this is sufficiently small to be neglected, and eq 2 reduces to
As we will develop later, F increases strongly at lower solute concentrations (since R is then much larger) and the correction for direct absorption by B must be reconsidered. Equation 5 was previously utilized for explaining the scintillation behavior of cyclohexane benzene TMPD ( M) solutions excited at 7.9 eV.6 These results are reproduced in Figure 1. The value of p extracted from the data was found to be -0.19. This, as previously noted, is quite close to the value of 0.21 that has been reported for the efficiency with which benzene makes internal conversion to its S1state from its state at 6.7 eV.lo The appropriateness of the 6.7-eV conversion efficiency is demonstrated in what follows. The energy distribution of the states of benzene that are initially populated via energy transfer from C* should approximate the energy distribution of the emission spectrum of C* but with a weighting factor proportional to the oscillator strength distribution of benzene in dilute cyclohexane divided by the fourth power of the energy.18 Although the emission spectrum (in photons per reciprocal centimeter) peaks at only 6.2 eV,19 the oscillator strength distribution rises so rapidly above this energy20that the weighted spectrum maximizes at about 6.7 eV. Utilizing the reported energy dependence of the benzene internal-conversion efficiency,14 its average value, when computed on this weighted distribution, turns out to be -0.26. To further confirm the appropriateness of our interpretation of p, we have determined its value in a series of C solvents with emission spectra that are increasingly red-shifted from the cyclohexane emission spectum. Since the benzene internal-conversion efficiency to S1increases monotonically as the excitation energy decreases from 6.2 eV,14 we would predict that /3 would similarly
+
+
~
~~
(14) Braun, C . L.; Kato, S . ; Lipsky, S. J . Chem. Phys. 1963, 39, 1645. (15) Schwarz, F. P.; Smith, D.; Lias, S. G.; Ausloos, P. J . Chem. Phvs. 1981, 75, 3800. (16) Raymonda, J. W. J. Chem. Phys. 1972, 56, 3912. (17) Koch, E. E.: Otto, A. Chem. Phvs. Lett. 1972. 12. 476. (18) Forster, Th. Ann. Phys. 1948, 2; 5 5 . (19) Rothman, W.; Hirayama, F.; Lipsky, S. J . Chem. Phys. 1973, 58,
1300. (20) American Petroleum Institute Research Project 44, Carnegie Institute of Technology, Catalog of Ultraviolet Spectral Data, Serial No. 1, 16, 19, 164, 172, 174, and 212.
2244
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
increase as the emission spectrum of C* red-shifts. This prediction is examined in Table I. The values of 0 presented in Table I were extracted from experimental values of (x - xc)/xc for 1W2M solutions of TMPD in aerated cyclohexane-benzene mixtures utilizing eq 5 and values of pBT, pCT, and 'pcB that were determined from their respective Stern-Volmer constants KBT, Ka, and KCB. These constants were estimated by scaling to those of cyclohexane (Le., KBT = 273 M-',6 KCT = 43 M-1,2'and KcB = 39 M-' 6 , 2 2 ) . The scaling parameter for KBT was taken to be the self-diffusion constant D of the C solvent (as estimated from the semiempirical equation of Dullien).23*24For Ka and KcB, the scaling parameter was taken equal to the product of D with the lifetime T of the C* emission.*' As will be noted from a comparison of the second and last columns in Table I, the predicted correlation of 0with ,A, appears to be well satisfied when considered within the context of the aforementioned approximations. Also, the value of /3 predicted from the internal-conversion efficiency when appropriately averaged over the product of the C* emission and B oscillator strength gives values of 0.35 for trans-decalin and 0.52 for 2,3-dimethylbutane. (It will be recalled that for cyclohexane this predicted value was 0.26.) These values also are in satisfactory agreement with those in Table 1. We turn our attention next to the PPO solutions excited at 7.9 eV. For the aerated cyclohexane-benzene solutions containing lo-* M PPO, the results shown in Figure 2 are similar to those shown in Figure 1 for TMPD at the same conditions. This is not unexpected on the basis of eq 5 since both /3 and KCB (=39 M-')6i22 are solute independent, and KBT and KCT have been reported to have values for PPO of KB, = 300 M-' 26 and K C T = 53 M-' 27-29 in air-equilibrated cyclohexane, which are quite close to those for TMPD (see Table I, row 1). The value of p extracted from the PPO data via eq 5 is 0.27, which agrees somewhat more closely with the theoretical value of 0.26 than does the value 0.19 extracted from the TMPD data. This difference is very likely attributable simply to the higher quality of the data using PPO due to its much larger emission quantum yield.30 Indeed we find that eq 5 with /3 = 0.27 and pCB,pBT, and pa calculated from their Stem-Volmer constants predicts the experimental data quite well. Thus at VB = 0.1, 1, and 2%, x/xc is predicted to be 0.91, 0.69, and 0.64, as compared to the experimental values (see Figure 2 ) of 0.90, 0.68, and 0.65, respectively. For nitrogenated solutions of PPO in cyclohexane KcB = 50 M-1?2 Ka = 67 M-1?8 and KBT e 1000 M-'.l0 Substituting these values into eq 5 and again using 0 = 0.27 predict that, for the M PPO solution, x/xc = 0.90, 0.70, and 0.66 at VB = 0.1, 1, and 2%, respectively. The experimental results show x/xc = 0.93,0.71, and 0.66 (see Figure 2). Again the agreement is quite good. Lowering the solute concentration from to M changes the scintillation behavior dramatically. This is illustrated in Figure 2 for the solute PPO. Two effects are to be particularly noted. (21) Choi, H.J.; Tweeten, D. W.; Lipsky, S. J . Phps. Chem. 1984, 88, 5863. (22) Barigelletti, F.;Dellonte, S.; Mancini, G.; Orlando, G.Chem.Phys. Lett. 1979, 65, 176. (23)Duliien, F. A. L. AIChE J . 1972, 18, 62. (24) Riddick, J. A.; Bunger, W. B. Organic Soluents; Wiley-Interscience: New York, 1970. (25) Katsumura, Y.; Tabata, Y.; Tagawa, S. Radiat. Phys. Chem. 1982, 19, 267. Katsumura, Y.; Yoshida, Y.; Tagawa, S.; Tabata, Y. Radial. Phys. Chem. 1983, 21, 103. (26) In neat liqtiid-air-equilibrated benzene this value has been reported to be 335 M-' (see ref loa), but in a 10% solution of benzene in cyclohexane the value is reduced to 300 M-l (see ref lob). (27) In ref 28,KCT= 67 M-l is reported for nitrogenated solutions. For air-equilibrated solutions this is reduced by a factor of 1.27(see ref 29) to give KCT = 53 M-I. (28) Hirayama, F.;Lipsky, S. Organic Scintillators and Liquid Scintillation Counters; Horrocks, D. L., Peng, C. T., Eds. Academic: New York, 1971;p 205. (29) Choi, H.T.; Askew, D.; Lipsky, S. Radiat. Phys. Chem. 1982, 19, 373. (30)Berlman, I. B. Handbook of Fluorescence Spectra of Aromatic Molecules; 2nd ed.; Academic: New York, 1971.
Yoshida and Lipsky First, in aerated solutions, the initial slope of x/xc vs VB becomes much more negative at the lower concentration, and second, nitrogenation now causes a rapid upswing in x/xc at relatively low VB. Equation 5 is incapable of accounting for either of these results. For example, if we use the same Stern-Volmer constants as were used in the successful prediction of the 1O-* M PPO results, M PPO that PBT = 0.23 we obtain now in aerated solutions at and pCT = 0.050 and at VB = 0.1% (Le., CB = 0.01 1 M), p C B = 0.29. Substitution of these into eq 5, with 0 = 0.27, predicts ( x - xc)/xc = +0.07. The experimental value is -0.20! For the M PPO solutions, pBT = 0.50 and pcr = 0.063 nitrogenated and, at VB = 0.1%, pCB= 0.34. These predict (x - xc)/xc = C0.39. The experimental value is -0.21! As we will note later, and as has been previously observed by others,' in P--particle-irradiated solutions of aerated cyclohexane-benzene-PPO, a lowering of the PPO concentration "deepens" the luminescence minimum. The early explanation of this provided by Burton and co-workers5 was rather straightforward and can be understood from an examination of eq 5. According to their theory, the parameter, 0,was implicitly taken equal to 1 and therefore negative values of (x - xc)/xc required the inequality pBT < pCT. Thus it followed from the usual Stern-Volmer forms of pBTand pcT, since PBT was less than pCT, that pBT/pCT would decrease as the T concentration was reduced and, accordingly, (x - xc)/xc would become more negative and the minimum would deepen. The problem with this explanation, however, is that pBT is simply not observed to be less than pcT. Certainly at VB = 1%, is quite significantly larger than pCT,6 and it is most unlikely that this inequality would reverse at lower benzene concentrations. Thus, as we have previously argued, (x - xc)/xc is negative not because is less than pCT but rather because PBT must be multiplied by the internal-conversion efficiency, p, and this is so small in dilute solution^.'^^^^ However, with /JBT greater than pcT, it would now follow from the usual Stern-Volmer expressions that, as the PPO concentration declines, PBT/PCT would increase and (since 0 cannot change) that (x xc)/xc would get less negative, and the minimum would become shallower instead of deeper. So we return to the dilemma. The most obvious solution to the problem is to seek an alteration in the Stern-Volmer form that only manifests itself at low T concentrations and then is in such a direction as to give an effectively smaller magnitude to pBT/pcT. Such an effect, at least on pCT (Le., to make it decrease with decreasing T concentration less rapidly than predicted by the Stern-Volmer form), has, in fact, been previously reported in studies of the emission from cyclohexane-PPO and cyclohexane-p-xylene solutions excited in the cyclohexane absorption band at 147 nm28and, more recently, for bicyclohexyl-p-xylene solutions excited at 175 r ~ m . ~The ' effect appears to derive from the existence of two states of C that are capable of transferring energy to T to form T*. One of these is identified as C* (Le., the lowest excited singlet state of C) and the other, which is produced from C* and appears to have a significantly longer lifetime, has been tentatively identified as Ct (the lowest triplet state of C).28,31*32 Thus the scintillation yield (of T* states) in C T systems, when optically excited in the C absorption band below the ionization potential. has been expressed as
+
=
-
XC
[PCT
+ (l
- PCT)6PtTIX1C
(6)
where 6 is the C* Ct transition probability in the absence of T, Xlc is the probability that C* is generated by optical absorption to some higher state of C, and pcT and ptT are the energy-transfer es to T from C* and Ct, respectively.28 Equation 6 was shown to explain the dependence of xc on T concentration from M when both pCT and ptT were given Stern-Volmer to forms with KtT = 100KcT (in nitrogenated solutions) and 6 = 0.01-0.05.28~3'
It is not difficult to accommodate this two-state mechanism into our previous expression for the scintillation efficiency of a (31) Walter, L. Ph.D. Dissertation, University of Minnesota, 1980. (32) Lipsky, S. Radiat. Res. Proc. Int Congr., 8th 1987, 2, 72.
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2245
Scintillation Process in Three-Component Systems three-component system. Thus if we identify, as before, pm and pCBas the transfer probabilities from C* to T and B, respectively (recall, however, pff is conditional on VB = 0) and define ptTand ptBas their analogues for energy transfer from Ct, then it follows directly that 2 (=x/Alc)can be expressed as
ii = 'PCBBPBT+ (1 - 'PCB)PCT + (1 - 'PCB)(l - PCT)6('PtBtPBT + ( l - ptB)PtT) (7) where p and j3f are the benzene internal-conversion efficiencies to SI from states sensitized by C* and Cf, respectively. Equation 7 ignores absorption of light by B. Recognizing that the scintillation efficiency in the absence of benzene, Le., xc, is given by eq 6, a simple rearrangement of eq 7 gives
x - xc -Xf-
+
where iiC = pm (1 - pcT)6/1tT. As we will demonstrate in what follows, eq 8 has all of the requisite properties for explaining our M PPO solutions of cyclohexaneresults for both and benzene mixtures under both aerated and nitrogenated conditions (see Figure 2). At benzene concentrations less than -2% by volume, the benzene internal-conversion efficiency to SI does not change significantly from its value at "infinite" dilution.I0 Therefore, below 2%, the entire dependence of (x - xc)/xc on benzene concentration in eq 8 resides in cpcB and ptB,each of which can be written in the Stern-Volmer form K i B C B / ( 1 KiBCB), where RiB = KiB/(l K i T C T ) with i = C or t and CBand CT are the concentrations of B and T, respectively. Defining
+
+
BPBT
sl--l
iiC
and (9) it follows that eq 8 will have a minimum at
when m p (sKcB+ t&) < 0 and mt > stKtB. As we will demonstrate below, in all of our PPO-cyclohexane-benzene solutions, t will be less than zero and, since KtB >> &B,28 the first inequality will always be satisfied. Therefore, a minimum will be guaranteed when s is positive (its sign in M but not M PPO solutions) and will nitrogenated possibly be observed when s is negative (its sign in aerated solutions) but with a second derivative of much smaller magnitude at the minimum. Also we will show that eq 8 properly predicts that the initial slope of x/xc vs VB will become increasingly negative as the PPO concentration declines. Considering first the nitrogenated solutions, we use K C T = 67 M-',28 K B T = 1000 M-',Io KcB = 50 M-',22and B = 0.27 as before. For the Cf state we use the values of KtT = 5600 M-l and KtB = 5200 M-'.'' Thus at lo-' and M PPO, KtB= 788 and 91 M-I and KCB= 47 and 30 M-', respectively, and similarly at these two concentrations pcT = 0.063 and 0.40, PBT = 0.50 and 0.91, and ptT = 0.85 and 0.98, respectively. For 6 we will initially use the value of 0.01228 (although later we will take 6 as a free parameter). Substituting into eq 6 gives iiC = 0.073 and 0.408 at lo-' and M, respectively. Since the cyclohexane triplet state is estimated to lie within a few tenths of an electronvolt below its first excited singlet state,33and @, as can be seen from Table
I (and also from its theoretical estimates), varies rather slowly with the energy of C*, we will assume Pt = /3 N 0.27 (the value that we extracted from the M PPO data). Thus at a PPO concentration of 10-3M we calculate for cyclohexane-benzene solutions that s = 0.85 and t = -0.12 and, therefore, both the inequalities are satisfied and a minimum is predicted. On the other hand, at a PPO concentration of IOm2 M, we calculate s = -0.40 and t = -0.014, and a minimum cannot exist since the second M, we note that since the inequality is unsatisfied. Also, at magnitude o f t is so much smaller than that of s, it follows from eq 8 that, so long as (1 - pcB)/~cB< 1, the second term on the rhs of eq 8 will contribute negligibly to (x - XC)/XC. Using KCB = 30 M-I, it then follows that in nitrogenated solutions of M PPO, when CBis greater than 0.011 M (Le., VB = 0.1%), (x - xc)/xc will be predicted to better than 5% by the use of eq 5 and to better than 3% for CB> 0.033 M (Le., VB = 0.3%). At concentrations lower than these, eq 5 should tend to proportionately underestimate the experimental value of (x - xc)/xc. Using 6 = 0.012, eq 8, although qualitatively predicting a M PPO solution, predicts it to occur minimum in nitrogenated at too low a VB (-0.006%) and, at higher VB, generally overestimates the experimental values of x/xc. To improve the quality of the fit, 6 may be taken as a free parameter. The value that 0.07. With this, s and t are best fits the data is found to be 6 recalculated to be 0.1 3, and -0.37, respectively. Substituting this into eq 10 then predicts a minimum at VB = 0.04% and of depth x/xc = 0.78. Also from eq 8, we calculate now at VB = 0.1 and 1% that x/xc = 0.82 and 1.06 as compared to the experimental values of 0.79 and 1.03, respectively. Clearly the fit is satisfactory. However, at VB = 2%, eq 8 estimates x/xc to be 1.09, whereas experimentally its value is 1.27. The disparity here is attributable to direct absorption of light by B. From eq 3 it may be noted that the contribution from direct absorption is strongly dependent on the value of R. Since R is proportional to pBT/pcT, it follows from the fact that PBT exceeds pcT that R will increase as T concentration declines. Also, since B* is longer lived than C*, nitrogen will enhance PBT more than pm and therefore also increase R. Thus R is expected, and indeed exhibits, a much larger value in nitrogenated M PPO solutions ( R = 9.1) than in the aerated M solutions ( R = 1.4). Recalculating F via eq 3 (which is adequate at VB = 2%) gives now F 31 1. Therefore, (x - xc)/xc must be increased by ~ 0 . 0 to 2 give a total value of 1.11. Although we remain thus shy by about 13% of the experimental value of 1.27, considering the various uncertainties in these calculations, the discrepancy is not considered particularly serious. We examine next our results for aerated solutions of M PPO in cyclohexane-benzene mixtures (see Figure 2) and again attempt an analysis via eq 8. The parameters Km = 53 M-1,27-29 K B T = 300 M-1,26and K c B = 39 M-' are as previously employed M PPO aerated solutions. Unfortuin our analysis for the nately, however, we do not have values available for K t T or K t B in the aerated solutions. Their nitrogenated valuesz8of K t T = 5600 M-' and K t B = 5200 M-' require a reduction by a factor that most plausibly will be somewhere in the range of 1.27 (the quenching factor for the C* state) to 28 (which assumes that the SternVolmer constant for O2 quenching of Ct scales to that for quenching of C* by the ratio K t T / K C T 100 28 in nitrogenated solution). Considering the range of this uncertainty, we use the reduction factor as a free parameter v and all other constants fixed. Thus at and M PPO, KtB = 5200/(v 5.6) M-I and 5200/(v + 56) M-', KcB = 37 and 25 M-I, pcT = 0.050 and 0.35, per = 0.23 and 0.75, and ptT = 5.6/(u 5.6) and 56/(u 56), respectively. Using 6 = 0.07 (the best fit value for the nitrogenated solutions), we compute Rc = 0.05 + 0 . 0 6 7 and ~ ~ 0.35 ~ +0 . 0 4 6 ~ ~ ~ M PPO, respectively. Substituting into eq 8 gives at lo-) and v = 7.3, and therefore s = -0.21 and t = -0.31 at M PPO M PPO. With these, eq and s = -0.48 and t = -0.079 at 8 predicts at VB = 0.1, 1, and 2% x/xc = 0.76, 0.77, and 0.78
-
+
+
+
(33) Robin, M. B. Higher Excited States of Polyatomic Molecules; Academic: New York, 1985; Vol. 3, Chapter 3.
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Yoshida and Lipsky
of aerated benzene but all excited with 8 particles. In Figure for 10-3 M PPO (whereas experimental values are 0.80,0.72, and 3, we contrast 8-particle with E = 7.9-eV-photon excitation for M PPO (as 0.72) and predicts 0.87, 0.63, and 0.58 for M PPO solutions of aerated toluene-cyclohexane, and in compared to the experimental values of 0.90, 0.68, and 0.65, Figure 6 we examine the effect of PPO concentration and O2 respectively). The general trends with change in PPO concenconcentration on P-particle-excited solutions of benzene-cyclotration are certainly correct, and the quantitative agreement is hexane. We consider first the M TMPD results. not unreasonable. There are two features in Figures 1 and 5 to which we wish We examine next the toluene results in Figure 3. From previous to call particular attention. The first of these is that the initial studies6 of aerated cyclohexane-toluene mixtures containing 10-2 slopes for 8-particle irradiation are about the same as for optical M TMPD excited at 7.9 eV, the ratio x/xc was found to exceed excitation at 7.9 eV and display about the same dependence on unity at all concentrations of toluene studied. Similar results are nature of the C solvent (see also Table I). The implication, of M PPO solutions. From the earlier shown in Figure 3 for course, is that, for both types of excitation, the initial loss in results with TMPD, the value of p extracted via eq 5 was 0.48.6 scintillation efficiency as benzene replaces cyclohexane has the This is in good agreement with the value of 0.51 for the efficiency same origin, namely, inefficiency in the production of B* via energy with which toluene internally converts to S, from its 6.7-eV state transfer from C* to B. For 8-particle excitation, C* is an inin infinitely dilute cyclohexane solution.1° For analysis of the termediate in what we have previously referred to as the channel M PPO solutions, eq 5 is inadequate and must be replaced by eq 1 process6 This involves recombination of C+ positive ions with 8. Since the second term on the rhs of eq 8 makes a negative their geminate electrons to produce C*, which then behave precontribution to ( x - xc)/xc, we would predict that the use of eq cisely as they do when generated optically (Le., transfer energy 5 with p = 0.48 would now strongly overestimate x/xc. This to B to produce B* with probability PpcBor transfer energy to indeed is the case. Taking KCB = 39 M-1,6*22 KBT = 470 M-’,j4 T to produce T* with probability (1 - pCB)pCT). and KCT = 53 M-’,27-29eq 5 predicts ( x - XC)/XC= 0.35 at VB The second feature to note in Figures 1 and 5 is that for p= 0.05%. On the other hand, using eq 8 at VB = 0.05% with the particle excitation, x/xc rather quickly recovers its initial loss quenching parameter, u = 7.3, and all other constants (except for and rises above unity at much lower benzene concentrations than KBT = 470 M-’ 34) the same as for benzene, predicts ( x - XC)/XC is observed for E = 7.9-eV excitation. Clearly this effect must = 0.03. The experimental value is 0.04. be attributable to channels other than channel 1 that also lead Before turning our attention to the results with 8-particle to T* but are more specifically ionic in character, Le., are not irradiation, we first comment briefly on the factor R. In Figure available below the ionization potential of C. We consider these 4 we show R as a function of excitation energy for M PPO channels below. solutions of cyclohexane-benzene and cyclohexane-toluene. It In the case of TMPD, as has been previously discussed,6 one will be recalled that R is the ratio of scintillation efficiencies in need consider only one other major route to T*. This involves pure B T to that in pure C T. Accordingly, it can be expressed the geminate process C+ T eC T+ + e- C + T*, as the ratio, for benzene to cyclohexane, of their internalanversion hereafter referred to as channel 3 and which is interfered with efficiencies for excitation at energy E (Le., XiB/Xic) multiplied C + B+ + eC+ by the geminate process C+ + B + eby the ratio of their energy-transfer efficiencies to produce T* B*, hereafter referred to as channel 2. In a previous analysis of N 1 for from T (Le., p;)T/p&). At 7.9 eV, the ratio X;,/X;, the channel 1, 2, and 3 processes it was derived that6 benzene-cy~lohexane’~*~~ and = 1.4 for toluene-cycl~hexane.~~~~~ The ratio P ~ T / P & = 8, 4.6, and 6.4 for nitrogenated benzene(11) x = xc + PCBXI(PPBT - PCT)+ ~ P ~ ( P B-T XC)- a n X C cyclohexane, aerated benzene-cyclohexane, and toluene-cyclohexane solutions of M PPO, respectively (see previous calwhere ‘p2 is the probability that C + decays via channel 2, p2,,is culations). Thus R is predicted to be i= 8,4.6, and 9, respectively, the probability that this decay does not generate T*, xc = X@CT as compared to experimental values of 9, 3.5, and 6.5. With the A,, and X1 and X3 are the probabilities that C+ decays via exception of toluene, the agreement is not u n r e a s ~ n a b l e . ~At~ channels 1 and 3, respectively, but conditional on the absence of 8.5 eV, XiB increases by ~ 3 0 % for benzene and by =lo% for B. Equation 11 is simply rearranged to toluene36 whereas X,; drops by about a factor of 1.7.16 Thus R should increase by ~ 2 . and 2 1.9 for benzene and toluene, respectively, at the higher energy, and as Figure 4 shows, these increases are about 1.95 for benzene and 1.5 for toluene. As the energy continues to increase to 10 eV, A;, continues to fall by about another factor of 2,” whereas Xi, does not alter signifiAs discussed previously,6 for TMPD X3
