Energy transfer from cyclohexane to benzene in their irradiated mixtures

OM-5724/91 $3.00 + 0.00 Copyright 0 1991 Pergamon Rcss plc

Radtar. Phys. Chem. Vol. 38, No. 1, pp. 51-60, 1991

ht. J. R&at. &I. Instrum., Part C Printed in Great Britain. All rights rcscrwd

ENERGY TRANSFER FROM CYCLOHEXANE TO BENZENE IN THEIR IRRADIATED MIXTURES DAVILI B. JOHNSTONand SANFORDLIPSKY Department

of Chemistry, University of Minnesota, Minneapolis, MN 55455, U.S.A. (Received 17 May 1990; in revised form 13 July 1990)

Ah&act-The fluorescence of both cyclohexane and benxcne in their irradiated mixtures has been studied as a function of benzene concentration from * 0.005 to 0.1 M. The quenching of the cyclohexane emission by benzene is found to be signikantly greater than obtained under optical excitation conditions suggesting an important role for benzene as a scavenger of the geminate ion-pair precursor of the fluorescing state of cyclohexane. From diffusion models, a lower bound is established for the scavenging rate constant. An

examination of the fluorescence from benzene leads to the conclusion that although the majority of benzene fluorescence drives from electronic energy transfer from excited cyclohexane, a large fraction (from 20 to 50% over the concentration range studied) is generated by recombining molecular ions. The intrinsic efliciency with which the recombining ions generate fluorescent states of benzene, however, appears to be peculiarly low.

toluene or p-xylene are considered to form negative ions with any significant probability and their concentrations, in these studies, were kept sufIiciently low as to avoid, presumably, any appreciable contribution from geminate positive charge transfer processes (Baxendale and Mayer, 1972; Busi and Casalbore, 1983). However, the G-values of excited solvent states thus obtained are found to be significantly lower than values determined by other methods (Choi et al., 1982a; Walter and Lipsky, 1975; Wojnarovits and F(ildiak, 1980; Yoshida et al., 1989). Although the question of possible origins for this disparity have been considered (Busi and Casalbore, 1983; Choi et al., 1982a), there appears still no definitive answer. In a recent investigation (Johnston and Lipsky, 1990), we have measured the quenching of cyclohexane fluorescence by benzene and the concomitant sensitization of benzene fluorescence by cyclohexane under optical (A, = 160 mn) excitation conditions. The analysis of this data have provided us with reliable quenching and energy transfer efEciencies over a range of benzene concentration from 0.0056 to 0.112 M. In the present investigation we have performed entirely similar experiments on this system but using fast electron rather than optical excitation. By comparing the two sets of measurements we are able to provide some new information pertinent to the mechanism of the formation of excited benzene.

INTRODUCI’ION The

formation of excited solute states in irradiated saturated hydrocarbon liquids derives from both neutral and ionic channels. The neutral channel involves the formation first of an excited solvent molecule (either formed directly or via geminate electron + positive ion recombination) followed by nonradiative transfer of this excitation to the solute. The ionic channels are more complex involving capture by the solute (hereafter referred to as B) of either the geminate electron, to form B-, or of the positive charge of the solvent (hereafter referred to as C), to form B+, followed by some or all of the possible ionic recombination processes (i.e. B+ + B-, B+ + e-, B- + C+). The relative contributions of these various channels to the observed yields of excited solute states has been considered by many investigators (Appleton and Brocklehurst, 1988; Brocklehurst, 1985; Busi et al., 1979; Hermann et al., 1980; Salmon, 1976; Tagawa et al., 1982), but remains generally unresolved. In only one case, that of biphenyl in cyclohexane, has there been some important progress made recently on this question using picosecond pulse radiolysis with analysis of both biphenyl negative ion and biphenyl fluorescence (Yoshida et al., 1989). In the case of benzene (or toluene or p-xylene) as solutes, the question of the mechanism of formation of excited aromatic takes on some additional relevance since the yields of these states (as deduced from their fluorescence) have been sometimes utilized to deduce G-values for excited solvent states (Baxendale and Mayer, 1972; Busi and Casalbore, 1983; Salmon, 1976) under the assumption that all of the ionic channels are ignorable. Neither benzene nor

ExPEREwENTAL All samples were irradiated with the /3- spectrum (E_ = 0.223 MeV) from a 05 Ci “‘Pm source. The source, purchased from Amersham, has the ““Pm incorporated in enamel and sealed with a 0.075 mm 51

52

DAVIDB. JOHNSTON and SANFORD LIPSKY

thick titanium window. The active area of the source is in the form of a narrow rectangle of length 50 mm and a width 3 mm. The source window was placed at a position of either 2.75 or 6.37mn-1 from the back window of the sample cell. The sample cell had an aluminum body to which was attached, in front, a 1 mm thick window of either LiF or U.V. grade quartz, via a 0.38mm diameter indium wire compression seal. The active diameter of the window was 20.6mm. Experiments were made using both windows, although the LiF window was somewhat inferior due to a weak background fluorescence (from 280 to 350 mn). The back window, through which the /I - spectrum entered, was made of 0.0254 mm thick aluminum foil. In initial experiments this window was attached using a compression fit on a raised polished circular edge that was machined onto the cell body. With this design, the separation between back and front windows was 4.26 mm. Since, as we show below most of the j? - spectrum is stopped in -0.6mm of the back window, rather severe corrections were required for benzene absorption of the cyclohexane emission even at the fluorescence wavelength .+= 222 nm (where the benzene absorption is minimal). Accordingly, the path length was reduced by means of an aluminum adapter which was used to push, from behind, the aluminum foil window to within 0.635 mm of the front window. Sealing was now accomplished by the compression of an o-ring (placed on the adapter) against the edge of the foil and the interior wall of the cell body. The emission from the cell was collected at an angle of 22.5” from the normal to the front window by a parabolic mirror and focused onto the entrance slit of a Spex 1680 double monochromator with grating blazed at 200 nm and operated at a band pass of 4 or 8 nm. The spectrally dispersed fluorescence was then focused with a CaF, lens onto the front surface of a thermoelectrically cooled Hamamatsu R955 photomultiplier and its signal amplified and counted. The entire analyzing system employed here was identical to that used in the previously reported optical studies (Johnston and Lipsky, 1990) on the same system. Using the empirical equation (Turner, 1986) R = 0.412 T’~274~wHhT to relate the electron range, R (g/cm*) to its kinetic energy, T (MeV), it is simple to compute that after passage through 0.0254mm of aluminum, a 0.223 MeV electron will have a range of about 0.55mm in cyclohexane. Accordingly, the solution fluorescence originated within a distance of from 0.64 to 0.09 mm from the front window. Within this distance, distortion of the emission spectra by reabsorption is negligible. This was confirmed by comparing the emission spectra of both cyclohexane and benzene obtained in this investigation with the spectra that were obtained by exciting the same solution optically at 160 nm in front-surface geometry (Johnston and Lipsky, 1990). From 185 to 320nm, the spectra were identical.

The intensities of fluorescence were monitored at either 210 or 222 mn for cyclohexane and at 287 nm for benzene. Since the spectral distribution of the cyclohexane fluorescence was found to be unaffected by the presence of benzene, the ratio of the cyclohexane fluorescence intensity with the benzene present to that without benzene was expected and, indeed, confirmed to be independent of the observation wavelength (i.e. 1, -210 or 222 nm). By virtue of our choice of i4’Em for excitation source, no Cerenkov radiation was observed and background was exclusively due to thermal noise from the photomultiplier (N 2-3 cps). Cyclohexane (Mallinckrodt, Spectrophotometic Grade) was further purified by percolation through activated silica gel. Benzene (Fischer, Spectranalyzed) was used without additional purification. All measurements were made on air equilibrated solutions at 20°C unless otherwise designated. Since we compare out results from this study with those from optical experiments performed on similarly constituted solutions, the effects of 0, to quench the excited states of cyclohexane and benzene are without consequence to our conclusions. A small effect of O2 to attach electrons is considered later. RESULTS The quenching of the cyclohexane fluorescence by benzene is presented in Table 1 as the ratio of Z$,,(S,)/Z&O(S,). The notation employed here uses the symbol Z$(S,) to represent the intensity of fluorescence from a solution S, excited with fi particles and observed at wavelength A,. The symbol S, refers to a cyclohexane + benzene mixture containing a benzene concentration equal to 0.0112n mol/l. Thus, for example, So refers to neat cyclohexane and S,,, to our highest concentration solution of 0.112 M. For comparison purposes, the same quenching ratio, but obtained using optical excitation at 1, = 160 nm, is Table 1. The quenching of the fluorescence of cyclohexane by benzene [(I$,&,)/l~,&)] and the sensitization of benzene fluorescence by cyclohexane [I$&,)/I$z,(S,)] as a function of benzene concentration, e, excited with either “‘Pm /3 particles (b = 8) or with 16Onm light &= 160) Solution label SO‘ -._

c (mW 5.60

2:: S0.1 S0.9 S 1.0 S 1.1 S2.0 S3.0

7.20 7.84 8.96 10.1 11.2 15.7 22.4 33.6

2:; S6.0 ST.0 SB.0 %a

S 10.0

44.8 56.0 67.2 78.4 89.6 101 112

MS”)/MS,) p=160’ rC=8 0.7% 0.833 0.751 0.720 0.687 0.660 0.642 0.561 0.460 0.351

0.802 0.786 0.734 0.725 0.707 0.624 0.541 0.425

0.272 0.223 0.180 0.152 0.132 0.114 0.0986

0.345 0.298 0.251 0.216 0.186 0.168 0.150

‘See Johnston and Lipsky (1990).

MS”)lMSO) ~=16@ P=8 0.321 0.368 0.372 0.425 0.402 0.475 0.436 0.521 0.494 0.566 0.533 0.609 0.676 0.754 0.823 0.926 1.170 0.968 1.13 1.38 I .23 1.52 1.26 1.66 1.31 1.78

1.88

1.43

I .98

1.49 1.50

2.08

Energy transfer

also shown in Table 1 as Z~~(S,)/Z~~(S,). The /Iratios have been averaged over at least three independent measurements, performed on fresh samples, often in different cells and over a period of several months. The standard deviation of each entry in Table 1 never exceeds N 3%. The sensitization of the benzene fluorescence is presented in Table 1 as the ratio of Z~~7(Sn)/Z~22(S,,). Since this ratio involves observation at two different A,, it has no absolute significance until corrected for the ratio of emission quantum yields and spectral densities for benzene and cyclohexane, respectively, and for the ratio of transmissions of the analyzing system at the two observation wavelengths. Since our analysis only requires relative values of these ratios, this correction was not applied. For comparison purposes, the analogue sensitization ratios for optical excitation, i.e. Z~~(S.)/Z$j(S,) are also presented in Table 1.

53

(Johnston and Lipsky, 1990) as I$@,) Zlt (S,). Thus if we define:

-PV(l

-axA

(1)

where (1 -pt) is defined to be the ratio of the probabilities that C+ + e- recombines in the presence of benzene to that in its absence (we assume now, but later relax this assumption, that the fraction of these recombinations that generates C* is the same with or without benzene), and 1 - pee is the probability that C* itself escapes quenching by benzene. If we now make the customary assumption that the spatial distribution of benzene that is “seen” by C* is independent of its mode of formation (and we will return to this point later), it then follows that 1 - rpc, can be obtained from the optical measurements

of

then, from equation (1),

Q& = 1 -it

(3)

Values of Q& are displayed in Table 2. The deviation of Q&, from unity is an indication of interference by benzene with the production of C+ in irradiated cyclohexane. The effect remains rather small to c IV0.01 M but is clearly not inconsequential at the higher concentrations. In the case that this interference is due to a scavenging of the geminate electron, then, as a number of experiments have con6rmed (Choi et al., 1983; Schwarz and Smith, 1985; Tweeten er al., 1989), over a limited concentration range, Qcxptl should be representable as a linear regression on c”, i.e.

Qcxpt, = a.4+ Bc”,

As is apparent from Table 1 (columns 3 and 4), benzene reduces the intensity of cyclohexane fluorescence to a signficantly greater extent when the solution is irradiated with /3- particles than when optical excitation is used at 160 run (1.1 eV below the cyclohexane liquid phase ionization potential; Casanovas et al., 1980). Since excited states of irradiated cyclohexane are generated almost entirely by geminate C+ + e- recombination (Choi et al., 1983; Jonah and Sauer, 1989; Le Motais and Jonah, 1989), it follows that benzene must somehow intrude on this recombination process. Either benzene attaches the electron and/or scavenges the positive charge or the benzene must otherwise somehow alter the geminate ion-pair so that in its subsequent annihilation to excited cyclohexane, there results a reduced probability for formation of C* (i.e. the emitting state of cyclohexane). We consider first an intrusion mechanism involving only electron attachment. In this case the ratio of the intensity of cyclohexane fluorescence at 210 mn in the presence of benzene to that in its absence can be written as:

ZMW %4w

ratio

(2)

DISCUSSION

-=(I

the

(4)

with n - 0.7 for the concentration range studied here. Such a plot is shown in Fig. 1 with the solid line representing an unweighted least square fit of Q@ to co.’ with A = 0.994, B = 2.44 M-i and a correlation coefficient of 0.995. The significance of B derives from a comparison of the Friauf et al., (1979) theoretical prediction of Q (hereafter referred to as QuKom) to Qexptl.The procedure for doing this has been previously described (Choi et al., 1983) and is briefly repeated here. Assuming that the geminate ion-pair separation distances are distributed with an exponential radial probability density (and we also return to this assumption later): j@)=T;

(5)

it can be shown (Choi et al., 1983) that the ion pair escape probability, pncr can be represented as: pcsc= (PC I”*4 PW,

$1;

(6)

Table 2. Values of Q&i,,, &‘a, K and F* as functions of benzene concentration, C, deduced bm experimental data in Table 1 Solution label

S,, S2.0 %a S,., S%Cl S6.0 ST.0 S*.0

7.84 8.96 10.1 11.2 15.7 22.4 33.6 44.8 56.0 67.2 78.4 89.6 101 112

See quations

0.915 0.936 0.910 0.909 0.899 0.850 0.826 0.788 0.747 0.717 0.704 0.710 0.682 0.657

1.18, I.193 1.14, 1.14, 1.11, 1.12, 1.20, 1.22,

1.23, 1.31, I .35, 1.31, 1.32, I .389

(2),’ (IS)? (2O)Eand (25)‘.

0.q

1.o, 0.72 0.7,

1.3, I .3, 1s, I .7, 1.7, I .6, 1.8,

0.23 0.22 0.21 0.21 0.19 0.24 0.32 0.35 0.40 0.46 0.48 0.46 0.49 0.53

DAVID

54

B. JOHNSTONand SANFORDLIPSKY was a bit poorer for n = 0.65 (giving A = 0.978, B = 2.23 and r = 0.995). The fact that Qlheorrtis somewhat better fit by a slightly lower value of n has been previously commented on (Choi et al., 1983). From the connection between B and B’ (Choi et al., 1983), i.e.

‘i5

E

.-E : Q

I

B = B’(k,rt/4D)”

0

Fig. 1. Q_, as a function of benzene concentration raised to the 0.7 power. The solid line is a linear least square fit of the data to equation (4).

l.O-

0

’

’ 0.4

s

’ 0.8

’

’ 1.2

’

S”

’ I.6

’

n 2.0

2.4

’

. 2.6

_

as a function of the dimensionless conFig. 2. Q,, centration variable, s, raised to the 0.7 power. The solid line is a linear least square fit of the theoretical points to equation (7).

where rr is the Onsager escape distance in cyclohexane (280A), and K, is the modified Bessel function of order 3 (Abramowitz and Stegun, 1970). Taking Gs - 0.15 for cyclohexane (Allen, 1976a) and assuming a total ion yield of Gr - 4 (Allen, 1976at) gives pcrc= 0.038 and, therefore, from equation (6), jr, 12. Since QtimEt has been tabulated as a function of br, and a dimensionless concentration variable, s = (k,rf/4D)c where k, and D are the electron + solute scavenging rate constant and mutual diffusion coefficient, respectively, our procedure is to fit Qtheorrt (for fir, = 12) to a linear regression on s”, i.e.

= A’ + B’s”; Q,,,corrt

(7)

and over a range in s such that Qtheorrthas about the same minimum and maximum values as Qexp,,.Such a regression is illustrated in Fig. 2 for n = 0.70. The points are from tables of Qthcorrt$and the solid line is an unweighted least square regression on these points with A’ = 1.016, B’ = 0.0925 and a correlation coefficient of 0.9997. A signficantly better fit was n = 0.65 (giving A’ = 1.010, obtained with B’ = 0.1000 and r = 0.99997) whereas for QsXptl the fit $Lc Motais and Jonah (1989) have recently suggested a CT= 5.1. However, use of this somewhat larger Gr has relatively small effect on our eventual estimates of the electron + benzene attachment rate constant. #Kindly supplied by Dr Noolandi.

(8)

we obtain k,/D - 9.6 f 0.5 x lo-* cm (using either 0.65 or 0.7 for n), and with D = 5.8 x 10-3cm2/s (obtained from an electron mobility in cyclohexane of 0.23 cm/Vsec; Allen 1976b), calculate a value of k,=34+0.2x lO”M-‘s-r for the electron+ benzene~avenging rate constant. Considering how large is D, this is not a particularly efficient reaction. Thus were the reaction diffusion limited, its encounter radius (i.e. kJ4xD) would be about 0.8& significantly less than the reduced de Broglie wavelength of the electron (i.e. h/J- 11 A). The radial probability density that we have used in equation (5) fits well the distance distribution of geminate electron-positive ion distances that are obtained from photoionization of aromatic solutes in saturated hydrocarbon liquids (Choi et al., 1982b; Lee and Lipsky, 1984). A number of radiation chemical studies, however, seem to indicate that a somewhat superior radial probability density to use in the present application is that given by the function (Jonah, 1983; Le Motais and Jonah, 1989; Yoshida et nl., 1984, 1989): f(r) = -$ e -y’.

(9)

Using this instead and following the same procedure as before, we would require yr, = 4.60 [to provide = 0.0381 and find that now the ap, = 2,/&K,(yr,) best linear regression of Qthcorrton s” (over a Q range from 1.05 to 1.80) is obtained with n = 0.5 (A’ = 0.999, B’ = 0.0868 and r = 0.9998) while I? = 0.7 is distinctly inferior (A’ = 1.05, B’ = 0.0405 and r = 0.989). Our experimental data, on the other hand, as we have previously remarked, fit an n = 0.7 regression somewhat better than n = 0.5 but, clearly the scatter is sufficiently large to accommodate either regression. Our preference for equation (5) derives from previous work (Choi et al., 1983; Tweeten et al., 1989) with pet-fluorocarbon scavengers where the scatter was substantially reduced below that in this experiment (due to the enhanced scavenging reactivity of the pet-fluorocarbon vis-a-vis benzene) and which clearly indicated the superiority of the n = 0.7 regression that the distribution function in equation (5) predicts. Nevertheless, if we now force our Q,rt, to n =0.5, we obtain A = 0.912, B = 1.77 and r = 0.995 and from this, together with the aforementioned results on Qtheorrt vs h”.s, predict a k, = 1.2 x lOi M-’ s-l, ca 4 times larger than our previous value. Scavenging of the geminate electron by benzene would tend to preferentially remove that portion of

Energy transfer

the benzene population that lies closest to where C* would have been generated by C+ + e- recombination. Accordingly, we might expect a somewhat reduced contribution to the C+ + B quenching rate constant from adventitiously located benzene molecules under radiation chemical conditions as compared to optical excitation conditions (where such an effect gives rise to a time dependent or so-called “transient” contribution to the quenching rate constant). This would have the effect that the optically determined values of 1 - (pee would be somewhat too small to use in the /I - experiment and, this in turn, would make the values of (1 -pt) = Q& that we have displayed in Table 2 to be too large, and, increasingly so, as the benzene concentration increases. Thus the data shown plotted in Fig. 1 may require a correction that would make it more concave upward and lead to a linearization at a higher power of n. The net effect would be to cause an increase in our evaluation of k,. As an upper-bound estimate of this effect, we might imagine all so-called transient elfects to disappear so that even in the presence of benzene, C* decays exponentially in time. In this case 1 - (P,-~would be given by the Stem-Volmer form (1 + ac)-’ with a = 22 M-’ (Johnston and Lipsky, 1990). However a more realistic upper bound estimate is obtained by requiring that only those transient contributions disappear which lead to the concavity of the optical quenching data. In this case, the same Stem-Volmer form would apply but with a larger coefficient, i.e. 1-cp,,=[l+(a+&c#l)c]-‘wherea=22M-’ and /I = 6.77 M-l (Johnston and Lipsky, 19901). Using this, we find that Qexptlvs c” is now concave downward for n = 0.7 (A = 0.891, B = 5.34, r = 0.996) and requires n = 1 for linearization (R = 1.01, B = 9.68, r = 0.999). Using the distribution function of equation (S), we obtain from the regression of on s” (for Qthwmfrom 1.05 to 2.11) for n = 0.7, Qthcom A’ = 1.03, B’ = 0.0832, r = 0.9996 and for n = 1, A ’ = 1.lO, B’ = 0.0286, r = 0.987. The large disparity between the two values of n required for linearization of Q,, (i.e. n = 1) and for Q-, (i.e. n = 0.7)# suggests that we have over estimated the correction. Nevertheless, proceeding as before with equation (8), we obtain for either value of n a value of k, - 1.O x lo’* M-’ s-l, cu 3 times greater than our earlier estimate. Thus the two major approximations that we

$In the case of optical quenching, the limiting slope of Z~$S,)/Z~$@,) as c-0 is a + /Ifi = 34 M-i (Johnston and Liuskv. 1990). For Qtixoretover this ran&, n = 0.65 is superior to n = 0.7 fi.e. A’ = 1.02. B’ = 0.0997. r = 0.99999). TAlthough our systems contain dissolved air, the electron attachment rate constant to 0, is sulliciently small (Bakale ef al., 1972) that at the ambient concentration of -2 x lo-) M, it can be estimated that only 2-3% of the geminate electrons will be. scavenged. Thus the recombination times for the ovetwhehning majority of geminate pairs are una&cted by air.

55

initially used in our estimate of k, (i.e. that of equation (5) and that of the “uncorrected” optical values of 1 - fpcB in equation (1)), both tend to increase the value of k,. Accordingly, at this point, it is our position that if the intrusion by benzene on the geminate recombination process is due exclusively to electron attachment, then its rate constant must have a lower bound of cu 3.4 x 10” M-‘s-l. This however, far exceeds reported upper bound estimates of the electron attachment rate constant for benzene in n-hexane of 109M-‘s-’ as determined from conductivity measurements (Bakale et al., 1972) and of 108M-’ s-’ from absorption measurements (Baxendale and Rasbum, 1974). Since it is unlikely that this rate would be so much larger in cyclohexane than in n-hexane, we now turn our attention to other possible mechanisms. An alternative to electron attachment is to have benzene scavenge the cyclohexane position ion via charge or proton transfer. As long as we stay within the same approximations that were utilized in our treatment of the electron attachment process, the same procedure as was used to evaluate k, there, would equally well be applicable now to the charge (or proton) transfer rate constant and, accordingly, we would again conclude that its value could not be less than -3.4 x 10” Me’s_‘. This value is not toodisparatefromavalueof -2x 10”M-‘s-‘that has been suggested for this rate constant from microwave absorption measurements in irradiated cyclohexane (Warman et al., 1976). However, from the results of more recent investigations (Trifunac et al., 1985; Sauer et al., 1988), it has been suggested that the species involved in the microwave measurements is not CsH& but rather some species derived from it, most plausibly, CsH& and that the measured rate constant of 2 x 10” M-’ s-’ should be associated with the transfer of charge (or of a proton) between it and benzene. Therefore, unless the fluorescence from the recombination of this species with e- has the same spectral distribution as that from C* (and for Cs HA this is extremely unlikely considering the magnitude of the proton affinity of CsH12) (Lias et al., 1988), the reaction between it and benzene would be inconsequential to the quenching of the observed fluorescence. Additional to this, it should be noted that one of the approximations implicit in equations (7) and (8) is that “transient” effects are unimportant in the reaction of the scavenger with the geminate ion-pair. For reaction with e- this is not unreasonable but for a C,H&_ ion, were its diffusion constant “normal”, the C+ + B-C + B+ reaction would, perforce, compete unfavorably with the very rapid reaction of C+ with e-.7 In such a case, as has been previously discussed (Choi et al., 1984b), transient effects would be dominant and the reciprocal of the recombination probability (i.e. Q,,,) should depend almost exponentially on benzene concentration. Our data, however, can be shown clearly not to support such a dependence. On the other hand, were the

DAVID

56

B. JOHNSTON and SANFORD LIPSKY

geminate ion-pair collapse time lengthened by electron scavenging by the benzene, it would then, of course, become immaterial to the intensity of cyclohexane fluorescence (although not to benzene fluorescence, as we discuss later) whether or not C+ is also scavenged by benzene. Accordingly pt would be controlled by the electron scavenging reaction. Similar conclusions have been reached by Yoshida et al. (1989). As a third possibility for a mechanism by which benzene might intrude on the geminate ion-pair recombination, we consider its effect to interact with the geminate ion-pair without capture of charge. The process envisioned here involves the formation of a metastable negative ion of benzene which then rapidly decays to neutral benzene and a thermal electron. To explain how this might lead to a quenching of cyclohexane fluorescence, only two possibilities suggest themselves. One is that during the time interval of temporary capture, the electron loses some of its spin coherence with C+ and, accordingly, on subsequent recombination of e- with C+ produces C* with a lower probability than would otherwise obtain. The problem with this view, however, is that there exists no obvious theoretical justification for a significant loss of spin coherence during the interval of temporary capture into a negative ion state (Brocklehurst, 1985). The second possibility requires that the electron be thermalized by the temporary capture at a separation from its sibling positive ion which is smaller than in neat cyclohexane (Lee and Lipsky, 1982) and, by virtue of this proximity, recombines with the positive ion before the latter can vibronically relax. A possible effect of this, as has been suggested recently by Jonah and Sauer (1989), is that strongly dissociating states of the neutral might then be generated with reduced probability for internal conversion to C*. The problem here, is that were we to adopt this view, then we would expect that even in neat cyclohexane there should exist a population of electrons sufficiently close to the geminate ions so as not to give fluorescence on recombination. But recent attempts to find evidence for such a “nonemitting” population of geminate electrons, at least in neohexane and isooctane, have been unsuccessful (Tweeten et al., 1989). To look further at the consequences of these various mechanisms, we turn next to an examination of our data on the intensity of benzene fluorescence. Under optical excitation conditions, the ratio of the intensity of benzene fluorescence at 287 nm to that from cyclohexane at 222 nm can be expressed as (Johnston and Lipsky, 1990):

I% CL) r207

-=--(PCB<88), G?

Gl)

(10)

r222

where r287/r222 is the ratio of the fluorescence quantum yields of benzene and cyclohexane multiplied by their fluorescence spectral densities at 287 and 222 nm, respectively, and multiplied by the

transmissions of the analyzing system at these two wavelengths, and (Bs) [ = 0.26 (Johnston and Lipsky, 1990)] is the probability that the states of benzene that are populated by the transfer of electronic energy from C* make a successful internal conversion to the emitting state of benzene, B*. In the case of high energy excitation, the mechansim of B* formation is much more complex, involving not only energy transfer from C* (generated by e- and C+ recombinations) but also ionic recombinations of B- + C+, B- + B+ and e- + B+ . To simplify our subsequent analysis we will assume now that C+ is always CsH& and ignore contributions to B* fluorescence from recombinations involving other positive ions (i.e. that may have derived from C,HA). However, we will later return to consider the effects of instability of C+. Thus the intensity of benzene fluorescence can be quite generally taken to be proportional to the sum of the probabilities that (i) no scavenging occurs, C* is formed, transfers its energy to benzene, which then converts to B* and (ii) scavenging occurs and B* is ultimately generated, i.e. Gs7(Sn) N r2s7[(l -mk4diu

+m;

(11)

where /?c is the probability that C+ + e- gives C* and p is the probability that, following the scavenging, B* is somewhat formed. The probability, p, contains imbedded in it, as we will discuss later, all of the parameters required for describing the ionic channels. In the absence of benzene, the intensity of cyclohexane fluorescence at 222 nm can be taken to be simply proportional to r222 and to the probability, t,-, that C+ + e- gives C*. This latter probability may be different from /Ic to accommodate the possible effects of the aforementioned loss in spin polarization and/or “prethermalization”. Thus & is simply the maximum value of /Ic, i.e. its value at c = 0. Using equation (1 l), we now express the ratio of benzene fluorescence to cyclohexane fluorescence as:

1 .

(1 -pt)c&B.)+P$ C

//?c .

(12)

where L = DC With the introduction of the parameter 6, equations (1) and (3) must also be modified. As is obvious from the discussion following equation (l), this modification only requires multiplication of the RHS of equations (1) and (3) by 6 to give: a,@“) m= 210

(1 -Fo(l

0

- rpcE&;

(13)

and

Q& = (1 -ptk.

(14)

Analgous to our definition of the quenching parameter Q,L in equation (2), we now define a sensitization parameter R,A, as: R_,

_

exp*’ -

Iht%)%%so) zk*

(So 1 Gw”

1.

(15)

Energy transfer

Values of R& are obtained from the entries in columns 5 and 6 of Table 1 and are displayed in Table 2. Substituting equation (10) and (12) into equation (15) gives:

R&l = (1 --Pt)E

+

PtP

(Pca/%
(1’4

We first consider equation (16) in the limiting case that pt = 0. The implication here is that benzene does not at all scavenge the geminate pair (either by electron attachment or by positive charge transfer) and, therefore, that the entire difference between the radiation chemical and photochemical process resides exclusively in 6 (i.e. in the effect of benzene to modify the recombination probability of C+ + e- to C* without capture of charge). With pt = 0, equation (14) requires that e = Q& which, from Table 2, is always less than unity and increasingly so as c increases. However from equation (16) it follows that with p t = 0, E must also equal R& and this, as Table 2 shows, is always greater than unity and increasingly so with increase in c. So, clearly, pt cannot equal zero. To determine, then, how small pt can be, we substitute equation (14) into equation (16), to give: Ptp = (~ce(K:~ -

Q&>&UW.

(17)

The RHS of equation (17) is simply evaluated using qcs = 1 - Z:$S,)/Z:E(S,) from Table 1, R& - Q& from Table 2, Bc N 0.30 [i.e. the internal conversion efficiency of cyclohexane to C* from the state generated at its liquid phase ionization potential (Schwarz et al., 1981)] and (&) = 0.26 (Johnston and Lipsky, 1990). Thus since p, from its definition, cannot be greater than unity, the RHS of equation (17) places a lower bound on pt. Since p will increase with c, the best estimate of this lower bound will be observed at the highest c studied of 0.112 M. This give pt 2 0.049. From Noolandi’s Tables and using either the distribution function of equation (5) or that of equation (9), it is then simple to compute that the lower bound on the scavenging rate constant must be -7 x 10’ M-l s-‘. Also, with pt > 0.049, equation (14) implies that c cannot be less than 0.69 at 0.112 M benzene. Equation (17) can also be utilized to obtain a lower bound on p. Substituting for pt from equation (14) into equation (17) gives:

Clearly when 6 = 1, the RHS of equation provides a lower bound on ZL.Thus P 2 @c<&)

57

a strong trend for increase in K and, therefore, via equation (19) in the probability p. From the increase in p with increase in benzene concentration we can conclude that there must be some contribution to B* formation from electron attachment to B. The argument for this can be developed as follows. Were there no electron attachment, then the only ionic channel that could generate B* would be B+ + e-. In this case, p must refer exclusively to the probability that the B+ + eannihilation gives B* and clearly there would be no reason for this to exhibit any dependence on benzene concentration. On other other hand, if we assume that B+ can only form if B- is tlrst generated (thereby providing more time for C+ + B to evolve into C + B+), it would then follow that p could be expanded as a sum of two terms representing the development of B* formation from the recombination of both C+ + B- and B+ + B- and with a concentration dependent branching ratio. Defining P to be the probability that C+ + B- evolves into B+ + B- during the process of the geminate ion-pair collapse, and p, and ZL,to be, respectively, the intrinsic probabilities that B* is produced when C+ + Band B+ + B- annihilate, it follows that p can be simply expressed as P, (1 - P) + p2 P and, therefore, that equation (19) can be recast as: PI +

(142 -

PI )P

2

WC<

BB >.

(21)

The increase in K with increase in c can now be accommodated by a concentration dependence of P. Since P is expected to increase with benzene concentration, it must follow that p2 is greater than p, (i.e. that B+ + B-+B* + B is more efficient than C+ + B-+B* + C). Also, from our highest value of K (1.81), it is clear that ~4~cannot be less than 0.14. To proceed one step further with this argument, suppose we assume that 6 = 1 (i.e. that the entire action of benzene on the geminate ion-pair is due to its scavenging action to attach the electron or to charge transfer with C’). Equation (21) therefore becomes an equality and, accordingly, if we knew the concentration dependence of P we could extract estimates of p, and ZL,.Although Tachiya (1987) has recently provided procedures for evaluation of P in terms of various rate constant parameters, our data on K are insufficient to warrant so elaborate a procedure at this time. Accordingly, we consider two simple, one parameter, limiting forms of P, i.e.

(18) (19)

where

Values of K are displayed in Table 2. Although the scatter is large, it is clear that as c increases, there is

which assumes transient terms are ignorable in the B + C++B+ + C reaction and p-

1 -e-c’;

(23)

which, at the opposite extreme, assumes that diffusive terms are ignorable. Substituting equation (22) or (23) into equation (21) provides an equation for K in three parameters

58

DAVID B. JOHNSTONand

pl, p, and C (or I’) and, considering the scatter in K, it is not surprising that we 6nd both forms for P can be made to fit the dependence of K on c. In both cases and P, -0.05 and P,- 0.2 with [ N 12M-l l’ N 10 M-i. Although it is not particularly pertinent to our subsequent discussion, it is interesting to note here that whereas [’ w 10 M-’ is unreasonably large for a static process (implying a reaction radius of N 16 A), the value t; N 12 M-l is not unreasonble for a diffusion controlled reaction that must occur within the few nsec time interval of the geminate ion-pair collapse. In attempting to understand the origin of these low values of ,u, and pr, we have considered the possibility, as was previously discussed in connection with C* fluorescence, that the optical values that we use for rpc, are overestimating the transient effects that exist in the high-energy irradiated solutions. To estimate a correction for this effect we have performed a similar calculation to that used in our discussion of C* fluorescence but find that it provides essentially, no change in the magnitudes of p, and p, . Of course, the low values for p are predicted on the assumption that E = 1. Thus, for example, at 0.112 M, were E = 0.69, then p would be unity. However, it is significant to note here, that similar low efficiencies for the recombination of ions to generate fluorescing states have been earlier reported. Thus, in the determination of the absolute yield of excited states of p-terphenyl and diphenyloxazole in irradiated cyclohexane, it appeared necessary (although here too the argument was not without its approximations) to take a rather low value of -0.25 for the intrinsic probability that ionic recombinations generated excited solute states (Choi et al., 1984a). Also, in a more recent study of the production of fluorescence from hexafluorobenzene in irradiated nonpolar solvents, it was concluded that the intrinsic probabilities for the recombination of CsF; with the solvent positive ion to yield excited hexafluorobenzene were in the range of 0.2-0.3 for the solvents cyclopentane, isooctane and neohexane (Tweeten et al., 1989). Still again, but in a more complex three component system involving both benzene and tetramethylphenylenediamine as solutes in cyclohexane (Yoshida and Lipsky, 1988), there were reported indications of inefficiencies in ionic recombinations leading to excited tetramethylphenylenediamine. The variety of systems that appear to exhibit low probabilities for ionic recombinations suggests that there may exist some rather general explanation. Spin relaxation would be a possibility were it not that the values of p are so low as to require essentially complete spin equilibration. From magnetic field effects on recombination fluorescence it seems fairly certain that on the time scale of geminate recombination (ca ns) such equilibration would be impossible for the majority of recombining pairs (Brocklehurst, 1985). Also a loss in spin coherence due to the presence of multiple ion-pairs would explain a p < 1

SANFORD LIPSKY

but to explain a p N 0.2 would require, according to most evidence, too large a population of such multiple pairs (Jonah and Sauer, 1982; Le Motais and Jonah, 1989). Instability of the solvent positive ion, C+, to decomposition to an ion, X+, of lower ionization potential might also explain a p < 1 if X+ +B-+X+B* and X+ +B+X+B+ were of much lower efficiency than the corresponding reactions with C+. A number of recent investigations have indeed suggested such instabilities of C+ (Jonah and Sauer, 1989; Le Motais and Jonah, 1989; Sauer et al., 1991; Trifimac et al., 1986; Werst et al., 1990). To pursue this possibility a bit further, suppose we assume the reactions with X+ produce no B* nor B+. In the absence of scavengers we letfo be the fraction of C+ positive ions that remain intact on the time scale of geminate e- + C+ recombination and, in the presence of scavengers, let fc and fe be the fractions of C+ that remain intact on the time scales of C+ + B- recombination and C+ + B charge exchange. Considering the various time scales involved, it is clear that f. > fB > fc. To get estimates on f we redevelop equations (1) and (11). Clearly equation (1) will not be affected by C+ instability (since f.will cancel in the ratios) but equation (12) will be modified in that p must now be replaced by either p&/fcor k&/f0 (depending on whether the ionic channel to B* is exclusively B+ + e- or B+ + B- and C+ + B-) and h is the probability that the ionic recombinations generate B*. In either case we see that were h N 1, then fe/fc or fc/fo would be N 0.2. However, there appears to be no evidence for the existence of such a large C+ instabilities in the presence of scavengers. Specific chemical channels for the annihilation process such as proton or hydride ion transfer (Sauer et al., 1991) are also possible ways for explaining a p < 1 and perhaps a combination of this and all of the aforementioned effects (including an E # 1) contribute together to generate the “apparent” p of -0.2-but the picture here certainly remains nebulous and a more careful investigation of these ionic recombination efficiencies is clearly indicated. Before leaving this topic, however, it is interesting to note that the ratio that we obtain for p, /pr w 0.25 is rather close to the value 0.26 that has been obtained for the internal conversion efficiency, (Be), (i.e. for the transition from the states of benzene populated by the C* + B energy transfer process to the fluorescing state, B*). If this agreement is not fortuitous, it would suggest that B+ + B- annihilation generates B* directly (albeit with a 0.2 efficiency) whereas the C+ + B- annihilation proceeds through the intermediate state of C* + B. Finally, we return to the original question of what fraction of benzene fluorescence in irradiated cyclohexane derives from recombining molecular ions and what fraction from C* + B energy transfer. From equation (ll), it is clear that the fraction, F*, of the

Energy transfer total benzene fluorescence that is due to recombining molecular ions can be written as: Crpt

F* = wt

+u

-PtvcrPce;

using equations (14), (17) and (20), equation rearranges to a particularly simple form; i.e.

59

Acknowledgements-This

work was supported in part by the U.S. Department of Energy, Division of Chemical

Science, ORice of Basic Energy Science.

(24) (24)

Fi=l-Gh; which, of course, could have been derived directly and more generally from the definitions of R and Q in terms of the /3- and 160 nm optical intensity ratios. The derived values of F* are displayed in Table 2 and indicate clearly that only at benzene concentrations much less than 0.005 M can ionic channels be ignomed and only at benzene concentrations much higher than 0.1 M will the neutral channel cease to be important. At any intermediate concentration, both ionic and neutral channels play important roles in the development of benzene fluorescence. CONCLUSION

Three possible mechanisms are considered for the interaction of benzene with a recombining geminate C+ + e- ion-pair in irradiated cyclohexane, namely (i) attachment of e- to form B-, (ii) electron transfer to C+ to form B+ + C and (iii) formation of a temporary negative ion that decays to a thermal electron +B. From an analysis of both the quenching of cyclohexane fluorescence by benzene and the concomitant sensitization of the benzene fluorescence by cyclohexane it is demonstrated that neither mechanism (ii) nor mechanism (iii) can be exclusively operating (i.e. there must be some nontrivial contribution from electron attachment). With the assumption that of the ionic routes to B*, only B- + C+ or B- + B+ are important (i.e. B+ + e- is ignorable), it is concluded that the rate constant for electron attachment to benzene in cyclohexane cannot be less than ca 7 x lo9 M-' s-’ and may be as large as 3 x 10” M-l s-l if mechanism (iii) is ignorable. Also it is demonstrated that the annihilations of B+ + Band of C+ + B- to give B* are required to have efficiencies much less than unity if mechanism (iii) is ignorable. The fraction of the total fluorescence from benzene that is attributable to electronic energy transfer from excited cyclohexane (formed by unperturbed C+ + erecombinations) is computed quite generally from the data to vary from 0.83 to 0.47 over the benzene concentration range from 0.0056 to 0.112 M. The remainder of this fluorescence is due to recombining molecular ions which clearly make a nontrivial contribution until concentrations much less than 0.0056 M are achieved. Accordingly, attempts to utilize benzene fluorescence to deduce the G-value for excited cyclohexane by totally ignoring the ionic contributions, may be seriously in error.

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