Study of the reactions of geminate ions in irradiated scintillator

hydrocarbon solutions using recombination fluorescence and stochastic simulations. Myran C. Sauer Jr., Charles D. Jonah, and Conrad A. Naleway. J...
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J . Phys. Chem. 1991, 95, 730-740

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bances of neat ethanol, cyclohexane, and n-hexane in the 200-nm region are considerably smaller than the absorbance of the same solvents containing scintillator. Therefore, the majority of the light is absorbed by the scintillator which means that G(Cer) should be approximately the same for the three solvents. The experimental values of G(Cer) are in basic agreement with the G value expected for absorption of Cerenkov light;'2-i4e.g., absorption of all of the eerenkov light generated in cyclohexane in the wavelength interval 200-320 nm results in a G value of 0.022. Geminate ion recombination involving positive or negative scintillator ions could also contribute to G(Cer), but this appears to be a relatively unimportant process. Measurements of the kinetics of the scintillator fluorescence in ethanol solutions using streak camera techniques show that the excited state appears to be formed entirely during the pulse, Le., the decay after the pulse follows the exponential decay expected on the basis of the known scintillator lifetime in ethanol.2*i5 This means that any significant contribution from geminate recombination would have to come from ion scavenging and recombination occurring during the pulse (ca. 30 ps or less). (It should be noted, however, that some geminate ion pairs must live for hundreds of nanoseconds because recombinations of such pairs have been observed in FDMR (fluorescence detected magnetic resonance) experiments.16 The experimental vairation of G(Cer) with solute at 0.001 M is not expected; it segms too large to be ascribed to variations in the absorption of Cerenkov light by the different solutes. The column labeled "other" in Table I1 represents the sum of contributions to solute excited singlet state formation from geminate recombination reactions and from energy transfer from solvent excited state@). These values will be discussed thoroughly in relation to experimental and theoretical results presented in the following paper.2 For a particular combination of solvent, solute, and concentration in Table I1 one can define G,, as the sum of the values labeled "Cer" and "Other". These can be compared with the yield determined in non-time-resolved experiments. Choi et aL9 have recently reported such results for (IS) Sauer, M. C.; Romero, C.; Schmidt, K. H. Radiat. Phys. Chem. 1987, 29, 261.

(16) Percy, L.T.; Wetst, D. W.; Trifunac, A. D. Radiat. Phys. Chem.

1988, 32, 209.

cyclohexane solutions of three scintillators and have summarized previously reported values. The values of GI& from Table I1 are expected to be smaller because any excited state produced after 5 ns, including that from free-ion recombination, is not included in G,a. For biphenyl in cyclohexane, our results are 0.32 and 0.12 for 0.01 and 0.001 M, respectively. Choi et al. obtained 0.42 and 0.1 1. For 0.001 M PPO in cyclohexane, we obtain 0.083, compared with 0.18 obtained by Choi et al. Thus, there is qualitative agreement for biphenyl. The reason for the disagreement for PPO is not known. Our previously reported values8 at 1 mM solute are more than twice as large as those we report here. The experimental technique used to obtain the present values was improved. In the previous work, correction was not made for the variation of sensitivity with wavelength of the spectrfluorimeter. An expected, lower sensitivity in the 300-nm region (where benzene fluoresces) would lead to an overestimate of photon yields at longer wavelengths where the other scintillators emit. Some additional features of the results in Table I1 should be mentioned here. At 0.001 M scintillator, the values in cyclohexane are about the same, as seems reasonable except possibly for DEA, for which a lower value might be expected if electron capture by DEA is inefficient. In the case of n-hexane, there is more variation with solute in G(other) than expected; for example, the factor of 2 between BP and PPO is not understood. At higher concentrations, there are fewer results because DPA is not sufficiently soluble, and the PPO experiments suffer from excimer formation which makes the determination of G values too uncertain. The results of 0.01 and 0.05 M show some variation with solute. These variations may be caused by inefficient electron capture of DEA, and inefficient positive charge capture of DFBP. For a complete understanding of the G values, information is needed on the rate constants for the electron reaction with DEA and of radical cations with DFBP. Also, the amount of the excited scintillator formed via energy transfer from solvent excited states must be included in the analysis of these G values; this is done in the following papers2 We will show there also that the G values presented here indicate a general inefficiency in the production of excited solute states, i.e., the ratio of the number of excited states formed to the number of ion pairs in which one or both of the charges react with a solute molecule is much less than unity, and possible reasons for this will be discussed.

Study of the Reactions of Geminate Ions in Irradiated Scintillator, Hydrocarbon Solutions Using Recombination Fluorescence and Stochastic Simulations Myran C. Sauer, Jr.,* Charles D. Jonah, and Conrad A. Nalewayt Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: April 17, 1990; In Final Form: August I O , 1990)

The fluorescence from electron beam pulse irradiated solutions of scintillatorsin n-hexane and cyclohexane has been measured. The experimental fluorescence vs time is compared to calculations utilizing a stochastic Monte Carlo model, in which three different distribution functions were tested to describe the initial electron-solvent" separation distance. This comparison indicates that the recombination fluorescence is markedly affected by fast reactions of the solvent radical cations, most likely proton transfer to the solvent, which prohibit eventual formation of the fluorescent state of the scintillator via ion recombination reactions. Results bearing on the contribution of energy transfer from the solvent-excited state to the scintillator are also presented. Measured G values of the fluorescent state of the scintillator are considerably lower than those calculated from the model, and possible reasons for this are discussed.

Introduction It is we&known that solutions of aromatic molecules in alkane liquids fluorwhen irradiated with ionizing radiation, and such solutions have been used for decades in scintillation counters, t b n t a d d m : DepafimentofChahtry, ~

21 I E. Chicago Ave., Chicago

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However, a detailed understanding of the processes involved does not exist. In particular, a quantitative description of the timedependent ionic reactions is lacking. A number Of efforts have been made in recent years to make time-resolved measurements of the fluorescence from such solutions, induced by a pulse of electrons, i ~ and to ~ relate such results to the dynamics Of the Scavenging and recombination of geminate ion pairs.'-" In principle,

0022-3654191 12095-0730%02.50/0 0 1991 American Chemical Society

Reactions of Geminate Ions such measurements allow derivation of the distribution of e-solvent'+ separation distances. Analysis of such data would be reasonably simple if we were dealing with isolated primary e-,solvent* ion pairs which were all identical, and if the fluorescence resulted only from scavenging of these ions by the solute and subsequent recombinations involving solute ions. However, several interfering processes occur which obfuscate the analysis of the time dependence of the fluorescence. For example, the fluorescent state of the solute can be produced both by the absorption of Cerenkov radiation generated by the liquids-10 and by energy transfer from the excited state of the solvent. A beginning has been made in modeling such processes." A further complication occurs because the creation of the fluorescent state may also be affected by the fact that the ion pairs are not all isolated.'* Due to the nature of the energy-deposition process, they sometimes occur in close proximity to other pairs. This has not been included in previous analyses of recombination fluorescence, nor is it treated explicitly here. In the present work we have used a new streak-camera system, which yields kinetically reliable results, to investigate solutions of several scintillators in alkane liquids (in most detail for cyclohexane and n-hexane). Improvements in our techniques of analysis and the use of theoretical simulations to compare with experimental results, along with experimental determinations of the G values of the solute fluorescent states, have resulted in new insights concerning the processes leading to this fluorescence. In particular, we find that the production of the solute fluorescent state is markedly affected, especially in cyclohexane, by transformations of the solvent radical cations into species which cannot lead to solute fluorescence. Furthermore, we are now able to interpret the process of energy transfer from the solvent excited state in a more quantitative manner. Despite the complexity of the processes noted above, comparison of experimental and calculated results will be seen to yield useful information on the distribution of e--RH'+ separation distances.

Experimental Section Electron Pulse. The pulse radiolysis results reported here are the first obtained by using the 5-ps pulse from the recently modified Argonne National Laboratory Chemistry Division LBand Linac.lsa Pulses of 5 ps fwhm and 6 nC of charge can be (1) Beck, G.; Thomas, J. K. J . Phys. Chem. 1972, 76, 3856. (2) Tagawa, S.; Katsumura, Y.; Tabata, Y. Chem. Phys. Le??.1979,64,

258. (3) Jonah, C. D.; Sauer, M. C., Jr.; Cooper, R.; Trifunac, A. D. Chem. Phys. Let?. 1979. 63, 535. (4) Tagawa, S.; Katsumura. Y.; Tabata, Y. Rudiur. Phys. Chem. 1980, 15, 287. (5) Sauer, M. C., Jr.; Jonah, C. D. J . Phys. Chem. 1980,84, 2539. (6) Katsumura, Y.; Tagawa, S.;Tabata, Y. J . Phys. Chem. 1980.84,833. (7) Tagawa, S.; Katsumura, S.;Tabata, Y. Radiut. Phys. Chem. 1982,19, 125.

(8) Katsumura, Y.; Tagawa, S.; Tabata, Y. Radial. Phys. Chem. 1982,

19. 243.

(9) Tabata, Y.; Katsumura, Y.; Kobayashi, H. Rudiu?.Phys. Chem. 1983, 21. 123. (IO) Sauer, M. C., Jr.; Romero, C.; Schmidt, K. H. Rudiu?. Phys. Chem. 1987,29, 261. (11) Yoshida, Y.; Tagawa, S.; Washio, M.; Kobayashi, H.; Tabata, Y. Radiat. Phys. Chem. 1989, 34, 493. (12) Information on the distribution of numbers of ion pairs in different size groups has km summarized recently in ref 13 and thmrctical calculations having to do with the effects of multiple-ion-pairgroups on the recombination kinetics are given in refs 13-17. (1 3) Hummel. A. In Ktnrtics o/Nonhomogmcour PmcesseG Freeman, G. R., Ed.; Wiley-Interscience: New York, 1987; Chapter 5, pp 215-275. (14) Bartczak, W. M.; Hummel. A. J . Radiounal. N u l . Chem.1986,101, 299. (15) Bartczak, W. M.;Hummel, A. J . Chem. Phys. 1987,87, 5222. (16) Hummel, A.; Bartczak, W. M.Rudia?. Phys. Chrm. 1988,32, 137. (17) Tachiya, M.; Hummel, A. Chem. Phys. h i t . 1989, 154, 497. (18) Mavrogencs, G.; Norem, J.; Simpson, J. Proceedings of the Stanford Linear Accelerator Conference, June 2-6.1988. Stanford Linear Accelerator Center Report, Stanford, CA; pp 429-430. (1 9) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: New York. 1970; p 88.

The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 731

n Linac

' 1

4 0.44 m e

2

.

5m

+

0.1 m

Figure 1. Optical system (not to scale). The sample cells are indicated by 1 and 2. MI is a front-surface AI mirror, as are M, and X, which are uscd in an alternate optical system (seetext). LI, L2,and L, are Supmil lenses of focal lengths 33,64, and 10 cm (at ca. 410 nm), and F is an optical filter. The distance from the cells to MI is 3.5 cm.

obtained routinely. The method by which a 30-nC, 30-ps fwhm pulse of 22-MeV electrons is compressed will not be discussed here. The results reported in this work were obtained on the longest time scale (nominally 5 ns) of the streak camera, so the streak camera, rather than the width of the electron pulse, limited the time resolution. Streak Camera The Hammamatsu streak-camera system used consisted of a C1587 temporal disperser, M1592 high speed streak unit, ClOOO SIT camera head (Type 18), C2280 temporal analyzer, and C2712 floppy and hard disk drive. The best time resolution of this system is 2 ps, using the shortest time-range setting of 0.15 ns. The time resolution is approximately inversely proportional to the time-range setting; therefore, for the 5-ns range used for the results reported here, the time resolution is approximately 60 ps. The signal recorded for the emission from a sample irradiated with a single electron pulse was usually quite noisy, and 100 pulses were typically averaged. This can easily be done, but any "jitter" in the time between the triggering of the streak camera and the occurrence of the electron pulse effectively degrades the time resolution. This was avoided by using part of the signal observed by the streak camera to determine the position of the pulse. (This will be explained further in the section on optics.) The computer of the temporal analyzer was programmed to determine the pulse position and shift the data accordingly as the data collection proceeded. The data from 100 pulses can be collected, shifted, and summed in less than 5 min. Optics. In the measurement of the electron-beam pulse widthm we found that the optical system shown in Figure 1 caused a minimal degradation of the time resolution. The electron beam, which is 2-3 cm wide and about 0.5 cm high, passes through the two sample cells labeled 1 and 2. The cells are rectangular (0.5 X 1 cm) in cross section, and made of Suprasil. One cell contains the liquid sample, and the other contains Xe at 0.5-1 atm. The light from both cells is focused on the slits (horizontal) of the streak camera. For optical alignment a mercury "penlamp" is placed at the position of the sample cells. The light from the Xe cell is used to determine the temporal position of the electron pulse for purposes of signal averaging. Wavelength discrimination is obtained by the optical filter, F. To discriminate against Cerenkov light from the irradiated liquid, which is emitted preferentially in the direction of the electron beam, the optics were modified. A thin mirror was placed at the position shown by the dashed line, so that the light was collected 180° from the direction of the electron beam. The lenses and the streak camera were, of course, also moved an appropriate distance. Also, because the Cerenkov light from Xe is emitted in a narrow cone in the direction of the electron beam, a mirror was placed directly behind the Xe cell parallel to the cell face, ~~~~~

(20) Cox, G. L.; Ficht, D. W.; Jonah, C. D.; Mavrogenes. 0. S.; Sauer, M.C., Jr. Proceedings of the 1989 IEEE Particle Accelerator Conference, Chicago, Mar. 20-23, 1989; pp 912-914.

132 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991

lZ01

Sauer et al. TABLE I: Fluorescence Lifetimes Used in Correction for Decry lifetime,' ns scintillator ethanol cvclohexane n-hexane biphenyl 16.0 16.0 (I6.Ob) 16.0 9,lO-diphenyl- 8.8 8.1 (9.4b) 8.6 anthracene anthracene 4.8 4.7 (4.99 4.8 2,5-diphenyl1.56 (1.60: 1 .64c) 1.43 (1 .4b) 1.52 oxazole p-terphenyl 1.18 1.07 (0.95: l.OSc) 1.15

z .- 1 0 0 80

'Values in parentheses are from the literature. bReference 22. CReference23. 0

1

2

3

4

5

Time (ns)

Figure 2. Raw_data and cumulative IPPO for 0.001 M PPO in cyclohexane. The Cerenkov signal from the solvent was subtracted before converting the raw data to the cumulative signal. 6s indicated by the arrow labeled X in Figure 1, to collect enough Cerenkov light from Xe. This arrangement degraded the time resolution somewhat, but it was particularly useful in the case of biphenyl which has a relatively long enjssion lifetime and therefore a weak signal. The reduction of the Cerenkov signal allowed the signal during the first few hundred picoseconds" to be more accurately measured; Le., the subtraction of the Cerenkov signal due to the neat solvent from the signal from the sample led to less uncertainty. Determination of Fluorescence Lifetimes. Fluorescence lifetimes of the scintillator solutions used were measured with a Photon Technology International, Inc. Model LS-1 single photon counting apparatus. The samples were purged of air by bubbling with nitrogen or argon. Fluorescence lifetimes were also obtained for ethanol solutions by pulse radiolysis using the streak-camera system (see Results and Discussion section). Calibration of the Streak Camera. The sensitivity of the streak camera in general varies with position on the yscreen*, i.e., where the light hits the photocathode. We have previously shown1° that this sensitivity can be calibrated by exciting with the electron beam an SF,-saturated solution of a scintillator, e.g., 0.001 M 9,lOdiphenylanthracene (DPA). The SF, captures electrons and prevents falrmation of the fluorescent state of the scintillator after the pulse. Independent measurement of the scintillator lifetime (8.5 ns for DPA in cyclohexane) in the same solution by single photon counting allows the streak sensitivity to be calibrated by setting the position of the electron pulse offscale (a few nanoseconds before the streak is triggered) and comparing the observed decay with the expected exponential decay. This calibration was performed at least once each day. Sample Preparation. The alkane solvents were purified by passage through columns of silica gel (Aldrich, grade 12, 28-200 mesh) which had been heated in an oven at 250 OC overnight. The solutions were degassed by bubbling with argon or helium immediately before radiolysis.

Results and Discussion Method of Analysis of the Data from the Streak Camera. Typical emission intensity vs time data from the streak camera are shown in Figure 2, along with the cumulative formation of the scintillator singlet state 'A as a function of time. The latter was calculated from the experimental data using the known lifetime of the scintillator. Display of the data in this way facilitates comparisons among different scintillators and allows one to visualize directly the rate at which excited states are being created as a function of time. The latter is the quantity of interest for understanding the dynamics of reactions and recombinations of the geminate ions. To display the experimental data in this manner, accurate values of the fluorescence decay times are needed. These were determined by optical excitation using a single photon counting apparatus and by streak camera measurements using radiolytic excitation of ethanol solutions. The values determined by single photon counting agreed within about 5% with

values in the literature. The values determined by using the streak camera should be the same as those determined by single photon counting if there is no significant amount of the fluorescent state formed after the pulse in ethanol solutions. Judging from the excellent fit to first-order decay kinetics observed, this seems to be the case.I0 The values from the streak are the same as those obtained from single photon counting within about 5%. The values used in the correction for decay are given in Table I, along with literature values. The values are based on the streak determinations and single photon counting results. The results show the differences in lifetime for the different solvents predicted by the dependence of the radiative lifetime on the square of the refractive index of the ~olvent.'~ The values given are for ca. 0.001 M solutions. There was no effect of concentration on the lifetime of biphenyl over the range of concentration used (0.001-0.05 M). For 2,5-diphenyloxazole (PPO), the decay kinetics were complicated at higher concentration (0.01-0.05 M) due to excimer formation; because of this complication, pulse radiolysis data which we obtained on PPO (which can be dissolved to about 0.1 M) at greater than 0.001 M were not tested. Rather, biphenyl was used to obtain data in 0.01-0.05 M concentration range. The other scintillators were studied in the pulse radiolysis experiments only at 0.001 M. As described previously,*' corrections were made for effects of density and refractive index on the relative amount of light obtained for the same radiation dose in the different solvents used. Mechanism for Solute Excited State Formation. There is common agreement'-" that the aromatic solute (A) singlet excited state (IA) formation occurs by the reactions 1-8, where R H represents the hydrocarbon solvent, and RH'+ and e- are formed by the electron pulse.

A'-

+ - + + + - + + - +

'RH

+ A-

eRH'+

A

eRH"

A

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A"

A'-

A'+

(2) RH

(3)

'A

(4)

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RH

A'+

'A

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-

IA

(8)

Some IRH may also be formed by direct excitation by the electron beam, but this process appears to be relatively unimp ~ r t a n t . ~Also, ~ , ~'A~ may be formed by direct excitation by the (21) Jonah, C. D.; Sauer, M. C., Jr.; Cooper,R.J . Phys. Chem., preceding paper in this issue. (22) Berlman, I. G. Handbook of Fluorescence Spectra of Aromaric Molecules, 2nd ed.; Academic Press: New York, 1971. (23) van den Zegel, M.;Boens, N.; Daems, D.; De Schryver, F. C. Chem. Phys. 1986, 101, 311. (24) Choi, H. T.; Wu,K. C.; Lipsky, S. Radia?.Phys. Chem. 1983, 21, 95. (25) Sauer, M. C., Jr.; Jonah, C. D.; LeMotais, B.C.; Chernovitz, A. C. J . Phyy. Chem. 1988, 92, 4099.

The Journal of Physicul Chemistry, Vol. 95, No. 2, 1991 733

Reactions of Geminate Ions

0.04-

c

o.oll/

- - oo . o 0

1

2

Time

3

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Figure 3. Cumulative 'A vs time for several solutes at 0.001 M in cyclohexane. The solutes are anthracene, 2,5-diphenyloxazole (PPO), pterphenyl (PT), 9.10-diphenylanthracene (DPA), and biphenyl (BP). The vertical scales for the different solutes have been adjusted to normalize the curves.

Allen, A. 0. Ylelds o Free Ions Formed in Liquids by Radiation; US.Government Printing Ofke: Washington, DC,1976; NSRDS-NBS 57.

2

3

4

5

Time (ns)

-..

Figure 4. Simulated results for 0.001 M solute in n-hexane: - and are duplicate runs; ---, the n-C6H14'+ion mobility is decreased to 0.45 of the value used in the other two simulations, and the ordinate values are multiplied by 1.20. 0.025

electron beam, but this process is small compared to (8), and because it is indistinguishable from it under the conditions of the experiments reported here, these two processes will be treated together. The amount of process 8 is estimated from experiments using ethanol solutions of A?' where the emission vs time profile over the first 5 ns can be fit for all scintillators (see Figure 3) assuming th_e formation of 'A only during the pulse by the absorption of Cerenkov light, followed by exponential decay with the fluorescence lifetime of the scintillator. The Simulation Method. To determine whether the experimentally observed cumulative IA vs time data agree with the mechanism given above, comparison with a model is needed. We have used a stochastic Monte Carlo model to describe the nonhomogeneous kinetics of the reactions of the geminate ions given by reactions 1-6. Details of this model are given in the Appendix. Briefly, the method involves using the known mobilities of electrons and positive ions in the hydrocarbon solvents to calculate the diffusional movements of the charged species, taking into account the Coulombic forces as well. A single ion pair is considered and the distance between the positive ion and the electron is sampled from either an exponential, or an ? exponential, or an ? Gaussian distance distribution whose parameters were selected to agree with the experimental free-ion yield (see eqs A-I-A-111). The solute molecules, A, are placed randomly at t = 0 in a volume containing the ion pair. Reactions 1-6 take place at t = 0 or later when the reactants are within the reaction radius used. This simulation method is convenient because new reaction mechanisms can be added to the system without major effort. For example, the effect of a transformation of RH'+ (see below, reaction 9) was easily included in the model, as well as energy transfer from 'RH to A (including effects of static scavenging and time-dependent rate constants). Figure 4 shows typical simulated results. To give the magnitude of the simulation error or noise for a typical computation, the cumulative yield of 'A is shown for two duplicate runs on 0.001 M solute in n-hexane (the solid curve and short-dashed curve). Also shown (long-dashed curve) is the result of decreasing the mobility of the n-C6H14'+ion to 0.45 of the value used for the other two curves. After multiplying the ordinate values by 1.20, the shape of the curve is seen to be indistinguishable from the other two curves within "experimental" error. Therefore, error in the mobilities of this magnitude will affect the calculated yields but will not significantly affect the shapes of the curves. Evidence for Chemical Transformation of the Solvent Radical Cation. Cyclohexane. The formation of ' A was simulated as indicated above, assuming a single-ion-pair model. (The possible effects of multiple ion pair "spurs" will be discussed in a later section.) For 0.001 M solutions of all scintillators (A) in cyclo(26)

1

(ns)

1 ....

0.000 0

simulation, x0.63 simulation. with translormation 01 S'

I

I

I

I

I

1

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Time (ns)

Figure 5. Comparison of simulated and experimental results for 0.001 M PPO and PT in cyclohexane. The simulated curves are for the exponential distribution with rlVs= 52 A. In this-and subsequent figures, the excitation of the solute by absorption of Cerenkov light has been subtracted unless otherwise shown, the scale of the ordinate is for the simulated curve, and the experimental results are normalized to the simulated curve at 4.5-5 ns.

hexane, the experimental results for the cumulative formation of 'A are in clear disagreement with the simulation. The experimental results are shown in Figure 3, and comparison with a simulated result is shown in Figure 5 . The experimental signal-to-noise ratio becomes worse for longer scintillator lifetime and smaller scintillator fluorescence quantum yield. However, the shape of the curve is clearly independent of the scintillator molecule, as is expected if the rates of reactions 1-8 are approximately the same for the different scintillator molecules used. The disagreement between experiment and simulations lie in the fact that experimentally there is essentially no formation of IA after about 2 ns. The formation of 'A using any of the three distributions given in the Appendix continues after 2 ns, as can be seen in Figure 5 where simulated data obtained by using an exponential distribution and the experimental data for PPO and p-terphenyl from Figure 3 are displayed. The shape of the simulated curve can be made to agree with the experimental result if reaction 9 is added to the mechanism, with the stipulation that

-

RH'+ products kg 13 x IO9 s-' (9) the products are not able to react in any way to produce IA. Reaction 9 can be assigned to the reaction of RH'+ with RH, resulting in C6H13+and the C6HII' radical (by proton transfer or H atom abstraction). Evidence supporting the general occurrence of such a reaction in hydrocarbon liquids has been presented by Trifunac and c o - w ~ r k e r s . ~ ~ - ~ ~ (27) Trifunac, A. D.; Werst, D. W. In Ionic Molecular Sysrems; Lund, A., Shiotani, M., Eds.; Topics in Molecular Organization and Engineering; J. Maruani, Ed.; Kluwer Academic: Dordrecht, The Netherlands, in press.

Sauer et al.

734 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 0.0201

0,000

_............I.

I

0

E2.I..................................................... ....... I I

I

I

I

1

2

3

4

A concentration of about 0.001 M scintillator is ideal for seeing the effect of such a reaction because the simulations show that a t this concentration a large fraction of the IA is expected to be produced by reaction 5. This is shown in Figure 6 where the components, calculated by using the exponential distribution (see eq A-I), due to reactions 4-7 are shown. The long-dashed curve shows the effect of introducing reaction 9 on the production of 'A from reaction 5. The component due to energy transfer from excited cyclohexane, reaction 7, is calculated by using the known G value of the fluorescent state of cyclohexane,Mthe known effect of electron scavengers on the production of this excited state,25 its known fluorescence lifetime,25-3'~32 and the known parameters*' for its reactivity with solutes. The reactivity with solutes includes the effects of time-dependent rate constant. The sums of the appropriate components from Figure 6 were used to obtain the two simulated curves shown in Figure 5. Note that at 0.001 M A there is no significant dependence of the shape of the simulated curve on distribution. All of the simulated curves shown at this concentration are for the exponential distribution. The simulations described above for cyclohexane solutions were done assuming that the cyclohexane radical cation (RH") is not the high-mobility cation (discussed below) which has been observed in both pulse radiolysis and pulse photoionization experiments on time scales considerably longer than that considered here. Other calculations, similar to those depicted in Figure 5, were made for the high-mobility cation and showed a similar variance from the experimental data. The question of the identity of the highmobility cation will be discussed in a later section. Other Solvents. Similar comparisons of experiment with simulation were done using n-pentane, n-hexane, isooctane, n-decane, cis-decalin, and trans-decalin. The rates of transformation (k,) are at least an order of magnitude slower than in cyclohexane; because of this, the estimation of k9 is not as accurate. In the latter three solvents, a large fraction of the 'A results from energy transfer (reaction 7) and thus the sensitivity of the signal to the ion-recombination reaction is lowered. (We plan to report on work using these solvents in a future publication.) For n-hexane the experimentally observed 'A formation is clearly slower than predicted by the simulation when no energy transfer from 'RH is introduced into the simulation (Figure 7). Introduction of a value of k9 = 3 X IO8 s-I allows the shapes of the experimental and simulated curves to agree. However, energy transfer from IRH (reaction 7) is likely to be significant despite the fact that the lifetime of 'RHfor n-hexane is approximately 0.3 ns. This value can be obtained from direct measurement" and from an (28) Trifunac, A. D.; Werst, D. W.; Percy, L. T. Radial. Phys. Chem. 1989, 34, 541. (29) Went, D. W.: Bakker, M. G.: Trifunac. A. D. J. Am. Chem. Soc. JIJ.

(31) Wickramaaratchi, M.,A,; Presea, J. M.; Holroyd, R. A.; Wesron, R. E.,Jr. J. Chem. Phys. 1985,82,4145. (32) Shinanka, K.; Koizumi, H.; Yoshimi, T.; Nakamura, Y.; Toriumi, M.; M d t a , M.;Hatano, Y.; Asaoka, S.: Niahimura, H. J . Chem. Phys. 1985,83, 4405.

0

5

Time (ns) Figure 6. Components of the simulated curves in Figure 5.

3

2

1

4

5

Time (ns) Figure 7. Comparison of simulated and experimental results for 0.001 M PPO in n-hexane. The simulated curves are for the exponential distribution with ravp= 52 A. The parameters for the transformation and energy transfer are given in the text.

ICerenkov excltatlon, no TMEl

2 L.................

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1

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2

Cerenkov Excitation, 10% TME 3

4

5

Time (ns) Figure 8. The effect of 10% by volume TME on the cumulative 'A vs time for 0.001 M PPO in cyclohexane. estimate based on measured quantum yields for fluorescence from excited states of saturated hydrocarbons,u the measured lifetimes for n-decane,j2 and a formula given by L i p ~ k yrelating ~ ~ quantum yields and the radiative and nonradiative decay constants. Making the further assumption that 30% of reaction 1 gives 'RH, one obtains a simulated curve (Figure 7) which is closer to the shape of the experimental curve. However, to get good agreement, a value of k9 = 2 X lo8 s-I must be used (Figure 7). The use of this technique to determine k9 is less certain for the remaining solvents, and we can only conclude that the values of k9 must be small enough (less than about 1 X lo8 s-I) to have little effect on the formation of 'A on the time scale of 0-5 ns. Effects of Tetramethylethylene (TME). To obtain additional insight concerning the transformation (reaction 9) to form cations that do not result in the excited state of the scintillator, we added a large concentration of a solute, TME, which should presumably undergo charge transfer (reaction 10) with the solvent radical cation to produce the TME radical cation. The TME radical cation should be relatively stable and lead to the scintillator excited state upon recombination (reaction 11). TME'+ is known to result

-

+ TME TME'+ + A'-

RH'+

TME'+ 'A

+ RH

+ TME

(10) (1 1)

in IA via reaction 11 for anthracene in n-hexane and methyl cy~lohexane.~~ (33) Preses, J. M.; Holroyd, R. A. J . Chem. Phys. 1990, 92, 2938. (34) Rothman, R.;Hirayama, F.; Lipsky, S. J . Chem. Phys. 1973, 58, 1300. (35) Lipsky, S. In Chemical Spectroscopy and Phorochrmisrry in rhe Ultraoiolet; Sandorfy,C., Ausloos, P. J., Robin, M. B., Eds. P r d i n g s of the Advanced Study Institute, held under the auspices of NATO and the Royal Society of Canada, Aug. 5-17, 1973, Valmorin, Quebec, Canada; D. Reidel: Boston, 1973.

The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 735

Reactions of Geminate Ions

TABLE II: Comparison of Mclwred, Relative, and Simulated G v 8 h of Solute Excited Singlet State' at 5 ns re1 G values G values GimC

solvent

solute

concn, M

n-hex n-hex n-hex c-hex

BP BP BP BP BP BP

0.05

c-hex c-hex

0.01 0.001 0.05 0.01 0.001

(hiah GW6 0.45 0.19 0.028 0.50 0.28 0.084

G,i,C 2.48 1.16 0.20 1.41 0.62 0.089

mo6.)

(iev

2.09 1.07 0.22

1.00 0.42 0.062 1.11 0.62 0.19

Cerenkov excitn

Gsim

Gd

.G,

(rel, high mob.)

G.i,

(GI)

(streak) I.O@

1* O F 0.50 0.086

0.38 f 0.03 0.035 f 0.0 1.10f0.02 0.58 f 0.0 0.16 f 0.01

1.1Ic

1.1Ie

0.49 0.070

0.58 0.12

G-1 (rei) 0.12 0.084 0.067 0.13 0.091 0.071

Gd

(streak) 0.14 f 0.03d 0.10 f 0.03 0.07 f 0.01 0.13 f 0.02 0.07 f 0.01 0.07 f 0.02

'The contribution from eerenkov excitation has been subtracted from all experimental values, except for the last two columns. bThe G values are in units of number of solute excited singlet states per 100 eV absorbed. CInthe case of cyclohexane, the simulated values include a contribution from energy transfer from the fluorescent state of cyclohexane based on values of the yield of this state and its lifetime and reaction rate with solutes from the literature (see text). Also, the solvent ion RH'+ is assumed to transform by reaction 9 with k9 = 3 X IO9 S-I. For biphenyl in n-hexane, the simulated values include an analogous contribution from energy transfer, but the arameters-for the n-hexane excited state are not well established (see text). The n-hexane radical cation is assumed to transform with k9 = 2 X lO!s-l. The Cerenkov excitation component has been subtracted on the basis of ethanol samples in obtaining the values in columns 4,7, and 8. A G value of 5 for ionization of the solvent was used, and the simulated values are for exponential distributions. dThe relative values from the streak camera measurements were normalized for each solute to the relative yield (column 7) in the 0.05 M solution in n-hexane. The average and average deviation for two sets of runs are given; an average deviation of fO.0 means the two values were the same. eThe simulated G values were normalized to the relative value of , G (column 7) for the 0.05 M solution for each solute/solvent combination. IRelative to 1.00 for ,G (in column 7) in 0.05 M BP in n-hexane. These experiments gave markedly different results in cyclohexane as compared with other hydrocarbons. Cyclohexane. To probe the time scale of the transformation reaction (reaction 9), TME was added at high concentration (10% by volume) to 0.001 M solutions of PPO (2,5-diphenyloxazole) in cyclohexane to compete with reaction 9. Some of the cyclohexane radical cation must proceed by reactions 10 and 11, because a fluorescence detected magnetic resonance (FDMR) signal of TME'+ has been observed in cyclohexane/anthracene solutions at lo-' M TME, and a structurally unresolved FDMR signal has teen observed at = I M TME.37 Therefore, we expected that IA would continue to increase in the 2-5-11s range due to reaction 11 and not level off as observed in Figure 3. The experimental result was dramatically different, as is seen in Figure 8, where the results with and without added TME are shown. With added TME, there is essentially no formation of 'PPO after the pulse (cyclohexene has essentially the same effect). In fact, the level of 'PPO with TME present is the sam? as the level due to excitation of the PPO by absorption of Cerenkov light, which is estimated by repeating the experiment with 0.001 M PPO and 10% TME inethanol (see above). Therefore, the TME has two effects. It prevents the production of 'A by energy transfer (reaction 7), which presumably means that if 'TME is produced by the analog of reaction 1 or by transfer of energy from 'RH, it does not transfer energy to A. Also, the production of 'A by ionic reactions is essentially eliminated, which means, contrary to our expectation, that the product of the reaction of RH" with TME does not react with A'- to produce IA. Therefore, the predominant products of reaction 10 must not be those written above, and we suggest instead, reaction 12.

+

-

+

RH'+ TME TMEH+ R' (12) n-Hexane. This effect of TME to eliminate the ionic production of 'A is not a general phenomenon in other hydrocarbon solvents. In the other solvents studied, the results indicate that the production of 'A by excitation transfer (reaction 7) is eliminated by 10% TME, but that reaction 11 simply replaced reaction 5 . The results for n-hexane are shown in Figure 9, where it is seen that 10% T M E has a much smaller effect on the cumulative yield of 'A at 5 ns than for cyclohexane, and the 'A formation rate is not markedly changed. Subtraction of the lower curve in Figure 9 from the upper one should indicate the relative amount of formation of 'A by energy transfer from IRH (in the absence of TME), if all RH'+ is converted to TME'+, if both ions have the same mobility, and if the value of the transformation rate constant, k9,for RH" is sufficiently small. The difference curve shown (36) Desroaiers, M.F.;Trifunac, A. D.J . Phys. Chem. 1986, 90,1560. (37) Went, D.W. Unpublished results.

Q 401 30

a a

c

E

'"1 0

I

I

I

I

I

1

2

3

4

5

Time (ns) Figure 9. The effect of 10% by volume TME on the cumulative 'A vs time for 0.001 M PPO in n-hexane. The difference curve is discussed in the text.

in Figure 9 has a formation period compatible with a lifetime of 'RH of about 0.3 ns, which, as we have discussed earlier, is a reasonable value. The fact that the difference curve shows a slight decrease at longer times is consistent with the value of k9 for n-hexane of =2 X lo8 P' estimated above (Figure 7); Le., the condition that k9 is small is not met, so the subtraction does not result in the energy-transfer component alone. If the TME,prevents the transformation of RH*+by reaction 9, and if the mobilities of the two ions are not greatly different, then the curve for the TME solution should have the same shape as the simulated curve. This comparison is shown in Figure 10, and the agreement is good. This supports the ideas that the TME radical cation behaves essentially the same as RH'+ in reaction 5 , and that the reason for the disagreement between experiment and simulation (with k9 = 0) in Figure 7 is due to the fact that the radical cation of n-hexane indeed undergoes a transformation as indicated. It is known that the TME" ion aggregates with one or more TME molecules at 10% TME.36 However, the decrease in mobility likely to result from this aggregation will not have a large effect on the shape of the cumulative 'A formation curve, as has been seen from the previous discussion of Figure 4.

Comparison of Measured and Simulated G Values of the Fluorescent State of the Solute. The absolute G values of 'A for several solutes in cyclohexane, n-hexane, and ethanol have been measured*I by using the known G value of the fluorescent state of benzene as a standard. The values obtained for biphenyl are reproduced from ref 21 in column 4 of Table 11. Likewise, column 11 gives relative G values obtained for eerenkov excitation of the solute, based on information from ref 21. Relative G values

Sauer et al.

736 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991

TABLE 111: Comparison of Experimental and Simulatedo C Values: Cyclohexane G('A)

_ _ _ _ _ _ _ ~ ~

simulated,

Ibiuhenvll. . . . > . M exptl

energy transfer

simulated, ionic

For the exponential distribution; the values for the are given in parentheses. 0

I

I

I

I

I

1

2

3

4

5

Time (ns)

Figure 10. Experimental and simulated results for 0.001 M PPO, 10% by volume TME in n-hexane. The simulated curve is for an exponential distribution with ravl= 52 A, with no energy-transfer component and no

transformation of RH'+.

obtained from the streak-camera results are also given in Table I1 and are seen to be fairly consistent with the absolute G values. The simulated values (Gsi,,,) are from our calculations, using G(ionization) = 5 ions per 100 eV absorbed; the simulated values designated "high mob" were calculated by using 0.095 cm2 V-' s-l for the mobility of the cyclohexane cation (see Table VI). The simulated G values given are for the exponential distribution. It is clear that there are large differences between the experimental and simulated G values. These differences cannot be explained by the transformation (reaction 9) of RH", because that has already been included in the simulation. Neither are the differences likely to be due to experimental error because of the agreement between the absolute G value measurements and the relative G value measurements obtained from the streak-camera measurements. Rationalization of the Differences between Experimental and Simulated G Values. Similar to the situation above for the effect of TME, we will see from the following that cyclohexane and n-hexane show dissimilar behavior with respect to C values, and therefore the discussion for these two solvents is separated. Cyclohexane. Because of the different rates of formation of excited scintillator by energy transfer and ion recombination, the relative amounts of these two pathways can be estimated by trial and error adjustment of the ratio and comparison of the resulting simulated curves with the experimental results. From the experimental results of Sauer et al.25the effect of the solute, A, on the G value of the fluorescent state of cyclohexane, G(IRH), can be estimated if one assumes that A scavenges electrons with about the same rate constant as N 2 0 or C 0 2 . On this basis, at 0.001 M A one obtains G(IRH) = 1.3, using a G('RH) in neat cyclohexane of 1.5.30 At 0.05 M A, G('RH) = 0.60 is obtained. The fraction of the excited states which transfer energy to A at each concentration was calculated taking into account static scavenging and timedependent rate constants, using 2.5 X cm2 s-' for the sum of the diffusion constants and 10.5 AZ5for the reaction radius, and a lifetime of 0.88 ns for 'RH.2s931332 This information is summarized in Table 111 along with simulated G values and experimental G values for A = biphenyl in cyclohexane. This summary of results displays unexpected effects. First, the yield of excited states is considerably lower at 0.05 M biphenyl than the simulation would predict. Second, the ratio of the experimental yield to the simulated yield depends strongly on concentration. To explore the reasons for these differences, let us first consider the possible explanations for 0.05 M biphenyl, where it is possible to estimate the fraction of the signal which is due to energy transfer (approximately 1 /3) and ion recombination (approximately 2/3) from the general shape of the experimental curve of 'A vs time. It might be thought the experimental data could be brought in line with the simulations if the literature value for G('benzene) were too low by approximately a factor of 3. This would cause

.

0.95 (1.26) 0.35 (0.33) 0.50 0.46 (0.26) 0.37 (0.35) 0.45 (0.47) 0.28 0.25 (0.251 0.084 0.045'(0.040) 0.044 (0.052) 0.94 (0.91)

0.05 0.01 0.001

0.00

GcXpll/ G s..i.. m w..., l\ . (..

exponential

our measured G value to be low by a factor of 1/3. However, because the same value of G('benzene) was used to determine G('RH),30that value would also be a factor of 3 too low and thus the yield of 'A from energy transfer would then be a factor of 3 larger. This would not help to explain the discrepancy. Clearly the measured G('A) shows that the amount of 'A formed by energy transfer is considerably smaller than the calculated value in 0.05 M biphenyl solutions. This could arise either if (1) the G value of IRH is much less than 1.5 or (2) the transfer from the excited state of cyclohexane to biphenyl produces IA with an efficiency significantly less than 100%. Although the G value of 1.5 for excited cyclohexane was also measured relative to G(lben~ene),~O the spectral range was sufficiently different that it is conceivable that the experimental errors might be large enough to reduce the value of 1.5 to a value of 0.5. Studies with tolueneBss9 (0.001~.01M) added to cyclohexane to accept the excitation from 'cyclohexane yield a limiting extrapolated value of C( Itoluene) of about 0.3. Assuming that the transfer reaction gives the fluorescent state of toluene with an efficiency (per reaction) of 1OO%, these experiments would indicate G('cyc1ohexane) = 0.3. On the other hand, if G(kyc1ohexane) = 1.5, these experiments would indicate that the efficiency is only 20%. However, we have examined the results of Laor and Weinreb@ for the transfer of energy from cyclohexane excited a t 150 nm to the solute PPO and find that those results support an efficiency of about 100% for this solute when interpreted in conjunction with the observation of Lipsky and ~ o - w o r k e r sthat ~ ~ *the ~ ~ quantum yield of the fluorescent state of cyclohexane is less than half as large at 150 nm as it is at the absorption edge (180 nm). The measured yield of 'A from ion recombination reactions is also considerably smaller than that expected from the calculations. This could be explained by (1) multiple-ion-pair spurs where much of the ion recombination will form triplets rather than singlets or (2) reactions 4, 5 and/or 6 creating excited states with a less than unit probability. The sum of the 'A produced by ionic reactions and energy transfer from 'cyclohexane is much less than expected on the basis of the simulated results at 0.05 M biphenyl; the difference becomes smaller at lower biphenyl concentrations. At 0.01 M biphenyl, the difference is only 50%, and at 0.001 M it is negligible. The tentative hypothesis (made on the basis of the 0.05 M results and the above discussion) that the production of 'biphenyl by energy transfer is only =30% efficient is not sufficient to rationalize the results shown in Table 111. With this factor and the values in Table I11 for the exponential distribution, the ionic component must be multiplied by an efficiency factor that is =1 at 0.001 M, 0.57 at 0.01 M, and 0.37 at 0.05 M to obtain values close to experimental. (Actually, the factor must be greater than 1 at 0.001 M, but this is physically unreasonable in that it would require two excited states to be formed in a recombination.) A similar trend results if the values for the $-exponential distribution are used. There is no obvious way to get such a trend; it seems to require an inefficiency in the production of 'biphenyl by recombination of biphenyl'- and biphenyl'+ which becomes more important as the concentration of biphenyl becomes higher. A possible basis for such an effect is the suggestion made in another section that proton ~

~~

(38) Baxendale, J . H.;Mayer, J. Chem. Phys. Lctr. 1972, 17, 458. (39) Walter, L.; Lipsky, S. Inr. J . Radial. Phys. Chem. 1975, 7 , 175. (40) Laor, U.;Weinreb, A. J . Chem. Phys. 1969, 50, 94.

The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 737

Reactions of Geminate Ions

0.7-1

TABLE IV: Comparison of Experimental and Simulateda G Values:

n-Hexane

[biphenyl], M 0.05 0.01 0.001

exptl

G('N simulated, energy transfer

simulated, ionic

Gcrptl/ Gsim(tou1)

- --.

0.60 (0.26) 1.88 (2.79) 0.218 (0.15) 0.45 0.86 (1.26) 0.16 (0.13) 0.30 (0.25) 0.19 0.028b 0.047 (0.046) 0.153 (0.22) 0.14 (0.11)

Values are for the exponential distribution. The values for the ? exponential are given in parentheses. The yield of excited states for the energy-transfer simulation was calculated assuming that 1/ 3 of the geminate recombinations of the electron with the unscavenged positive-ion yield excited states (similar to cyclohexane where the yield of excited state is 1.5 and the ion recombination approximately 4.5). The energy-transfer simulation is done using an RH lifetime of 0.3 ns (as discussed in the text) and describing the effects of static scavenging and time-dependent rate constants using 7.5 X IO-' cm2 s-l for the sum of the diffusion constants and 10 A for the reaction radius. bValues for other scintillators at 0.001 M are significantly higher? the reason for this is not known, but 0.028 should be considered as a lower limit.

transfer to T M E is responsible for the observed effect of TME in drastically reducing the 'A yield in cyclohexane; Le., perhaps the reaction of cyclohexane'+ with biphenyl proceeds partially by proton transfer. However, this seems to be ruled out by the fact that the shapes of the calculated curves do not fit with experiment at 0.05 M biphenyl if the component from biphenyl'+ biphenylis reduced by the amount corresponding to the relative decrease in G value. n-Hexane. For n-hexane, the ratio of the observed to simulated G value decreases with decreasing concentration, contrary to the case of cyclohexane, and the experimental values are lower than the simulated values by a factor of 5 or 6. The results for A = biphenyl in n-hexane are shown in Table IV. Qualitatively, these results mean that there must be a large inefficiency factor in the ionic reactions leading to IA, Le., only 15-20% of the initial positive ions can ultimately lead to 'A, due either to there being positive ions other than the C6HI4*+ created initially which are incapable of leading to 'A, or to inefficiencies in the recombination reactions 4-6. The effect of multiple-ion-pair regions (spurs) would be to reduce the efficiency of 'A formation because in the limit of random recombination only one recombination in four would give 'A. Although the contribution of multiple-ion-pair events is thought to be quite significant,'*-'' it is not sufficient to explain the observed factor of 5 or 6 for nhexane. In the case of cyclohexane, where the factor is smaller, multiple-ion-pair regions could be invoked to explain most, if not all, of the observed inefficiency, but not the effect of solute concentration. What Can We Conclude about the "Distribution"? Comparison of Experimental and Simulated Curves. So far we have only discussed the kinetic comparison of the simulated and measured cumulative IA curve^ for 0.001 M solutions, where the results were used to show that the solvent radical cations undergo transformations. In those comparisons, the distribution (see eqs A-I, A-11, and A-111) used made little difference because the results at low concentration are insensitive to the distribution. At 0.05 M solute, the distribution used has a greater effect on the shape of the simulated curve, so we can probe the nature of the distribution by comparison with the shape of the experimentally observed curve. Clearly, the creation of 'A by energy transfer (reaction 7), and the occurrence of the transformation of the radical cation (reaction 9) makes the derivation of such information difficult. The information derived above on the transformation of the radical cations and the contribution to 'A formation by energy transfer from excited solvent is used in the simulations a t 0.05 M shown in Figures 1 1 and 12, where experimental and simulated results are displayed for solutions of 0.05 M biphenyl in n-hexane and cyclohexane, respectively. The simulated curves are normalized to the experimental data at about 5 ns. For n-hexane, the exponential distribution does not fit the experimental data;

?exponential ?Gaussian

....... exponential

Time (ns)

Figure 11. Experimental results for 0.05 M biphenyl in n-hexane and simulated results. Two sets of experimental results are represented by the broad black and gray curves. The parameters for the simulation were rave = 52, 66, and 71 A for the exponential, ? exponential, and 9 Gaussian, respectively; k9 = 2 X IO* s-I; energy transfer from excited solvent was included by assuming the efficiency of reaction 1 to give IRH is 0.33, the lifetime of 'RH is 0.35 ns, the reaction radius (fiRH + fdFtc) is 10 A, and using for the sum of the diffusion constants of the reacting species 7.5 x IO-' cmz s-I.

+

0.15

c O

-.-

p,,,,,,

r'exponential ?Gaussian -exponential

I

0.0611

* (JI

0.00

0

1

2

3

4

5

Time (ns)

Figure 12. Experimental results for 0.05 M biphenyl in cyclohexane and simulated results. Two sets of experimental results are represented by the broad black and gray curves. The parameters for the simulation were r,v8 = 52, 66, and 71 A for the exponential, ? exponential, and 9 Gaussian, respectively; k, = 3 X IO9 s-I; energy transfer from excited of IO A solvent was included by using a reaction radius ( f ' R H + rdudutc) and a yield of 0.1 1 IRH per ion pair, estimated from the results of Sauer et al.?' a lifetime of 'RH of 0.88 ns,25*31,32 and using for the sum of the diffusion constants of the reacting species 2.5 X 10" cm2 s-l.

the 3 exponential distribution gives a reasonably good fit, and the 9 Gaussian is marginally poorer. We wondered whether the shape of the curve for the exponential distribution would change appreciably if ravgwere changed from 5 2 to 47.3 A, which corresponds to the change needed to get the same separation into free ions if the ions within the first 10 A are removed from our consideration in calculating the separation probability. This is equivalent to introducing a cutoff radius to the distribution. No significant change in the shape of the simulated curves was observed for such changes in ravg. In the case of cyclohexane, none of the distributions gives a good fit with experiment; the 9 Gaussian has the correct slope at later times but does not fit well during the first half nanosecond. The Production of Solvent Excited State via Recombination. The simulations also give us information about F,,the fraction of the electrons that recombine by reaction 1 with RH". F, in turn can be used to calculate G('RH), if one assumes a value of F,, the probability of production of 'RH in reaction 1. Conversely, if G('RH) is known as a function of electron-scavenger concentration, the value of F, can be calculated. The resulting values can be used to draw conclusions concerning the efficacy of the three distributions in describing the experimental system. The results for cyclohexane with 0.05 and 0.001 M solute are given in Table V.

138 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 TABLE V Calculated Electron-RH'+ Recombination and Excited Solvent Production [solute], M 0.05 0.05 0.05

0.001 0.001 0.00 1

distribution exponential 9 exponential 9 Gaussian exponential 9 exponential 9 Gaussian

Fr

Fe

0.434 0.204 0.149 0.897 0.868 0.854

0.276 0.588 0.805 0.290 0.300

0.304

F, was calculated from F, by using values of G(IRH) in cyclohexane as a function of electron-scavenger concentrati~n.~~ At 0.05 M solute, G(IRH) = 0.6, and at 0.001 M solute, G('RH) = 1.3. More than 90% of the excited states originate via the recombination reaction in neat cyclohexane.2s Taking G(ionization) = 5 , the values for F, were calculated, Le., F, = G(IRH)/(F,G(ionization)). From the table one sees that the type of distribution has only a small effect (5%) on F, at 0.001 M, but has a large effect at 0.05 M. The value determined for F, at 0.05 M is very dependent on the distribution assumed. If all e-,RH'+ pairs are equal with respect to the probability of production of 'RH, F, should be constant; therefore, this analysis favors the exponential distribution for cyclohexane. Comparison with Previous Evidence Concerning the Distribution. From the results of this work, as discussed above, the rz exponential distribution is preferred for n-hexane. For cyclohexane the kinetic results are not conclusive, but the analysis given concerning solvent excited state formation favors the exponential distribution. Previous evidence in the radiolysis of cyclohexane and n-hexane is predominantly in favor of the exponential distribution. Abell and Funabashi4' analyzed experimental results on electron sca~ e n g i n gand ~ ~the electric field dependence of the escape probab i l i t ~ ~ and ~ - @concluded that the exponential distribution was appropriate. M o z ~ m d e has r ~ ~presented an analysis indicating that this distribution fits most of the observations on electric field effects on the escape probability in radiolysis. The results of Jonah4 on the decay of positive ions in n-hexane were interpreted to support the exponential distribution, but if the observed species (n-hexane") undergoes transformation at 2 X lo8 s-I, the results should be reexamined. A summary as of 1982 of evidence concerning the distribution in radiolysis has been given by Choi et aL4' Later, Choi et al.48 presented an analysis of their results on the quenching of solvent excited state fluorescence by an electron scavenger in terms of the &exponential or &Gaussian distributions (by implication, they favor these over the exponential). Yoshida et aI.l1 used an exponential distribution to fit their results on emission from excited biphenyl and absorption by biphenyl anions in cyclohexane in work similar to that reported here. Other Observations. Comparison with Previous Work. The emission results of Yoshida et al.," obtained by techniques similar to those used here, on biphenyl in cyclohexane are given only for a 0.1 M solution. At this concentration, the effects of the ion transformation (reaction 9) are not expected to be easily discerned because positive ion scavenging by biphenyl occurs at approximately the same rate as reaction 9. They were able to fit their emission results and results on optical absorption of the biphenyl anion (at 0.01 and 0.5 M biphenyl) without including an iontransformation reaction in their mechanism. They assumed the cyclohexane radical cation to be the high-mobility (0.095 cm2 V-I s-I) species. Also, the exponential distribution they used was broader than that used here (eq A-I, Appendix, r,,, = 61 A vs 52 A); their distribution predicts a 40% larger separation prob(41) Abell, G.C.; Funabashi, K. J . Chem. fhys. 1973, 58, 1079. (42) Warman, J. M.; Rzad. S . J. J. Chem. fhys. 1970.52, 485. (43) Schmidt, W. F. Radial. Res. 1970, 42, 73. (44) Mathieu, J.; Blanc, D.; Caminade, P.; Patau, J. P. J. Chim. Phys. 1967, 64, 1679. (45) Mozumder, A. J . Chem. fhys. 1974,60, 4305. (46) Jonah, C. D. Radial. fhys. Chem. 1983, 21, 53. (47) Choi, H.T.; Sethi, D. S.;Braun, C. L. J . Chem. Phys. 1982,77,6027. (48) Choi, H. T.; Haglund, A.; Lipky, S . J . Phys. Chem. 1983.87, 1583.

Sauer et al. ability. In view of our experience that the fit between experiment and simulation is not very sensitive to such changes in the distribution or to the mobility of RH'+, and the fact that the data at 0.001 M solute are essential in establishing the occurrence of reaction 9, we suggest that their results are probably consistent with our mechanism. Cerenkov Excitation of the Solute. In a previous reportlo on recombination fluorescence, we were puzzled by the observation that for IO-" M solutions of a scintillator the amount of excitation which occurred essentially instantaneously (during a 30-ps pulse) was approximately twice as great in cyclohexane and n-hexane as in ethanol. To explain this result the suggestion was made that an initial excitation of A of unknown origin occurred in the hydrocarbon solutions. Since that time, we have determined that the reason for the difference is that ethanol has a greater optical absorbance in the 200-nm region than do the two alkane liquids. This has a major effect on the excitation of A by absorption of Cerenkov light (reaction 8); Le., in ethanol a larger part of the Cerenkov light is absorbed by the solvent. Because of this, in the present work we have not used solutions less than M. At M and higher, the absorption of the scintillator, A, is large enough in the 200-nm region that the differences between ethanol and the alkanes with respect to the amount of Cerenkov excitation of A appear to become negligible. Energy Transfer from Excited Solvent. With the realization that solvent ion transformation has a major effect in reducing the recombination fluorescence, especially in cyclohexane, it is now clear that the relative importance of reaction 7, energy transfer from excited solvent, should be greater than was previously thought. Also, the fact that the experimentally determined G values for 'A formation are considerably smaller than those predicted from the simulations means that the energy-transfer process may be further enhanced in importance if there is some 'built-in" inefficiency in the ionic pathway. The High-Mobility Ion in Cyclohexane. That there is an ion in cyclohexane, which can be produced by r a d i o l y s i ~or~ pho~-~~ toionization" and has abnormally high mobility, is well established. One of the aims of the work reported here was to determine whether the effects of this high mobility could be seen in the recombination-fluorence kinetics and G value. However, if our conclusion that a rapid transformation of the cyclohexane'+ radical cation is required is correct, the idea that the high-mobility cation is cyclohexane" is untenable because the high-mobility ion is known to live for hundreds of nanoseconds, whereas the transformation of c - C ~ H . ~ ~is' +complete within a few nanoseconds. Therefore, it seems likely that the high-mobility ion is the product of the transformation, i.e., c-C6HI3+,which is required by our results to be unable to result in excited scintillator. As we have already mentioned, the ion-molecule reaction of the solvent radical cation with the solvent is one which occurs generally, and the evidence for this has been recently presented by Trifunac and c o - w o r k e r ~ . ~From ~ - ~ ~the results reported here, Le., the reaction of cyclohexane" with cyclohexane (k = 3 X IO9 s-I) and with TME, the cyclohexane radical cation has a great propensity to give up a proton. Consequences of the Solvent Radical-Cation Transformation. The interpretation of any experiment designed to probe the geminate-ion recombination process which depends on the product of a reaction of an additive with the radical cation of the solvent will have to take into account the transformation. On the other hand, experiments which depend only on measurement of a product of electron scavenging will be negligibly affected. For cyclohexane, the question may be asked as to how the transformation modifies our thinking concerning interpretations of results on the effect of electron scavengers on the yield of the fluorescent state of c y c l o h e ~ a n e . ~The ~ * ~experimental ~ resultsZ5 (49) de Haas, M. P.; Warman, J. M.; Infelta, P. P.;Hummel, A. Chem. Phys. k i t . 1975, 31, 382. (50) de Haas, M. P.; Hummel, A.; Infelta, P. P.; Warman, J. M. J . Chem. Phys. 1976, 65, 5019. (51) Sauer, M. C., Jr.; Trifunac, A. D.;McDonald, D. B.; Cooper, R. J . Phys. Chem. 1984,88,4096.

The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 739

Reactions of Geminate Ions

TABLE VI electron mobility, cm2 V-l 5-l positive ion mobility, cm2 V-l

n-hexane cyclohexane 0.071 0.23 s-l

1.1

x 10-3

0.4

x 10-3

(9.5 x 10-')4 0.8 x 10-3 0.3 x 1 0 - 3

negative Bcintillator ion mobility. cm2 V-1 s-I positive scintillator ion mobility, cm2 V-I s-I 0.8 reaction radius for ion recombinations, A 10

X

0.3 X lW3 10

'High-mobility ion.

showed that scavenging of the fluorescence was more efficient than scavenging of the electron, and this was shown to be explainable by a mechanism involving an initially excited cyclohexane'+ ion which does not result in the fluorescent state upon recombinations2 (arguments against this mechanism have been recently advanceds3). The ion transformation does not offer an alternate rationalization of the observations, because it would make fluorescence scavenging less efficient than electron scavenging. More importantly, the effect of the transformation would be minimal because most of the geminate ion pairs recombine or are scavenged by the electron scavenger in such experiments before the transformation can occur.

Conclusions The experimental results from the radiolysis of cyclohexane and n-hexane differ markedly in several respects. For this reason cyclohexane appears to be a poor choice as a paradigm for hydrocarbon radiolysis. Comparison between experimental data and a theoretical simulation of the experiments suggests that a very rapid proton transfer from the solvent radical cation of cyclohexane will explain the different behavior in cyclohexane. A similar process, although considerably slower, is also needed to explain the experimental observations in n-hexane. The yields of the fluorescent states of the scintillators are considerably smaller than predicted theoretically. These differences can be only partially explained by multiple-ion-pair regions (multiple-ion-pair spurs) and suggest that some positive ions from the solvent are unable to produce scintillator excited states. Further experiments are needed to explain completely the differences between cyclohexane and n-hexane, particularly the variation of the G value of the fluorescent state as a function of scintillator concentration. Measurement of fluorescence G values and kinetics in other hydrocarbon solvents are also important. Work with scintillators which have appreciably reduced rates of either electron or positive charge capture will be important with respect to verifying effects predicted by the model. The effect on the G values and kinetics of including multiple-ion-pair spurs in the model should also be determined. The effects of such spurs should also be further investigated by quantitative measurements of the time evolution and yield of the scintillator triplet state. Acknowledgment. We thank Drs.Alexander D. Trifunac, David Went, and Martin Bakker for unstinting advice, discussion, and suggestions. We also acknowledge the helpful comments of Professor Sanford Lipsky. We gratefully acknowledge the work of Donald T. Ficht and George L. Cox in running the 5-ps linac pulse. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, US-DOE, under contract no. W-31-109-ENG-38.

Appendix The dynamics of an electron-positive-ion pair in the presence of scavengers which can react with either the electron or the positive ion are simulated. The initial separation of the electron and the positive ion is determined by a predefined function as discussed in the main body of the paper. The movement of the charged particles due to random diffusive motion and to the attractive Coulombic force is calculated by using known properties (52) Jonah, C. D.; Sauer, M. C., Jr. Radiat. Phys. Chcm. 1989,34,497. (53) Tweeten, D. W.; Lee. K.: Lipky, S. Radial. Phys. Chem. 1989,34,

771.

of the charged species and of the liquid. The volume of space that is studied is a box with sides of approximately twice the Onsager radius, r,, for the solvent. The electron is placed at the center of the cube and the positive ion is placed at a distance determined by randomly sampling the distance-distribution function. The distributions described by the following equations were used to describe the distance between the electron and its sibling positive ion after thermalization of the electron. The same values of rav8(see below) were used for cyclohexane and n-hexane. These values give the experimentally determined probabilities of separation into free ions for the radiolysis of cyclohexane and n-hexane with low LET radiation. These probabilities are estimated on the basis of known G values for free ionsx and a G value for ionization of 4.5. In the following equations, F(r) is the probability of finding the electron between r and r + dr. exponential: F(r) dr = b-' exp(-r/b) dr;

9 Gaussian: F(r) dr 9 exponential:

r,,, = b = 52 A (A-1)

= (4?/7r1/*b3) exp(-9)/b2) dr; ray, = 2b/7r'l2 = 71 A

F(r) dr = (r2/2b3) exp(-r/b) dr; r,,, = 36 = 66 A

(A-11) (A-111)

Because of the size of the box, the maximum initial distance between the electron and positive ion is r,. This will eliminate approximately 3 in lo00 ion pairs for (A-I), 1 in loo00 for (A-III), and considerably fewer for (A-11). An appropriate number of scavengers, determined by the scavenger concentration, are placed randomly within the box. The motion of the positive and negative species within a time interval At includes both a diffusive term and a Coulombic term. The time step for each movement is ad'usted based on the ion mobilities to give a diffusive step of 1 I t . The Coulombic step Ar is calculated from qpFAt

= -(4*~r)rJ where r' is the distance between the positive and negative ion, q is the elementary charge, p is the mobility of the charged species under consideration, e, is the dielectric constant, and 4m0 is used to create appropriate units. The diffusive motion is determined by a random selection from an array of possible motions. An array of 26 vectors, each 1 A in length, was created. These vectors are in the six axes directions (+x and -x, etc), the eight corners of the cube ( f d 3 / 3 , f d 3 / 3 , * d 3 / 3 ) and the corners of the XY,XZ,and YZ squares [for example, for the XY square, (*d2/2, f d 2 / 2 , O)]. A random number from 1 to 26 was obtained and used to select one possible motion. Simulations have shown that this will be equivalent to selecting the step direction randomly if the number of steps is sufficiently large (greater than 10). After the electron and positive ion are moved, it is necessary to determine whether a reaction will take place. A reaction will take place if the separation between reacting species is less than the reaction radius for the reaction. This could be a time-consuming step in the calculation because of the large number of scavengers that can be in the volume under study. To facilitate the search for potentially reactive pairs, the reaction space is broken up into 8000 smaller cubes, each O.lr, on a side (approximately 30 A in a hydrocarbon). Initially, each scavenger is assigned to a cube based on its coordinate (more than one scavenger molecule can be in a given cube). After each step, the positive ion and negative ion are also each assigned to a cube. Because the size of a cube is greater than the reaction radius (approximately 10 A), only species that are in the same cube or one of the adjacent 26 cubes need be checked to see if the distance is less than the reaction distance. Thus, only very few distances need to be calculated. This allows one to run quite high scavenger concentrations without slowing the program inordinately.

740

J. Phys. Chem. 1991, 95, 740-743

If the pasitive and negative ion react, the calculation for that ion pair is terminated, and calculations on a new ion pair are initiated. If a charged species reacts with one of the solute molecules, the program treats the resultant ion pair identically, except that the diffusion rate and mobility for the new product species are used and the time increment is changed appropriately. The process of moving the charged species and checking for reaction continues until ( I ) the charged pair is neutralized and the event is terminated; or (2) a maximum time is reached which corresponds to the experimental time window ( t , = 5 ns for these experiments). If one of the reactive species undergoes a displacement moving it outside the large box, the charged pair is moved so that the negative ion is at the center of the large box

The Prlmary Process C103- (+hv) Solutions

-

CIO‘

and the same separation distance is maintained. This rarely occurs under our conditions. For 0.05 M solution of scavenger, 1000 ion pairs were sufficient to obtain good statistics, while, for a concentration of 0.001 M scavenger, 8000 ion pairs are studied. Because we are observing the neutralization of a scavenger ion, at lower concentrations of scavenger more ion pairs must be studied to improve the statistics. A run for 8000 steps takes approximately 25 h on a DEC Microvax I1 (approximately equivalent to a VAX 11-780). Table VI contains the parameters that were used for the calculations. Note that the results are only very weakly dependent on the reaction radius as long as the reaction radius is considerably smaller than rc.

+ O2 in the Photolysis of Aqueous C103-

U. K. Klaning* Chemistry Department, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark

and K. Sehested Rise National Laboratory, Risa, DK-4000 Roskilde, Denmark (Received: April 19, 1990)

-

- -

The quantum yield, in the primary process CI03-(+hu) CIO- + O2( I ) and the sum of the quantum yields @2 + @3 in the primary processes C103- (+,hu) C102 + 0-(2) and C103- C102- + O(’P) (3) were measured in the steady-state photolysis of aqueous CI03- solutions at 214 and 229 nm. The ratio of the yields of CIO- and C103- in the reactions ClOz CIO- + O2 and C102 + 0- CIO; (4) was determined by y-radiolysis of aqueous solutions of C102 at varying pH. The finding that the ratio between the yields of CIO- and CI03- in reactions 4 equals the ratio between 0,and the quantum yield, a0= 1 - - a2- a3,for CIO3- returning to the ground state is taken as evidence that process 1 results from a cage-back reaction. This result combined with recent studies of the radiolysis of KC103 crystals suggest that the primary processes in the photolysis of aqueous CI03- originate in a common process by which 0-is expelled from CI03- upon photoexcitation. The expelled 0-may escape the solvent cage containing CIOz (process 2), or react in a cage-back reaction (process 0 and I ) . During the expulsion of 0-the photoproducts may convert to C102- and O(’P) (process 3).

-

-

Introduction Formation of O2by a primary photochemical process has teen observed in the photolysis of aqueous solutions of C103-,192 Mn04-,3-5 Br0