J. Phys. Chem. 1984,88, 1921-1926
1921
there are usually more sites than cations available, and any rearrangement causes a change in the site energy. This formalism remains useful to understand that no sites should be excluded from cation occupancy, even if the occupancy level is below the detection limit.
(allowing the purchase of a high-temperature X-ray diffractometer camera), as well as research financing by the “Fonds voor Kollektief en Fundamenteel Onderzoek”. Registry No. H,O, 7732-18-5; NH,, 7664-41-7; acetone, 67-64-1; benzene, 71-43-2; ethanol, 64-17-5.
Acknowledgment. W.J.M. ackowledges a research position as Senior Research Associate (Onderzocksleider) from the “Belgisch Nationaal Fonds voor Wetenschappelijk Onderzoek”. The authors also acknowledge financial support from the same institution
Supplementary Material Available: A listing of the observed and calculated structure factors, and tables of selected interatomic distances and bonding angles (35 pages). Ordering information is available on any current masthead page.
Parallel Study between Electron Scavenger Effects on Positronium Formation Probability and Fluorescence Intensity in Cyclohexane Yasuo Ito,* Research Center for Nuclear Science and Technology, University of Tokyo, Tokai-mura, Ibaraki, 319-11 Japan
Yosuke Katsumura, Toshiyuki Azuma, and Yoneho Tabata Nuclear Engineering Research Laboratory, University of Tokyo, Tokai-mura, Ibaraki, 31 9- 11 Japan (Received: April 18, 1983) In order to clarify the mechanism of Ps formation, the effects of various electron scavengers on the intensities of both positronium and recombination fluorescence in cyclohexane have been studied. The scavenger effects on the fluorescence intensity have been found to be described adequately by the Warman-Asmus-Schuler empirical equation for the electron scavenging reactions, making it possible to determine the reactivity parameters of the scavengers. The same equation applied to a simple model of positron spur has been found to describe the gross feature of the inhibition of Ps formation by several scavengers (C2H5Br, C2H51,CHC13,and CH2C12),but a systematic deviation from the equation is observed at a low scavenger concentration range, Anomalously stronger inhibition effects have been found for CC14,CBr.,, CHBr,, CH2BrZ,and CCl,CCl,. CS2was an opposite case, being less efficient to inhibit Ps formation than expected. According to these results, it is proposed to classify the electron scavengers into four groups: normal, strong, and partial inhibitors and an enhancer. Discussion is made of the mechanisms of these different inhibition effects in cyclohexane within the framework of the spur reaction model of Ps formation.
Introduction The mechanism of Ps formation in a condensed substance has been the subject of many recent studies.’-’ There are basically two different models of Ps formation; the Ore model* and the spur reaction modeL9 The latter model seems to be supported by a large number of experimental results recently. But in spite of so many works which indicate excellent parallelism between Ps formation and radiation chemistry, little work has been done to compare directly and quantitatively the data of these two different fields. It has been shown in our previous paperlo that the effects of C2HSBrand CHJ (as inhibitors) and of C6F6(as an anti-inhibitor) on Ps formation in cyclohexane can be explained by using the WAS (Warman-Asmus-Schuler) empirical equation’ to a simple model of the positron spur. The value of the reactivity parameter, a,reported in the literature of radiation chemistry could be used successfully. The same treatment failed when CCI4 was used as
’
(1) M. Eldrup, V. P. Shantarovich, and 0. E. Mogensen, Chem. Phys., 11, 129 (1975). (2) B. Levay and 0. E. Mogensen, J . Phys. Chem., 81, 373 (1977). (3) B. Djermouni and H. J. Ache, J . Phys. Chem., 82, 2378 (1978). (4) V. M. Byakov, V. L. Bugaenko, V. I. Grafutin, 0. V. Koldaeva, E. V. Minaichev, and Yu. V. Obukhov, Khim. Vys. Energ., 12, 346 (1978). ( 5 ) A. G. Maddock, J. Ch. Abbe, G. Duplatre, and A. Haessler, Chem. Phys., 58, 1 (1981); Radiat. Phys. Chem., 1 1 , 199 (1978). (6) 0.A. Anisimov, S.V. Vocel, and Yu. N. Molin, Chem. Phys., 53, 123 (1980). ( 7 ) (a) G. Wikander, Chem. Phys., 66, 227 (1982); (b) ibid., 39, 309 (1979). ( 8 ) V. I. Gol’danskii, At. Energy Reu., 6,3 (1968). (9) 0. E. Mogensen, J . Chem. Phys., 60,998 (1974). (10) Y. Ito, M. Miyake, and Y. Tabata, Radiat. Phys. Chem., 19, 315 ( 1 982). -~ ( l i ) J. M. Warman, K. D. Asrnus, and R.H. Schuler, Adu. Cfiem.Ser., No. 82, 25 (1968).
.-
0022-3654/84/2088-1921$01.50/0
the inhibitor, and we had to assume an additional pathway of the inhibition, namely a positron capture by CC1,. Stimulated by the recent works by Gol’danskii et a1.,12we have recently started experiments of electron scavenger effects on Ps formation and on solute fluorescence in cyclohexane and have found that the scavenger effects on the recombination fluorescence in 10 mM PPO (2,5-diphenyloxazole) solution in cyclohexane can be well described by the WAS equation and that this technique can provide us with simple and reliable means to determine the reactivity parameter, a,of the scavenger. In this paper we will first show how the measurements of fluorescence by the single photon counting can be carried out to determine the reactivity parameters and then examine quantitatively the Ps formation data using the reactivity parameters thus obtained.
Experimental Section The photon counting experiments of fluorescence were carried out using a pair of photomultipliers (HTV-R1246 and HTVR1294U). About 20 pCi of @ C o‘ was used as the radiation source. The R1246 photomultiplier coupled to a 40 mm X 10 mm diameter Pilot U plastic scintillator was used to detect 1.17 and 1.33 MeV y rays which served as a start signal. The R1294U photomultiplier, sensitive between 280 and 750 nm, detected the fluorescence photons (ranging 330-450 nmI3), to provide stop signals. The start and stop signals were fed to a time-to-amplitude converter whose output was analyzed by a 1000-channel pulse height analyzer. The fluorescence intensity was obtained from (12) L. G. Aravin, V. I. Gol’danskii, M. K. Filimonov, and V. P. Shantarovich, Kfiim. Vys. Energ., 14, 188 (1980); ibid., 16,282 (1982). (13) I. E. Berlman, “Handbook of Fluorescence Spectra of Aromatic Molecules”, Academic Press, New York, 1971.
0 1984 American Chemical Society
1922 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 M'-e-
1-P
P
e-
e-'
Ito et al.
Ps
3
Figure 1. A simple model of Ps formation in a positron spur composed of three charged particles: a parent ion M+, an electron, and a positron. p is the probability with which e- combines with e+ to form Ps. The electron scavenger S captures a fraction of e-, and the captured electron may be transferred to e* to form Ps with a probability A , depending on the energetical conditions. The arrows indicate the electron flow.
the total counts of the time profile. The system time resolution as determined by measuring the time profile of Cerenkov light in H 2 0was about 500 ps. The concentration of PPO was chosen to be 10 mM since the fluorescence intensity levels off above 20 mM due to self-quenching and/or excimer formation. When the absorption band of the dissolved scavenger overlaps the emission band of PPO, a quartz cell containing the neat scavenger liquid was placed in front of the R1294U photomultiplier as an optical filter. The positron lifetime measurements were carried out as described previously." Cyclohexane and all the electron scavengers used in this experiment were of Tokyo Kasei's guaranteed grade reagents and were used without further purification. It was not necessary to purge air from the sample solutions, because it became clear by our preliminary experiments, and in agreement with the statement by others,6 that the presence of saturated air does not affect Ps formation probability significantly.
Treatment of the Data All of the data were analyzed by using the WAS equation. The model of the positron spur" used in the present study is illustrated in Figure 1; it is assumed to be composed of a parent ion M', an electron e-, and a positron e'. The electron goes to e+ with a probability p to form Ps or otherwise goes back to M' (with a probability 1 - p ) . Thus, the Ps formation probability with regard to unit excess electron production is p . The value of p = 0.75 was found to give reasonable results for the case of anti-inhibition of C,F6 in C2H5Brsolution of cyclohexane." An electron scavenger, S, introduced to this reacting system captures e-, and according to the WAS equation, its efficiency is given by
Channel Number ( 56pslch)
Figure 2. The fluorescence time profile for 10 mM PPO (2,s-diphenyloxazole) solution in cyclohexane (upper spectrum) and the effect of addition of 40 mM CC1, to it (lower spectrum). The two spectra are normalized for the same counting time.
WAS equation may not explain details of the geminate recombination process. This, however, does not invalidate the present treatment, because we are interested in examining gross parallel relationships with radiation chemistry data at a wide concentration range. Also, the use of eq 3 is not recommendable, especially if the inhibition is supposed to take place via several pathways as, for example, in the case of CCl4.l0 Strictly speaking, furthermore, the experimental results for, for example, C2H5Bras shown in Figure 5 cannot be described even by eq 3 adequately. For the case of the recombination fluorescence, the scintillator molecule PPO (we will denote its reactivity and concentration by a. and co, respectively) is an electron scavenger and the fluorescence intensity is, as will be discussed later, proportional to the fraction of electrons captured by PPO. When an electron scavenger S is added, PPO and S compete to capture e-. The fluorescence intensity is then given by
The scavenger S sometimes can quench the excited state of PPO (reaction 15), and the lifetime of PPO* decreases from l / X o in neat PPO solution to 1 / X = l / ( X o k,c) in scavenger solution. By multiplying a correction factor due to this effect to eq 4, we can derive an expression for the luminescence intensity relative to that in neat PPO solution, IFo:
+
The Ps formation probability is then p(1 - f(c)), and the 0-Ps intensity relative to that in neat solvent is
Xo
1
(lc/l=')-
where I , and I,' are the intensities of the long-lived component of the e+ lifetime spectra in scavenger solutions and in neat cyclohexane, respectively. The lifetime of this component, X30 (= 0.385 ns-l in aerated cyclohexane), increases only slightly on addition of the scavengers, but its amount is no more than 10% up to the scavenger concentration of 1 M. This normally does not bring forth a significant error in the estimation of I,; hence, we can relate it to 0-Ps intensity. Sometimes a function (eq 3) which is more flexible than eq 2 13/13'
=
1
1
+ (ac)"
(3)
is used with both a and u taken as adjustable parameter^.^^'.'^ There is indeed an argument in radiation chemistry15 that the exponent u is 0.6 at a low-concentration region. Probably the (14) Zhang Man-wei and Wu Wen-yuan, Radiat. Phys. Chem., 20, 223 (1982). (15) J. M. Warman, "The Study of Fast Processes and Transient Species by Electron Pulse Radiolysis", J. M.Baxendale and F. Buci, Eds., Reidel, Dordrecht, The Netherlands, 1981, pp 433-533.
+ k,c
(~OC~)'~~
=
1
+ (aOco)l/' + acp2
t (a0co
(5)
The reactivity parameter of PPO is not known. We found beforeI7 that PPO is as efficient an anti-inhibitor as biphenyl (Ph,), for which the a value is known (= 15 M-' 16). Although this does not necessarily mean that PPO and Ph2 have the same a value (e' reactivity is involved as well as e- capture), we have assumed a. = 15. This choice of the a. value is thought to be valid when the electron abstraction probability from PPO- and Ph2- is 1 (see Figure 3 of ref 10). As shown in Figure 2, the fluorescence time profile is not simple but can be roughly approximated by a main exponential decay component and slower ones. The fluorescence rate determined from the slope of the main component was ho = 0.53 ns-'. The quenching rate constant k, can in principle be estimated from the slope of fluorescence time profile in the scavenger solutions. The plot of X vs. scavenger concentration is in fact not linear (see Figure 3). This is because the formation of the PPO* excited state takes
-
(16) J. M. Warman, K. D. Asmus, and R. H. Schuler, J . Phys. Chem., 73, 931 (1969). (17) Y . Ito et al., paper presented at the 22nd Radiation Chemistry Symposium in Japan, 1979 (in Japanese).
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1923
Scavenger Effects on Ps and Fluorescence Intensity
TABLE I: Classification of Electron Scavengers according to Their Effects on Ps Formation, together with Their Reactivity (cy) Parameters and the Rate Constants of Quenching (k,) Excited-State PPO* in Cyclohexane
lo9 S-1
0.8
It
,
109k
scavenger normal inhibitor
f
strong inhibitor
1 , , , , , 20 CCl,
40
60
80
concentration
mM/dm3
Figure 3. The slope, A, of the fluorescence time profile in 10 mM PPO solution in cyclohexane as a function of the concentration of added CC4. The broken line corresponds to A. = 0.6 X lo9 S-I and k, = 2.0 X lo9 M-' s-' from ref 19.
partial inhibitor enhancer a
CHCI, CH,CI, C,H,Br C,H,I CCI. Ccl;CCI, CBr, CHBr, CH, Br, CS, C, F'
cy,
M-'sq;
M-'
I .3 5.3
0
0 0
7.2 (7.8)'
14.5
2.4 2.0
12.8 (12)'
12.0
2.5 13
17.6
I
10.2 7.3 16.6 15b
1.2
5
The value in the parentheses is from ref 11,
Reference 10.
\
\ 001
Reduced I
I
0.01
Reduced
0.1 concentration
I
1 MC
10
Figure 4. Plot of (IF/I&')(A,, + @)/Ao as a function of the dimensionless concentration parameter CYC (reduced concentration) for the electron scavengers. The a and k, values listed in Table I are used for each scavenger in this plot. The solid curve corresponds to the right-hand side of eq 5 with CY^ = 15 M-' and co = 10 mM: (0)C2H5Br,(m) CHCI,, (0) CH2CI2,(0) CS2,(0) C2H51,( 0 )CH2Br2,(4CCL, (X) CCI,CCI,, ( e )CHBr,.
place over a long time range due to the distribution in the initial separation between the geminate ion pairs, electron capture by PPO,diffusion of PPO-and M', etc.'* The rate constant of quenching photochemically produced PPO* by CCl, (k, = 2.0 X lo9 s-I M-' 19) is shown in Figure 3 by the broken line. Apparently, the previous results show this slope of k, only at a high-concentration region of CC14. We can, however, use such a plot to make an approximate guess of k,. Since the correction factor due to the quenching becomes significant only at high scavenger concentrations, we can determine the values of a and kq without much arbitrariness. Our procedure was to see at first whether eq 5 can be used to fit the experimental data of fluorescence intensity. Since k, can be determined separately from the time profile of fluorescence, CY is basically the only parameter that has to be adjusted. After finding a best fit of the a value, we examine whether eq 2 gives a good fit to the Ps formation data with this same a value. Results The results of the fluorescence measurements are summarized in Figure 4 where (ZF/ZFo)(Xo + k,c)/Xo is plotted against the reduced concentration ac. Clearly, the experimental points of all the scavengers can be placed well on the curve of eq 5 with a suitable selection of a values. The values of a and k, thus determined are summarized in Table I. It is important to note that (18) (a) S . J. Rzad, J . Phys. Chem., 76, 3722 (1972); (b) M. C. Sauer and C. D. Jonah, ibid., 84, 2539 (1980). (19) (a) T. Takahashi, K. Kikuchi, and H. Kokubun, J . Photochem., 14, 67 (1980); (b) Y . Katsumura, S . Tagawa, and Y . Tabata, J . Phys. Chem.,
84, 833 (1980).
IO
01 conceritration
100
aC
Figure 5. Inhibition effects of the "normal inhibitors". The concentration of the scavengers are normalized to a reduced concentration ac by using the CY values listed in Table I. The solid curve corresponds to eq 2: (0) C2H51,(X) CH2CI2,( 0 )CHCI,, (0) C,H,Br.
the a values for C2H5Br (= 7.2) and CC14 (= 12.8) are very close to 7.8 and 12, respectively, which are the values often found in literature, and thus are considered to be established for these scavengers.' 1,20 This strongly proves how the previous photon counting technique can provide a reliable method to determine the a values. The CY values thus determined were used to examine the Ps formation data in terms of eq 2, and the electron scavengers have been found to be adequately divided into four groups with respect to their inhibition effects. The first group consists of scavengers whose inhibition effect is described approximately by eq 2. C2H5Br,C2HSI,CHC13,and CHzClzbelong to this group (Figure 5 and Table I). These scavengers have moderate a values and do not, with the exception of C2H51,quench PPO*.The agreement with eq 2 is, however, not complete, and a much better fit over the entire concentration range can be derived by taking smaller a values. Defining the a value thus determined by a', we have a/ = 4.8 (as compared to 7.2 in Table I) for C2H5Br,a' = 11 (14.5) for C2H51,a' = 4 (5.3) for CH2C12,and a' = 6.8 (7.3) for CHCI,. Thus, the a' values directly determined from the Ps data are up to about 30% smaller than those in radiation chemistry. We note, however, a systematic trend: for all scavengers the data points at a low-concentration range are found above eq 2, while the agreement is well at intermediate concentrations. It was due to this that we claimed before, in our experiments which were carried out in this intermediate concentration region,I0 that the Ps formation data can be described well by eq 2. We will call this group of scavengers "normal inhibitors", emphasizing that their inhibition effects are well described, especially at the intermediate concentrations, by the WAS equation with the a values essentially the same as those in radiation chemistry. The second group consists of CCl,, CBr,, CHBr,, CH2Br2,and CC13CC1, (see Figure 6 and Table I). Clearly, they are more ~
~
~~~
(20) G. W. Klein and R. H. Schuler, J . Phys. Chem., 77, 978 (1973).
1924 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
efficient inhibitors of Ps formation than expected from eq 2, the deviation from which becoming more significantly downward at higher concentrations. The scavengers of this group have large a values and also quench PPO* quite efficiently. We note also that the data points at a low-concentration region tend to come above eq 2 as in the case of normal inhibitors. Emphasizing their efficient inhibition behavior above intermediate concentrations, however, we will call this group “strong inhibitors”. Our data for CC1, and CC13CC13can be compared to those reported by Wikander:7b for CC14 the data were almost the same; for CC13CCl, there was some small difference, but both data agreed in that this scavenger is a strong inhibitor. The third group, which we will call ”partial inhibitors”, exhibits a less efficient inhibition effect than expected from eq 2 (see Figure 7 ) . CS, is the only example of this group at present. In spite of its large cy value (= 16.6 M-I), Ps formation probability decreases only slightly on addition of CS,, the data points being found far above the solid curve corresponding to eq 2. After passing a minimum at about 1 M, Z3increases again, which agrees with that reported by Jansen et aL21 The latter authors discussed the minimum in Z3 in detail, but the partial nature of the inhibition below 1 M was not recognized at that time due to lack of knowledge of the parameters of electron capture by CS,. The fourth group consists of those scavengers which exhibit anti-inhibition and antirecombination22effects. Biphenyl, C6F6, and naphthalene are the examples.23 We will call this group of scavengers “enhancers”. Since the behavior of this group of scavengers has been d i s c u ~ s e d , ’we ~ ~will ~ ~ not repeat it here. Discussion Recombination Fluorescence. First we will discuss why the scavenger effects of fluorescence intensity can be described by the WAS equation. Energy transfer from solvent excited states and delayed recombination of ion pairs are the two major mechanisms of producing solute excited states in organic liquids. But in saturated hydrocarbons, the latter is more important and the excited state, PPO*, is formed mainly via charge scavenging reactions in the geminate recombination process:I8 M e-
-
M+
w-
+ PPO
+ e-
(6)
PPO-
(7)
+ + + -
PPO-
+ M+
M+
PPO
e-
PPO+ PPO+
+M PPO+ + M PPO*
PPO*
PPO-
(8)
(9) (10)
PPO*
PPO* -,hv
(11) (12)
Reactions 7 and 8 are the major pathway of producing PPO* since the mobility of e- is 2515 and several hundred times larger than that of M+ and PPO-, respectively, in cyclohexane. Whichever pathway it may take, however, one of the precursors of PPO* is e-. Electron scavenging by S (reaction 13) will e-
+ S (or RX)
-
S- (or R
+ X-)
(13)
eliminate e- by an amount described by the WAS equation. And thus, the fluorescence intensity can be described by using the WAS equation for two-scavenger systems as in eq 4. The scavenger S may also be involved in electron-transfer (reaction 14) or energy-transfer (reaction 15) PPO-
+s
-
PPO
+ s-
(14)
(21) P. Jansen and 0. E. Mogensen, Chem. Phys., 25, 75 (1977). (22) B. Levay and 0.E. Mogensen, ”The Structure and Properties of Solid Surfaces” (Proceedings of the 4th International Materials Symposium held at the University of California, Berkeley, June 17-21 (1968); Wiley: New York, 1969. (23) Y. Ito and Y. Tabata, Radiat. Phys. Chem., 15, 319 (1980).
PPO*
+s
-
Ito et al. PPO
+s
(15)
reactions. Since the rate constant of reaction 14 is expected to be of the order of 108-109 M-] s-l, it is not efficient to inhibit PPO* formation. We will disregard contribution from this reaction, as will be justified by the reasonable final results of this treatment. The lifetime of PPO* is long enough for reaction 15 to become significant, and we have to include a correction term as in eq 5 . The solute fluorescence can also occur by other mechanisms. It is reported that PPQ* is formed as a result of direct excitation of PPO molecules by Cerenkov light.24 Indeed, it was observed in our experiments that the fluorescence was not completely suppressed even at very high concentrations of scavengers. For 10 mM PPO solutions of CHCl3 and CH2CI2,for example, the fluorescence time profile was such that a decay cqmponent with a very small intensity was superimposed on the Cerenkov light pattern. The solute fluorescence may also result from volume recombination of free ions. But its fraction is small, and moreover, the fluorescence will be overwhelmed by intersystem crossing or phosphorescence. We will disregard contribution from these processes as being of minor importance. Normal Inhibitors. For the normal inhibitors, the inhibition effect is interpreted mainly in terms of electron scavenging reactions, and contribution from any other reactions may not be important. The agreement of Ps formation data with eq 2 for the normal inhibitors would be rather surprising for several reasons. Firstly, the form of the WAS equation is considered to come from the inhomogeneous nature of the initial separation between geminate ion pairs and can be derived theoreticallyZ5for single-ion-pair spurs under a suitable assumption of the initial distribution of M+-e- distance. In the positron spur, e+ itself is a reactive entity which is also distributed inhomogeneously with respect to e-, but there is no reason to expect the WAS-type of expression to apply. The model illustrated in Figure 1 supersimplifies the e+ spur, and e- is assumed to be divided into two parts, each with fraction p and 1 - p . It is further assumed that the WAS-type of function applies to electron-scavenging reactions for the e+-e- pairs. We will recall an expression for the reactivity parameter theoretically given for single-ion-pair spurs.26
k, is the rate constant of the electron capture reaction, rc is the Onsager’s critical distance, D is the relative diffusion constant of the ion pair (D = D+ D-),and Gfi and Ggiare the G values of free and geminate ions. Even if this expression is assumed to be extrapolated to e+-e- pairs, the a value may be different from that of usual radiation chemistry: D = D+ D-may be larger for e+-e- pairs, and Gfi/Ggimight also be different. The fact that the a’ values directly obtained from the Ps formation data are about 30% smaller than those in radiation chemistry might mean that the distance between e+ and e- is, on the average, smaller than that between geminate ion pairs in radiation chemistry. Secondly, the positron spur can be different in structure from the usual spurs in radiation chemistry. Since LET of e+ is considered to become larger at its final stage of energy loss process, the terminal positron spur is expected to be composed of many ion pairs. The significant upward deviation of the data points at the low-concentration range (Figure 5) conforms to the concept either that the positron spur is composed of many ion pairs or that the distribution of e+-e- distance is different from that of M+-edistances in radiation chemistry. Before going into this kind of argument, however, it will be necessary to refine the simple model of the positron spur of Figure 1. Detailed discussion of this problem will be done in a forthcoming paper with results of more extensive measurements.
+
+
(24) Y. Katsumura, S. Tagawa, andd Y. Tabata, Radiat. Phys. Chem., (26) (a) J. A. Crumb, J . Phys. Chem., 83, 1130 (1979); (b) M . Tachiya, J . Chem. Phys., 70, 4701 (1979).
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1925
Scavenger Effects on Ps and Fluorescence Intensity 1311;
001
01
10
I
Reduced concentration
100
aC
Figure 6. Inhibition effects of the “strong inhibitors”. The concentration of the scavengers are normalized to a reduced concentration ac by using the LY values listed in Table I. The solid curve corresponds to eq 2. Note that the experimental points are found below this curve as compared to the results in Figure 5 : (0)CHBr3,(e) CH2Br2,(X) C2CI6,(A) CC14.
DBPA line width. This cannot, however, explain the insufficient anti-inhibition effect of C6F6 in Ccl4solutions in cyclohexane. It must be explained further why then e+ is not captured by the anions formed from the normal inhibitors. There is a tendency that the strong inhibitors are, on the average, more efficient electron acceptors than the normal inhibitors, since their 01 values are larger and they can quench PPO*. Another tendency to be noted is that the molecular size of the strong inhibitors is larger than that of the normal inhibitors. Partial Inhibitors. In order to explain the partial nature of the inhibition by CS2, we will reconsider the simple model of Figure 1. The electron scavenger S (CS2 in the present case) captures e- to form S-. We assume further that e+ can abstract the captured e- and form Ps. e+
I
01
001 CS,
concentration
1
10
(mol / dm3i
Figure 7. Effect of CS2 on 0-Ps formation probability in cyclohexane. The minimum of the Ps intensity is seen around 1 M. The solid curve corresponds to eq 2, and the broken curve to eq 18 with p = 0.75 and A = 0.48 and 0.6.
Strong Inhibitors. The inhibition effects of the second group of scavengers are much stronger than expected from eq 2. Such an anomalously strong inhibition effect was known for CC14.10327 It was pointed that the line shape of the Doppler broadened positron annihilation (DBPA) radiation was broader for CCll solutions than for C2H5Bror CH31 solutions. This suggests a possible formation of some e+-containing compound. Another important observation was that, while the anti-inhibitor c6F6 could suppress the inhibition effect of C2H5Brcompletely, it could only insufficiently suppress the effect of CC14. These observations lead us to postulate an additional pathway of the inhibition of Ps formation: a positrion capture by CC14 like e+ + CC14
-
PsCl
+ CC13+
The possibility of this reaction has not yet been confirmed experimentally nor theoretically. We will simply mention for the present that the existence of PsCl is well established2*and that CC13’ also seemed to have been observed recently.29 It is seen from Figure 6 that the downward devation from eq 2 differs for different scavengers. This fact may give some support to the postulated et capture, because the efficiency of the et capture should depend on the specific nature of the scavengers. From this point of view, the efficiency of e+ capture is, in the increasing order, CH2Br2,CCI4, c2c16, and CHBr,; Le., a scavenger with larger molecular size is a ”stronger” inhibitor. An alternative explanation for the “strong inhibition” may be to suppose that e+ reacts with, in the case of CC14 for example, C1- formed as a result of the electron scavenging in multi-ion pair spurs. At a glance this seems quite probable. It can indeed explain both the “strong” nature of the inhibition and the change in the (27) Y. Ito, Y. Miyake, Y. Tabata, and M. Hazegawa, Radiat. Phys. Chem., 21, 217 (1983). (28) (a) A. Farazdel and P. E. Cade, J . Chem. Phys., 66,2612 (1977); (b) 0. E. Mogensen and V . P. Shantarovich, Chem. Phys., 6, 100 (1974). (29) R. E. Buhler, Radiat. Phys. Chem., 21, 139 (1983).
-
Ps
+S
(17)
This kind of reaction has quite often been suggested to explain the anti-inhibition or the antirecombination effects of C6F6or many aromatic compounds.23 Defining the probability of this abstraction reaction by A , we can write the Ps formation probability as
4/I,O =
0001
+ S-
1
1 (1 + $(ac)’!’) + (ac)’/2
(18)
A similar expression with A = 1 was successfully used to explain the anti-inhibition effects of an enhancer, C6F6.lo For the normal inhibitors, A should certainly be close to 0. CS2 is considered to be an intermediate case between the normal inhibitor and the enhancer. The broken lines in Figure 7, corresponding to eq 18, agree with the data only at limited regions. However, if we take into account the fact that Z3 somehow becomes larger at the low concentrations (Figures 5 and 6), we may get a good fit with A 0.48. It will not be productive, however, to go into further arguments on this point until we get a better picture of the positron spur. The thermodynamic criterion for reaction 17 may be written as follows.
-
EA(S) - P(S-)
< Vo(e+) + 6.8 eV
(19)
EA(S) is the electron affinity of S , Vo(e’) is the positron work function in the solvent, P(S-) is the solvation energy of S-, and 6.8 eV is the binding energy of Ps. According to the Born expression, P(S-) is given by
p(s-) =
-“( ;) 2a 1 -
where a is the average radius of S- and t is the static dielectric constant. We have little knowledge of Vo(e+) in organic substances, but it is known to be negative in many metals.30 Recently e+ mobility in n-hexane has been reported to be large,,’ a result which suggests a negative work function of e+. Taking Cl- as an example, EA(C1) - P(Cl-) = 3.61 + 1.99 = 5.6 eV. It is known that the anion Cl- never transfers e- to e+, and thus the right-hand side of eq 19 is probably smaller than 5.6 eV. In the case of C6F6, the left-hand side of eq 19 is much smaller (EA = 1.2 - 1.8 eV32 and P = -1 eV), a favorable condition for the criterion. This explains why C6F6 behaves as an enhancer. CS, may have a somewhat larger absolute value of P due to smaller size then C6F6, but its electron affinity is smaller instead (0.5-1.0 eV3,), and the (30) W. Brandt, Adu. Chem. Ser., No. 158, 129 (1976). (31) F. Heinrich and A. Schlitz, ”Proceedings of 6th International Conference on Positron Annihilation, April 3-7, 1982, Arlington, TX”, P. G. Coleman, S. C. Sharma, and L. M. Diana, Eds., North-Holland Publishing Co., 1982, p 705. (32) (a) F. M. Page and G . C. Goode, “Negative Ions and Magnetron”, Wiley-Interscience, New York, 1969; (b) C. Lifshitz, T. 0. Tierman, apd B. M. Hughes, J . Chem. Phys., 59, 3182 (1973); (c) E. C. M. Chen an4 W. E. Wentworth, ibid., 63, 3183 (1975). (33) (a) K. Kraus, W. Muller-Duysing, and H. Neuert, Z . Naturforsch., A , 16A, 1385 (1961); (b) H. Disert and K. Lachmann, Hahn-Meitner Ins!. Kernforsch. Berlin, HMI-B 198, 34 (1975); (c) R. N. Compton, P. W. Reinhardt, and C. D. Cooper, J. Chem. Phys., 63, 3821 (1975).
1926 The Journal of Physical Chemistry, Vo1. 88, No. 9, 1984
criterion of eq 19 is expected to hold as well. Thus, it seems quite reasonable to think that reaction 17 can occur for CS2. The problem may be why CS2 exhibits a partial nature ( A < 1) in reaction 17 while CsF6, biphenyl, etc. seem to have unit abstraction probability ( A 1). At present we lack exact data even of the electron affinity to discuss this problem. The rise of Z3 after passing the minimum might be explained, without referring to an assumption of increased electron mobility as in ref 21, in terms of the criterion of eq 19. Firstly, the positron work function may change at high CS2 concentrations. Secondly, at high CS2 concentrations, ion clusters (CS2); will be formed, and such cluster formation should result in a reduction in the absolute value of the solvation energy. These situations can well be expected to lead to an enhanced e- abstraction by e+ in such a naive case of partial inhibition. CS2 seems to be the only partial inhibitor known at present. We note, however, that the data points of some of the normal inhibitors, especially C2HSBr(see Figure 5 ) , tend to come above eq 2 at very high concentrations. There is some possibility of reaction 17 to be taking place for such scavengers, the abstraction probability A being very small, but not zero.
Conclusion The present parallel study between Ps formation and fluorescence has made it possible to classify the electron scavengers adequately into four groups with regard to their effects on Ps formation in cyclohexane: normal, strong and partial inhibitors and enhancers. There may not be fundamental mechanistic differences among the normal inhibitor, the partial inhibitor, and the enhancer, an important difference possibly being in the
Ito et al. magnitude of the electron abstraction probability A . The effects of the normal inhibitors seem to be described fairly well by eq 2 with the LY values derived from radiation chemistry, but much remains to be studied to see what such surprising agreement implies. Detailed information concerning the struture of the positron spur and the processes occurring in it is believed to be included in the deviations (as in Figure 5 ) from the radiation chemistry data, and this is going to be the subject of our future investigation. The effects of the strong inhibitors might be explained by assuming e+ capture, but such an assumption has to be tested by further studies. Detailed study of the partial nature of the inhibition by CS, will also be important for the understanding of the processes occurring in the positron spur. Although the previous results strongly favor the spur reaction model of Ps formation, it does not necessarily exclude entirely the possibility of Ps formation by the Ore model. It is difficult to think that all Ps are formed by the spur reaction model. We would better ask why there seems to be no or little Ps formation by the Ore model in the condensed phase.34 The present comparative study between recombination fluorscence and Ps formation is very useful to clarify the mechanism of Ps formation. Further experiments using other electron scavengers are under way. Registry No. CHC13,67-66-3; CH,CI,, 75-09-2; C,H5Br, 74-96-4; C2H51,75-03-6; CCI,, 56-23-5; CC1,CCI3, 67-72-1; CBr,, 558-13-4; CHBr3, 75-25-2; CH2Br2,74-95-3; c s 2 , 75-15-0; C6F6, 392-56-3; Ps, 12585-87-4; e+, 12585-85-2; cyclohexane, 110-82-7. (34) 0.A. Anisimov, V. L. Bizyaev, S. V. Vwel, and Yu.N. Molin, Chem. Phys. Let?., 76,273 (1980).
