2370
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
B. Djermounl and H. J. Ache
Positronium Formation Process in Organic Liquids Belkacem Djermounl and Hans J. Ache” Department of Chemistry, Virginia Polytechnic Institute and State Unjverslty, Blacksburg, Vlrglnia 2406 1 (Received May 3 I, 1978) Publlcatlon costs assisted by the Petroleum Research Fund
The formation of positronium in benzene solutions containing a variety of halogenated compounds, such as CC4, CH2C12,C2HC13,l,l,l-C2H3C13,o-C6H4CH3Br,o-C6H&l2, o-C6H4CH3C1,C6H&1, and other mono- and dihalobenzene, was studied in the presence and absence of C6Fsadditives. The observed Iz values, which are indicative of the number of thermalized positronium atoms formed, showed in each system a good correlation with dissociative electron attachment parameters of the solute species. C6F6additives increased the number of Ps atoms reaching thermal energies. The experimental results are discussed in terms of a reaction scheme in which Ps is formed as a result of electron abstraction from the surrounding molecules by energetic positrons. These Ps atoms can either react rapidly with solute species if their excess kinetic energy favors such a reaction, or with species generated in the reactions of free electrons produced in the positron spur with solute molecules via dissociativeelectron attachment. The number of these reactive species is mainly determined by the number of free electrons having sufficient energies to undergo dissociative electron attachment. A compound such as C6F6,which has a high cross section for nondissociative electron attachment, competes for free electrons with the solute, and protects the latter from radiolysis. Thus in the presence of c$F, fewer reactive species are formed in the spur with which the Ps can rapidly react and more Ps atoms will reach thermal energies. An alternative to this reaction scheme is the previously reported spur reaction model which assumes positronium formation via free positron and free electron combination in the positron spur. The results will be also discussed within the framework’of this latter model.
Introduction Positrons (e’) are formed with high kinetic energies as a result of the radioactive decay of certain neutron deficient nuclides. They lose most of their kinetic energy in collision with surrounding matter before they annihilate as free positrons with an electron under emission of photons. A fraction of them, however, will combine with electrons to form the bound state of positronium (Ps), which can exist in two ground states, the singlet or para-Ps with antiparallel orientation of positron and electron spin, and the triplet or ortho-Ps with parallel spin orientation; the two species are usually generated in the ratio ortho to para 3:l.I The exact mechanism for the formation of positronium is still the subject of considerable discussion. While for the formation of Ps atoms in gases the Ore gap mode1,l which assumes that positrons slowing down from higher energies pass through an energy gap in which they are capable of abstracting electrons from the surrounding matter to form Ps, is the generally accepted model, other authors suggested that in liquids and solutions other mechanisms such as the combination of a positron and a secondary electron in the positron spur must be considered, which led to the postulation of the spur reaction2 and the modified spur reaction models3 Most of the studies on the Ps formation process were carried out via positron lifetime measurement^.^ These studies have shown that the number of 0-Ps atoms reaching thermal energies and reacting as such with surrounding matter can be correlated with the intensity, 12,of the long-lived component in the positron lifetime spectra. They also revealed that certain compounds when added to a solution facilitate a strong reduction in 12. Several mechanisms have been proposed to account for this experimental o b ~ e r v a t i o n . ~ - ~ ~ In terms of the “Ore” model for Ps formation, this phenomenon could be explained in (1)reactions of “hot” (nonthermal) Ps atom^"'^^^^ which will reduce the number of 0-Ps reacting with thermal energies or by (2) inhibition 0022-3654/78/2082-2378$0 1.OO/O
of 0-Ps formation (in the Ore gap) either by “slowing down” or by positron capture.7b Alternatively, consistent with the spur reaction model, (3) inhibition of Ps formation may be caused by electron scavenging, which reduces the number of electrons available for combination with the positron,2311-1h19-23 The “modified spur reaction model”8 combines the concept of Ps formation in the positron spur with subsequent fast interactions between the (hot) Ps atom and substrates present in the spur, e.g., radicals generated by the positron or others which can form Ps compounds. According to this model I 2 can be reduced either as the result of electron scavenging by solutes, which suppresses Ps formation, or in “hot” Ps reactions, or by both mechanisms. The experimental results obtained so far appear to indicate that none of these models can explain satisfactorily all the experimental details without making several ad hoc assumptions. One of the criticism of the “Ore” or “modified Ore” model is among others that it is not capable of explaining the so-called “anti-inhibition effect”23 of substances such as C6F6,which when added to solutions containing C C 4 cause an increase of 12,without making some speculative assumptions about positron or positronium affinities, or the sharp decrease of I2 when small amounts of CS2are added to certain hydrocarbons and the subsequent increase of I 2 a t higher CS2 concentrations.20 On the other hand the spur reaction model,2 which tries to relate radiation chemical phenomena occurring in electron spurs to the Ps formation process fails to provide an explanation for the fact, e.g., that the I2 values in solutions of halogenated halobenzenes in organic solvents level off at higher solute concentrations,lga behavior which does not conform with a model which considers competition between positron-electron combination process and the removal of electrons by the solute, acting as electron scavengers. However, in other aspects there are clear parallels between radiation chemical processes in electron spurs and the positronium formation process, e.g., as far as the dependence of I2 on the nature and composition of Q 1978 American Chemical Society
The Journal of Physical Chemistty, Vol. 82, No. 22, 1978 2379
Positronium Formation Process in Organic Liquids
the solvent is concerned.12*20 Thus in order to formulate a model which can more accurately describe the detailed mechanism of the Ps formation we have carried out several series of experiments, in which we further assessed the parameters responsible for changes in the observed I2 values in various solutions of compounds, such as the halogenated aliphatic and aromatic hydrocarbons. For these compounds the electron attachment cross sections have been previously measured as a function of electron energy (in the gas phase) and an attempt was made to correlate these parameters with I2 in order to further elucidate the exact Ps formation process.
Experimental Section The experimental procedures were essentially the same as previously described.28 (a) Positron Lifetime Measurements. Positron lifetime measurements were carried out by the usual delayed coincidence meth0d.l The resolution of the system as measured by the prompt time distribution of "Go source and without changing the 1.27- and 0.511-MeV bias was found to be less than 0.4 ns fwhm. Data analysis was carried out by using computational methods originally described by C ~ m r n i n gand , ~ ~subsequently modified by Corrections for the positrons annihilating in the source material were made. (b) Purity and Source of Reagents. The solvents were of highest available purity and when necessary dried by means of a molecular sieve and redistilled. The other compounds used in these investigations were purified by suitable methods: distillation, recrystallization, and preparative gas chromatography (until subsequent tests showed a purity of better than 99.5%). (c) Preparation of Samples. Specially designed sample vials (cylindrical glass tubes 100 mm long and 10 mm i.dJ were filled with about 1 mL of solution. The positron sources were 3-5 pCi 22Naprepared by evaporating carrier-free solutions of 22NaC1onto a thin aluminum foil. The foils were suspended in the center of the ampoule and all solutions carefully degassed by vacuum freeze-thaw techniques to remove oxygen. (The vials were subsequently immersed in a specially designed thermostat which allowed control of the temperature within f1.0 "C.) Results and Discussion In the first series of experiments positron lifetime spectra were obtained in various benzene solutions containing 0.1 mole fraction of chlorinated or brominated hydrocarbons. Consistent with previous resultdBin each case the I2 values are significantly reduced in comparison with the I? observed in neat benzene (Table I). A typical plot of I2 vs. mole fraction of an additive, in this case 0 - , p-, and m-dibromobenzene, is shown in Figure 1. If electron-positron combination in the positron spur can be compared with electron-ion recombination in the electron spur, as postulated by the spur reaction model, a simple competitive model can be derived to describe the removal of free electrons by the scavenger, and the following correlation between 0-Ps formation probability P at a given solute concentration [MI is obtained:21 P = P / ( 1 + K[M]) (1) ( P / P - 1) = K[M]
(2)
K is the scavenging or inhibition constant for the scavenging reaction between solute and electrons and P is the 0-Ps formation probability in the neat solvent. Since Po and P can be correlated with I2 and I: the results shown
TABLE I: 1, (%) and AI, ( X )Values Observed in Benzene Solutions of Various Compoundsa peak energy, compd eV 0.038 CCl, 0.78 0.038 CHCl, 0.215 0.038 CH,Cl, 0.45 0.39 C,HCl, l,l,l-C2H3C13 0.038 o-C,H,CH,Br 0.95 o-C,H,Cl, 0.36 C,H,Br 0.84 o-C,H,ClCH, 1.10
I,St., % (10 mol I,, % peak cross % in (pla- AI,, section, cmz benzene) teau) %
2.62 X lo-', 2.3 12.9 28.3 5.2 X 3.66 X 5.7 27.5 13.7 7.32 X 1.48 x lo-'* 9.9 33.8 7.4 3.18 X lo-'* 2.84 x 7.2 30.6 10.6 1.51 x lo-'' 5.2 26.8 14.4 6.0 x lo-'' 9.75 33.5 7.7 4.3 x 8.5 26.9 14.9 9.6 x lo-'' 8.2 32.4 8.8 2.2 x lo-'' 13.6 36.2 5.0 C6F6 1 ~ 0 . 0 1.23 x lo-', 40.5 41.2 0.73 8.04 X C6H,C1 0.86 1.4 X lo-'' 13.7 35.5 5.7 For comparison peak cross sections and peak energies for electron attachment to these compounds in the gaseous state are listed. References 31-34. The I, plateau values are the I, values observed in these solutions in the presence of 10-15 mol % of C,F6. AI, is given by the difference of the I, plateau's observed in a mixture of 0.15 mole fraction C6F6and 0.85 mole fraction C6H6in the absence and presence of 10 mole % additive. I, &. % is I, observed in the presence of > 10 mole % of substrate in benzene solution. (All measurements were made at room temperature. )
DEPENDENCE OF I2 ON MOLE F R A C T I O N O F DIEROMOBENZENES I N BENZENE
I EXPTL
ERROR
30
0 ORTHO 0
META 0 PARA
2ol!
1
0
01
02
03
04
05
06
07
OB
09
IO
MF
Flgure 1. I, vs. mole fraction o-, p-, or mdibromobenzene in benzene (at room temperature).
in Figure 2, where 120/12- 1 is plotted as a function of solute concentration, m-dichlorobenzene or m-dibromobenzene in benzene solution, indicate that the simple correlation between positronium formation probability and inhibition constant as formulated in eq 2 does not apply even at low solute concentrations in nonpolar solvents. Levay and Mogensen,21who investigated similar systems, claimed that the empirical expression using a second adjustable parameter, a, in the exponent, provides a better fit: P = P/(l + (K[M])") (3) We find it very difficult to fit our results as shown in Figures 1 and 2 to this expression, or to a modified version of eq 2, which was suggested by Eldrup et a l . I 3 for aqueous solutions of certain inorganic ions: P = P(1- A ) / ( l + K[M]) + A (4)
2380
B. Djermouni and H. J. Ache
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
L
12 SAT. v s LOG PEAK ENERGY FOR DISSOCIATIVE e- ATTACHMENT
5
IO
N
H
5
k[ ij
I
0
om-DICHLOROBENZENE 0m -DIBROMOBENZENE (IN BENZENE SOLUTION1
1
0 cc14 I
F 01
03 0 4 0.5 0 6 M IN MOLE/LITER
-10
02
Figure 2. I:! I2 - 1 vs. [MI in benzene solutions of mdichlorobenzene and m-dibromobenzene (at room temperature).
where A is a constant related to the saturation value of I2 obtained at higher solute concentration. Since there is no strict theoretical justification for either one of these expressions, we have not further pursued this line of interpretation and conclude that these results do not provide any evidence for a positronium formation mechanism which involves simple competition for electrons between positrons and solute species. In the past, similar results, e.g., the variance in the I2 observed for neat halogenated hydrocarbons, were explained qualitatively in terms of hot Ps reactions5 (modified Ore model for Ps formation) and related to the C-halogen bond energies by using the correlation
I9
-
DRX - D P s X RX
where IRx is the ionization potential of the halogenated hydrocarbon, DM the C-halogen bond dissociation energy, and Dpsx the Ps-halogen bond energy. Since according to the Ore model Ps atoms are formed in the Ore gap with energies from 6.8 eV to thermal, only the fraction of P s atoms with kinetic energies above DRX - Dpsx can effectively react with the compound and undergo subsequent rapid annihilation in the reaction product. I z should therefore vary as a function of DRx. While this trend has been qualitatively observed in a number of solutions and is also in qualitative agreement with the results of the present study, and would easily explain the saturation values, IzSat,,which I2 assumes at higher solute concentrations, as shown for C6H4Br2-C6H6solutions in Figure 1,one would also have to consider the possibility that the electron attachment to these compounds followed by dissociation which would remove electrons from the spur may show a similar trend: e-
-I .5
+ CeHbX
-+
C6H5 + X-
(6)
which can reduce the number of available electrons in this manner. Thus in a second series of experiments we tried to correlate the total reduction of the number of thermalized 0-Ps atoms, which is proportional to (Izo- 128at.), caused by the presence of the solute with the properties of the solute molecules which control the dissociative electron attachment process. In a previous paperlg we have found that the logarithm of the inhibition constant K increases linearly with the free
I
I
-0.5 0.0 LOG PEAK ENERGY ( e V )
I
05
Figure 3. IFt vs. maximum peak energy (in eV) for e- attachment in benzene solutions containing 10 mole % of the various compounds. (e- attachment peak energies obtained from ref 31-34 for the gas phase.)
-
energy change, -AG, for the one electron transfer process +A :, + efor the corresponding scavenger ions in aqueous solutions and suggested that the energy maximum of the cross section curve for electron attachment co-incides with the free energy change in this process. In analogy to this relationship we tested whether a similar correlation would apply for organic compounds in a relative inert solvent such as benzene. Thus as mentioned above I2 was measured in various benzene solutions containing 0.1 mole fraction of a chlorinated or brominated hydrocarbon known to undergo dissociative electron attachment resulting in the formation of C1- or Br- ions. The concentration of 0.1 mole fraction of solute was chosen because a t that point in practically every case the I2 saturation value, IZsat.,was already reached while on the other hand the solute concentration is still reasonably low so that it is not expected to change significantly the spur properties if indeed the spur model applies. The results are listed in Table I. In order to correlate IZsat.with the solute properties, one would need to know the electron attachment cross section of these compounds as a function of energy in benzene solution. Since these values have never been measured we had to rely on the corresponding cross section found for these compounds in the gas The limitations of such a comparison have been thoroughly discussed by Christophorou et al.33 and by Allen et It is clear that this approach can be only a first approximation. Thus in order to correlate IZSat.with the parameters responsible for the electron attachment to these compounds, IQSat, was plotted as a function of the previously reported peak energies for (dissociative) electron attachment (Figure 3) and also shown in Figure 4 as a function of the peak cross section^.^^-^^ The results would suggest that both factors, i.e., peak energy as well as peak cross section, have a distinct effect on the capability of the additives to suppress thermal 0-Ps formation. A perhaps even better correlation exists if is plotted as a function of the activation energy E* for the dissociative electron attachment to these compounds (Figure for a series of aliphatic 5). As shown by Wentworth et halogenated compounds E* is linearly related to the change in internal energy AE occurring during this process. AE = DAB - EAB where DAB is the A-B bond dissociation energy and EAB is the electron affinity of B. Further evidence for the possible dependence of the number of thermal Ps atoms formed by solute or solvent
The Journal of Physical Chemistry, Vola82, No. 22, 1978 2381
Positronium Formation Process in Organic Liquids 1 2 SAT. vs PEAK CROSS-SECTION FOR
DISSOCIATION ELECTRON ATTACHMENT 14
o-C6H4CH3CI~C6H~CI
/
12
-8
IO
t
v)
8
RI
Y
6
4
0
I
I
- I3
I
I
I
I
I
-17
-15
-19
LOG PEAK CROSS-SECTION (crn2)
Figure 4. vs. peak cross section for e- attachment in benzene solutions containing 10 mole % of the various compounds (at room temperature). (e- attachment cross sections obtained from ref 31-34 for the gas phase.)
0.2 0.4 0.6 0.8 0.9 MOLE FRACTION C6Fg
Flgure 0. I, vs. mole fraction of C,F, in solutions of benzene and cyclohexane containing 0,l mole fraction CCI.,.
I, vs
MOLE FRACTION ADDITIVE
I EXPTL
45
ERROR
1 2 SAT. vs ENERGY OF ACTIVATION FOR
DISSOCIATIVE e- ATTACHMENT (E') 14
40
-
I
e 9 12
-
-
2
10 r
30
+a ?J
H
35
s25
0
02
04
06
08
I
MOLE FRACTION ADDITIVE
Figure 7. I, vs. mole fraction of additive in solutions of C6FBin C,H6, m-C,H,F, in C&, and CeF, in CsH5F.
-
1
0
1
2
4
6 8 E ' (kcal/mole)
IO
I2
Figure 5. Insat. vs. E" (energy of activation for thermal electron attachment, from ref 36-37).
interactions with free electrons can be obtained from the results obtained upon addition of compounds such as hexafluorobenzene which exhibit an extremely large cross section for nondissociative electron attachment. In this series of experiments positron lifetime spectra were obtained in various C6H6-C6F6mixtures which contained a constant amount, i.e., mole fraction of CC14 (10 mole %) while the mole fraction of C6H6and C6F6was varied. As can be seen from Figure 6 where Iz is plotted as a function of [C6F6]/[C6F6]+ [C6H6],I2increases from 2.3% in pure benzene (+lo mole % CC4) to reach a plateau of 12.9% a t about 0.1 mole fraction of C6F6. A higher C6F6
concentrations Iz slightly decreases before it further increases to approach eventually 41.2% in pure C6F6(+lo mole % CC14) solutions. Similar results are obtained in cyclohexane solution although the plateau region is reached in this case only a t higher C6F6concentrations. These experiments differ from those carried out previously by Anisimov et al.23in that in our studies the mole fraction of CC14was kept constant while the other authors used a constant volume fraction of CC14 solution which leads to considerable changes of the number of CC14 molecules present in the various solutions. The slight decrease of Iz in the concentration range of 0.4-0.5 mole fraction C6F6 in C6H6-C6F6-CC14solutions is real and probably a result of the sharp decrease of I2 in neat C6F6-C6H6mixtures as indicated in Figure 7. One can assume that electrons formed in the positron spur in C6H6-CC14mixtures become preferentially attached to C C 4 , which dissociates into CC13 and C1-. In the presence of increasing amounts of C6F6which has also a high cross section for electron attachment more and more
2382
B. Djermouni and H. J. Ache
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
I
I
A I2 v s PEAK CROSS-SECTION
1
FOR e- ATTACHMENT 7Ccl4
1 EXPTL ERROR
Y 0.I
0
02 [C6F614C6F61
0.3 +
Figure 8. I2 in [C,F,-C,H,-additive] mixtures as a function of [C6F6]/([C6F6] [CBH6]). The mixtures contain consistentiy 10 mole % additive.
+
electrons will become attached to C6F6which competes for electrons with CC14. In contrast to CC14, however, the attachment to C6F6is nondissociative. Thus the overall result of adding C6F6or similar compounds to solutions is that fewer free electrons are available in the positron spurs to undergo dissociative attachment processes. This again emphasizes the role of free electrons in determining the number of thermal positronium atoms reaching thermal energies as indicated by the effect of these former compounds on the I , values. These experiments were extended to study positron annihilation in benzene solutions of a series of compounds which are known to undergo dissociative electron attachment, such as CHCl,, CHZCl2,C2HC13,1,1,1-C2H3Cl3, o-C6H4CH3Br,O-C&&C12, O-C&&CH3Cl, C6H&h, and C&&1. As in the case of the C6F6-C6H6-CC14system I 2 was determined as function of the mole fraction [C6F,]/([C6F6] [C&,]) in so~utionscontaining 10 mole 70of the additive. Similar to the system small amounts of C6F6result in a drastic increase of I z leveling off to a plateau at about 0.1 mole fraction of C6F6 present, followed by a second increase of Iz with about 0.8 mole fraction of C6F6 added. The Iz's observed in the plateau region are listed in Table I. As a measure of the effectiveness of these solutes to compete with C6F6for electrons we defined, as AIz, the difference between the Iz's of the plateau observed in each of these mixtures and Iz in C6H6-C6F6 solutions without any other additive present, measured over the same C6H,-C6F6 composition range. This procedure is schematically shown for CC14and C6H5Br additives in Figure 8 and the AI,'s are listed in Table I. A large AI2 would indicate that the additive effectively competes with C6F6for electrons and vice versa. A first qualitative evaluation of these data can be obtained by plotting AI2 as a function of the peak energies, peak cross section, or E* the activation energy for e- attachment (Figures 9-11). The smooth correlation between AIzand these electron attachment parameters seems to confirm the expected trends. These results are in line with the observations that if a compound with a higher nondissociative electron attachement peak energy and a definitely
+
-13
[C6H61)
-15
-17
LOG PEAK CROSS-SECTION ( c m 2 )
Figure 9. AI, vs. log peak cross section for e- attachment in C6H,-C,Fa solutions at room temperature containing 10 mole % of additive. (eattachment cross section from ref 31-34.) A I , vs ENERGY OF ACTIVATION FOR DISSOCIATIVE e - ATTACHMENT (E')
I
30
EXPTL. ERROR
-8
1
cu 20
H
a
IC
2
0
-I
4
6 8 E * (kcal/mole)
IO
12
Figure 10. Ai, vs. log peak energy for e- attachment in CBH,-C6F, solutions at room temperature containing 10 mol % additive (peak energies taken from ref 31-34). A I 2 v s LOG PEAK ENERGY FOR DISSOCIATIVE e- ATTACHMENT
I
om14 c
9
eN 20
2
EXPTL. ERROR
l\
IO
I
-I .5
-I 0
I
I
-05 0.0 LOG PEAK ENERGY ( e V )
I
0.5
Figure 11. AI, vs. E",the activation energy for electron attchment ( E " from ref 36-37).
less expanded energy range in which it can attract electrons combined with a smaller attachment cross section such as rn-C6H4F2is added to a solution containing CC14it cannot
Positronium Formation Process in Organic Liquids
l5F7!
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978 2383
react with one of the transient species again leading to rapid annihilation. The fact that the addition of C6F6increases the number of Ps atoms makes it very doubtful that the “hot” Ps reactions with CC14 are the only processes occurring. As discussed above C6F6 will scavenge electrons and thus reduce the number of electrons which could directly interact with Ps or the number of products formed in the reactions between electrons and the solute, CC14etc., with which the Ps may subsequently react. The good correlation between I$at.and the dissociative electron attachment parameters especially the activation energies (as IN BENZENE SOLUTIONS shown in Figure 5 ) determined from thermal electron CONTAINING 0.1 MF ADDITIVE attachment would suggest that the reactive products I EXPTL ERROR formed in this radiolysis are organic radicals and halogen ions. Since halogen ions have been shown to be fairly unreactive it stands to reason that the reactions between the freshly formed Ps and these radicals are responsible for the rapid positron annihilation. If one wants to adopt this mechanism one would also have to consider the fact that I2 shows a saturation behavior. To explain this observation one can postulate that 02 04 06 0 0 0.9 the number of electrons in the spur and their kinetic MOLE FRACTION m-CgHqF2 energy distribution is a constant for all systems; it will be also small compared with the number of solute concenFigure 12. I2 vs. mole fraction of rn-C6H,F, in benzene solutions containing 0.1 mole fraction additive. trations where I , levels off. Benzene will not significantly interfere with the electron compete with CC14 for electrons and I z does not increase. attachment to the solute (or C6F6)since the onset energy On the other hand a partial effect is seen in the case of for dissociative electron attachment to benzene in the gas C6H5Br or C6H4C12solutions, where the solutes have phase is comparatively large31-34P7.9 eV) and the thermal comparable cross sections for electron attachment and a attachment rate for nondissociate attachment is very small slight enhancement in I 2 can be observed as demonstrated compared with fluorinated compound (see, e.g., table 6.8, in Figure 12. p 501, in ref 31). Summarizing the results so far one would have to draw Under these conditions it seems reasonable to assume the conclusion that the kinetic analysis of the I z data that all electrons which are energetically capable of carobtained with increasing amounts of chlorinated or brorying out this process, i.e., those which have kinetic enminated hydrocarbons present in neat benzene as solvent ergies in excess of the required activation energy for provides little evidence for a competition between solute electron attachment, will become attached to the solute species and positrons for free electrons as formulated in or C6F6molecules. eq 2, 3, or 4 which casts some doubt on the applicability values and their of the spur reaction model. On the other hand the IZsat. This would explain the observed IZSat. dependence on the electron attachment parameters, which values observed a t somewhat higher solute concentration, in turn are related to the corresponding bond dissociation as well as the effect of CC14, clearly suggest that the energies. presence or absence of free electrons in the solutions has A distinction between the direct “hot” Ps reactions with a profound effect on I,, i.e., on the number of Ps atoms the substrate and the reactions of Ps with the reactive reaching thermal energies. species formed in the spur via electron attachment which It seems reasonable to consider the observed results in both should show the same dependence on the bond terms of two reaction schemes. In the first one the asdissociation energies of the solute3-10molecules involved, sumption shall be made that Ps is formed by energetic can be derived from the experiments in which C G Fhas ~ positrons abstracting electrons from the surrounding. This been added. would correspond to the classical Ore mode1,l whose apBecause of its low activation energy for nondissociative plicability has been supported in gas phase experiments. electron attachment, C6F6should (at a concentration of In any solvent the Ps formed in this manner will, however, 0.1-0.2 mole fraction) have effectively scavenged the be surrounded by transient species, such as dry or solvated available free electrons and protected the solute molecules electrons and other reactive species formed in the positron from radiolysis via dissociative electron attachment. spur by radiolysis. Rapid reactions of the Ps with these However, under these conditions where no reactive species may occur so that in a given solvent only a certain species should have been formed in the spur the results number of these Ps atoms reach thermal energies. As an showed that I 2 does not increase to the level observed in overall result I,, i.e., the number of Ps atoms reaching the absence of the solute. We suggest that this fraction thermal energies in the neat solvent, will not only be of Ps, which is AI2, is lost due to direct interaction of Ps governed by the number of Ps initially formed, which as a hot species with the solute, in accordance with the depend on the nature of the solvent, but also by the “modified Ore model” (vide ~ u p r a ) . ~ - l ~ subsequent reactions of the “hot” Ps with radiolytic species, which prevent the Ps from reaching thermal Thus as discussed above a similar dependence should energies. The effect of an added solute such as C C 4 on exist between the energies of activation for dissociative ethe number of thermal Ps atoms could in this case be attachment and AI2, if this latter fraction corresponds to explained by either assuming that “hot” Ps react with CC14 hot Ps reactions with solute molecules. This correlation itself, very rapidly followed by almost immediate positron has indeed been observed (Figure 10). This model would annihilation from the reaction products, or that Ps atoms also be in agreement with a number of experimental results
2304
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
obtained in aqueous solutions of simple inorganic i~ns.~-’O It would be, however, beyond the scope of this paper to review all the experimental observations made in this area within the framework of this work. The starting point of the second reaction scheme is that Ps is formed by a combination of a free positron with an electron2 (spur reaction model). Its various a s p e ~ t s ~ J ~have - ~ ~been J ~ +discussed ~~ in several papers and shall not be repeated. This model can provide an explanation for most of the experimental observations made in this study. The effect of C6F6additives can again be understood as nondissociative electron attachment of electrons to form C6FC which have a relatively long lifetime (12 ~s at -0.0 eV and
