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Positronium quenching and inhibiting properties of the CN-, Fe(CN)64- and Fe(CN)63- ions in aqueous solutions
Radiat. Phys. Chem. Vol. 23, No. 5, pp. 531 536, 1984 Printed in Great Britain.
0146-5724/84 S3.00+ .00 Pergamon Press Ltd.
POSITRONIUM QUENCHING A N D INHIBITING PROPERTIES OF THE C N - , Fe(CN)6 4AND Fe(CN)6 3- IONS IN AQUEOUS SOLUTIONS G. DUPL.~TRE, J. TALAMONI,t J. CH. ABa~ and A. HAESSLER Labor~toire de Chimie Nucl6aire, Centre de Recherches Nucl6aires et Universit6 Louis Pasteur, B.P. 20 67037 Strasbourg Cedex, France
(Received 1 February 1983; in revised form 25 March 1983) Abstract--The effects of the C N - , Fe(CN)64- and Fe(CN)63- ions on positronium (Ps) formation and their rate constants of reaction with Ps in water have been studied using both the lifetime spectroscopy and the Doppler broadening of the annihilation lineshape techniques. Quenching reactions are observed with the ferricyanide ion and attributed to Ps oxidation. Inhibition of Ps formation occurs by positron scavenging with all three solutes, with the formation of an e ÷ bound-state, and also by electron scavenging in the case of Fe(CN)63-. The various inhibition constants are derived as well as the Doppler broadened spectra of the bound-states, and the variations of their intensities with solute concentration.
1. I N T R O D U C T I O N
inhibition of Ps formation resulting from these anions been reported. It thus seemed interesting to reconsider the overall effects of these ions as concerns Ps formation and reactions in aqueous solutions, using both the LS and D B A R L techniques. F o r the sake of comparison, the inhibition promoted by C N - was also examined.
RECENXLV, the reactions of muonium (Mu) with Fe 2 +, Fe 3+ and the ferro- and ferricyanide ions in aqueous solutions have been investigated3 ~) The rate constants for the reactions with the paramagnetic solutes are higher by one to two orders of magnitude than that with Fe(CN)64- , which is diamagnetic, and spin exchange reactions have been hypothesized to be at the origin of these differences. In the case of positronium (Ps) reactions, the rate constants follow the same trend: Fe(CN)64- is unreactive while Fe 2+ has been reported as a typical spin converter and oxidation reactions were suggested for Fe 3+ and Fe(CN)63 .(2-5) When using the m u o n spin rotation technique, one measures exclusively the rate of depolarisation of the triplet M u so that the determination of the reaction mechanism may be rather speculative. In Ps chemistry, the changes of the relative amounts of both the triplet and singlet states of Ps can be measured, which allows a firmer assignment to the reaction mechanism. However, this requires the combined use of two measuring techniques, namely lifetime spectroscopy (LS) and the Doppler broadening of the annihilation lineshape ( D B A R L ) or the angular correlation (AC) techniques. The distributions of the momenta of the positron bound-states have not been measured for Fe(CN)64- and Fe(CN)63-, nor has the
2. E X P E R I M E N T A L The experimental equipment and data processing have already been described. ¢6-8) The resolutions of the lifetime apparatus and of the Ge/Li detector were 300 ps and 1.45 keV (at 511 keV), respectively. The intensities li and lifetimes ~ (or decay rate constants, 2~= l/zi) related to the various positron species are identified by subscripts 1, 2, 3 and 4 referring to p.Ps, e+, o.Ps and an e + bound-state, respectively. Parameters wit]l superscript "0" refer to the pure solvent. The lifetimes in pure water were z~°=0.12ns, ~2°=0.40ns and T3° = 1.80 ns. The DBARL data are expressed in terms of the full width at half-maximum (fwhm) of the annihilation line, in keV. Following a procedure previously described, ~7) the experimental lines can be corrected for the resolution of the detector and then decomposed into the sum of Gaussians, each characteristic of a positron species, and which are described by their full width at half-maximum, Fi. Conversely it is possible, knowing these latter values and the resolution function of the detector, to calculate from the LS data the expected variations of fwhm with the concentration C of solute. A good matching with the experimental determinations is a good test of the overall consistency of the measurements and of the interpretation of the results. The F I (0.99keV), F2(2.66keV ) and F3(2.39keV ) values have been determined previously,o).
tOn leave of absence from the Instituto de Fisica e Quimica de Sao Carlos, Universidade de Sao Paulo, Brazil. 531
532
G. DUPL.$,TREet al.
For all solutes, the potassium salts were used. The chemicals were pure grade from Merck and used"without any further purification. The sample ampoules were degassed by the usual freeze-thaw technique.
inhibited, the variations of I 3 with C can be described by the empirical expression • -oo)
3. RESULTS AND DISCUSSION
where K is the inhibition constant. The resulting fitted parameters are given in Table 1. In comparison with our previous measurements in water, fappears lower by about 35~, which would indicate that if this inhibition mechanism is correct, f is not constant in a given solvent, contrary to our previous assumption which was based on numerous observations.0°, Il) (ii) Combined limited inhibition and enhancement reactions. Based on the observation that k(OH + C N - ) is relatively high (4.5 × 10 9 M Is- ~),(~2)it may be expected that CN would promote enhancement reactions concurrently with the inhibitionY°) In this case, an empirical expression to describe the variations of 13 with C is"°'")
3.1 CN solutions The variations of I 3 and of fwhm with the concentration C of solute are shown in Figs. 1 and 2, respectively. No quenching is observed and the data can be analyzed directly in terms of inhibition and possibly enhancement reactions of Ps formation, exclusively. As was the case for the halides and SCN-,(6) the concomitant decreases of 13 and of fwhm when C increases indicate that the inhibition proceeds through positron scavenging. This result agrees with recent data reported by Mogensen et al. (9) The LS data can be considered on two different basis: (i) Inhibition reactions only. The inhibition is "limited", i.e. its effect saturates with increasing C. Denoting f as the fraction of Ps whose formation is
.~2| t.
I
"
'
I
....
i
[
,
,
i ....
I
~
•
•
i ....
~
i
i~p
o
- - ~
i
err
•
o 0£2 ........ 0~ 00~ o;2'0os'b'l
o12
o's
i
i
C (MI
FIG. 1. Variations of 13, the intensity of the long-lived component, with concentration C of: Q, CN-; (3, Fe(CN)64-; A, Fe(CN)6"~-.
i
I
I
]
. . . .
]
I
I
~exp err
=E296
I
~
,
J'--~-i
29O 285 2B(]
.....
tr_~-
L
2 75 27C b-
265
00'02 'o~ oh1 062 ' 'o~5'"dl
o'2~'o!s'"'l C IN)
FIG. 2. Variations of fwhm with concentration C of: O, CN--; O, Fe(CN)64 ; A, Fe(CN)63-.
(l)
(2)
13/130 = f / ( l + KC) + 1 - f
.01 + a C t /
/3 = ,3
f
+ 1
-
f)
where fl and ~/fl are the enhancement constant and coefficient, respectively. Clearly, the use of this expression with four adjustable parameters may not be very conclusive, owing to the very smooth experimental variations of 13 as compared to those obtained with, e.g. I y3) Consequently, the fitting was performed by fixing f and the ratio ~/fl which were determined by previous measurementsY°) The derived parameters are displayed in Table 1. The Z2 test does not allow one to choose between hypotheses (i) or (ii). Besides the consistency of the f value with the previous measurements, two arguments are however in favour of the latter: all positron scavengers characterized so far are also rather efficient hole scavengers and the derived fl value is well in line with the reported correlation between k(OH + S) vs fl,oo) where S is a solute. With regard to the DBARL data, the problem of determining the values of ['4 and 14 for the positron bound-state arises. To this end, measurements were carried out using 2 M C N - in a concentrated (4M) NO3 aqueous solution. Besides ea~, an extra component is observed with ['4 = (2.37 + 0.05) keV and with a corresponding relative intensity of (85 + 12) ~ . This is in good agreement with recent AC results by Mogensen et al. (9) who find 2.40 keV for the fwhm of the AC curve related to pure C N and 14 = 100~ under conditions similar to ours. Using the F4 value so determined, the deconvoluted annihilation lines related to the various CN solutions in water were analyzed so as to derive I4. If /)4 represents the percentage of free positrons entering
Positronium quenching and inhibiting properties into bound-state formation, the variations of P4 with C are well described by the following empirical relation:
--
0 25
--
533
0.1
0.2
0.3
0.~
0.5
i
~
,
,
,
05 C(M) 0.6/, ~,.n
•
0.62
k4C l + k,C where p~ax is the maximum value which P4 reaches at high concentration, and k4 is a constant related to the rate constant for the formation of the positron bound-state. We find p ~ x = (83 _ 15)% with k4= 18.2M -~. Very significantly, the P~'~ value coincides with that obtained in the concentrated NOa- solution. Furthermore, the k4 constant is quite close to the inhibition constant K determined assuming combined enhancement and inhibition reactions (equation (2); Table 1), which lends strong support to this mechanism. Using the values of P4 vs C and of F4, the LS data plus the 1 - ' 1 , 2 , 3 values known from previous measurements, the expected variations of fwhm with C can be calculated. The resulting curve is shown as a solid line in Fig. 2 and is in good agreement with the experimental points. (3)
--
max
P4 -- P4
3.2 Fe(CN)64- solutions A very small quenching reaction is observed (Fig. 3). The reaction rate constant derived from the expression
~3--A3°q-k'C
(4)
is k ' = (0.05 + 0.005) M - i n s - ~ . Corrections to the experimental values of 13 due to this quenching are negligible. The variations of 13 and of fwhm with C are shown in Figs. 1 and 2, respectively. As in the case of C N - , the data can be analyzed in terms of limited inhibition alone or of combined inhibiting and enhancing reactions. The parameters derived when fitting expressions (1) and (2), respectively, to the data are given in Table 1. In either case, the inhibition constant is
O.
).58
0.56 0.;3v~e
0
•
;
l
0.010
i
1
i
0.020
I
0.030
C(M)
FIG. 3. Variations of 1/% with concentration C of: O, Fe(CN)64-; A, Fe(CN)63-.
very high. Very significantly, when using equation (2), Kis about six times higher than that for C N - and the derived fl value inserts, well into the k(OH + S) = f ( f l ) correlation, tl°) as k(OH + Fe(CN)64-) = 1.2 x 101°M - l s-1. 02) The small decrease of fwhm with increasing C can only be correlated with the LS data by supposing the formation of a positron bound-state. A complete treatment of the D B A R L data requires the determination of F 4 related to the e + bound-state. A measurement in a mixed 0.5M Fe(CN)64- and 4M NO3- solution leads to F4 -- (2.52 + 0.05) keV, which is significantly broader than the corresponding value for C N - and intermediate between F2 and F3. The associated intensity is such that all the free positrons have reacted to form the bound-state. Back-calculation for 0.5M Fe(CN)64- using this value of F 4 and supposing that all free positrons are converted into the bound-state leads to a calculated value of fwhm in fair agreement with the experimental one. The variation with C of the percentage of free positrons participating in bound-state formation is well described by equation (3) with P ~ ' = 100% and k4 = 140 M - 1. The identity of this latter value with that of the inhibition constant K
TABLE 1. LS AND DBARL PARAMETERSFOR CN-, Fe(CN)64- AND Fe(CN)63- IN WATER Solute
(M - t)
K
f
CN-
42.3 18.4 325 142 0t 140t 96
0.18 0.28t 0.21 0.28t
Fe(CN)64Fe(CN)63-
?Fixed values.
0.28t 0.28t
[3
a/[3
1.5
1.18t
4.1
1.18t
(M - i)
k
k"
k4
F4 (keV)
0.05 0.05 20.0 20.0 20.0
18.2 18.2 140 140 140 140 140
2.37 2.37 2.52 2.52 2.48 2.48 2.48
(M - l) (M - Ins- a) (M - t)
23.8 11.4 14.8
534
G. DUPL.~TREet al.
derived from the LS data is quite noticeable, confirming that the same process is responsible for both the inhibition of Ps formation and the formation of the positron bound-state. The calculated fwhm vs C curve (solid line in Fig. 2) is in good agreement with the experimental values. 3.3 Fe(CN)63- s o l u t i o n s With this solute, 7:3 decreases rapidly with increasing C, indicating quenching reactions. The variation of 1/7:3 VS C is linear, as shown in Fig. 3. Using equation (4), the quenching rate constant derived, k ' = (20.02 + 0.05) M - ~ n s ~, is in good agreement with the value reported by Tao ~5) but significantly higher than those given in Refs (3 and 4). Equation (4) implies that oxidation or Ps complex formation are involved. Pure spin conversion reactions would lead to curved variations of 23 with C; however, from these data alone it cannot be excluded that a small fraction of the quenching reaction may be due to spin conversion. To obtain definite information on the inhibiting ability of Fe(CN)63 - , it is necessary to know precisely the mechanism of the quenching reaction(s) so as to apply the relevant corrections to the experimental 13 values. ~7) Nevertheless, whatever the quenching process, the decrease of 13 with increasing C at low concentration (Fig. 1) implies that ferricyanide is also a very efficient inhibitor. Furthermore, the fact that fwhm levels off at about 2.95 keV (Fig. 2), which is significantly lower than the fwhm measured in a concentrated Cr207 = solution where only e~ is present (fwhm2 = 3.15 keV), definitely indicates the formation of either a Ps (by Ps complexation) or a e + (by e ÷ scavenging) bound-state. However, the former possibility appears to be ruled out since a 1M Fe(CN)63 solution in the presence of a strong inhibitor, 3M NO 3-, or of a strong Ps oxidizer, 0.4M Cr207-, when no Ps can be present, leads to the same fwhm value of 2.95 keV as in the solution containing ferricyanide alone. Analysis of the corresponding annihilation lines corrected for the detector resolution gives F 4 = 2.48 keV with a correlated intensity 14 of 100%. Due to the limited resolution of the measuring device it is only for/1 that the analysis of the annihilation lines (without any constraints other than Fz) leads to a consistent determination in solutions containing ferricyanide alone; this is because of the markedly different value of F~ compared to the others. I1 decreases steadily with increasing C. Such a variation is not compatible with Ps spin conversion reactions proceeding at a high rate, confirming the conclusion drawn from the LS data. Since oxidation appears to be the dominant quenching process, let us suppose as a working
hypothesis that all Ps reactions proceed via oxidation. Equation (4) is then strictly valid and the corrected intensity, I~Or~, can be calculated from the experimental I3 values, from ~7~ (5)
(
Ie3°rr = I 3 1
.~ ~ -
~ 0 "
"2 - - r~3 /
It may be noted at this point that the variations of 1/% and 1/I~ °rr with C do not appear to show any remarkable change in the slope around 0.003 M, in contrast to what has been found for the rate constant of reaction with the hydrated electron/4) It is likely that ion pairing has no influence on the inhibiting ability of the ferricyanide ion, as is the case for the NO3 ion in aqueous solutions/51 The corresponding values of the intensities relating to the DBARL data, I f , can be calculated ~v)and the DBARL curves analyzed on the basis of four components, leading to the determination of 14, related to the e + bound-state, at each concentration. In terms of the percentage of free positrons entering into the bound-state and using equation (3), we find p ~ x = 100% and k4= 140M *. This latter value agrees remarkably well with k4 and K found for the ferrocyanide ion (Table 1), pointing to a quite similar ability of the C N - moieties to scavenge the positrons in either case. The calculated variations of fwhm with C are shown as a dashed line in Fig. 2; the agreement with the experimental points is very good, strongly supporting the starting hypothesis. Although definitely pointing to oxidation as the most important process in the quenching reactions, the preceding analysis cannot rule out the possibility of a minor contribution from either Ps complex formation or spin conversion reactions. Owing to the limitations in the resolution of the measuring device, it is difficult to gain further information in the former case, as new parameters need to be introduced, namely the lifetime and the momentum distribution of the additional positron species. In an extreme case, where the z and F parameters associated with a proposed Ps-solute complex would be very close to those for eaq+ , the distinction between Ps complex formation and oxidation would not be possible. An extensive study of the change of k ' with temperature might hopefully provide some enlightenment. To test for the contribution of spin conversion reactions, we have performed similar calculations as described for the pure oxidation case, applying the corresponding relevant equations to correct the LS data. These calculations show that spin conversion reactions should represent less than about 5% of the overall quenching reactions. Having thus established the nature of the quench-
Positronium quenching and inhibiting properties ing reactions with fair confidence, it is interesting to consider the inhibition promoted by the ferricyanide. The DBARL data unambiguously show the formation of a positron bound-state. However, as the "rate constant for the reaction of Fe(CN)6 3- with the solvated electron is about 2 x 10~°M - ~s - ~, it may be expected at the concentrations used °6) that part of the inhibition would arise from electron scavenging. The LS data can, therefore, be analyzed on the basis of the following expression °7)
(6) I]orr=i30g(C~l+_l+~g(C)+ 1 -fg(C)) with g(C)= 1/(1 + kC). Owing to the number of parameters involved, several treatments have been attempted by fixing one or more of these. The resulting values are displayed in Table 1. It may be noted that when K is taken as zero, the "total" inhibition constant, k, is very high and the inhibition would have to be due solely to positron scavenging. This would be the first example of such a reaction leading to total inhibition. However, the fact that the derived value, k = 23.8 M -~, is very different from k 4 = 1 4 0 M -t deduced from the DBARL data strongly suggests that this hypothesis is not valid. In fact, a much lower Z2 value is obtained when both K and k are varied. The K value derived is consistent with that for k4, within the accuracy of the data, pointing to a limited inhibition by positron scavenging as found for the cyanide and ferrocyanide ions. Obviously, the additional presence of some enhancement cannot be disclosed in the complex case of Fe(CN)63 , but this would lead to a higher K and thus to a closer agreement with k4. The value of k remains rather high, in the range 11 M - t - 1 5 M - t , which appears much higher than expected on the basis of the correlation k(e~ + S) = f ( k ) when using values of k(e~+S) obtained at low ionic strength.00. ~s) It may be noted though that the latter reaction rate constant increases drastically with C for the highly charged Fe(CN)63- ion, passing from 3 x 109M -I s -1 at zero ionic strength og) to about 2 x 10t° M - t s - ~in the decimolar range. °6) However, within the framework of the spur model for Ps formation, it is possible that the ferricyanide ion would be a more efficient quasi-free electron scavenge~ ~°) than expected from the Hunt correlation,09) thus behaving similarly to the SeO4 = ion.~20) 4. CONCLUSIONS With regard to the quenching reactions, this work confirms the great difference in reactivity between the
535
ferro- and ferricyanide ions as already found by Goldanskii et al.(2) and also observed in Mu chemistry. °) It is shown that the Ps quenching promoted by the latter arises from oxidation and not from spin conversion reactions. Clearly, it cannot be excluded that the quenching mechanism would be different for Ps and for Mu. However, it has been noted that the rates of reaction of either Ps or Mu with paramagnetic species were often high but not correlated with the number of unpaired electrons. °,2~) It seems that part of this anomaly might in fact be due to an incorrect assignment of the mechanism of the observed reactions. This work shows that the difference between the reactivities of the ferro- and ferricyanide ions does not arise from the paramagnetic properties of the latter but from its reducibility. The second aspect of this paper refers to the inhibition process. Both Fe(CN)64- and Fe(CN)63appear to be very effective inhibitors of Ps formation, although for Fe(CN)64- the inhibition saturates at about 0.02 M. Eldrup et al.~22)have suggested that Ps could be formed through the reaction of e + (or e - ) with either a free e - ( e +) or with the latter species delocalized over several solute molecules or ions. This second pathway of Ps formation would be favoured with increasing solute concentration and would eventually counterbalance the inhibition originally promoted by the solute, leading to a limited inhibition (in fact, one would rather expect a marked increase of the Ps yield after an initial decrease at low concentration). Such an interpretation does not seem to hold in the present case as delocalization should not be important at the very low concentrations where 13 levels off. In the model we have proposed, °°) it is also suggested that Ps could be formed via two pathways, involving either quasi-free or localized (not fully solvated) particles; the difference between "total" and "limited" inhibitors would rely upon the selectivity of their reactivity towards either of these particles. On this basis, however, it is not clear why all the solutes investigated so far which react with the positron do so only with the localized positron. Perhaps, the localization process is extremely fast for e + in the polar solvents. In contrast to what has been found for several other solutes, including the halide ions, ~6) it appears that all free positrons can react with the C N - , ferroand ferricyanide ions, as the bound-state intensity, 14, approaches 100% at high concentration. The presence of excited bound-states or of chemical reactions which interfere in the positron spur do not account for the limiting value, well below 100%, reached by 14 in the former cases. (6,23) Within our model, °°) the formation of the bound-states would occur by the reaction of the solute with the localized positrons.
G. DUPL~.TRE et al.
536
This is consistent with theoretical calculations predicting t h a t the reaction of the halide ions, X - , with the fully h y d r a t e d positron, ea+, should be endothermic, t6) On this basis, the plateauing o f 14 (or P4) with increasing C can plausibly arise from the annihilation of the (X e +) b o u n d - s t a t e c o m p e t i n g with its decomposition to yield e,q.
Acknowledgement--J. Talamoni is grateful to CNPq (Brazil) for financial support.
REFERENCES 1. Y. C. JEAN, J. H. BREWER, D. C. FLEMING and D. C. WALKER, Chem. Phys. Lett. 1978, 60, 125. 2. V. I. GOt.DANSKII, V. G. FIRSOV and V. P. SHANTAROVICH,Kin. Kat. 1965, 6, 495. 3. V. I. GOLDANSKnand V. P. Sr~ANTAROVICH,Appl. Phys. 1974, 3, 335. 4. A. L. NICHOLS, R. E. WILD, L. J. BARTAL and H. J. ACHE, Appl. Phys. 1974, 4, 37. 5. S. J. TAO, Appl. Phys. 1976, 10, 67. 6. G. DVPL~,~E, J. CH. ABB~, A. G. MADOOCK and A. HA~SLER, J. Chem. Phys. 1980, 72, 89. 7. G. DUPLATRE, J. CH. AaaL J. TALAMONI, J. C. MACHADO and A. HAESSLER,Chem. Phys. 1981, 57, 175. 8. A. G. MADDOCK, J. CH. Aaa~ and A. HAESSLER, Chem. Phys. 1976, 17, 343.
9. O. E. MOGENSEN,N. J. PEDERSEN and J. R. ANDERSEN, Chem. Phys. Lett. 1982, 93, 115. 10. J. CH. ABBfi, G. DUPL,~TRE, A. G. MADDOCK, J. TALAMONIAND A. ]-{AESSLER,J, Inorg. Nucl. Chem. 1981, 43, 2603. I I. J. CH. ABB~, G. DUPL,~TRE, A. G. MADDOCK and A. HAESSLER, Radial. Phys. Chem. 1980, 15, 617. 12. FARHATAZ1Zand A. B. Ross, Nat. Stand. Ref. Data Ser. 59, Nat. Bur. Stds U.S., 1977. 13. G. DUPLATRE, J. CH. ABBE, A. G. MADDOCK and A. HAESSLER, Radiat. Phys. Chem. 1978, ll, 199. 14. M. S. MATHESON, Phys. Chem. Vol. VII, Academic Press, New York, 1975. 15. J. CH. ABB~, G. DUPL,~TRE, A. G. MADDOCK and A. HAESSLER, Radiochem. Radioanal. Lett. 1979, 38, 303. 16. G. DUPE~TRE and C. D. JONAH, Private communication. 17. G. DUPL,~TRE, J. CH. AaB/~, J. TALAMONI and A. G. MADDOCK, Chem. Phys. Lett., 1983. 18. M. ANBAR, M. BAMaENEK and A. B. Ross, Nat. Stand. Ref. Data Ser. 43, Nat. Bur. Stds U.S., 1973. 19. K. Y. LAM and J. W. HUNT, Radiat. Phys. Chem. 1975, 7, 317. 20. C. D. JONAH, J. R. MILLER and M. S. MATHESON, J. Phys. Chem. 1977, 81, 1618. 21. J. GREEN and J. LEE, Positronium Chemistry, Academic Press, 1964. 22. M. ELDRUP, V. P. SHANTAROVICHand O. E. MOGENSEN, Chem. Phys. 1975, II, 129. 23. J. TALAMONI,J. CH. ABB~, G. DUPL~.TRE and A. HAESSLER, Radiat. Phys. Chem. 1982, 20, 275.
0146-5724/84 S3.00+ .00 Pergamon Press Ltd.
POSITRONIUM QUENCHING A N D INHIBITING PROPERTIES OF THE C N - , Fe(CN)6 4AND Fe(CN)6 3- IONS IN AQUEOUS SOLUTIONS G. DUPL.~TRE, J. TALAMONI,t J. CH. ABa~ and A. HAESSLER Labor~toire de Chimie Nucl6aire, Centre de Recherches Nucl6aires et Universit6 Louis Pasteur, B.P. 20 67037 Strasbourg Cedex, France
(Received 1 February 1983; in revised form 25 March 1983) Abstract--The effects of the C N - , Fe(CN)64- and Fe(CN)63- ions on positronium (Ps) formation and their rate constants of reaction with Ps in water have been studied using both the lifetime spectroscopy and the Doppler broadening of the annihilation lineshape techniques. Quenching reactions are observed with the ferricyanide ion and attributed to Ps oxidation. Inhibition of Ps formation occurs by positron scavenging with all three solutes, with the formation of an e ÷ bound-state, and also by electron scavenging in the case of Fe(CN)63-. The various inhibition constants are derived as well as the Doppler broadened spectra of the bound-states, and the variations of their intensities with solute concentration.
1. I N T R O D U C T I O N
inhibition of Ps formation resulting from these anions been reported. It thus seemed interesting to reconsider the overall effects of these ions as concerns Ps formation and reactions in aqueous solutions, using both the LS and D B A R L techniques. F o r the sake of comparison, the inhibition promoted by C N - was also examined.
RECENXLV, the reactions of muonium (Mu) with Fe 2 +, Fe 3+ and the ferro- and ferricyanide ions in aqueous solutions have been investigated3 ~) The rate constants for the reactions with the paramagnetic solutes are higher by one to two orders of magnitude than that with Fe(CN)64- , which is diamagnetic, and spin exchange reactions have been hypothesized to be at the origin of these differences. In the case of positronium (Ps) reactions, the rate constants follow the same trend: Fe(CN)64- is unreactive while Fe 2+ has been reported as a typical spin converter and oxidation reactions were suggested for Fe 3+ and Fe(CN)63 .(2-5) When using the m u o n spin rotation technique, one measures exclusively the rate of depolarisation of the triplet M u so that the determination of the reaction mechanism may be rather speculative. In Ps chemistry, the changes of the relative amounts of both the triplet and singlet states of Ps can be measured, which allows a firmer assignment to the reaction mechanism. However, this requires the combined use of two measuring techniques, namely lifetime spectroscopy (LS) and the Doppler broadening of the annihilation lineshape ( D B A R L ) or the angular correlation (AC) techniques. The distributions of the momenta of the positron bound-states have not been measured for Fe(CN)64- and Fe(CN)63-, nor has the
2. E X P E R I M E N T A L The experimental equipment and data processing have already been described. ¢6-8) The resolutions of the lifetime apparatus and of the Ge/Li detector were 300 ps and 1.45 keV (at 511 keV), respectively. The intensities li and lifetimes ~ (or decay rate constants, 2~= l/zi) related to the various positron species are identified by subscripts 1, 2, 3 and 4 referring to p.Ps, e+, o.Ps and an e + bound-state, respectively. Parameters wit]l superscript "0" refer to the pure solvent. The lifetimes in pure water were z~°=0.12ns, ~2°=0.40ns and T3° = 1.80 ns. The DBARL data are expressed in terms of the full width at half-maximum (fwhm) of the annihilation line, in keV. Following a procedure previously described, ~7) the experimental lines can be corrected for the resolution of the detector and then decomposed into the sum of Gaussians, each characteristic of a positron species, and which are described by their full width at half-maximum, Fi. Conversely it is possible, knowing these latter values and the resolution function of the detector, to calculate from the LS data the expected variations of fwhm with the concentration C of solute. A good matching with the experimental determinations is a good test of the overall consistency of the measurements and of the interpretation of the results. The F I (0.99keV), F2(2.66keV ) and F3(2.39keV ) values have been determined previously,o).
tOn leave of absence from the Instituto de Fisica e Quimica de Sao Carlos, Universidade de Sao Paulo, Brazil. 531
532
G. DUPL.$,TREet al.
For all solutes, the potassium salts were used. The chemicals were pure grade from Merck and used"without any further purification. The sample ampoules were degassed by the usual freeze-thaw technique.
inhibited, the variations of I 3 with C can be described by the empirical expression • -oo)
3. RESULTS AND DISCUSSION
where K is the inhibition constant. The resulting fitted parameters are given in Table 1. In comparison with our previous measurements in water, fappears lower by about 35~, which would indicate that if this inhibition mechanism is correct, f is not constant in a given solvent, contrary to our previous assumption which was based on numerous observations.0°, Il) (ii) Combined limited inhibition and enhancement reactions. Based on the observation that k(OH + C N - ) is relatively high (4.5 × 10 9 M Is- ~),(~2)it may be expected that CN would promote enhancement reactions concurrently with the inhibitionY°) In this case, an empirical expression to describe the variations of 13 with C is"°'")
3.1 CN solutions The variations of I 3 and of fwhm with the concentration C of solute are shown in Figs. 1 and 2, respectively. No quenching is observed and the data can be analyzed directly in terms of inhibition and possibly enhancement reactions of Ps formation, exclusively. As was the case for the halides and SCN-,(6) the concomitant decreases of 13 and of fwhm when C increases indicate that the inhibition proceeds through positron scavenging. This result agrees with recent data reported by Mogensen et al. (9) The LS data can be considered on two different basis: (i) Inhibition reactions only. The inhibition is "limited", i.e. its effect saturates with increasing C. Denoting f as the fraction of Ps whose formation is
.~2| t.
I
"
'
I
....
i
[
,
,
i ....
I
~
•
•
i ....
~
i
i~p
o
- - ~
i
err
•
o 0£2 ........ 0~ 00~ o;2'0os'b'l
o12
o's
i
i
C (MI
FIG. 1. Variations of 13, the intensity of the long-lived component, with concentration C of: Q, CN-; (3, Fe(CN)64-; A, Fe(CN)6"~-.
i
I
I
]
. . . .
]
I
I
~exp err
=E296
I
~
,
J'--~-i
29O 285 2B(]
.....
tr_~-
L
2 75 27C b-
265
00'02 'o~ oh1 062 ' 'o~5'"dl
o'2~'o!s'"'l C IN)
FIG. 2. Variations of fwhm with concentration C of: O, CN--; O, Fe(CN)64 ; A, Fe(CN)63-.
(l)
(2)
13/130 = f / ( l + KC) + 1 - f
.01 + a C t /
/3 = ,3
f
+ 1
-
f)
where fl and ~/fl are the enhancement constant and coefficient, respectively. Clearly, the use of this expression with four adjustable parameters may not be very conclusive, owing to the very smooth experimental variations of 13 as compared to those obtained with, e.g. I y3) Consequently, the fitting was performed by fixing f and the ratio ~/fl which were determined by previous measurementsY°) The derived parameters are displayed in Table 1. The Z2 test does not allow one to choose between hypotheses (i) or (ii). Besides the consistency of the f value with the previous measurements, two arguments are however in favour of the latter: all positron scavengers characterized so far are also rather efficient hole scavengers and the derived fl value is well in line with the reported correlation between k(OH + S) vs fl,oo) where S is a solute. With regard to the DBARL data, the problem of determining the values of ['4 and 14 for the positron bound-state arises. To this end, measurements were carried out using 2 M C N - in a concentrated (4M) NO3 aqueous solution. Besides ea~, an extra component is observed with ['4 = (2.37 + 0.05) keV and with a corresponding relative intensity of (85 + 12) ~ . This is in good agreement with recent AC results by Mogensen et al. (9) who find 2.40 keV for the fwhm of the AC curve related to pure C N and 14 = 100~ under conditions similar to ours. Using the F4 value so determined, the deconvoluted annihilation lines related to the various CN solutions in water were analyzed so as to derive I4. If /)4 represents the percentage of free positrons entering
Positronium quenching and inhibiting properties into bound-state formation, the variations of P4 with C are well described by the following empirical relation:
--
0 25
--
533
0.1
0.2
0.3
0.~
0.5
i
~
,
,
,
05 C(M) 0.6/, ~,.n
•
0.62
k4C l + k,C where p~ax is the maximum value which P4 reaches at high concentration, and k4 is a constant related to the rate constant for the formation of the positron bound-state. We find p ~ x = (83 _ 15)% with k4= 18.2M -~. Very significantly, the P~'~ value coincides with that obtained in the concentrated NOa- solution. Furthermore, the k4 constant is quite close to the inhibition constant K determined assuming combined enhancement and inhibition reactions (equation (2); Table 1), which lends strong support to this mechanism. Using the values of P4 vs C and of F4, the LS data plus the 1 - ' 1 , 2 , 3 values known from previous measurements, the expected variations of fwhm with C can be calculated. The resulting curve is shown as a solid line in Fig. 2 and is in good agreement with the experimental points. (3)
--
max
P4 -- P4
3.2 Fe(CN)64- solutions A very small quenching reaction is observed (Fig. 3). The reaction rate constant derived from the expression
~3--A3°q-k'C
(4)
is k ' = (0.05 + 0.005) M - i n s - ~ . Corrections to the experimental values of 13 due to this quenching are negligible. The variations of 13 and of fwhm with C are shown in Figs. 1 and 2, respectively. As in the case of C N - , the data can be analyzed in terms of limited inhibition alone or of combined inhibiting and enhancing reactions. The parameters derived when fitting expressions (1) and (2), respectively, to the data are given in Table 1. In either case, the inhibition constant is
O.
).58
0.56 0.;3v~e
0
•
;
l
0.010
i
1
i
0.020
I
0.030
C(M)
FIG. 3. Variations of 1/% with concentration C of: O, Fe(CN)64-; A, Fe(CN)63-.
very high. Very significantly, when using equation (2), Kis about six times higher than that for C N - and the derived fl value inserts, well into the k(OH + S) = f ( f l ) correlation, tl°) as k(OH + Fe(CN)64-) = 1.2 x 101°M - l s-1. 02) The small decrease of fwhm with increasing C can only be correlated with the LS data by supposing the formation of a positron bound-state. A complete treatment of the D B A R L data requires the determination of F 4 related to the e + bound-state. A measurement in a mixed 0.5M Fe(CN)64- and 4M NO3- solution leads to F4 -- (2.52 + 0.05) keV, which is significantly broader than the corresponding value for C N - and intermediate between F2 and F3. The associated intensity is such that all the free positrons have reacted to form the bound-state. Back-calculation for 0.5M Fe(CN)64- using this value of F 4 and supposing that all free positrons are converted into the bound-state leads to a calculated value of fwhm in fair agreement with the experimental one. The variation with C of the percentage of free positrons participating in bound-state formation is well described by equation (3) with P ~ ' = 100% and k4 = 140 M - 1. The identity of this latter value with that of the inhibition constant K
TABLE 1. LS AND DBARL PARAMETERSFOR CN-, Fe(CN)64- AND Fe(CN)63- IN WATER Solute
(M - t)
K
f
CN-
42.3 18.4 325 142 0t 140t 96
0.18 0.28t 0.21 0.28t
Fe(CN)64Fe(CN)63-
?Fixed values.
0.28t 0.28t
[3
a/[3
1.5
1.18t
4.1
1.18t
(M - i)
k
k"
k4
F4 (keV)
0.05 0.05 20.0 20.0 20.0
18.2 18.2 140 140 140 140 140
2.37 2.37 2.52 2.52 2.48 2.48 2.48
(M - l) (M - Ins- a) (M - t)
23.8 11.4 14.8
534
G. DUPL.~TREet al.
derived from the LS data is quite noticeable, confirming that the same process is responsible for both the inhibition of Ps formation and the formation of the positron bound-state. The calculated fwhm vs C curve (solid line in Fig. 2) is in good agreement with the experimental values. 3.3 Fe(CN)63- s o l u t i o n s With this solute, 7:3 decreases rapidly with increasing C, indicating quenching reactions. The variation of 1/7:3 VS C is linear, as shown in Fig. 3. Using equation (4), the quenching rate constant derived, k ' = (20.02 + 0.05) M - ~ n s ~, is in good agreement with the value reported by Tao ~5) but significantly higher than those given in Refs (3 and 4). Equation (4) implies that oxidation or Ps complex formation are involved. Pure spin conversion reactions would lead to curved variations of 23 with C; however, from these data alone it cannot be excluded that a small fraction of the quenching reaction may be due to spin conversion. To obtain definite information on the inhibiting ability of Fe(CN)63 - , it is necessary to know precisely the mechanism of the quenching reaction(s) so as to apply the relevant corrections to the experimental 13 values. ~7) Nevertheless, whatever the quenching process, the decrease of 13 with increasing C at low concentration (Fig. 1) implies that ferricyanide is also a very efficient inhibitor. Furthermore, the fact that fwhm levels off at about 2.95 keV (Fig. 2), which is significantly lower than the fwhm measured in a concentrated Cr207 = solution where only e~ is present (fwhm2 = 3.15 keV), definitely indicates the formation of either a Ps (by Ps complexation) or a e + (by e ÷ scavenging) bound-state. However, the former possibility appears to be ruled out since a 1M Fe(CN)63 solution in the presence of a strong inhibitor, 3M NO 3-, or of a strong Ps oxidizer, 0.4M Cr207-, when no Ps can be present, leads to the same fwhm value of 2.95 keV as in the solution containing ferricyanide alone. Analysis of the corresponding annihilation lines corrected for the detector resolution gives F 4 = 2.48 keV with a correlated intensity 14 of 100%. Due to the limited resolution of the measuring device it is only for/1 that the analysis of the annihilation lines (without any constraints other than Fz) leads to a consistent determination in solutions containing ferricyanide alone; this is because of the markedly different value of F~ compared to the others. I1 decreases steadily with increasing C. Such a variation is not compatible with Ps spin conversion reactions proceeding at a high rate, confirming the conclusion drawn from the LS data. Since oxidation appears to be the dominant quenching process, let us suppose as a working
hypothesis that all Ps reactions proceed via oxidation. Equation (4) is then strictly valid and the corrected intensity, I~Or~, can be calculated from the experimental I3 values, from ~7~ (5)
(
Ie3°rr = I 3 1
.~ ~ -
~ 0 "
"2 - - r~3 /
It may be noted at this point that the variations of 1/% and 1/I~ °rr with C do not appear to show any remarkable change in the slope around 0.003 M, in contrast to what has been found for the rate constant of reaction with the hydrated electron/4) It is likely that ion pairing has no influence on the inhibiting ability of the ferricyanide ion, as is the case for the NO3 ion in aqueous solutions/51 The corresponding values of the intensities relating to the DBARL data, I f , can be calculated ~v)and the DBARL curves analyzed on the basis of four components, leading to the determination of 14, related to the e + bound-state, at each concentration. In terms of the percentage of free positrons entering into the bound-state and using equation (3), we find p ~ x = 100% and k4= 140M *. This latter value agrees remarkably well with k4 and K found for the ferrocyanide ion (Table 1), pointing to a quite similar ability of the C N - moieties to scavenge the positrons in either case. The calculated variations of fwhm with C are shown as a dashed line in Fig. 2; the agreement with the experimental points is very good, strongly supporting the starting hypothesis. Although definitely pointing to oxidation as the most important process in the quenching reactions, the preceding analysis cannot rule out the possibility of a minor contribution from either Ps complex formation or spin conversion reactions. Owing to the limitations in the resolution of the measuring device, it is difficult to gain further information in the former case, as new parameters need to be introduced, namely the lifetime and the momentum distribution of the additional positron species. In an extreme case, where the z and F parameters associated with a proposed Ps-solute complex would be very close to those for eaq+ , the distinction between Ps complex formation and oxidation would not be possible. An extensive study of the change of k ' with temperature might hopefully provide some enlightenment. To test for the contribution of spin conversion reactions, we have performed similar calculations as described for the pure oxidation case, applying the corresponding relevant equations to correct the LS data. These calculations show that spin conversion reactions should represent less than about 5% of the overall quenching reactions. Having thus established the nature of the quench-
Positronium quenching and inhibiting properties ing reactions with fair confidence, it is interesting to consider the inhibition promoted by the ferricyanide. The DBARL data unambiguously show the formation of a positron bound-state. However, as the "rate constant for the reaction of Fe(CN)6 3- with the solvated electron is about 2 x 10~°M - ~s - ~, it may be expected at the concentrations used °6) that part of the inhibition would arise from electron scavenging. The LS data can, therefore, be analyzed on the basis of the following expression °7)
(6) I]orr=i30g(C~l+_l+~g(C)+ 1 -fg(C)) with g(C)= 1/(1 + kC). Owing to the number of parameters involved, several treatments have been attempted by fixing one or more of these. The resulting values are displayed in Table 1. It may be noted that when K is taken as zero, the "total" inhibition constant, k, is very high and the inhibition would have to be due solely to positron scavenging. This would be the first example of such a reaction leading to total inhibition. However, the fact that the derived value, k = 23.8 M -~, is very different from k 4 = 1 4 0 M -t deduced from the DBARL data strongly suggests that this hypothesis is not valid. In fact, a much lower Z2 value is obtained when both K and k are varied. The K value derived is consistent with that for k4, within the accuracy of the data, pointing to a limited inhibition by positron scavenging as found for the cyanide and ferrocyanide ions. Obviously, the additional presence of some enhancement cannot be disclosed in the complex case of Fe(CN)63 , but this would lead to a higher K and thus to a closer agreement with k4. The value of k remains rather high, in the range 11 M - t - 1 5 M - t , which appears much higher than expected on the basis of the correlation k(e~ + S) = f ( k ) when using values of k(e~+S) obtained at low ionic strength.00. ~s) It may be noted though that the latter reaction rate constant increases drastically with C for the highly charged Fe(CN)63- ion, passing from 3 x 109M -I s -1 at zero ionic strength og) to about 2 x 10t° M - t s - ~in the decimolar range. °6) However, within the framework of the spur model for Ps formation, it is possible that the ferricyanide ion would be a more efficient quasi-free electron scavenge~ ~°) than expected from the Hunt correlation,09) thus behaving similarly to the SeO4 = ion.~20) 4. CONCLUSIONS With regard to the quenching reactions, this work confirms the great difference in reactivity between the
535
ferro- and ferricyanide ions as already found by Goldanskii et al.(2) and also observed in Mu chemistry. °) It is shown that the Ps quenching promoted by the latter arises from oxidation and not from spin conversion reactions. Clearly, it cannot be excluded that the quenching mechanism would be different for Ps and for Mu. However, it has been noted that the rates of reaction of either Ps or Mu with paramagnetic species were often high but not correlated with the number of unpaired electrons. °,2~) It seems that part of this anomaly might in fact be due to an incorrect assignment of the mechanism of the observed reactions. This work shows that the difference between the reactivities of the ferro- and ferricyanide ions does not arise from the paramagnetic properties of the latter but from its reducibility. The second aspect of this paper refers to the inhibition process. Both Fe(CN)64- and Fe(CN)63appear to be very effective inhibitors of Ps formation, although for Fe(CN)64- the inhibition saturates at about 0.02 M. Eldrup et al.~22)have suggested that Ps could be formed through the reaction of e + (or e - ) with either a free e - ( e +) or with the latter species delocalized over several solute molecules or ions. This second pathway of Ps formation would be favoured with increasing solute concentration and would eventually counterbalance the inhibition originally promoted by the solute, leading to a limited inhibition (in fact, one would rather expect a marked increase of the Ps yield after an initial decrease at low concentration). Such an interpretation does not seem to hold in the present case as delocalization should not be important at the very low concentrations where 13 levels off. In the model we have proposed, °°) it is also suggested that Ps could be formed via two pathways, involving either quasi-free or localized (not fully solvated) particles; the difference between "total" and "limited" inhibitors would rely upon the selectivity of their reactivity towards either of these particles. On this basis, however, it is not clear why all the solutes investigated so far which react with the positron do so only with the localized positron. Perhaps, the localization process is extremely fast for e + in the polar solvents. In contrast to what has been found for several other solutes, including the halide ions, ~6) it appears that all free positrons can react with the C N - , ferroand ferricyanide ions, as the bound-state intensity, 14, approaches 100% at high concentration. The presence of excited bound-states or of chemical reactions which interfere in the positron spur do not account for the limiting value, well below 100%, reached by 14 in the former cases. (6,23) Within our model, °°) the formation of the bound-states would occur by the reaction of the solute with the localized positrons.
G. DUPL~.TRE et al.
536
This is consistent with theoretical calculations predicting t h a t the reaction of the halide ions, X - , with the fully h y d r a t e d positron, ea+, should be endothermic, t6) On this basis, the plateauing o f 14 (or P4) with increasing C can plausibly arise from the annihilation of the (X e +) b o u n d - s t a t e c o m p e t i n g with its decomposition to yield e,q.
Acknowledgement--J. Talamoni is grateful to CNPq (Brazil) for financial support.
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