45 1
Lifetimes of Positrons in Positronium Complexes
and performed with the technical assistance of Mr. T. H. Meyer.
=B f4ssao/Wt
s68oa(p)
b = @2E/Q(l- 6t)b&.oSssoa(~)
References and Notes (1) Contribution No. 549 from the Charles F. Kettering Research Laboratcry. (2) G. R. Seely, J. Phys. Chem., preceding paper in this issue. (3) G. R. Seely, J. Phys. Chem., 74, 219 (1970). (4) G. R. Seely, J. Phys. Chem., 71, 2091 (1967).
(5) To derive eq 1, note first that if both chlorophylls a and b are present, the measured fluorescences excited by 460-nm irradiation are each composed of two parts, and in the absence of reabsorption and secondary fluorescence, can be expressed as the sum of two components, = f$, :$2 and = &$.!: Application of eq 1 of viz. the previous paper to each fluorescence component separately, with neglect of reabsorption and dissymmetry (R = 0, D = I), gives the following:
+
6, = f245600/n(9tb)45oSs5o~P)
+
= t2$:/n(1
- @t)ioFbs80Se80a(p)
ti::,
f;$;, ,# ,: and cancellation of the common Elimination of factors n, io, and a(p), and rearrangement of the remainder glves eq 1. In effect, the subtractive terms in eq 1 correct for the mutual overlap of chlorophyll a and b fluorescences. (6) C. S . French, J. S. Brown, and M. C. Lawrence, Plant Physioi., 49, 421 (1972). (7) G. R. Seely, J. Theor. Bioi., 40, 173 (1973). (8)T. M. Cotton, A. D. Trifunac. K. Ballschmiter, and J. J. Katz, Biochim. Biophys. Acta, 366, 181 (1974). (9) C. E. Strouse, Proc. Naf.Acad. Sci. U.S.A.,71, 325 (1973). (IO) G. R . Seely and R. G. Jensen, Spectrochim. Acta, 21, 1835 (1965). (11) G. R. Seely, Specfrochim. Acta, 21, 1847 (1965).
On the Annihilation Lifetimes of Positrons Bound in Positronium Complexes' William J. Madia and Hans J. Ache* Department of Chemistry, Virginia Polytechnic institute and Sfafe University, Blacksburg, Virginia 2406 1 (Received July 29, 1975)
An experimental approach is described to determine the annihilation lifetimes, T ~ of, positrons in Ps complexes of p-dinitrobenzene and p-benzoquinone in organic solvents. It is based on the dependence of I z , the intensity of the long-lived component in the positron lifetime spectra, on the chemical reaction rates of the Ps atoms with the substrate molecules, which in turn vary as a function of temperature. From the experiments an average value for rC = 0.36 f 0.10 ns has been obtained.
Introduction A positron may combine with an electron to form a electron-positron bound state, the positronium atom (Ps). to s which is This species has a lifetime of about too short for its reactions to be followed by conventional product analysis. The chemical reactions of positronium can be studied by observing changes in its average lifetime and decay modes which are dependent on the chemical reactivity and physical composition of its environment.2 By using these methods Madia, Nichols, and Ache3 have been able to show that Ps undergoes reversible molecular complex formation in solutions with compounds which are known in conventional chemistry as strong complex formers, such as nitrobenzene, benzoquinone, etc. Temperature studies were carried out which resulted in an assessment of the kinetics and the activation parameters of these processes. Very little, however, is known about the exact nature of the Ps ~ o m p l e xespecially ,~ about the annihilation lifetime of the positron in the Ps complex. At the present time only a few quantum mechanical calculations have been published, which would predict lifetimes of about 0.31 ns for P S L ~ + 0.33 , ~ , ~ns for P ~ N a + , ~5f ns j for P S C ~ ,and ~ ? 0.45 ~ ns for P S H . ~ Thus in the following we wish to report the results of a preliminary experimental study from which an estimate of the positron annihilation lifetimes in Ps complexes of com-
pounds such as dinitrobenzene and p-benzoquinone may be derived.
Experimental Section The experimental procedures were essentially the same as previously d e ~ c r i b e d . ~ J ~ (a) Positron Lifetime Measurements. Positron lifetime measurements were carried out by the usual delayed coincidence method.2 The resolution of the system as measured by the prompt time distribution of 6oCosource and without changing the 1.27- and 0.511-MeV bias was found to be less than 0.4 ns (b) Purity and Source of Reagents. All solvents were of highest available purity. They were 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 Sample. Specially designed sample vials (cylindrical glass tubes 100 mm long and 10 mm i.d.) were filled with about 1 ml of solution. The positron sources were 3-5 WCi 22Na prepared by evaporating carrier free neutral solutions of either 22NaHC03 or 22NaC1 (obtained from ICN) onto a thin aluminum foil. The radioactive foils were suspended in the solutions and all solutions were carefully degassed by freeze-thaw techniques to reThe Journal of Physical Chemistry, Vol. 80, No. 5, 1976
.
William J. Madia and Hans J. Ache
452
move oxygen. The vials were subsequently sealed off and immersed in a specially designed thermostat which allowed control of the temperature within f1.0 "C. Special care has been taken to evaluate the potential effects of heat and irradiation (by the 22Na source) on the sample. Thus data points were first obtained at increasing temperatures, then the cycle was reversed and data were obtained at decreasing temperatures. The data were found to be reproducible throughout the full cycle which clearly indicated that no significant changes had occurred in the samples.
1
Koas
-
I
FOR Ps REACTIONS WITH p-DINITROBENZENE AND p.BENZOQUINONE I N TOLUENE AND n-PENTANOL SOLUTIONS VI IOOO/T
I
I
\%I
Results a n d Discussion As discussed in our previous paper3 the experimental results obtained in solutions of diamagnetic organic compounds, such as nitrobenzene derivatives and p-benzoquinone, provide strong evidence that thermal Ps atoms react with these molecules via a mechanism which involves the reversible formation of a Ps complex. It can be formulated as follows: annihilation in solvent K 2Y Ps+M A, Kz
&
p s x", ~ 2y (annihilation in complex) (1) According to the above reaction scheme the following reactions have been considered: (1) reaction of Ps with substrate M to form a Ps complex PsM (rate constant K1); (2) decomposition of PsM (rate constant Kz); (3) positron annihilation in complex (decay constant i,);(4) annihilation of Ps in bulk solvent with rate A,. Since the concentration of M, the substrate, remains essentially constant throughout the experiment the mechanism can be simplified to 27
2Ps
-K I'
2y
(KI' = K[M])
p-BENZOOUINONE IN TOLUENE (13 I5 mM1
Io92 0
(3)
Figure 1 shows a plot of K&sd vs. 1/T (the reciprocal of the absolute temperature). The Arrhenius behavior of the various systems observed at lower temperature suggested that in this region K2
