Positronium Chemistry: Present and Future Directions - Advances in

1 Positronium Chemistry: Present and Future Directions

Downloaded by 201.202.128.182 on November 29, 2015 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0175.ch001

HANS J. ACHE Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

In this review an attempt has been made to critically assess the present status of positronium chemistry and positron an nihilation techniques as a chemical probe in general. Spe cifically, the concept that the interactions between positro nium atoms and substrate occur primarily via positronium complex formation and that the rate of this reaction is there fore dependent on the nature of the environment in which they occur, has been developed to a method of determining the position of probe molecules in micelles and to evaluate formation constants for inclusion and acceptor-donor com plexes of biological interest. Furthermore the positronium formation process was very sensitive to microphase transi tions and was used for the assessment of critical micelle concentrations in aqueous and reverse micellar systems.

A mong the various combinations of elementary particles and their antiparticles, which have become known during the recent years as exotic atoms, the positronium ( P s ) , which is the bound state of an electron and positron (e e"), is undoubtedly the most thoroughly investigated species. This is probably owing to the fact that Ps atoms can be produced easily following the β decay of certain radioactive nuclides, such as N a . T h e properties of this species have been discussed i n previous reviews (1-7). Positrons emitted as a result of such a radioactive decay lose most of their (initially several hundred K e V ) kinetic energy i n inelastic and elastic collision until they reach nearly thermal energies at which point they can combine w i t h electrons to form the Ps atom, whose binding M

+

2 2

+

0-8412-0417-9/79/33-175-001$11.25/l © 1979 American Chemical Society

In Positronium and Muonium Chemistry; Ache, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

POSITRONIUM A N D M U O N I U M CHEMISTRY


2

energy is 6.8 eV. The positronium formation probability depends on the nature of the environment: i n water about 3 6 % of a l l positrons form Ps, whereas i n benzene the corresponding number is 5 7 % . Ps can be visualized as an analog of the hydrogen atom, i n w h i c h the proton is substituted by a positron, and thus can be considered as the lightest isotope of the hydrogen (Figure 1 ) . However, i n contrast to the hydrogen atom which is a one-center system, the equal masses of the electron and positron make the positronium a two-center system, which leads to drastic differences not only i n the physics but also i n the chemistry of these two species. Ps exists i n two ground states, the singlet (para) Ps w i t h antiparallel spin orientation ( j j ) (its self-annihilation lifetime is i n free space 1.25 X 1 0 ' sec and it decays b y two-photon emission), and the triplet (ortho) Ps with parallel spin orientation ( î f ) w i t h a considerably longer intrinsic lifetime of 1.4 χ 10" sec (Figure 2 ) . Its self-annihilation occurs v i a three-photon emission. Ortho and para Ps are formed normally i n the ratio of 3:1. Despite this short lifetime, which rules out conventional product analysis as e.g. used i n the reactions of tritium, the Ps is an excellent labelled hydrogen atom for the investigation of the properties and the chemical and physical processes i n matter; this is because its lifetime and the mechanism of its annihilation process are determined by the chemical and physical states of the environment. The potential of the positron annihilation and the Ps atom to the solution of physical problems has been recognized rather early b y physi cists, and here especially, i n the area of solid-state physics, where this method is now w e l l advanced and has become a standard technique e.g. for defect studies and for F e r m i surface determinations i n metals (8). O n the other hand, the development of the positron annihilation 10

7

POSITRONIUM

HYDROGEN ATOM

REDUCED M A S S : « m

e

me 2

BOHR RADIUS: 0.53 A

1.06 οA

IONIZATION POT.: 13.6 eV

6.8 eV

ο

Angewandte Chemie (English)

Figure 1. Characteristics of hydrogen and Ps atoms (5)


1.

ACHE

Positronium Chemistry Ps

(e-e+)J|

0.512 MeV/ / θ . 5 Ι 2 MeVy

SINGLET-Ps (PARA)

Vcl80°'

τ ? = 1.25 X IO- sec.

(FOR FREE PARA-Ps)


,0

(e- e+)

Ps. 7,

ÎÎ

Ε

Χ (+

Ε χ + Ε = Ι . 0 2 MeV 2

/ 3

TRIPLET-Ps (ORTHO) τ ° = 1.4 X I0 sec. _7

( FOR FREE ORTHO-Ps) Angewandte Chemie (English)

Figure 2.

Ρs annihilation characteristics (5)

method as a probe for chemical properties, i.e. the Ps chemistry, has proceeded rather slowly since the discovery of Ps b y Martin Deutsch in 1951 ( 9 ) . It is interesting to note that in the early stages a major contribution i n the area of Ps chemistry was and still is made by scientists trained by physicists. However, despite all the pioneering efforts by these groups, chemists remained rather indifferent to this new atom and it was only during the past five to seven years that chemists of all persuasions have become more and more involved i n the chemistry of this exotic atom, and have provided the diversity and expertise to develop this technique to a new general tool for the solution of chemical problems. Thus I believe it is rather appropriate at this point in time to assess what has been accomplished so far i n Ps chemistry, what we know about the reaction of the Ps, and where we are going from here. As i n the case of any new technique one can distinguish two stages. The first stage can be considered as the study of the basic features of this particular effect, or, as i n this case, as the study of the underlying fea tures, chemical or physical processes, w h i c h alter the fate of the Ps atom. T h e second stage of research carries more significance for the chemist and is concerned w i t h the question of how we can i n turn utilize



4


the knowledge gained i n the first stage to develop this new technique, or the reactions of the new atom to obtain new chemical information, over and above that of what can be assessed by other conventional techniques. It is my contention that we have successfully finished the first stage and that we have to direct our attention now to the second stage, a task for which we need the cooperation of chemists in all areas of chemistry reaching from nuclear and radiation chemistry to bio- and enzyme chemistry. However, before I venture into a discussion of where or into w h i c h areas I see a special advantage i n applying this nuclear technique, I would like to sumamrize briefly some of the essential features of Ps chemistry. Basically the chemical information about the environment i n w h i c h positron or Ps is formed comes from the observation of two processes: the Ps formation and the reactions of the Ps atom. Let me explain the second process first and let us concentrate on the question of w h i c h reactions the ortho Ps (o-Ps) can undergo. (Because of the extremely short lifetime of the para species, the following discussion is restricted to the reaction of the o-Ps ). Basic Features of Positronium Interactions with Matter Quantum mechanics predicts that the annihilation lifetime of the positron is determined basically by the degree of overlapping of positron and electron wave functions, w h i c h leads e.g. to the intrinsic lifetime of o-Ps o f l . 4 X l O - s e c . The laws of conservation of energy and momentum also require that the self-annihilation of the o-Ps occurs via three-quantum annihilation. In the past, several reaction mechanisms were discussed, such as pickoff annihilation, oxidation, and spin conversion. A l l these processes result i n a definite shortening of the positron lifetime and i n a drastic increase of the two-photon annihilation rate (Figure 3 ) . (Previous reviews can be found i n References J - 7 ) . Unfortunately, some of the concepts such as pick-off annihilation and the bubble model are foreign to the vocabulary of the organic or biochemist. Thus i n order to describe the various reaction types between Ps atoms and molecules we more recently have discussed these reactions i n a scheme w h i c h is based on simple gas kinetic principles familiar to every chemist (JO). As shown i n Figure 4 the basic assumption is that i n a collision between o-Ps and another molecule a more or less long-lived collision complex is formed, i n which the electron density at the positron of the positron is increased drastically. The average time that the Ps spends i n this complex w i l l depend on the stability of this complex. If only weak (van der Waals) forces are operative i n holding this complex together, 7


In Positronium and Muonium Chemistry; Ache, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979. _ l

°

Figure 3.

H O

2 y / 3 y = 372/1

2 y / 3 y =372/ 1

2 / / 3 y =372/1

PHOTONS EMITTED

Angewandte Chemie (English)

SHORTER

SHORTER

SHORTER

SHORTER

AVERAGE LIFETIME OF o - P s APPEARS TO BE

τ

7

Quenching reactions of o-Ps (The ratio 2γ/3γ represents the ratio of annïhûation events occurring via 2-photon and 3-photon emission). (Intrinsic lifetime τ ° = 1.4 X 10 sec (5).)

- l

est. ~ 0 . 5 x l O (COMPLEX)

I.25x I O (p-Ps)

COMPOUND FORMATION

_l

—

~0.5 X I O ° (IN COND. PHASE) (FREE POSITION*

L

MECHANISM

OXIDATION

CONVERSION

PICKOFF

REACTION

AVERAGE LIFETIME OF PRODUCT (sec)



7

(RAPID ANNIHILATION)

RAPID

+

2

X

(RAPID ANNIHILATION FROM COMPLEX)

2/

ANNIHILATION)

Journal of the American Chemical Society

(RAPID ANNIHILATION)

2/

—·Ζδ M + e" + ) becomes more probable than Ps formation (e + M —> M + P s ) , so that V constitutes the upper boundary of the Ore gap (Figure 24). Ps atoms can be formed in the Ore gap with kinetic energies of up to 6.8 e V and react as a kinetically excited species or after reaching thermal equilibrium. P s

P s

+

+

+

+

e +

Kinetic energy of positron ( E ) k

Major type of interaction with substrate ( M ) (Ionization pot. of subst. = V ) (Excitation pot. of subst. = E * )

E >V

e

k

+ + M->M++e-+e+

V E >E*

α

E >V-6.8eV

0

k

e+ + M - > M * + e+ or e+ + M - > M + + (e+e~)

E* k

e+ + M - > M + + (e+e-)

V-6.8 e V E < V-6.8 e V k

N o positronium formation

Thermal energies

Figure 24. Schematic of Ore gap model (energetics of Ps formation)



38


The experimental results, however, suggest that not all positrons form Ps and several factors have been discussed which could interfere with and inhibit this process. The Ore model is based on the simplified assumption that all posi trons whose kinetic energy lies in the Ore gap produce Ps. In practice, however, the Ps formation process in the Ore gap has to compete w i t h all other processes that can cause moderation of the positron to energies below the lower Ore limit. The most important of these elastic and i n elastic collisions w i t h substrate molecules, the energy transferred in the second case possibly stimulating molecular vibrations and rotations. This category also includes processes that lead to the positron capture by addi tion of positrons to the substrate molecule A B . e + A B -> e A B or A + e Β +

+

+

If the compound formation occurs above or within the Ore gap, the cap tured positrons are no longer available for the formation of Ps; therefore the yield decreased. A second model for Ps formation which has been suggested recently by Mogensen is the spur reaction model (71). H e assumes that Ps is formed as a result of a spur reaction between the positron and a secondary electron i n the positron spur. In this model a correlation should exist between the Ps formation probability and the availability of the electrons in the spur. The Ps formation must compete with electron-ion recom bination and with electron and positron scavenging by the surrounding molecules as well as with other processes. A model which combines certain features of both models is Tao's modified spur model (72). In this model Tao considers both the possibil ity of combination of a positron with an electron created i n the spur as well as the direct formation of a Ps, similar to the mechanism discussed in the Ore model, if the total kinetic energy of the resulting electronpositron pair is less than the potential energy between them. The processes mentioned here, such as elastic scattering, stimulation of molecular vibrations and rotations i n the electron volt range, and the addition of low-energy electrons (or positrons) to molecules or genera tion of electrons ih the spur and their subsequent reactions with scaven gers, etc., are of the greatest importance to the understanding of elemen tary processes i n radiation chemistry. Thus several investigations have been carried out by Mogensen et al. (73, 74, 75), Tao (72), Byakov et al. (76,77), M o l i n et al. (78,79), Maddock et al. (80,81), and our labora tory (82, 83) to demonstrate the interrelationship between the Ps forma tion process and radiation-chemical phenomena. In the past we have interpreted our experimental results i n solutions of inorganic ions i n terms qf the (modified) Ore gap model (21, 22,33).



1.

ACHE

Positronium Chemistry

39

It was assumed that the energetic o-Ps, which is formed in the Ore gap with kinetic energies varying between 6.8 eV and thermal energies, has, as any other hot atom, two alternatives. It may undergo chemical reactions while still hot, followed by a rapid annihilation of the positron i n the resulting reaction products, or it can lose its excess kinetic energy i n moderating collisions, becoming a thermalized Ps-atom and reacting as such. O n the other hand, hot reactions between solute and Ps-atoms have to take place shortly after the birth of the Ps before it becomes thermalized. Thus, the lifetime of the positrons incorporated i n Ps atoms taking part in hot reactions w i l l become indistinguishable from that of the free positrons or p-Ps. By using this approach the experimental results obtained i n aqueous solutions of inorganic ions were interpreted by assuming that only a certain fraction of all Ps-atoms formed hâve sufficient energy (i.e., hot Psatoms ) to overcome the reaction barrier to react with the inorganic ions (A - f e" - » A ) . In this way the redox potential of the Ps-atom could be approximated (32, 33). If one wants to interpret the experimental results in terms of the simple spur reaction model ( 71 ) one would have to consider the competition between positron and electron combination and the reaction of the electron with the scavenger (inorganic ions). Thus in analogy with the approach used by H a m i l l and several other authors (84,85) for a simple competition for dry or solvated electrons in a solution one could derive the following correlation between the o-Ps formation probability Ρ at a given solute concentration [ M ] , if the o-Ps formation probability in the pure solvent is P ° ; a q

n +

( n _ 1 ) +

P —P°/(l + K[M]) where Κ is the rate constant for inhibition of o-Ps formation. The Κ values assessed from this kinetic analysis are summarized i n Table V I I I (83) and plotted i n Figure 25 on a logarithmic scale as a func tion of — AG for the one-electron transfer process. A reasonable correlation exists between the free energy changes and the inhibition constants Κ as seen from Figure 25. No apparent correlation, however, seems to exist between the inhibi tion constants Κ and the reported rate constants for the reactions of hydrated electrons (Table V I I I ) with these compounds, w h i c h makes an interpretation of the observed inhibition in terms of a competition for solvated electrons between positron and scavenger, i.e. the inorganic ions, rather unlikely. Another possibility would involve the combination of dry electrons and positrons, i n which case scavenger and positron compete for the dry 0


40


Table VIII.

Correlation Between the Free Energy Changes and the Inhibition Constants Κ (83)

Ion

κ(Μ-η

Pb Sn" Cd Ag H ΊΤ Zn" Na NO3-

2.5 1.2 0.37 0.35 0.22 0.10 0.10

Positronium Chemistry: Present and Future Directions - Advances in

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