1288 (60) (61) (62) (63) (64)
(65) (66) (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) (77) (78) (79) (80) (81) (82) (83)
J. Phys. Chem. 1980, 84, 1286-1294 D. C. Walker, Can. J. Chem., 55, 1987 (1977). S. A. Rice and L. Kevan, J. Phys. Chem., 81, 947 (1977). S. A. Rice, G. Doliio, and L. Kevan, J. Chem. Phys., 70, 18 (1979). T. Nguyen and D. C. Walker, J. Chem. Phys., 67, 2309 (1977). L. Kevan, M. K. Bowman, P. A. Narayana, R. K. Boekman, V. F. Yudanov, and Yu. D. Tsvetkov, J. Chem. Phys., 63, 409 (1975). P. A. Narayana, M. K. Bowman, L. Kevan, V. F. Yudanov, and Yu. D. Tsvetkov, J. Chem. Phys., 63, 3365 (1975). S. Schlick, P. A. Narayana, and L. Kevan, J. Chem. Phys., 64, 3153 (1976). P. A. Narayana and L. Kevan, J. Chem. Phys., 65, 3379 (1976). D.P. Un and L. Kevan, Chem. Phys. Lett., 40, 517 (1976); J. Phys. Chem., 81, 1498 (1977). R. F . Khairutdinov and K. I. Zamaraev, Dok/. Akad. Nauk. SSSR, 222, 654 (1975). R. F. Khahtdlnov, R. B. Shutkovskii, and K. I. Zamaraev, Sov. Phys. SolM State, 17, 594 (1975). R. F. Khairutdinov and K. I. Zamaraev, Bull. Acad. Scl. USSR, Dlv. Chem. Scl., 24, 2667 (1975). R. F. Khairutdinov, N. A. Sadowskii, V. N. Parmon, M. G. Kuzmln, and K. I. Zamaraev, Dokl. Acad. Nauk. SSSR, 220, 888 (1975). I. V. Alexandrov, R. F. Khairutdinov, and K. I. Zamaraev, Chem. Phys., 32, 123 (1978). N. R. Kestner, J. Logan, and J. Jcftner, J. Phys. Chem., 78, 2148 (1974). S. Efrima and M. Bixon, J. Chem. Phys., 64, 3639 (1976). G. V. Buxton and G. A. Salmon, unpublished work. G. Dolivo and L. Kevan, J . Chem. Phys., 70, 2599 (1979); and to be published. N. F. Moll and E. A. Davis, “Electronic Processes in Non-Crystalline Materials”, Clarendon Press, Oxford, 1971. K. Weiser, Prog. Solid State Chem., 11, 403 (1976). J. Tauc, Phys. Today, 23 (1976). J. M. Marshall, Phll. Mag. B , 38, 335 (1978). J. Noolandi, Phys. Rev. B, 16, 4466, 4474 (1977). W. D, Gill, “Photoconductivlty and Related Phenomena”, Elsevier, Amsterdam, 1976, p 303.
(84) (85) (86) (87) (88) (89) (90) (91) (92) (93) (94) (95) (96) (97) (98) (99) (100) (101) (102) (103) (104) (105) (106) (107) (108)
J. Hirsch, J. Phys. C , 12, 321 (1979). R. C. Hughes, Phys. Rev. B, 15, 2012 (1977). D. L. Dexter, J. Chem. Phys., 21, 836 (1953). V. L. Ermolaev, Sov. Phys. Usp., 80, 333 (1963). A. N. Terenln and V. L. Ermolaev, Dokl. Akad. Nauk SSSR, 85, 547 (1962). G. Porter and F. Wilkinson, R o c . R. SOC.London, Ser. A , 264, 9 (1961). F. S. Dainton, M. S. Henry, M. J. pilllng, and P. C. Spencer, J. Chem. Soc., Faraday Trans. 1 , 73, 243 (1977). V. L. Ermolaev, E. 0. Syeshnikova, and T. A. Shakhverdov, Russ. Chem. Rev.. 44. 26 11975). H. Sternlicht,’G. C. Nieman, and G. W. Robinson, J. Chem. Phys., 36, 1326 (1963). F. B. Tudron and S. D. Colson, J. Chem. Phys., 65, 4184 (1976). K. Godzik and J. Jortner, Chem. Phvs.. 38. 227 (1979). Th. Forster, Ann. Phys. 2, 55 (1948). Y. Elkana, J. Feitebn, and E. Katchalski, J. Chem. Phys., 48, 2399 (1968). I. L. Berlman, “Critical Transfer Distances between Molecules”, Academic Press, New York, 1973. P. Avouris, A. Campion, and M. A. El-Sayed, Chem. Phys. Lett., 50, 9 (1977). G. S. Beddard and G. Porter, Nature (London), 260, 367 (1976). K. B. Eisenthal, Chem. Phys. Lett., 6, 155 (1971). R. S. Knox, Physlca (Utrecht), 36, 361 (1968). S. A. Rice and G. A. Kenney-Wallace, Chem. Phys., accepted for publication. R. P. F. Qqpry, “8iochemistry of Photosynthesls”, Wiley, New York, 1977. A. Hengleln, Ber. Bunsenges. Phys. Chem., 78, 1078 (1974). R. P. Hemenger and R. M. Pearlstein, J. Chem. Phys., 56, 4064 (1973). S. W. Haan and R. Zwanrig, J. Chem. Phys., 68, 1879 (1978). R. M. Noyes, Prog. React. Klnef., 1, 129 (1961). F. S. Dainton, M. J. Pilling, and S. A. Rice, J. Chem. Soc., Faraday Trans. 2 , 71, 1333 (1975). .
I
Positron Annihilation in Liquids. A Brief Review and a Reflection on Metal-Ammonia Studies R. N. West School of Mathematlcs and Physics, Universlty of East Anglle, Norwlch, Unlted Klngdom (Received November 20, 1979)
The basic physics and chemistry of positrons and positronium in liquids are outlined. The extent to which positron studies can provide information about reactive dry and solvated species is briefly discussed in order to provide a background for subsequent papers in these proceedings. Existing positron data on metal-ammonia solutions are shown to have most bearing on fundamental positron problems rather than the indigenous species of the solution in question.
1. Introduction Positron annihilation studies of condensed matter now have a history of some 30 years and are today finding increasing application to problems throughout solid and liquid state physics and ~hemistry.l-~The history of positron studies of aqueous and similar solutions is almost as long but until quite recent times has been largely a story of relatively modest rewards. Today this field is seeing considerable activity and, as we should see in this coming session, if the major breakthrough in understanding has yet to come, the potential is certainly there. Energetic positrons are readily available in the form of a variety of commercial radioisotope (nNa, 58Co,64Cu,etc.) sources. When such positrons enter matter they are raps) idly slowed by electrons and ions and quickly ( attain thermal equilibrium with the containing medium. After a further and markedly longer period (s) the annihilation of each positron is announced to the external N
0022-3654/80/2084-1286$0 1.OO/O
observer by the appearance of y-ray photons whose energies, relative directions, and time of emission can all be measured with high precision with modern detector systems. The utility of such measurements in investigations of the physics and chemistry of both the material in question and the “foreign” light charged particle in it derives from the fact that, notwithstanding the complexity of the underlying quantum electrodynamical problem, the results of such measurements depend essentially only on the initial state of the positron-many electron system. 2. Two-Photon Annihilation (i) The Basic Physics. Because the positron is rapidly thermalized and is excluded by Coulomb repulsion from regions deep within heavy atom or ion cores where both it and potential electron partners could have large kinetic energy, annihilation in condensed matter is confined to relatively slowly moving (u Vi - 6.8 eV. If E > Vi inelastic wattering with ionization will be more probable because of the greater density of final states associated with two free particles. If E > V,, the lowest excitation potential, this excitation will again compete with Ps formation. Thus Ps formation is most probable for the positron energy range V , > E > Vi - 6.8 eV (3) This is the “Ore Gap”l2the size of which is relevant to the ultimate Ps yield. The extension of this model to even a homogeneous condensed medium must take account of various and inevitable energy changes such as a modified Ps binding energy and possibly significant Ps-, positron-, and electron-medium affinities. Within the consequent range of preferred energies other factors such as the excitation of molecular vibrational and rotational modes and the formation of positron-molecule complexes may further inhibit Ps f0rmation.l The introduction of impurities producing additional excitation and ionization mechanisms can affect the Ps yield in either direction. Furthermore, since Ps atoms can be formed with kinetic energies ranging from thermal to E the atoms may undergo rapid chemical reactions whifzstill “ h ~ t ” . ~Such ~ - ~reactions ~ may result in a final positron state in which all memory of its Ps past is lost to both it and its observer at later times. The reader by now should have discerned the considerable flexibility of this complete Ore plus “hot Ps” model. Its major weaknesses which confine its adherents to purely qualitative interpretation are its implicit and unsatisfied needs for both an adequate description of the energy loss spectra of the thermalizing positrons and the various possible energy states of its potential electron partners. Nevertheless it does provide a plausible picture off Ps formation in situations in which all of the system except the positron is in equilibrium. The “spur” model of Ps formationla provides a further degree of freedom. Here Ps is assumed to be formed in a reaction between the positron and a spur electron in the positron spur. The spur is the group of reactive species (the positron, electrons, positive ions, etc.) created in the later stages of positron energy (100 200 eV) loss. Within this spur Ps formation must compete with electron-ion recombination, electron and positron reactions with scavenger molecules, and with electron and positron diffusion out of the spur. The apparent advantage of this view of Ps formation is that complementary data on such spur phenomena are available from radiation chemistry data.19@ Mogensen and colleagues8~10~20‘zz have established various correlations between such data and Ps formation fractions in a variety of pure liquids and solutions. Nevertheless it must be admitted that the correlations established sometimes defy a really transparent interpretationz0and in other cases might equally well be used in a qualitative justification of the “hot Ps” modified Ore Gap model. It is not possible in an article of this sort to do justice to the various detailed discussions contained in the references cited above. Instead, we shall content ourselves with the following general observations. The spur and Ore Gap models should be regarded as complementary rather than alternative views of Ps formation. Neither can provide much more than qualitative pictures at the present time. In respect to the effects of solutes or additives in solution they both provide a similar picture, namely, that centers having a strong affinity for electrons or positrons will inhibit Ps formation whereas electron donors or positive-ion scavengers will likely enhance such formation. As we shall see in the following section the positron data taken in isolation can seldom discriminate between the pictures offered by the two
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models. Nevertheless the advent of the spur model has provoked renewed theoretical interest in the problem and much increased experimental activity in respect to both the inhibition and the quenching aspects of Ps chemistry. (iii) Quenching of Positronium. Chemical and physical processes occurring in times greater than s following the positrons injection into the sample affect both the rates and intensities in lifetime spectra. Such quenching processes if nothing else invariably shorten the lifetime of the longest-lived 0-Ps atoms. The pickoff process will always occur whether or not other quenching mechanisms are present. The observed rate for the pickoff of 0-Ps atoms can be most simply regarded as the result of a simple competition between the intrinsic three-photon rate A, (-7 X lo6 s-l) and a two-photon rate, A, = Kt, where K is the rate of collision with the surrounding molecules (K >> A,) and 6 (> A,. In the absence of alternative quenching processes this, which usually appears as the longest-lived lifetime component, has an intensity (usuallyI3 in the literature) almost equal to three quarters of the Ps fraction (P). Few of the remaining l14P p-Ps atoms suffer the pickoff process because their intrinsic decay is so fast. This fast decay of the para atoms is also in principle present in the lifetime spectrum but seldom can be reliably resolved and its intensity is often more easily found from that, I,, of the already mentioned narrow component in the momentum density. Then in view of the picture offered above, I, = 13/3= P/4. The separation of this component from the somewhat broader distributions that result from pickoff, positrons bound to medium molecules, or positrons that have throughout remained essentially free is usually possible by the PAACFrr7 or similar methods. Of course these last two mentioned modes of decay also contribute lifetime components with rates that normally lie in the range 2 X lo9 5 X lo9 s-l. This simple pattern of events and observables will break down in the presence of other quenching mechanisms. A simpIe rate equation d e s c r i p t i ~ nof~ ?the ~ ~interaction of Rs atoms with various quenching centers is usual but if too many mechanisms are included in the analysis the solutions obtained are far from transparent and usually lie well beyond the resolving power of the present experimental techniques. The equations and solutions appropriate to ortho para (and, of necessity, the simultaneortho) c o n v e r s i ~ nor ~ ~simpler ,~~ ously occurring para unidirectional processes such as ionization (oxidation) or capture10~23~25 have been well discussed elsewhere. Here we shall merely content ourselves with a description of the predicted trends in observables as the quenching rate increases. An ortho para conversion analysis is usually based on a triplet to singlet conversion rate y. Since in any collision the probability of a singlet to triplet conversion is, for purely statistical reasons, three times that for triplet to singlet, there is an inherent bias toward the ortho state. On the other hand, the probability of annihilation while in the para state, A,, is some ten times that of the typical 0-Ps pickoff rate. Thus, whereas when y is zero the relative populations of the para and ortho states are in the ratio 1:3, as y increases, and all Ps atoms experience a similar life history, there is a correspondingly increased probability that they decay from the para state. Eventually, as y (or more modestly y >> &) the decay rate of the longest lived of two exponential components
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A3
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'/44x,+ 74Ap
(4)
West
which is close to the spin-averaged Ps vacuum rate,2 and its intensity 13(m) = 4/J3(0). Concomitantly the intensity I , of the narrow component in the momentum density grows by a factor -4. A similar pattern of lifetime changes can result from unidirectional transitions. If at time t = 0, no0-Ps atoms are born and subsequently annihilate at a rate A, or interact at a rate k with various centers with the consequence that they then can more quickly decay at an alternative rate Xf, the entire population decays in time as
Thus as k increases so also do both A3 = A + k , and 1, until, when k approaches the value (Af - A!, the part of the spectrum described by (5) degenerates to a single component exp(-Aft). Around this limiting value the spectrum is complex but in any realistic case is unlikely to be resolved into discrete components or from other modes of fast decay. This type of quenching mechanism can be most easily distinguished from conversion via the behavior of I,. As k (A, - A,) and thus the intrinsic p-Ps rate A, (-4Af) the para atoms will also be appreciably quenched. Thus I , will initially remain unchanged but ultimately decrease, in contrast to its growth when fast conversion obtains. Other more complex patterns of quenching induced changes in lifetime rates and intensities can easily be envisaged and may, in particularly favorable circumstances, be experimentally resolved but the simplest examples given above provide sufficient basis for most of the coming discussion.
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4. Water, Aqueous, and Other Solutions The positron lifetime spectrum for water is generally The agreed to approximate well to three components.10J1,26 longest-lived component has an intensity 1, 26% and a lifetime 7, (A3-l) 1.9 ns and is attributed to pickoff annihilation of 0-Ps atoms. Thus I , = 3/4Pas described in section 3iii. The separation of the faster components arising from p-Ps decay and the annihilation of quasi-free positron or similar states is difficult and generally requires some specific assumptions about the underlying rates of these components. The usual a s s u m p t i ~ n , "guided ~ ~ ~ by the results of quenching studies, is that the lifetime of the intermediate free positron component is -400 ps. There then emerges a short-lived component with r1 130 ps and, as expected, I, I3 E 8.5%. A similar picture of the distribution of Ps and positron states is also obtained from PAACFIT7 analyses of angular distributions.26 Here and in other liquids a useful, albeit not always entirely adequate, model assumes the Ps atoms exist in bubbles or cages created by a balance between the Ps localization energy and the various intermolecular and Ps-molecule forces. A continuum view of the bubble state suggests a correlation between the 0-Ps pickoff rate and surface tension which has been experimentally verified.28 The fwhm of the momentum density p-Ps component for water is very much greater than that for the corresponding delocalized state in ice and suggests a bubble of the order 5-A radius. A description of the positron state underlying the intermediate lifetime component is less ameniable to such a continuum analysis but here, inevitably, in polar fluids, one is concerned with a solvated particle.26 The introduction of various solutes into water, and other solvents, vastly increases the interpretational possibilities.
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Fi ure 4. Quenching of 0-Ps by iodoacetic acid. (From Maddock et
al.s 7)
The following three major areas of endeavor can then be distinguished: (1)the study of the inhibition of Ps formation by various solutes which, as earlier suggested, means rapid (
