J. Phys. Chem. 1996, 100, 14161-14165
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Vacancies in the Solids of Low Molecular Weight Organic Compounds Observed by Positron Annihilation Yasuo Ito* and Hamdy F. M. Mohamed† Research Center for Nuclear Science and Technology, The UniVersity of Tokyo, Tokai, Ibaraki 319-11, Japan
Masaru Shiotani Faculty of Engineering, Hiroshima UniVersity, 1-4-1 Kagamiyama, Higashi Hiroshima 739, Japan ReceiVed: February 8, 1996; In Final Form: April 29, 1996X
Positron lifetime spectra were measured for several low molecular weight organic compounds, normal and cyclic hydrocarbons and their perfluorinated versions, from room temperature down to about 40 K, and information about the vacancies in them has been extracted from the lifetime and intensity of the orthopositronium (o-Ps) component. Normally the sizes of vacancies were larger in the solids comprising larger molecules, showing that o-Ps can represent the vacancy size. In the special case of perfluorocyclohexane, the solid of which had to be prepared by sublimation, the vacancy size was larger than expected. In all of the solid molecules studied, two o-Ps states could be observed and their relative importance could easily change, showing a hysteresis-like behavior. At lower temperatures of around 40 K the o-Ps state with longer lifetime and larger intensity became overwhelming for all of the molecules. A further remarkable observation is that o-Ps lifetime and intensity were not very sensitive to most of the phase transitions, including the melting points.
Introduction A positron injected into insulating materials can pick up an electron from the material and form a neutral particle called positronium (Ps), with para-positronium (p-Ps, e+ and e- spins antiparallel) and ortho-positronium (o-Ps, the spins parallel) forming in the ratio of 1:3. The probability of Ps formation depends on the physical and chemical properties of the substance. For example, Ps formation is considered to be favorable in the regions where there is enough space to accommodate Ps, but various trapping sites, of both chemical and physical nature, can affect Ps formation.1,2 Ps once formed feels the repulsive molecular force of the constituent molecules of the substance and selectively gets into free spaces. The lifetime of p-Ps (0.125 ns) is too short to be influenced by the volume factors, but the lifetime of o-Ps (140 ns in vacuum) is long enough so that e+ in o-Ps can annihilate one of the electrons in the surrounding medium. The rate of this process, called pick-off annihilation, is determined by the probability density of the surrounding electrons at the position of e+. Thus, o-Ps lifetime is reduced in smaller volumes and its lifetime becomes as short as several nanoseconds in liquids and solids. Excellent short reviews for the Ps trapping into molecular vacancies were given by Eldrup3 and Goworek.4 A simple model originally proposed by Tao5 to describe the rate of the pick-off annihilation, λp, was extended to a spherical potential well with radius R and with infinite height6 as
λp )
2πR 1 R 1 )21ns-1 (1) + sin τp R + ∆R 2π R + ∆R
[
(
)]
where ∆R is the thickness ()0.166 ns7) of the electron layer that constitutes the wall of the hole and can overlap with the o-Ps wave function. It is due to this particular sensitivity of Ps toward vacancy size that positron annihilation has attracted attention with regard to the problems associated with free spaces † X
On leave from El-Minia University, Egypt. Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00400-5 CCC: $12.00
in substances. Although much is left to be clarified about the relationship between the o-Ps parameters (its intensity and lifetime) and the free volume characteristics (the size and the number density), “vacancy spectroscopy” using Ps is considered promising. The present study was motivated by an electron spin resonance (ESR) study of radical cations of organic molecules,8 where simple organic molecules such as cyclohexane (c-C6), methylcyclohexane (Me-cC6) and methylsilocyclohexaene (MecSiC5) are dissolved as guest molecules in a matrix (or host molecules) of perfluorocyclohexane (PFCH, cC6F12) or perfluoromethylcyclohexane (PFMCH, CF3-cC6F11) and the solidified mixture is irradiated with gamma-rays. The positive charges produced by the irradiation are transferred to the guest molecules, and excess electrons are trapped by the matrix. Hence, radical cations of the guest molecule are stabilized, which can be observed by optical and ESR spectroscopy.9 One of the authors (M.S.) has been investigating the ESR spectra of radical cations and found a phenomenon that suggests that the radical cations produced in this way are accommodated in a larger space in PFCH than in PFMCH.10 For example, the ESR spectra of the radical cation of Me-cSiC5 varied with the temperature of the measurement. This could be reproduced by an ESR spectral line shape simulation method using a program for calculating exchange-broadened spectra, in which a parameter describing the frequency of the exchange oscillation of the C-Si-C bondings was involved. The frequency of the oscillation was found to be larger in PFCH matrix than in PFMCH matrix, and this in turn suggests that the space provided for the Me-cSiC5 radical cations is larger in the former matrix. This is opposite to what can be expected from a simple consideration of molecular size. Because PFCH is smaller in size than PFMCH, the size of vacancy, if any, should be larger for the latter. The experiments to be described here have been carried out with a hope of finding an answer to this paradox. Furthermore, several new findings have been obtained for the solids of the low molecular weight compounds studied: (1) o-Ps © 1996 American Chemical Society
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Ito et al.
is not very sensitive to the thermochemical and crystallographic phase changes; (2) Ps can take two different states, the o-Ps parameters of one of them being as large as those in liquid; and (3) o-Ps appears to see vacancies in microcracks formed at low temperature solids. Experimental Section At first, PFCH and PFMCH and their mixtures were used as the samples, but other nonfluorinated low molecular organic compounds, such as methylcyclohexane, n-hexane, cyclohexane, and benzene, were also measured. The purest grades of these compounds were purchased and were used without further purification in most cases. For n-hexane the purest grade chemicals were further distilled, or mixture (hexanes) were used to see the effect of impurity. Excepting PFCH, liquid of these samples was put in a glass tube containing a positron source (22Na enveloped in thin Kapton film) and was evacuated by freeze-pump-thaw method, and then the glass tube was sealed. PFCH is solid at room temperature but is easily sublimated. Thus, it was transferred by sublimation into the glass tube containing the positron source. The sealed glass tube containing the sample and the positron source was set in a low-temperature cryostat designed for the positron annihilation lifetime (PAL) measurements. For each sample the PAL measurements were performed first in a cooling direction from room temperature down to about 40 K and then in a heating direction from 40 K to room temperature at intervals of 10 K. At each temperature it took 7 h to take one PAL spectrum and about 30 min to change the temperature to the next stable level. The temperature was controlled (0.2 K during the measurements. Results The results for PFCH and PFMCH are shown in Figures 1 and 2, respectively. The open circles show the results of the cooling direction, and the solid circles those of the heating direction. The points to be noticed are as follows. 1. The solid PFCH made by sublimation showed long o-Ps lifetime and low intensity (point A in Figure 1). However, the next experimental point appears to have settled to a shorter lifetime and higher intensity. Apparently the solid PFCH as formed by sublimation had a loose structure with abundant large spaces. The initial small I3 value should be an experimental artifact since the solid could not be packed well between the source and the glass tube, and many positrons must have been annihilated in the wall of the glass tube. 2. Literature values for the phase transitions of PFCH and PFMCH measured by various methods are indicated in the figures. The PAL parameters did not show any observable change at these transitions. In the case of PFMCH, even the melting point was not reflected in the o-Ps parameters. 3. At temperatures between 140 and 120 K the o-Ps parameters show a dramatic decrease, and at an even lower temperature of about 40 K they rise again. Hysteresis appears in this variation of o-Ps parameters for the cooling and the heating runs, but the behaviors are not the same. For PFCH the o-Ps parameters decrease in the cooling run, and in the heating run the high-temperature value is restored more quickly. For PFMCH in the cooling run they do not drop readily, as if to show supercooling effect, and in the heating run they remain at the low value in a wide temperature range. Similar data for the nonfluorinated molecules are shown in Figures 3-5. The results are basically the same as for the perfluorinated ones. For Me-cC6 o-Ps parameters do not change at the melting point. However, for cyclohexane and occasionally for n-hexane the melting point is reflected in the PAL. For
Figure 1. o-Ps lifetime τ3 and its intensity I3 as a function of temperature for perfluorocyclohexane. The measurement was started from near room temperature down to the lowest attainable temperature (open circles) and then in a heating direction back to room temperatue (solid circles). The temperatures of phase transitions taken from the literature are indicated. Point A is for the sample as prepared by sublimation, and point A′ indicates how point A relaxed to thermal equilibrium (see text).
n-hexane the experiments were repeated several times with different samples: nonpurified purest grade n-hexane, further carefully distilled, and spectroscopic grade hexanes (mixture of saturated hexane isomers but without double-bond impurities). The results were similar, and thus it appears that the results are not the outcome of some impurity effect. It was a rare case when the o-Ps parameters changed at the melting point, and mostly both τ3 and I3 changed continually. In one experiment, the liquid of pure n-hexane was rapidly solidified in liquid nitrogen (point B in Figure 5) and, by repeated warming and cooling, a nontransparent solid was prepared and the PAL measured. In this case the lifetime τ3 and I3 showed the lower values of Figure 5 (point B′). An earlier work on n-hexane11 reported only the values corresponding to the open circles of Figure5. The data for benzene are shown in Figure 6. Similar to the literature data12 o-Ps lifetime decreased at the melting point and its intensity decreased to 26-23% at low temperatures. The lifetime spectra of the solid benzene could be decomposed into only two components. In such a case the longer lifetime has been called τ2 (with I2), but we plot it on the same graph as the data of τ3 and I3 since it may be a kind of positronium. Our data for solid benzene agree with those of Goworek et al.,13 in that the o-Ps intensity does not decrease even at very low temperatures, but differ in detailed behaviors: our data do not show temperature dependence while in ref 13 the o-Ps lifetime
Vacancies in Solids Observed by Positron Annihilation
Figure 2. o-Ps lifetime τ3 and its intensity I3 as a function of temperature for perfluoromethylcyclohexane. The symbols and the inset numbers are the same as in Figure 1.
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Figure 4. o-Ps lifetime τ3 and its intensity I3 as a function of temperature for cyclohexane. The symbols and the inset numbers are the same as in Figure 1.
from one of these two states to another takes place in the cooling and the heating runs, but the temperature at which the transition takes place appears to be unstable and has a hysteresis-like behavior. Discussion
Figure 3. o-Ps lifetime τ3 and its intensity I3 as a function of temperature for methylcyclohexane. The symbols and the inset numbers are the same as in Figure 1.
was seen to decrease below 100 K and the o-Ps intensity showed oscillatory change. Most compounds except benzene and cyclohexane showed two different o-Ps states in the solid state. In one state both τ3 and I3 change smoothly from the liquid values as if to indicate the existence of a kind of supercooled state. Another is the state with short lifetime (1-1.4 ns) and low intensity. Transition
The initial purpose of the experiments was to compare the sizes of vacancies in solid PFCH and PFMCH. The o-Ps lifetime τ3 is 2.7 and 3.2 ns for PFCH and PFMCH, which from eq 1 correspond to the vacancy diameters of 0.68 and 0.76 nm, respectively. A question may arise whether eq 1 applies to the perfluorinated molecules, since the electron negativity of the F atoms that should constitute the wall of the vacancies might affect the thickness (∆R ) 0.166 nm is used in eq 1) of the electron surface layer. As will be discussed later, there is some evidence that the F atoms do not affect significantly the hole characteristics toward Ps. Since the sizes (the long axis) of PFCH and PFMCH molecules are 0.71 and 0.80 nm, respectively, they will not be accommodated in the pre-existing vacancies of PFCH and PFMCH. Furthermore, the vacancy size measured by o-Ps is larger for PFMCH than for PFCH. This is reasonable since the molecular size of PFMCH is larger but is opposite to the expectation deduced from the ESR study. This paradox is settled if we notice the large value of τ3 ) 3.8 ns (corresponding diameter is 0.82 nm) in PFCH as prepared by sublimation (point A in Figure 1). This is large enough to accommodate the radical cations of, for example, Me-cSiC5 and allow for the selective C-Si-C exchange oscillation. Since the sample for the ESR measurement was prepared by rapidly
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Figure 5. o-Ps lifetime τ3 and its intensity I3 as a function of temperature for n-hexane. The symbols and the inset numbers are the same as in Figure 1. The results for the second cooling run (triangles) are also indicated. In one experiment the state with large o-Ps parameters (point B) was brought to the low value state (B′) by repeated warming and cooling treatment within the solid state.
cooling the mixture of the guest molecules and the sublimated host PFCH, the space around the guest molecule may be large. In PFMCH, however, the guest molecules are enclosed in the matrix solidified from the liquid state, and thus the space should not be as large as in the sublimated PFCH solid. The paradox may thus be attributed to the very fact that the solid PFCH was the one as prepared by sublimation. The previous results provide a practical example as to how the vacancy spectroscopy using Ps works. The o-Ps lifetimes in methylcyclohexane and cyclohexane (Figures 3 and 4) are smaller compared to those of the corresponding perfluorinated compounds PFMCH and PFCH. The ratios of the vacancy diameter, calculated from eq 1, are 0.91 for cC6 and PFCH and 0.88 for Me-cC6 and PFMCH. Since these values are close to the ratio of the molecular size, the o-Ps lifetime is considered to be reflecting the size of vacancy fairly well through eq 1 irrespective of whether there are F atoms or not. Probably, F atoms do not affect significantly the electron surface layer in the hole. The second important point is the insensitivity of o-Ps parameters toward phase changes observed by thermochemical and spectroscopic methods. For PFCH the transition at 178 K observed by broadline NMR15 is considered to be the rotational transition and that at 168 K observed by calorimetry16 is presumed to involve internal molecular motion. For cyclohexane the phase transition at 186 K17 is not observed, either. For PFMCH the change of the o-Ps parameters occurs at temperatures close to but not exactly the same as the two transition
Ito et al.
Figure 6. o-Ps lifetime τ3 and its intensity I3 as a function of temperature for benzene. The symbols and the inset numbers are the same as in Figure 1.
temperatures at 174 and 226 K observed by specific heat,18 X-ray diffraction, and broadline NMR.19 This temperature range is considered to correspond to plastic crystals. The insensitivity of o-Ps parameters toward melting point is the most notable of the present results. Such has rarely been reported. For example, in the PAL study of sulfolane14 τ3 did not change at all on going from liquid to plastic phase, but I3 exhibited a monotonous decrease. In the present results, however, the lifetime τ3 and the intensity I3 change in accord; that is, when τ3 becomes small, I3 also becomes small. The appearance of the long-lived state in the solid should involve vacancies, and the hysteresis-like behavior suggests that such vacancies are controlled by a condition that is unstably realized. Indeed, in one of the experiments with solid n-hexane having a long-lived component (point B in Figure 5), we changed the temperature of the sample up and down within the limit of the solid state and observed that the PAL shifted to the small value (B′ in Figure 5). Apparently the vacancies are annealed out by the heat cycle treatment. The vacancy in question may be similar to those that would be seen in supercooled liquid, but it is not necessary to assume for the present case that the whole of the substance is in a supercooled state. Even if the solid is mostly crystallized, Ps may be trapped in disordered regions, if any. In the solids of low molecular weight compounds, Ps trapped in vacancies may be able to expand the vacancy size in a similar manner as it creates “Ps bubbles” in liquids. In welldeveloped good crystals, however, Ps will not find such a site to create large vacancies. Existence of a short lived o-Ps component of about 1 ns appears to be common for molecular solids and liquids, but it
Vacancies in Solids Observed by Positron Annihilation
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is not understood well. They were found in many molecular solids and assigned to dense packing in crystals20 or to atomic size defects.21 They have also been found in liquid molecular compounds and assigned to secondary reaction products of Ps in the positron spur.22 The short-lived state ranging from 1.0 to 1.4 ns in the present results may be correlated with them. We note that τ3 values of these short-lived components are, although crudely, reflecting the molecular size (hence the vacancy size); that is, they are larger for the solids of larger molecules. Another important fact is that its intensity is always smaller than that of the long-lived o-Ps. We try to explain these observations by the model23 recently revised from the spur model of Ps formation,1 where Ps is assumed to form when the free energy for the reaction
e+matter + e-matter f Pshole
(2)
is positive, taking into account the energy levels of e+ and ein matter and of Ps in the hole. Since the zero-point energy of Ps, E0, is larger in smaller holes [for a spherical potential well with radius R (nm) with infinite height E0 ) 0.188/R2 eV], the Ps yield should be smaller in a substance containing small holes. Goworek et al.13 noted that solid benzene has the component of around 1 ns at all of the temperatures while polyphenyls larger than biphenyl show no long-lived component at very low temperatures. They remarked that free volume type defects are necessary for the formation of Ps in polyphenyls, and such free volumes are thermally generated at higher temperatures. However, the existence of the ∼1 ns component in solid benzene at very low temperatures was not explained. Our present results strongly support the idea, mentioned in ref 13 as a possibility, that Ps may enlarge the pre-existing free volume in solid benzene. The appearance of the long-lived and intense o-Ps state at very low temperatures below 40 K is also a result of great importance. This component looks as if a supercooled state is connected from liquid to the very low temperature. We have been performing PAL measurements for macromolecules in the same temperature range, too, but have not observed a similar phenomenon. In an old literature reference25 an increase in the o-Ps lifetime and intensity in poly(tetrafluoroethylene) was observed below 1.2 K, which, although the authors suggested possible phase transition, has been left unclarified. Considering that the long-lived o-Ps state at very low temperature has been found for most low molecular compounds studied except benzene, we suggest extending the argument made for the two different o-Ps states in the solids at intermediate temperaturess; that is, at the very low temperature microcracks start to form in the crystals and provide efficient sites for Ps trapping and formation of “bubble-like” holes. Conclusion The large vacancies in perfluorocyclohexane supposedly expected from the results of ESR measurements have turned out to be related with the particularly soft spongy structure as prepared by sublimation. This illustrates how vacancy spectroscopy using Ps can be used for practical purposes. In normal solids composed of well-relaxed good crystals the vacancy size measured by o-Ps lifetime roughly reflects the molecular size, in accord with the observation of Eldrup et al. that o-Ps lifetime in solid molecular compounds near the melting point can be correlated with the molecular size.6 In the solids of most of
the molecules studied Ps can take two different states, one being a bubble-like Ps state, with the Ps hole size and the intensity resembling those in supercooled liquid, and the other being Ps at a much smaller site and with a lower intensity. It is also a new observation that at even lower temperatures around 40 K Ps tends to take the bubble-like state, probably due to the fragile and easily cracked structure of the crystals of the low molecular compound molecules. These new aspects of o-Ps behavior might be particular to the solids of low molecular weight compounds, in which molecules can be displaced by the incoming positronium atoms. In the solids of larger molecules or macromolecules, however, there can be an argument whether Ps can “dig” vacancies, and the study of low molecular weight compounds may provide a good test for it. We have recently started PAL measurements with much larger statistics than the present results and have been able to decompose them into four lifetime components, confirming the existence of short-lived components in liquids and solids of the molecules studied. Detailed analysis of the four-component analysis will be published in due course. References and Notes (1) Mogensen, O. E. Positron Annihilation in Chemistry; Springer Series in Chemical Physics 58; Springer-Verlag: Berlin, 1995. (2) Ito, Y. Positron and Positronium Chemistry (studies in physical and theoretical chemistry); Elsevier: Amsterdam, 1988; Chapter 4. (3) Eldrup, M. Positron Annihilation; Coleman, P. G., Sharma, S. C., Diana, L. M., Eds.; North-Holland Publishing: Amsterdan, 1982; pp 753762. (4) Goworek, T. Proceedings of the 3rd Internationl Workshop on Positron and Positronium Chemistry; World Scientific: Singapore, 1990; pp 533-550. (5) Tao, S. J. J. Chem. Phys. 1972, 56, 5499. (6) Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51. (7) Nakanishi, H.; Jean, Y. C. Positron and Positronium Chemistry (studies in physical and theoretical chemistry); Elsevier: Amsterdam, 1988; Chapter 5. (8) Shiotani, M.; Lindgren, M.; Ichikawa, T. J. Am. Chem. Soc. 1990, 112, 967. (9) Shiotani, M. Magn. Res. ReV. 1987, 12, 333. Lindgren, M.; Shiotani, M. Radical Ionic SystemssProperties in Condensed Phases; Kluwer: Dordrecht, The Netherlands, 1991; Chapter 15. (10) Shiotani, M.; Komaguchi, K.; Ohshita, J.; Ishikawa, M. Chem. Phys. Lett. 1992, 188, 93. Komaguchi, K.; Shiotani, M. J. Phys. Chem. 1996, in press. (11) Kajcsos, Zs.; De´zsi, I.; Horva´th, D. Appl. Phys. 1974, 5, 53. (12) Chuang, S. Y.; Tao, S. J. Appl. Phys. 1976, 11, 247. (13) Goworek, T.; Rybka, C.; Wawryszczuk, J.; Wasiewicz, R. Chem. Phys. Lett. 1984, 106, 482. (14) Abbe´, J. Ch.; Duplaˆtre, G.; Machado, J. C. Positron Annihilation (Proceedings of the 7th ICPA); World Scientific: Singapore, 1985; pp 620622. (15) Fratiello, A.; Douglass, D. C. J. Chem. Phys. 1964, 41, 974. (16) Christofers, H. J.; Lingafelter, E. C.; Cody, G. H. J. Am. Chem. Soc. 1947, 69, 2502. (17) Aston, J. G.; Szasz, G. J.; Fink, H. L. J. Am. Chem. Soc. 1943, 65, 1135. (18) Dworkin, A. C. R. Acad. Sci. 1969, 269C, 73. (19) Buu Ban, Chachaty, C.; Renaud, M.; Fourme, R. Can. J. Chem. 1971, 49, 2953. (20) Lightbody, D.; Sherwood, J. N.; Eldrup, M. Chem. Phys. 1985, 93, 475. (21) Jain, P. C.; Eldrup, M.; Pedersen, N. J. Chem. Phys. 1986, 106, 303. (22) Hirade, T.; Mogensen, O. E. Chem. Phys. 1993, 170, 249-256, and references cited therein. (23) Ito, Y.; Okamoto, K. I.; Tanaka, K. J. Phys. IV 1993, 3, 241. (24) Mogensen, O. E. Positron Annihilation; Coleman, P. G., Sharma, S. C., Diana, L. M., Eds.; North-Holland: Amsterdam, 1982; p 763. (25) Kelly, T. M.; Canter, K. F.; Roellig, L. O. Phys. Lett. 1965, 18, 115.
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