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Positronium formation reaction of trapped electrons and free positrons: delayed formation studied by AMOC
ARTICLE IN PRESS
Radiation Physics and Chemistry 68 (2003) 647–649
Positronium formation reaction of trapped electrons and free positrons: delayed formation studied by AMOC N. Suzukia, T. Hiradeb,*, F. Saitoc, T. Hyodod a
Henkel Research Center of Advanced Technology, Molecular Engineering Institute, Kinki University, 11-6 Kayanomori, Iizuka, Fukuoka 820-8555, Japan b Department of Materials Science, Japan Atomic Energy Research Institute, Tokai, Naka, Ibaraki 319-1195, Japan c The Institute of Physical and Chemical Research, Cyclotron Center, Hirosawa 2-1, Saitama 351-0198, Japan d Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, 3-8-1, Komaba, Tokyo 153-8902, Japan
Abstract Positronium (Ps) can be formed by the reaction of trapped electrons and free positrons at low temperatures in molecular solids. While Ps formation by spur process must be fast, Ps formation by trapped electrons and free positrons is possible even at positron age of several hundreds pico-seconds. Age–momentum correlation measurement of electron–positron pair annihilation g-rays was applied to investigate the delayed Ps formation, and an evidence for the existence of the delayed Ps formation was successfully observed. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Positron; Positronium; Polyethylene; Polymer; Trapped electrons; Low temperature; AMOC; Delayed Ps formation
1. Introduction The mechanism of positronium (Ps) formation in condensed matter has been studied for a long time. The spur model (Mogensen, 1974) proposed by Mogensen qualitatively explains a wide range of Ps formation data in condensed matter. In 1980s, very large increment of Ps formation at low temperatures during positron annihilation lifetime (PAL) measurement was observed in some materials, such as cyclohexane (Eldrup et al., 1980) and polyethylene (Kindl and Reiter, 1987). It was a phenomenon that could not be explained by the spur model. Hirade et al. successfully explained it by the Ps formation reaction of trapped electrons accumulated during PAL measurement and free positrons escaped from the Ps formation in the terminal spur of the positron track. Moreover, they obtained the experimental evidence successfully (Hirade et al., 1998, 2000). *Corresponding author. Fax: +81-29-282-6716. E-mail address: [email protected] (T. Hirade).
Ps binding energy is 6.8 eV in vacuum and a little lower, probably about 4–5 eV, in materials such as polyethylene. Some of the excess electrons produced by the positron irradiation are trapped with a binding energy of 0.5–3 eV at low temperatures and live for a long time. If a free positron finds one of the trapped electrons before its lifetime, the positron will pick up an electron to form Ps. One of the phenomena expected for the Ps formation by accumulation of trapped electrons is visible light effect. The binding energy of the electrons on the trapping sites is 0.5–3 eV. Therefore, the visible light can quench the trapped electrons. Hence the visible light effect on Ps formation should be a good evidence for the existence of new Ps formation mechanism. Hirade et al. successfully obtained inhibition by visible light of the enhancement of Ps formation (Hirade et al., 1998, 2000). Hirade et al. also indicated that there is a good correlation between the density of the trapped electrons (and anions) observed by electron paramagnetic resonance (EPR) and the increment of the Ps formation in polymethylmethacrylate (PMMA) and polyethylene (Hirade et al., 2000). For polyethylene, free positrons
0969-806X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0969-806X(03)00286-X
ARTICLE IN PRESS N. Suzuki et al. / Radiation Physics and Chemistry 68 (2003) 647–649
2. Experimental The polymer sample used for this study was linear high-density poly(ethylene) (PE, Mitsui Petrochemical, Japan). It has a molecular weight of M w ¼ 60; 000; a density of 0.968 g/cm, and a crystallinity of 0.72. Commercial samples usually contain additives to prevent thermal and oxidative degradation, which are specific for the type and application purposes of the polymer. These additives can in general affect chemical reactions. The details of the AMOC system used in the present work are described elsewhere (Suzuki et al., 2000). In the present study, the S-parameter (uncorrelated with the lifetime measurements) was continuously measured simultaneously with the AMOC measurements. All AMOC measurements were performed at 20 K.
3. Results and discussion Fig. 1 indicates S-parameter change with elapse of the AMOC measurement time in polyethylene at 20 K in the darkness and under visible light. It is possible to divide it into three stages: (I) increment and (II) saturation in the darkness and (III) quenching of o-Ps intensity by the visible light, respectively. The density of the trapped electrons increases in stage (I) and the density is saturated in stage (II), and there are no trapped electrons in stage (III). AMOC results were analyzed to give age dependence of S-parameter as shown in Fig. 2. The larger the value
0.57
S-parameter
can find one of the trapped electrons at a density of B1015 spins/g. The mean distance between the trapped electrons is about B100 nm for that concentration. Brusa et al. estimated that the diffusion distance of free positron before annihilation in polyethylene was about 80 nm (Brusa et al., 1995). It indicates that at least some of the free positrons can diffuse freely in polyethylene before their annihilation. The other expected phenomenon is the ‘‘delayed Ps formation’’. In order to see this phenomenon, we applied age–momentum correlation (AMOC) technique. Only the self-annihilation of para-Ps (p-Ps: 14 of Ps is formed as p-Ps) gives large SðtÞ-parameter. If the Ps formation by the trapped electrons is possible up to just before the free positron annihilation, it must be clearly observed by AMOC measurement, because annihilation from delayed p-Ps formation can give large SðtÞ values even at the positron age of B400 ps. In the present study, we performed the AMOC measurement for polyethylene at 20 K under visible light and in the darkness. The results strongly suggest the existence of the delayed Ps formation.
0.56
I
0.55
II
III
0.54 0
5
10
15
20
25
30
time (days) Fig. 1. AMOC measurement time dependence of S-parameter in polyethylene at 20 K. Measurements were performed in darkness at stages I and II, and under visible light at stage III, respectively.
0.54 0.52
S (t)
648
0.50 0.48 0.46 0.44 0
1
2
3
4
5
positron age (nsec) Fig. 2. Positon age dependence of SðtÞ-parameter in polyethylene at 20 K. The closed circles represent the results obtained in darkness (stage II in Fig. 1) and the open circles represent the results obtained under visible light (stage III in Fig. 1). Solid lines were the simulation curves without delayed Ps formation.
of S-parameter, the lower the total momentum of the electron–positron pairs annihilates. The open circles and the closed circles indicate the results for stages (II) and (III) in Fig. 1, respectively. The solid line through the open circles represents the result of the fit to a model without delayed Ps formation. The parameters used here are shown in Table 1. The fit is good, which is consistent with the fact that no delayed Ps formation is expected under visible light because of no trapped electrons at (III). The solid line through the closed circles represents the result of the fit to a model in which only the Ps formation probability is different from that for (III). In the case of stage (II), there is a delayed increment at early age region. Moreover, the decrement appeared at later age region than the decrement in the case of stage (II). This is more clearly seen by the comparison with the
ARTICLE IN PRESS N. Suzuki et al. / Radiation Physics and Chemistry 68 (2003) 647–649 Table 1 Parameters for the simulations indicated in Fig. 2 S
p-Ps o-Ps e+ Kapton a
0.676 0.477 0.453 0.429
t (psec)a
129.6 1310 320 384
649
Tohoku University and Dr H. Saito at University of Tokyo for valuable discussions.
Intensity(%) Stage II
Stage III
14 42 30 14
5.15 15.45 65.4 14
These values were obtained by the measurement at stage III.
fitted curve with no delayed Ps formation. Hence those observed in stage (II) can only be explained by the delayed Ps formation. There is a minimum of SðtÞ at positron age of about 1 ns in polyethylene especially for measured under visible light. Such a minimum is not observed in nhexane at room temperature (Stoll et al., 1995). It is probably caused by positron complex. It is known that a minimum of o-Ps intensity is seen after large decrement by elevating temperature for some materials (Wang et al., 1998; Ito et al., 1999; Chen et al., 2001). Hirade et al. mentioned that it could be caused by the positron scavenging by stable anions, i.e. by a formation of positron complex (Hirade et al., 1998). It is quite natural to have this kind of positron complex at stage (III) because it was measured after large increment of o-Ps intensity. The positron complex formation should give low SðtÞ values around 1 ns. Further investigations are needed to identify the cause of this minimum on SðtÞ:
4. Conclusion Delayed Ps formation was clearly observed for polyethylene at 20 K by AMOC measurement. Hence it is clear that the Ps formation is possible by the trapped electrons and the free positrons having escaped from the Ps formation by spur process and moving freely in polyethylene.
Acknowledgements We are very grateful to Prof. T. Suzuki in KEK for supplying PE samples. We also thank Dr. Y. Nagai at
References Brusa, R.S., Duarte Naia, M., Margoni, D., Zecca, A., 1995. Positron mobility in polyethylene in the 60–400 K temperature range. Appl. Phys. A 60, 447–453. Chen, Z.Q., Suzuki, T., Uedono, A., Tanigawa, S., Ito, Y., 2001. Temperature and irradiation effects on positronium formation in polycarbonate. Mater. Sci. Forum 363–365, 297–299. Eldrup, M., Lightbody, D., Sherwood, J., 1980. Studies of phase transformation in molecular crystals using the positron annihilation technique. Faraday Discuss. 69, 175–182. Hirade, T., Wang, C.L., Maurer, F.H.J., Eldrup, M., Pedersen, N.J., 1998. Visible light effect on positronium formation in PMMA at low temperatures. Abstract Book for the 35th Annual Meeting on Radioisotopes in the Physical Science and Industries, Tokyo, Japan, June 30–July 1, p. 89 Hirade, T., Maurer, F.H.J., Eldrup, M., 2000. Positronium formation at low temperatures: the role of trapped electrons. Radiat. Phys. Chem. 58, 465–471. Ito, Y., Hirade, T., Hamada, E., Suzuki, T., Ito, Y., 1999. The effect of visible light irradiation on positronium formation in polyethylene at low temperature. Acta Phys. Pol. A 95 (4), 533–538. Kindl, P., Reiter, G., 1987. Investigations on the lowtemperature transitions and time effects of branched polyethylene by the positron lifetime technique. Phys. Stat. Sol. A 104, 707–713. Mogensen, O.E., 1974. Spur reaction model of positronium formation. J. Chem. Phys. 60 (3), 998–1004. Stoll, H., Koch, M., Lauff, U., Maier, K., Major, J., Schneider, H., Seeger, A., Siegle, A., 1995. Annihilation of incompletely thermalized positronium studied by age-momentum correlation. Appl. Surf. Sci. 85, 17–21. Suzuki, N., Nagai, Y., Hyodo, T., 2000. Can a newly developed AMOC technique be applied to determine the para-positronium lifetime. Radiat. Phys. Chem. 58, 777–780. Wang, C.L., Hirade, T., Maurer, F.H.J., Eldrup, M., Pedersen, N.J., 1998. Free-volume distribution and positronium formation in amorphous polymers: temperature and positron-irradiation-time dependence. J. Chem. Phys. 108 (11), 4654–4661.
Radiation Physics and Chemistry 68 (2003) 647–649
Positronium formation reaction of trapped electrons and free positrons: delayed formation studied by AMOC N. Suzukia, T. Hiradeb,*, F. Saitoc, T. Hyodod a
Henkel Research Center of Advanced Technology, Molecular Engineering Institute, Kinki University, 11-6 Kayanomori, Iizuka, Fukuoka 820-8555, Japan b Department of Materials Science, Japan Atomic Energy Research Institute, Tokai, Naka, Ibaraki 319-1195, Japan c The Institute of Physical and Chemical Research, Cyclotron Center, Hirosawa 2-1, Saitama 351-0198, Japan d Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, 3-8-1, Komaba, Tokyo 153-8902, Japan
Abstract Positronium (Ps) can be formed by the reaction of trapped electrons and free positrons at low temperatures in molecular solids. While Ps formation by spur process must be fast, Ps formation by trapped electrons and free positrons is possible even at positron age of several hundreds pico-seconds. Age–momentum correlation measurement of electron–positron pair annihilation g-rays was applied to investigate the delayed Ps formation, and an evidence for the existence of the delayed Ps formation was successfully observed. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Positron; Positronium; Polyethylene; Polymer; Trapped electrons; Low temperature; AMOC; Delayed Ps formation
1. Introduction The mechanism of positronium (Ps) formation in condensed matter has been studied for a long time. The spur model (Mogensen, 1974) proposed by Mogensen qualitatively explains a wide range of Ps formation data in condensed matter. In 1980s, very large increment of Ps formation at low temperatures during positron annihilation lifetime (PAL) measurement was observed in some materials, such as cyclohexane (Eldrup et al., 1980) and polyethylene (Kindl and Reiter, 1987). It was a phenomenon that could not be explained by the spur model. Hirade et al. successfully explained it by the Ps formation reaction of trapped electrons accumulated during PAL measurement and free positrons escaped from the Ps formation in the terminal spur of the positron track. Moreover, they obtained the experimental evidence successfully (Hirade et al., 1998, 2000). *Corresponding author. Fax: +81-29-282-6716. E-mail address: [email protected] (T. Hirade).
Ps binding energy is 6.8 eV in vacuum and a little lower, probably about 4–5 eV, in materials such as polyethylene. Some of the excess electrons produced by the positron irradiation are trapped with a binding energy of 0.5–3 eV at low temperatures and live for a long time. If a free positron finds one of the trapped electrons before its lifetime, the positron will pick up an electron to form Ps. One of the phenomena expected for the Ps formation by accumulation of trapped electrons is visible light effect. The binding energy of the electrons on the trapping sites is 0.5–3 eV. Therefore, the visible light can quench the trapped electrons. Hence the visible light effect on Ps formation should be a good evidence for the existence of new Ps formation mechanism. Hirade et al. successfully obtained inhibition by visible light of the enhancement of Ps formation (Hirade et al., 1998, 2000). Hirade et al. also indicated that there is a good correlation between the density of the trapped electrons (and anions) observed by electron paramagnetic resonance (EPR) and the increment of the Ps formation in polymethylmethacrylate (PMMA) and polyethylene (Hirade et al., 2000). For polyethylene, free positrons
0969-806X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0969-806X(03)00286-X
ARTICLE IN PRESS N. Suzuki et al. / Radiation Physics and Chemistry 68 (2003) 647–649
2. Experimental The polymer sample used for this study was linear high-density poly(ethylene) (PE, Mitsui Petrochemical, Japan). It has a molecular weight of M w ¼ 60; 000; a density of 0.968 g/cm, and a crystallinity of 0.72. Commercial samples usually contain additives to prevent thermal and oxidative degradation, which are specific for the type and application purposes of the polymer. These additives can in general affect chemical reactions. The details of the AMOC system used in the present work are described elsewhere (Suzuki et al., 2000). In the present study, the S-parameter (uncorrelated with the lifetime measurements) was continuously measured simultaneously with the AMOC measurements. All AMOC measurements were performed at 20 K.
3. Results and discussion Fig. 1 indicates S-parameter change with elapse of the AMOC measurement time in polyethylene at 20 K in the darkness and under visible light. It is possible to divide it into three stages: (I) increment and (II) saturation in the darkness and (III) quenching of o-Ps intensity by the visible light, respectively. The density of the trapped electrons increases in stage (I) and the density is saturated in stage (II), and there are no trapped electrons in stage (III). AMOC results were analyzed to give age dependence of S-parameter as shown in Fig. 2. The larger the value
0.57
S-parameter
can find one of the trapped electrons at a density of B1015 spins/g. The mean distance between the trapped electrons is about B100 nm for that concentration. Brusa et al. estimated that the diffusion distance of free positron before annihilation in polyethylene was about 80 nm (Brusa et al., 1995). It indicates that at least some of the free positrons can diffuse freely in polyethylene before their annihilation. The other expected phenomenon is the ‘‘delayed Ps formation’’. In order to see this phenomenon, we applied age–momentum correlation (AMOC) technique. Only the self-annihilation of para-Ps (p-Ps: 14 of Ps is formed as p-Ps) gives large SðtÞ-parameter. If the Ps formation by the trapped electrons is possible up to just before the free positron annihilation, it must be clearly observed by AMOC measurement, because annihilation from delayed p-Ps formation can give large SðtÞ values even at the positron age of B400 ps. In the present study, we performed the AMOC measurement for polyethylene at 20 K under visible light and in the darkness. The results strongly suggest the existence of the delayed Ps formation.
0.56
I
0.55
II
III
0.54 0
5
10
15
20
25
30
time (days) Fig. 1. AMOC measurement time dependence of S-parameter in polyethylene at 20 K. Measurements were performed in darkness at stages I and II, and under visible light at stage III, respectively.
0.54 0.52
S (t)
648
0.50 0.48 0.46 0.44 0
1
2
3
4
5
positron age (nsec) Fig. 2. Positon age dependence of SðtÞ-parameter in polyethylene at 20 K. The closed circles represent the results obtained in darkness (stage II in Fig. 1) and the open circles represent the results obtained under visible light (stage III in Fig. 1). Solid lines were the simulation curves without delayed Ps formation.
of S-parameter, the lower the total momentum of the electron–positron pairs annihilates. The open circles and the closed circles indicate the results for stages (II) and (III) in Fig. 1, respectively. The solid line through the open circles represents the result of the fit to a model without delayed Ps formation. The parameters used here are shown in Table 1. The fit is good, which is consistent with the fact that no delayed Ps formation is expected under visible light because of no trapped electrons at (III). The solid line through the closed circles represents the result of the fit to a model in which only the Ps formation probability is different from that for (III). In the case of stage (II), there is a delayed increment at early age region. Moreover, the decrement appeared at later age region than the decrement in the case of stage (II). This is more clearly seen by the comparison with the
ARTICLE IN PRESS N. Suzuki et al. / Radiation Physics and Chemistry 68 (2003) 647–649 Table 1 Parameters for the simulations indicated in Fig. 2 S
p-Ps o-Ps e+ Kapton a
0.676 0.477 0.453 0.429
t (psec)a
129.6 1310 320 384
649
Tohoku University and Dr H. Saito at University of Tokyo for valuable discussions.
Intensity(%) Stage II
Stage III
14 42 30 14
5.15 15.45 65.4 14
These values were obtained by the measurement at stage III.
fitted curve with no delayed Ps formation. Hence those observed in stage (II) can only be explained by the delayed Ps formation. There is a minimum of SðtÞ at positron age of about 1 ns in polyethylene especially for measured under visible light. Such a minimum is not observed in nhexane at room temperature (Stoll et al., 1995). It is probably caused by positron complex. It is known that a minimum of o-Ps intensity is seen after large decrement by elevating temperature for some materials (Wang et al., 1998; Ito et al., 1999; Chen et al., 2001). Hirade et al. mentioned that it could be caused by the positron scavenging by stable anions, i.e. by a formation of positron complex (Hirade et al., 1998). It is quite natural to have this kind of positron complex at stage (III) because it was measured after large increment of o-Ps intensity. The positron complex formation should give low SðtÞ values around 1 ns. Further investigations are needed to identify the cause of this minimum on SðtÞ:
4. Conclusion Delayed Ps formation was clearly observed for polyethylene at 20 K by AMOC measurement. Hence it is clear that the Ps formation is possible by the trapped electrons and the free positrons having escaped from the Ps formation by spur process and moving freely in polyethylene.
Acknowledgements We are very grateful to Prof. T. Suzuki in KEK for supplying PE samples. We also thank Dr. Y. Nagai at
References Brusa, R.S., Duarte Naia, M., Margoni, D., Zecca, A., 1995. Positron mobility in polyethylene in the 60–400 K temperature range. Appl. Phys. A 60, 447–453. Chen, Z.Q., Suzuki, T., Uedono, A., Tanigawa, S., Ito, Y., 2001. Temperature and irradiation effects on positronium formation in polycarbonate. Mater. Sci. Forum 363–365, 297–299. Eldrup, M., Lightbody, D., Sherwood, J., 1980. Studies of phase transformation in molecular crystals using the positron annihilation technique. Faraday Discuss. 69, 175–182. Hirade, T., Wang, C.L., Maurer, F.H.J., Eldrup, M., Pedersen, N.J., 1998. Visible light effect on positronium formation in PMMA at low temperatures. Abstract Book for the 35th Annual Meeting on Radioisotopes in the Physical Science and Industries, Tokyo, Japan, June 30–July 1, p. 89 Hirade, T., Maurer, F.H.J., Eldrup, M., 2000. Positronium formation at low temperatures: the role of trapped electrons. Radiat. Phys. Chem. 58, 465–471. Ito, Y., Hirade, T., Hamada, E., Suzuki, T., Ito, Y., 1999. The effect of visible light irradiation on positronium formation in polyethylene at low temperature. Acta Phys. Pol. A 95 (4), 533–538. Kindl, P., Reiter, G., 1987. Investigations on the lowtemperature transitions and time effects of branched polyethylene by the positron lifetime technique. Phys. Stat. Sol. A 104, 707–713. Mogensen, O.E., 1974. Spur reaction model of positronium formation. J. Chem. Phys. 60 (3), 998–1004. Stoll, H., Koch, M., Lauff, U., Maier, K., Major, J., Schneider, H., Seeger, A., Siegle, A., 1995. Annihilation of incompletely thermalized positronium studied by age-momentum correlation. Appl. Surf. Sci. 85, 17–21. Suzuki, N., Nagai, Y., Hyodo, T., 2000. Can a newly developed AMOC technique be applied to determine the para-positronium lifetime. Radiat. Phys. Chem. 58, 777–780. Wang, C.L., Hirade, T., Maurer, F.H.J., Eldrup, M., Pedersen, N.J., 1998. Free-volume distribution and positronium formation in amorphous polymers: temperature and positron-irradiation-time dependence. J. Chem. Phys. 108 (11), 4654–4661.