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Ortho-Ps annihilation in resorcinol at high pressure
ARTICLE IN PRESS
Radiation Physics and Chemistry 68 (2003) 577–579
Ortho-Ps annihilation in resorcinol at high pressure T. Goworek*, J. Wawryszczuk, R. Zaleski Institute of Physics, Maria Curie-Sklodowska University, Pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland
Abstract The effect of high pressure on positron lifetime spectra in resorcinol was investigated. The o-Ps lifetime decreases with pressure continuously reaching the value which needs redefinition of DR value used in the Tao–Eldrup model. The intensity of long-lived component unexpectedly rises with pressure increase, but at 450 MPa a drop of that intensity can indicate the approach of the minimal size of free volume able to trap Ps. Preliminary data for hydroquinone are also presented. r 2003 Elsevier Ltd. All rights reserved. Keywords: Dihydroxybenzenes; High pressure; Positronium formation
1. Introduction Temperature dependence of Ps formation probability in molecular crystalline media can be classified into three groups: (a) Ps formed at all temperatures, its intensity increasing slowly with temperature; (b) Ps formed at all temperatures, its intensity decreasing with temperature; (c) Ps not formed at low temperatures, its intensity being a sigmoidal function of temperature. In group (c) positronium seems to be formed on thermally produced defects of free volume type. In the case of equilibrium the concentration of defects is proportional to expðH=kTÞ; where H is the enthalpy of the defect activation H ¼ E þ pV (E—activation energy, p—pressure, V—defect volume), thus one can expect that the influence of pressure on Ps intensity is opposite to that of temperature. As a measure of Ps formation probability we assume, as usual, the intensity I3 of o-Ps component in the lifetime spectrum. In the experiment with biphenyl (Goworek, 2000) we observed *Corresponding author. Tel.: +48-815376225; fax: +48 815376191. E-mail address: [email protected] (T. Goworek).
rather a stepwise I3 decrease indicating a shrink of free volume below the size at which the energy level in the potential well still existed. Group (b) seems to follow the predictions of the spur model: with temperature rise the radius of Onsager sphere diminishes reducing also I3 : It was interesting to us to observe how I3 depended on pressure in this case; we were seeking for the point of possible break down of positronium formation at high pressure. Typical representatives of group (b) are dihydroxybenzenes. Temperature variations of their PAL spectra were investigated by us earlier (Goworek, 1996,1997). In catechol the long-lived component is of low intensity, thus the subjects of this study were resorcinol (low temperature phase a) and hydroquinone only.
2. Experimental The spectra were registered using a standard fast–slow spectrometer with BaF2 crystals; the resolution time was 216 ps. The positron source, 22Na, was sealed in Kapton envelope. Scintillators were placed outside the pressure chamber and shifted slightly aside to avoid the summing effects. This kind of geometry and thick chamber walls reduce significantly the rate of count. Two series of measurements were performed, 1.1 106 counts were collected per each spectrum. All components were close
0969-806X/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0969-806X(03)00235-4
ARTICLE IN PRESS T. Goworek et al. / Radiation Physics and Chemistry 68 (2003) 577–579 0.4 0.35 0.3 0.25 0.9 0.85
τ3, ns
to each other, below 1 ns, thus it was necessary to limit the number of free parameters. The data from earlier papers (Goworek, 1996, 1997) allowed us to assume that p-Ps component in resorcinol has the lifetime t1 ¼ 125 ps and this value was fixed during the data processing. The spectra were analysed using the LT program (Kansy, 1996). Note that the positron lifetime in Kapton foil under pressure decreased, the rate of that decrease being determined as about 65 ps/GPa.
τ2, ns
578
0.8 0.75
3. Results and discussion
0.7
ð1Þ
where m0 is the electron rest mass, the numerical value of R is given for V0 in electronvolts. We do not expect V0 larger than 3 eV, thus the minimal radius of Ps trap is about 0.125 nm. If we accept the Tao–Eldrup model (Eldrup, 1982) with usual values 36
32
I3, %
28
24
20
16 200
24
20
16
12
0
100
200
300
400
500
PRESSURE, MPa
p_ 0:216 nm Rmin ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffi ; 4 m0 V 0 V0
150
0.65
I3, %
Fig. 1 shows the temperature dependence of I3 in resorcinol and hydroquinone at a normal pressure (0.1 MPa). With lowering the temperature the intensities of o-Ps component in both dihydroxybenzenes increase; the lifetime shows a very weak temperature dependence. In Fig. 2 the o-Ps lifetime t3 ; the lifetime of free positrons t2 and o-Ps intensity I3 in resorcinol (low temperature phase a) are shown as a function of pressure. The lifetime t3 decreases monotonously with pressure increase and at about 400 MPa reaches the value 0.72 ns. In the potential well of finite depth V0 ; the minimal well radius at which the energy level exists (i.e. the well is able to trap positronium) is
250
300
350
TEMPERATURE, K Fig. 1. Intensities of long-lived components in resorcinol and hydroquinone as a function of temperature. Three component fit. Squares—resorcinol phase a, circles—resorcinol phase b, diamonds—hydroquinone.
Fig. 2. The lifetime spectrum parameters for rersorcinol as a function of pressure. The solid line represents simple polynomial drawn as an eye-guide only. For the sake of comparison the intensity of o-Ps component in biphenyl is shown (crosses and dashed curve).
of lb and DR parameters the shortest o-Ps lifetime, which we should observe, is 0.78 ns. The experimental data for p > 300 MPa are below that limit. The value of o-Ps decay rate in the bulk lb is assumed 2 ns1, i.e. the largest possible, thus the appearance of lifetimes below 0.8 ns can be explained only as a result of increased DR: That parameter is an equivalent of mean Ps penetration depth into the bulk. The model ofp finite potential depth ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gives the penetration range d ¼ _= 4m0 ðV0 EÞ; where E is the zero-point energy of the particle in the well. That energy increases with the reduction of well radius and, if it approaches V0, the I becomes larger; that should be reflected by the DR increase. The intensity of long-lived component rises slowly with pressure increase. In the range 0–430 MPa the increase is about 20%. In the framework of the spur model such an effect requires the assumption that average electron–positron distance in the spur decreases slightly under the pressure. The number of free volume holes in the structure of solid resorcinol should remain unchanged, or can be even reduced, thus, the result of this experiment can serve as one argument more that I3
ARTICLE IN PRESS T. Goworek et al. / Radiation Physics and Chemistry 68 (2003) 577–579
hydroquinone. However, the lifetime spectrum of positrons in hydroquinone is rather complex, indicating a distribution of o-Ps lifetimes or the existence of several long-lived components (Goworek, 1997). In an attempt to examine the dependence of spectrum parameters on pressure, we have assumed that there exist two longlived components of the lifetimes at normal pressure 0.7 and 1.2 ns. Due to a close location of the components (the difference of the longest and shortest lifetime is 1 ns only) we fixed, as previously, the shortest lifetime as 155 ps (that one found in the paper cited above). Fig. 3, showing the pressure dependence of the intensities of two longest components, is the result of our preliminary measurements, still loaded with large experimental uncertainities. Nevertheless, one can notice that the shorter of the two discussed components is almost insensitive to the pressure, while the longer one collapses at about 280 MPa.
45 40
I3, %
35 30 25 20 15 20
I4, %
579
15 10 5
Acknowledgements
0
0
100
200
300
400
500
PRESSURE, MPa Fig. 3. The intensities of two longest-lived components in PALS spectrum of hydroquinone. Four component fit. Dashed lines show average I4 for the pressures below and above 280 MPa.
intensity cannot be a direct measure of the number of free volume sites, as it is often assumed in polymer studies. At the end of the pressure range obtainable in our experimental arrangement a decrease of I3 was observed. Such a drop of intensity can be a sign that the free volume size approaches the minimal dimensions (1), the zero-point level is located near the upper rim of the potential well, the trap becomes shallow and trapping is ineffective. In order to check it, an extension of the pressure range is needed in the search for total disappearance of I3 : A strong temperature dependence of o-Ps formation intensity can be observed in other dihydroxybenzene,
This work was supported by the Polish Committee for Researches (KBN) grant 5 P03B 031 21.
References Eldrup, M., Lightbody, D., Sherwood, J.N., 1982. The temperature dependence of positron lifetimes in solid pivalic acid. Chem. Phys. 63, 51. Goworek, T., Jasin˜ska, B., Wawryszczuk, J., Ciesielski, K., 1996. Positrons in resorcinol. Chem. Soc. Faraday Trans. 92, 1573. Goworek, T., Jasin˜ska, B., Wawryszczuk, J., Ciesielski, K., 1997. Positronium formation in dihydroxybenzenes. Chem. Soc. Faraday Trans. 93, 1573. Goworek, T., Suzuki, T., Hamada, E., Kondo, K., Ito, Y., 2000. Pressure quenching of positronium in solid biphenyl. Chem. Phys. 255, 347. Kansy, J., 1996. Microcomputer program for analysis of positron annihilation lifetime spectra. Nucl. Instrum. Methods. A374, 235.
Radiation Physics and Chemistry 68 (2003) 577–579
Ortho-Ps annihilation in resorcinol at high pressure T. Goworek*, J. Wawryszczuk, R. Zaleski Institute of Physics, Maria Curie-Sklodowska University, Pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland
Abstract The effect of high pressure on positron lifetime spectra in resorcinol was investigated. The o-Ps lifetime decreases with pressure continuously reaching the value which needs redefinition of DR value used in the Tao–Eldrup model. The intensity of long-lived component unexpectedly rises with pressure increase, but at 450 MPa a drop of that intensity can indicate the approach of the minimal size of free volume able to trap Ps. Preliminary data for hydroquinone are also presented. r 2003 Elsevier Ltd. All rights reserved. Keywords: Dihydroxybenzenes; High pressure; Positronium formation
1. Introduction Temperature dependence of Ps formation probability in molecular crystalline media can be classified into three groups: (a) Ps formed at all temperatures, its intensity increasing slowly with temperature; (b) Ps formed at all temperatures, its intensity decreasing with temperature; (c) Ps not formed at low temperatures, its intensity being a sigmoidal function of temperature. In group (c) positronium seems to be formed on thermally produced defects of free volume type. In the case of equilibrium the concentration of defects is proportional to expðH=kTÞ; where H is the enthalpy of the defect activation H ¼ E þ pV (E—activation energy, p—pressure, V—defect volume), thus one can expect that the influence of pressure on Ps intensity is opposite to that of temperature. As a measure of Ps formation probability we assume, as usual, the intensity I3 of o-Ps component in the lifetime spectrum. In the experiment with biphenyl (Goworek, 2000) we observed *Corresponding author. Tel.: +48-815376225; fax: +48 815376191. E-mail address: [email protected] (T. Goworek).
rather a stepwise I3 decrease indicating a shrink of free volume below the size at which the energy level in the potential well still existed. Group (b) seems to follow the predictions of the spur model: with temperature rise the radius of Onsager sphere diminishes reducing also I3 : It was interesting to us to observe how I3 depended on pressure in this case; we were seeking for the point of possible break down of positronium formation at high pressure. Typical representatives of group (b) are dihydroxybenzenes. Temperature variations of their PAL spectra were investigated by us earlier (Goworek, 1996,1997). In catechol the long-lived component is of low intensity, thus the subjects of this study were resorcinol (low temperature phase a) and hydroquinone only.
2. Experimental The spectra were registered using a standard fast–slow spectrometer with BaF2 crystals; the resolution time was 216 ps. The positron source, 22Na, was sealed in Kapton envelope. Scintillators were placed outside the pressure chamber and shifted slightly aside to avoid the summing effects. This kind of geometry and thick chamber walls reduce significantly the rate of count. Two series of measurements were performed, 1.1 106 counts were collected per each spectrum. All components were close
0969-806X/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0969-806X(03)00235-4
ARTICLE IN PRESS T. Goworek et al. / Radiation Physics and Chemistry 68 (2003) 577–579 0.4 0.35 0.3 0.25 0.9 0.85
τ3, ns
to each other, below 1 ns, thus it was necessary to limit the number of free parameters. The data from earlier papers (Goworek, 1996, 1997) allowed us to assume that p-Ps component in resorcinol has the lifetime t1 ¼ 125 ps and this value was fixed during the data processing. The spectra were analysed using the LT program (Kansy, 1996). Note that the positron lifetime in Kapton foil under pressure decreased, the rate of that decrease being determined as about 65 ps/GPa.
τ2, ns
578
0.8 0.75
3. Results and discussion
0.7
ð1Þ
where m0 is the electron rest mass, the numerical value of R is given for V0 in electronvolts. We do not expect V0 larger than 3 eV, thus the minimal radius of Ps trap is about 0.125 nm. If we accept the Tao–Eldrup model (Eldrup, 1982) with usual values 36
32
I3, %
28
24
20
16 200
24
20
16
12
0
100
200
300
400
500
PRESSURE, MPa
p_ 0:216 nm Rmin ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffi ; 4 m0 V 0 V0
150
0.65
I3, %
Fig. 1 shows the temperature dependence of I3 in resorcinol and hydroquinone at a normal pressure (0.1 MPa). With lowering the temperature the intensities of o-Ps component in both dihydroxybenzenes increase; the lifetime shows a very weak temperature dependence. In Fig. 2 the o-Ps lifetime t3 ; the lifetime of free positrons t2 and o-Ps intensity I3 in resorcinol (low temperature phase a) are shown as a function of pressure. The lifetime t3 decreases monotonously with pressure increase and at about 400 MPa reaches the value 0.72 ns. In the potential well of finite depth V0 ; the minimal well radius at which the energy level exists (i.e. the well is able to trap positronium) is
250
300
350
TEMPERATURE, K Fig. 1. Intensities of long-lived components in resorcinol and hydroquinone as a function of temperature. Three component fit. Squares—resorcinol phase a, circles—resorcinol phase b, diamonds—hydroquinone.
Fig. 2. The lifetime spectrum parameters for rersorcinol as a function of pressure. The solid line represents simple polynomial drawn as an eye-guide only. For the sake of comparison the intensity of o-Ps component in biphenyl is shown (crosses and dashed curve).
of lb and DR parameters the shortest o-Ps lifetime, which we should observe, is 0.78 ns. The experimental data for p > 300 MPa are below that limit. The value of o-Ps decay rate in the bulk lb is assumed 2 ns1, i.e. the largest possible, thus the appearance of lifetimes below 0.8 ns can be explained only as a result of increased DR: That parameter is an equivalent of mean Ps penetration depth into the bulk. The model ofp finite potential depth ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gives the penetration range d ¼ _= 4m0 ðV0 EÞ; where E is the zero-point energy of the particle in the well. That energy increases with the reduction of well radius and, if it approaches V0, the I becomes larger; that should be reflected by the DR increase. The intensity of long-lived component rises slowly with pressure increase. In the range 0–430 MPa the increase is about 20%. In the framework of the spur model such an effect requires the assumption that average electron–positron distance in the spur decreases slightly under the pressure. The number of free volume holes in the structure of solid resorcinol should remain unchanged, or can be even reduced, thus, the result of this experiment can serve as one argument more that I3
ARTICLE IN PRESS T. Goworek et al. / Radiation Physics and Chemistry 68 (2003) 577–579
hydroquinone. However, the lifetime spectrum of positrons in hydroquinone is rather complex, indicating a distribution of o-Ps lifetimes or the existence of several long-lived components (Goworek, 1997). In an attempt to examine the dependence of spectrum parameters on pressure, we have assumed that there exist two longlived components of the lifetimes at normal pressure 0.7 and 1.2 ns. Due to a close location of the components (the difference of the longest and shortest lifetime is 1 ns only) we fixed, as previously, the shortest lifetime as 155 ps (that one found in the paper cited above). Fig. 3, showing the pressure dependence of the intensities of two longest components, is the result of our preliminary measurements, still loaded with large experimental uncertainities. Nevertheless, one can notice that the shorter of the two discussed components is almost insensitive to the pressure, while the longer one collapses at about 280 MPa.
45 40
I3, %
35 30 25 20 15 20
I4, %
579
15 10 5
Acknowledgements
0
0
100
200
300
400
500
PRESSURE, MPa Fig. 3. The intensities of two longest-lived components in PALS spectrum of hydroquinone. Four component fit. Dashed lines show average I4 for the pressures below and above 280 MPa.
intensity cannot be a direct measure of the number of free volume sites, as it is often assumed in polymer studies. At the end of the pressure range obtainable in our experimental arrangement a decrease of I3 was observed. Such a drop of intensity can be a sign that the free volume size approaches the minimal dimensions (1), the zero-point level is located near the upper rim of the potential well, the trap becomes shallow and trapping is ineffective. In order to check it, an extension of the pressure range is needed in the search for total disappearance of I3 : A strong temperature dependence of o-Ps formation intensity can be observed in other dihydroxybenzene,
This work was supported by the Polish Committee for Researches (KBN) grant 5 P03B 031 21.
References Eldrup, M., Lightbody, D., Sherwood, J.N., 1982. The temperature dependence of positron lifetimes in solid pivalic acid. Chem. Phys. 63, 51. Goworek, T., Jasin˜ska, B., Wawryszczuk, J., Ciesielski, K., 1996. Positrons in resorcinol. Chem. Soc. Faraday Trans. 92, 1573. Goworek, T., Jasin˜ska, B., Wawryszczuk, J., Ciesielski, K., 1997. Positronium formation in dihydroxybenzenes. Chem. Soc. Faraday Trans. 93, 1573. Goworek, T., Suzuki, T., Hamada, E., Kondo, K., Ito, Y., 2000. Pressure quenching of positronium in solid biphenyl. Chem. Phys. 255, 347. Kansy, J., 1996. Microcomputer program for analysis of positron annihilation lifetime spectra. Nucl. Instrum. Methods. A374, 235.