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Positron annihilation in argon intercalated n-alkanes at high pressure
Chemical Physics 320 (2006) 207–213 www.elsevier.com/locate/chemphys
Positron annihilation in argon intercalated n-alkanes at high pressure B. Zgardzin´ska, J. Wawryszczuk, T. Goworek
*
Institute of Physics UMCS, Marie Curie-Sklodowska University, 20-031 Lublin, Poland Received 5 April 2005; accepted 6 July 2005 Available online 15 August 2005
Abstract Positron annihilation lifetime spectroscopy was used to observe the effects of argon intercalation in some solid long-chain alkanes at high pressure. The ortho-Ps lifetime rises with argon pressure, which means increase of free volumes in the alkane structure. The range of pressures in which the rotator phase exists increases, comparing to pure alkane. In n-heptadecane, n-nonadecane, and possibly n-heneicosane, a stepwise change of ortho-Ps lifetime and intensity at 12 MPa is observed, suggesting the transition to a new kind of the rotator phase. The transition rate is low, final lifetime value is 3.3 ns. Despite a large size of free volumes corresponding to such a lifetime, their compressibility is found negligible up to the pressure of 90 MPa. At low pressures the compressibility of free volumes in the rotator phase is negative. 2005 Elsevier B.V. All rights reserved. Keywords: Positronium; Alkane; High pressure; Argon intercalation
1. Introduction Positron annihilation lifetime spectroscopy (PALS) is a method commonly used in determination of intermolecular free volume sizes in solids, particularly in polymers [1,2]. Such free spaces exist also in crystalline media, e.g., in long-chain n-alkanes some free volumes are located in the vicinity of nonplanar conformers. At low temperature (‘‘rigid’’ phase) n-alkane molecules have the form of straight rods; with temperature rise the concentration of nonplanar conformers increases. It concerns predominantly the rotator phases existing in a narrow range 5–12 K below the melting point [3– 5]. In n-alkanes with the chain length of about 20 carbon atoms, 20% of molecules in the rotator phase have the form of kinked chains [5]. The crystalline structure of odd numbered n-alkanes is lamellar, with molecular chains settled parallel to one another and perpendicular to the lamella surface. The free volume created in the *
Corresponding author. Fax: +48 81 5376191. E-mail address: [email protected] (T. Goworek).
0301-0104/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.07.008
vicinity of kinked molecules is relatively large in relation to other abundant conformers (end-gauche type) and has the form of a channel running along the molecule. The location of the kink is movable, and the expected average length of an empty channel is about half of the lamellae spacing. The PALS spectroscopy bases on the relation between the free volume size and the lifetime of orthopositronium located in it. Positronium (Ps) is the bound state of a positron with an electron. Due to its negative work function it is trapped in free (electron-less) volumes. The lifetime of triplet ortho-positronium (o-Ps) is determined mainly by the overlap of its wavefunction with the surrounding bulk (pick-off process). The larger the trap is – the longer is the lifetime; details of this relation are determined by the void geometry. In the case of free volumes near the kinked molecules the most suitable approximation of the void shape seems to be an elongated channel of circular or square cross-section. The equation describing the o-Ps lifetime in a rectangular channel is given by Jasin´ska et al. [6], in a cylindrical one – by Goworek et al. [7].
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The properties of molecular solids often depend on the size and concentration of the free volumes in their structure; e.g., the compressibility concerns mainly free spaces, not the molecular volume. It was found by Sirota et al. [8] that in the rotator phase RI of n-alkanes linear negative compressibility can be observed. The effect of expansion under high pressure accompanies the intercalation of gases into alkanes and their derivatives. It seemed to us worthwhile to observe the modification of free volumes in selected n-alkanes subjected to a high pressure. Our partial results for n-nonadecane were published recently [9].
2. Materials and experimental techniques n-Nonadecane C19H40 and its odd numbered neighbouring alkanes: n-heptadecane C17H36 and n-heneicosane C21H44 were chosen due to a convenient range of temperatures in which the rotator phase exists (in our experimental conditions we had no possibility to change the temperature of the pressure chamber within broad limits). At normal pressure (0.1 MPa) the rotator phase RI exists in the range 283–295 K for n-heptadecane, 296–305 K for n-nonadecane and 305.5–313.5 K for n-heneicosane [5]; in even-numbered neighbours the rotator phase does not appear. The limiting values of the temperature and pressure between which the rotator phase exists can be found in the paper by Wu¨rflinger and Schneider [10] or Forsman and Anderson [11]. The samples were produced by Sigma–Aldrich, their purity was tested using the gas chromatography/mass spectrometry setup (ThermoFinnigan Trace DSQ) and found better than 99%; no additional purification was performed. The polycrystalline samples had the form of disc shaped pellets 2 mm thick, sufficient to stop all positrons from the radioactive source. The pressure was produced by the gas compressor U-11 (Unipress, Warsaw); the working gas in the pressure chamber was argon. The lifetime spectra were registered with a conventional fast-slow coincidence spectrometer with time resolution of 220 ps. The positron source was 22Na (0.5 MBq) in a Kapton envelope. The statistics collected per one spectrum was about 1.5 · 106 coincidences. Low source activity and c ray absorption in thick walls of the pressure chamber resulted in low counting rate; the statistics given above needed the collection time of 6 h per spectrum. The spectra were processed by LT programme [12] fitting to the data a sum of three or four exponential components convoluted with the instrumental resolution curve. The shortest-lived component, s1 120 ps, belonged to the singlet para-Ps decay, the intermediate one, s2, to annihilation of unbound positrons, the long-lived component, s3 1.5–3.5 ns, was attributed to the ortho-Ps decay. The length of the empty channel near the kinked molecule depends on kink location, thus
we had a certain distribution of o-Ps lifetimes. For the sake of simplicity this distribution was ignored; the s3 values were thus the average over possible void sizes. We could expect that in certain conditions some o-Ps atoms can escape from the medium and annihilate in the surrounding argon atmosphere. The longest-lived component, s4, if any, represented the o-Ps annihilation in argon. If such a component existed, the intermediate component (s2) contained also the events of free positron annihilation in argon. Two kinds of measurements under pressure were performed: (a) The samples were exposed to the pressure producing gas. A sandwich of samples and the positron source pressed together was placed directly in the chamber of compressor. (b) The sandwich was inserted into a small thin-wall steel tube 10 mm of inner diameter (the same as that of the samples), closed by two pistons; the container volume was tightened by O-rings. Before placing into the compressor, one piston was in high position enabling evacuation of the container to the pressure of about 1 Pa through a side opening, and then the piston was pushed down. In this way the volume between the pistons was gas free and entirely filled by the samples. The gas pressure was transmitted via the pistons. In this measurement version we avoided gas penetration into the samples. The temperature of the samples inside the high pressure chamber was controlled with the accuracy ±0.1 K using Shimaden FP21 unit.
3. Results and discussion Fig. 1 presents the results for three discussed nalkanes without gas permeation to the samples at 292.5 K (n-heptadecane), 302 K (n-nonadecane) and 310.5 K (n-heneicosane), i.e., roughly at the same distance from the melting point for all media. In the range of pressures p 6 50 MPa the s3 dependence on pressure follows a similar dependence on temperature; pressure increase by 1 MPa corresponds to the temperature decrease by 0.22 K; this agrees well with the estimate given by Sirota et al. [8]. With pressure increase the lifetime s3 shortens, which means that no anomalies are observed: the volume of free spaces diminishes. The transition from the rotator to ‘‘rigid’’ phase is well visible as a drop both of o-Ps lifetime s3 and intensity I3. In the rigid phase the concentration of kink-conformers is greatly reduced; long empty channels disappear and the remaining positronium is now located in small spaces between the molecular lamellae [13]. Further increase of
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Fig. 2. Ortho-Ps lifetime and intensity in pure (without argon intercalation) n-nonadecane in an extended range of pressures.
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Fig. 1. Ortho-Ps lifetime and intensity in pure alkanes (without argon intercalation) as a function of pressure. Traingles – n-heptadecane (temperature 292.5 K), open circles – n-nonadecane (302 K), asterisks – n-heneicosane (310.5 K).
pressure brings a little effect (Fig. 2). In the range 200– 1300 MPa the intensity I3 in n-nonadecane practically does not depend on the pressure, and above 500 MPa the lifetime s3 changes negligibly. Close packed structure of lamellae composed of straight nondeformed molecules is resistant against externally applied pressure. No phase transitions are observed up to 1300 MPa. When the pressure is applied directly to the samples in gaseous atmosphere, gas penetration changes the oPs lifetime and intensity in the rotator phase in another way than in pure alkane samples. Fig. 3 shows the pressure dependence of s3 and I3 for n-heptadecane at 292.5 K. The same parameters for n-nonadecane at two selected temperatures: 298 and 302 K are shown in Figs. 4 and 5, whereas for n-heneicosane at 310.5 K in Fig. 6. For comparison the same figures show the lifetime and intensity values for pure samples, without intercalation of argon. Generally, one observes an increase of o-Ps lifetime with pressure. A particularly strong effect is visible in n-heptadecane and n-nonadecane at 302 K. According to Sirota et al. [8] argon atoms locate between the lamellae, but do not enter the free volumes near the kinked molecules, which remain still empty. The rise of s3 from (2.4–2.6) to 3.3 ns
seen in Figs. 3 and 5 results from the changed free volume dimensions: its length and cross section. The length increases with pressure due to the increase of lamellae spacing; this dimension increases by 1.75 · 10 3 nm/ MPa [8], being insufficient to explain the observed lifetime rise. According to the pick-off annihilation model [6], the rise of s3 to 3.3 ns means that the void crosssection has to increase by about 40%, too, in comparison to a pure sample. Increase of the dimensions is visible also at 298 K in n-nonadecane and 310.5 K in n-heneicosane (note that 310.5 K in this case is equivalent to 302 K for n-nonadecane), however, the effect is much smaller. A striking feature of s3 and I3 pressure dependences in n-heptadecane is a stepwise increase of these parameters at 12 MPa. During several hours they rise with the time to a new high values. It can be explained as a result of phase transition. At that pressure (and temperature) the low pressure phase RI transforms into a new one, which is characterized by the presence of still larger defects. The lifetime 3.3 ns belongs to the longest observed in solids. Surprising is its constancy in a very broad range of pressures; the size of free volumes once achieved is not too sensitive to further pressure increase. A similar stepwise and slow change of o-Ps parameters can be seen also in n-nonadecane at 302 K and 12 MPa (Fig. 4). Thus, large differences in PALS parameters as a function of pressure, seen in Figs. 3–6, made us to study also the temperature variation of the observed effect. The
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Fig. 3. Ortho-Ps lifetime and intensity in argon intercalated nheptadecane as a function of pressure (dots). Triangles denote the series of successive spectra taken at fixed pressure. For comparison the experimental data for nonintercalated samples are shown by open circles. Temperature 292.5 K. The intensity of additional fourth component in PALS spectrum, appearing above the transition to the rigid phase, is shown at the bottom.
temperature of our pressure chamber could be changed from room temperature upwards, so measurements were done for n-nonadecane and n-heneicosane only. The pressure was set fixed, 18 MPa, and the temperature increased in 1 K steps. At each temperature two spectra were taken successively, i.e., in 6 h spacing. The lifetime and intensity of the long-lived component for n-nonadecane are shown in Fig. 7. One can see the step both of s3 and I3 at the transition from the rigid to rotator phase at 298 K (shifted, as expected, by 4 K comparing to zero pressure), then a slow rise up to 302 K when again one observes a step similar to that seen in pressure dependences. At both these temperatures the values of parameters are not stable in time, they rise slowly. Note that only at those two points two successive spectra give different values of parameters. Above the step, like in pressure experiment, the lifetime is perfectly temperature independent. Analogous data were collected for n-heneicosane at 18 MPa. Fig. 8 shows that the effect of transition to
Fig. 4. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane as a function of pressure (full circles). For comparison the experimental data for nonintercalated samples are shown by open circles. Temperature 298 K.
the proposed new phase exists also in n-heneicosane (step at 310 K), but is much less pronounced. The points in Figs. 7 and 8 represent the spectrum parameters averaged over 6 h duration of the spectrum collection. More detailed observation of their variation in time was undertaken. An amplitude window at the output of time-to-amplitude converter (Ortec 567) of the PALS spectrometer was placed as shown by the insert in Fig. 9, selecting the events of positron annihilation delayed by (2.1–5.9) ns, i.e., belonging to o-Ps decay. The number of counts in that window collected at 10 min intervals was recorded in the multichannel analyser working as a multiscaler. The result shown in Fig. 9 indicates that in n-nonadecane at 302 K and 40 MPa the equilibrium is reached not earlier than 7 h after pressure switching on. In [8] the time needed to reach equilibrium after argon penetration is estimated for about 0.5 h, thus the slow variation must be of other origin. The stepwise change of the parameter values, instability with the time, change of the form of temperature dependence above the instability point are strong arguments in favour of the existence of a new high-pressure rotator phase in the investigated n-alkanes. The new postulated (rotator) phase is characterized by still larger free volumes than those
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PRESSURE, MPa Fig. 5. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane as a function of pressure (full circles). The data for nonintercalated samples are shown by open circles. Temperature 302 K.
in RI phase without pressure and without argon intercalation. The results shown in Fig. 4 are collected below the proposed new phase transition point. It is seen (as well as in the Fig. 5) that the normal RI phase is moderately sensitive to argon intercalation, and negative compressibility of free volumes is faintly marked. In the argon intercalated samples the transition to the rigid phase is shifted toward higher pressures comparing to nonintercalated ones. Phase transition is accompanied by the appearance of a new component in PALS spectrum. It is very long-lived and the lifetimes, 7– 8 ns, observed for various pressures, are identical with those for argon alone filling the chamber (Fig. 10). One can suppose that this component is produced by Ps escaping from the sample. In the rigid phase gas intercalation is not observed [8]. In the rotator phase argon atoms are accumulated in the interlamellar gaps, 0.26 nm thick, locally enlarged due to a possible longitudinal shift of molecules and reduced total length of nonplanar conformers. At transition to the rigid phase the gap is narrowed by 0.06 nm and the kink molecules are straightened; reduction of interlamellar free spaces leads to argon atom escape. The samples are damaged,
Fig. 6. Ortho-Ps lifetime and intensity in argon intercalated nheneicosane as a function of pressure (full circles). The data for nonintercalated samples are shown by open circles. Temperature 310.5 K.
a great number of microcracks makes them sponge-like, which can be noticed even visually. In such a damaged structure o-Ps can migrate to the gaseous surrounding outside the crystalline structure. The lifetime of o-Ps remaining in the crystal is slightly shorter than in pure alkane. That can be explained as a result of additional probability of Ps disappearance (besides decay) by transition to the outside. Four component analysis shows that in the rotator phase, the ‘‘argon component’’, if it exists, has an intensity of a fraction of a percent only. As can be seen in Figs. 3–6 the shift of the rotator-rigid phase transition point in the samples after intercalation by argon is from 6 to 18 MPa. An additional series of measurements was performed with nnonadecane sample at 306 K changing the pressure from 18 MPa upwards (without pressure the sample would be molten). The expected transition point without argon penetration should be approximately at 47 MPa. Fig. 11 shows that in argon atmosphere the transition occurs not earlier than at 84 MPa, i.e., by 37 MPa higher than in a pure sample. It seems that with increasing temperature the range of pressures in which the rotator phase exists becomes broader. It is in contrast to pure alkanes where that range reduces, and for n-nonadecane the rotator phase disappears at 348 K and 220 MPa [11]. In our measurements the
B. Zgardzin´ska et al. / Chemical Physics 320 (2006) 207–213
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Fig. 9. n-Nonadecane. The number of counts registered in the delay range 2.1–6 ns (long-lived component range), as shown on the spectrum in the inset in right bottom corner, as a function of time. Pressure 40 MPa, temperature 298 K. The zero of time scale means the moment of pressure application.
TEMPERATURE, K Fig. 7. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane at 18 MPa as a function of temperature. Full circles mean the first measurement at given temperature, open symbols – repeated measurement, 6 h later. Vertical broken line shows the transition point from rigid to rotator phase.
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Fig. 10. Ortho-Ps lifetime in argon as a function of pressure at 300 K.
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Fig. 8. Ortho-Ps lifetime and intensity in argon intercalated nheneicosane at 18 MPa as a function of temperature. Full circles mean the first measurement at given temperature, open symbols – second measurement, 6 h later. Vertical scale in this figure is the same as in Fig. 7.
transition is preceded by a slight decrease of s3 lifetime and growth of the intensity of the fourth (argon) component, and then, at 88 MPa the whole long-lived part of the spectrum reduces to one component living about 5 ns, i.e., like for gaseous argon at these pressures. It means that practically all positronium escapes to the outside. Several spectra were taken with decreasing pressure. The data shown in Fig. 11 indicate that the spectra return roughly to the same shape as in the series with rising pressure, except one point, p = 80 MPa, which may indicate hysteresis.
B. Zgardzin´ska et al. / Chemical Physics 320 (2006) 207–213
methods. Also the nature of large defects characteristic of that phase should be explained. The temperature of transition to the rigid phase after intercalation of argon is shifted toward higher values; that shift is particularly large in n-nonadecane at 306 K. At this temperature and pressures above 88 MPa all positronium escapes from the samples to argon surrounding. It is interesting that relatively large free volumes producing the o-Ps component with s3 3.3 ns show no tendency to reduce even at pressures as high as 90 MPa. The rate of s3 decrease with pressure in the range 50–80 MPa is os3/op = 4 · 10 3 ns/MPa, which, according to the pick-off model [6], corresponds to a relative volume decrease 1.4 · 10 3 per MPa. Without intercalation the shortening of s3 with pressure is evident (Fig. 1), os3/op being in that case almost by two orders of the magnitude larger. Pressure lowering restores the shape of PALS spectrum.
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Fig. 11. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane as a function of pressure at 306 K (dots). The intensity of ‘‘argon component’’ is shown at the bottom of figure. Full symbols – pressure up run, open circles – pressure down; diamond relates to the spectrum taken at 309 K. An arrow indicates the expected phase transition point rigid – rotator in nonintercalated samples.
4. Conclusions A general tendency to increase the free volume in n-alkanes after argon intercalation is observed. The effect of s3 and I3 increase is particularly strong at about 12 MPa in n-heptadecane (292.5 K) and in n-nonadecane (302 K). Such a negative compressibility of free volumes at these temperatures can be attributed to the creation of a new variant of the rotator phase, characterized by large size of free volumes, in n-heptadecane and n-nonadecane much larger than in the phase without argon intercalation. It seems that free volume created near the kinked chain of alkane molecule is not sufficient to explain the size of defects appearing in the discussed phase. The existence of a new phase has to be confirmed by other, independent
The authors thank Dr. M. Mardarowicz (Faculty of Chemistry UMCS) for GCMS tests of our samples. The assistance by R. Zaleski in data processing is gratefully acknowledged.
References [1] Y.C. Jean, P.E. Mallon, D.M. Schrader (Eds.), Positron and Positronium Chemistry, World Scientific, Singapore, 2003. [2] O.E. Mogensen, Positron Annihilation in Chemistry, SpringerVerlag, Berlin, 1995. [3] J. Doucet, I. Denicolo`, A. Craievich, J. Chem. Phys. 75 (1981) 1523. [4] A.F. Craievich, I. Denicolo`, J. Doucet, Phys. Rev. B30 (1984) 4782. [5] M. Maroncelli, Song Ping Qi, H.L. Strauss, R.G. Snyder, J. Am. Chem. Soc. 104 (1982) 6237. [6] B. Jasin´ska, A.E. Koziol, T. Goworek, J. Radioanal. Nucl. Chem. 210 (1996) 617. [7] T. Goworek, K. Ciesielski, B. Jasin´ska, J. Wawryszczuk, Chem. Phys. 230 (1998) 305. [8] E.B. Sirota, D.M. Singer, H.E. King Jr., J. Chem. Phys. 100 (1994) 1542. [9] T. Goworek, J. Wawryszczuk, R. Zaleski, Chem. Phys. Lett. 402 (2005) 367. [10] A. Wu¨rflinger, G.M. Schneider, Ber. Bunsenges. Phys. Chem. 77 (1973) 121. [11] H. Forsman, P. Anderson, J. Chem. Phys. 80 (1984) 2804. [12] J. Kansy, Nucl. Instrum. Meth. A 374 (1996) 235. [13] T. Goworek, R. Zaleski, J. Wawryszczuk, Chem. Phys. 295 (2003) 243.
Positron annihilation in argon intercalated n-alkanes at high pressure B. Zgardzin´ska, J. Wawryszczuk, T. Goworek
*
Institute of Physics UMCS, Marie Curie-Sklodowska University, 20-031 Lublin, Poland Received 5 April 2005; accepted 6 July 2005 Available online 15 August 2005
Abstract Positron annihilation lifetime spectroscopy was used to observe the effects of argon intercalation in some solid long-chain alkanes at high pressure. The ortho-Ps lifetime rises with argon pressure, which means increase of free volumes in the alkane structure. The range of pressures in which the rotator phase exists increases, comparing to pure alkane. In n-heptadecane, n-nonadecane, and possibly n-heneicosane, a stepwise change of ortho-Ps lifetime and intensity at 12 MPa is observed, suggesting the transition to a new kind of the rotator phase. The transition rate is low, final lifetime value is 3.3 ns. Despite a large size of free volumes corresponding to such a lifetime, their compressibility is found negligible up to the pressure of 90 MPa. At low pressures the compressibility of free volumes in the rotator phase is negative. 2005 Elsevier B.V. All rights reserved. Keywords: Positronium; Alkane; High pressure; Argon intercalation
1. Introduction Positron annihilation lifetime spectroscopy (PALS) is a method commonly used in determination of intermolecular free volume sizes in solids, particularly in polymers [1,2]. Such free spaces exist also in crystalline media, e.g., in long-chain n-alkanes some free volumes are located in the vicinity of nonplanar conformers. At low temperature (‘‘rigid’’ phase) n-alkane molecules have the form of straight rods; with temperature rise the concentration of nonplanar conformers increases. It concerns predominantly the rotator phases existing in a narrow range 5–12 K below the melting point [3– 5]. In n-alkanes with the chain length of about 20 carbon atoms, 20% of molecules in the rotator phase have the form of kinked chains [5]. The crystalline structure of odd numbered n-alkanes is lamellar, with molecular chains settled parallel to one another and perpendicular to the lamella surface. The free volume created in the *
Corresponding author. Fax: +48 81 5376191. E-mail address: [email protected] (T. Goworek).
0301-0104/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.07.008
vicinity of kinked molecules is relatively large in relation to other abundant conformers (end-gauche type) and has the form of a channel running along the molecule. The location of the kink is movable, and the expected average length of an empty channel is about half of the lamellae spacing. The PALS spectroscopy bases on the relation between the free volume size and the lifetime of orthopositronium located in it. Positronium (Ps) is the bound state of a positron with an electron. Due to its negative work function it is trapped in free (electron-less) volumes. The lifetime of triplet ortho-positronium (o-Ps) is determined mainly by the overlap of its wavefunction with the surrounding bulk (pick-off process). The larger the trap is – the longer is the lifetime; details of this relation are determined by the void geometry. In the case of free volumes near the kinked molecules the most suitable approximation of the void shape seems to be an elongated channel of circular or square cross-section. The equation describing the o-Ps lifetime in a rectangular channel is given by Jasin´ska et al. [6], in a cylindrical one – by Goworek et al. [7].
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The properties of molecular solids often depend on the size and concentration of the free volumes in their structure; e.g., the compressibility concerns mainly free spaces, not the molecular volume. It was found by Sirota et al. [8] that in the rotator phase RI of n-alkanes linear negative compressibility can be observed. The effect of expansion under high pressure accompanies the intercalation of gases into alkanes and their derivatives. It seemed to us worthwhile to observe the modification of free volumes in selected n-alkanes subjected to a high pressure. Our partial results for n-nonadecane were published recently [9].
2. Materials and experimental techniques n-Nonadecane C19H40 and its odd numbered neighbouring alkanes: n-heptadecane C17H36 and n-heneicosane C21H44 were chosen due to a convenient range of temperatures in which the rotator phase exists (in our experimental conditions we had no possibility to change the temperature of the pressure chamber within broad limits). At normal pressure (0.1 MPa) the rotator phase RI exists in the range 283–295 K for n-heptadecane, 296–305 K for n-nonadecane and 305.5–313.5 K for n-heneicosane [5]; in even-numbered neighbours the rotator phase does not appear. The limiting values of the temperature and pressure between which the rotator phase exists can be found in the paper by Wu¨rflinger and Schneider [10] or Forsman and Anderson [11]. The samples were produced by Sigma–Aldrich, their purity was tested using the gas chromatography/mass spectrometry setup (ThermoFinnigan Trace DSQ) and found better than 99%; no additional purification was performed. The polycrystalline samples had the form of disc shaped pellets 2 mm thick, sufficient to stop all positrons from the radioactive source. The pressure was produced by the gas compressor U-11 (Unipress, Warsaw); the working gas in the pressure chamber was argon. The lifetime spectra were registered with a conventional fast-slow coincidence spectrometer with time resolution of 220 ps. The positron source was 22Na (0.5 MBq) in a Kapton envelope. The statistics collected per one spectrum was about 1.5 · 106 coincidences. Low source activity and c ray absorption in thick walls of the pressure chamber resulted in low counting rate; the statistics given above needed the collection time of 6 h per spectrum. The spectra were processed by LT programme [12] fitting to the data a sum of three or four exponential components convoluted with the instrumental resolution curve. The shortest-lived component, s1 120 ps, belonged to the singlet para-Ps decay, the intermediate one, s2, to annihilation of unbound positrons, the long-lived component, s3 1.5–3.5 ns, was attributed to the ortho-Ps decay. The length of the empty channel near the kinked molecule depends on kink location, thus
we had a certain distribution of o-Ps lifetimes. For the sake of simplicity this distribution was ignored; the s3 values were thus the average over possible void sizes. We could expect that in certain conditions some o-Ps atoms can escape from the medium and annihilate in the surrounding argon atmosphere. The longest-lived component, s4, if any, represented the o-Ps annihilation in argon. If such a component existed, the intermediate component (s2) contained also the events of free positron annihilation in argon. Two kinds of measurements under pressure were performed: (a) The samples were exposed to the pressure producing gas. A sandwich of samples and the positron source pressed together was placed directly in the chamber of compressor. (b) The sandwich was inserted into a small thin-wall steel tube 10 mm of inner diameter (the same as that of the samples), closed by two pistons; the container volume was tightened by O-rings. Before placing into the compressor, one piston was in high position enabling evacuation of the container to the pressure of about 1 Pa through a side opening, and then the piston was pushed down. In this way the volume between the pistons was gas free and entirely filled by the samples. The gas pressure was transmitted via the pistons. In this measurement version we avoided gas penetration into the samples. The temperature of the samples inside the high pressure chamber was controlled with the accuracy ±0.1 K using Shimaden FP21 unit.
3. Results and discussion Fig. 1 presents the results for three discussed nalkanes without gas permeation to the samples at 292.5 K (n-heptadecane), 302 K (n-nonadecane) and 310.5 K (n-heneicosane), i.e., roughly at the same distance from the melting point for all media. In the range of pressures p 6 50 MPa the s3 dependence on pressure follows a similar dependence on temperature; pressure increase by 1 MPa corresponds to the temperature decrease by 0.22 K; this agrees well with the estimate given by Sirota et al. [8]. With pressure increase the lifetime s3 shortens, which means that no anomalies are observed: the volume of free spaces diminishes. The transition from the rotator to ‘‘rigid’’ phase is well visible as a drop both of o-Ps lifetime s3 and intensity I3. In the rigid phase the concentration of kink-conformers is greatly reduced; long empty channels disappear and the remaining positronium is now located in small spaces between the molecular lamellae [13]. Further increase of
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Fig. 2. Ortho-Ps lifetime and intensity in pure (without argon intercalation) n-nonadecane in an extended range of pressures.
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Fig. 1. Ortho-Ps lifetime and intensity in pure alkanes (without argon intercalation) as a function of pressure. Traingles – n-heptadecane (temperature 292.5 K), open circles – n-nonadecane (302 K), asterisks – n-heneicosane (310.5 K).
pressure brings a little effect (Fig. 2). In the range 200– 1300 MPa the intensity I3 in n-nonadecane practically does not depend on the pressure, and above 500 MPa the lifetime s3 changes negligibly. Close packed structure of lamellae composed of straight nondeformed molecules is resistant against externally applied pressure. No phase transitions are observed up to 1300 MPa. When the pressure is applied directly to the samples in gaseous atmosphere, gas penetration changes the oPs lifetime and intensity in the rotator phase in another way than in pure alkane samples. Fig. 3 shows the pressure dependence of s3 and I3 for n-heptadecane at 292.5 K. The same parameters for n-nonadecane at two selected temperatures: 298 and 302 K are shown in Figs. 4 and 5, whereas for n-heneicosane at 310.5 K in Fig. 6. For comparison the same figures show the lifetime and intensity values for pure samples, without intercalation of argon. Generally, one observes an increase of o-Ps lifetime with pressure. A particularly strong effect is visible in n-heptadecane and n-nonadecane at 302 K. According to Sirota et al. [8] argon atoms locate between the lamellae, but do not enter the free volumes near the kinked molecules, which remain still empty. The rise of s3 from (2.4–2.6) to 3.3 ns
seen in Figs. 3 and 5 results from the changed free volume dimensions: its length and cross section. The length increases with pressure due to the increase of lamellae spacing; this dimension increases by 1.75 · 10 3 nm/ MPa [8], being insufficient to explain the observed lifetime rise. According to the pick-off annihilation model [6], the rise of s3 to 3.3 ns means that the void crosssection has to increase by about 40%, too, in comparison to a pure sample. Increase of the dimensions is visible also at 298 K in n-nonadecane and 310.5 K in n-heneicosane (note that 310.5 K in this case is equivalent to 302 K for n-nonadecane), however, the effect is much smaller. A striking feature of s3 and I3 pressure dependences in n-heptadecane is a stepwise increase of these parameters at 12 MPa. During several hours they rise with the time to a new high values. It can be explained as a result of phase transition. At that pressure (and temperature) the low pressure phase RI transforms into a new one, which is characterized by the presence of still larger defects. The lifetime 3.3 ns belongs to the longest observed in solids. Surprising is its constancy in a very broad range of pressures; the size of free volumes once achieved is not too sensitive to further pressure increase. A similar stepwise and slow change of o-Ps parameters can be seen also in n-nonadecane at 302 K and 12 MPa (Fig. 4). Thus, large differences in PALS parameters as a function of pressure, seen in Figs. 3–6, made us to study also the temperature variation of the observed effect. The
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Fig. 3. Ortho-Ps lifetime and intensity in argon intercalated nheptadecane as a function of pressure (dots). Triangles denote the series of successive spectra taken at fixed pressure. For comparison the experimental data for nonintercalated samples are shown by open circles. Temperature 292.5 K. The intensity of additional fourth component in PALS spectrum, appearing above the transition to the rigid phase, is shown at the bottom.
temperature of our pressure chamber could be changed from room temperature upwards, so measurements were done for n-nonadecane and n-heneicosane only. The pressure was set fixed, 18 MPa, and the temperature increased in 1 K steps. At each temperature two spectra were taken successively, i.e., in 6 h spacing. The lifetime and intensity of the long-lived component for n-nonadecane are shown in Fig. 7. One can see the step both of s3 and I3 at the transition from the rigid to rotator phase at 298 K (shifted, as expected, by 4 K comparing to zero pressure), then a slow rise up to 302 K when again one observes a step similar to that seen in pressure dependences. At both these temperatures the values of parameters are not stable in time, they rise slowly. Note that only at those two points two successive spectra give different values of parameters. Above the step, like in pressure experiment, the lifetime is perfectly temperature independent. Analogous data were collected for n-heneicosane at 18 MPa. Fig. 8 shows that the effect of transition to
Fig. 4. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane as a function of pressure (full circles). For comparison the experimental data for nonintercalated samples are shown by open circles. Temperature 298 K.
the proposed new phase exists also in n-heneicosane (step at 310 K), but is much less pronounced. The points in Figs. 7 and 8 represent the spectrum parameters averaged over 6 h duration of the spectrum collection. More detailed observation of their variation in time was undertaken. An amplitude window at the output of time-to-amplitude converter (Ortec 567) of the PALS spectrometer was placed as shown by the insert in Fig. 9, selecting the events of positron annihilation delayed by (2.1–5.9) ns, i.e., belonging to o-Ps decay. The number of counts in that window collected at 10 min intervals was recorded in the multichannel analyser working as a multiscaler. The result shown in Fig. 9 indicates that in n-nonadecane at 302 K and 40 MPa the equilibrium is reached not earlier than 7 h after pressure switching on. In [8] the time needed to reach equilibrium after argon penetration is estimated for about 0.5 h, thus the slow variation must be of other origin. The stepwise change of the parameter values, instability with the time, change of the form of temperature dependence above the instability point are strong arguments in favour of the existence of a new high-pressure rotator phase in the investigated n-alkanes. The new postulated (rotator) phase is characterized by still larger free volumes than those
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PRESSURE, MPa Fig. 5. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane as a function of pressure (full circles). The data for nonintercalated samples are shown by open circles. Temperature 302 K.
in RI phase without pressure and without argon intercalation. The results shown in Fig. 4 are collected below the proposed new phase transition point. It is seen (as well as in the Fig. 5) that the normal RI phase is moderately sensitive to argon intercalation, and negative compressibility of free volumes is faintly marked. In the argon intercalated samples the transition to the rigid phase is shifted toward higher pressures comparing to nonintercalated ones. Phase transition is accompanied by the appearance of a new component in PALS spectrum. It is very long-lived and the lifetimes, 7– 8 ns, observed for various pressures, are identical with those for argon alone filling the chamber (Fig. 10). One can suppose that this component is produced by Ps escaping from the sample. In the rigid phase gas intercalation is not observed [8]. In the rotator phase argon atoms are accumulated in the interlamellar gaps, 0.26 nm thick, locally enlarged due to a possible longitudinal shift of molecules and reduced total length of nonplanar conformers. At transition to the rigid phase the gap is narrowed by 0.06 nm and the kink molecules are straightened; reduction of interlamellar free spaces leads to argon atom escape. The samples are damaged,
Fig. 6. Ortho-Ps lifetime and intensity in argon intercalated nheneicosane as a function of pressure (full circles). The data for nonintercalated samples are shown by open circles. Temperature 310.5 K.
a great number of microcracks makes them sponge-like, which can be noticed even visually. In such a damaged structure o-Ps can migrate to the gaseous surrounding outside the crystalline structure. The lifetime of o-Ps remaining in the crystal is slightly shorter than in pure alkane. That can be explained as a result of additional probability of Ps disappearance (besides decay) by transition to the outside. Four component analysis shows that in the rotator phase, the ‘‘argon component’’, if it exists, has an intensity of a fraction of a percent only. As can be seen in Figs. 3–6 the shift of the rotator-rigid phase transition point in the samples after intercalation by argon is from 6 to 18 MPa. An additional series of measurements was performed with nnonadecane sample at 306 K changing the pressure from 18 MPa upwards (without pressure the sample would be molten). The expected transition point without argon penetration should be approximately at 47 MPa. Fig. 11 shows that in argon atmosphere the transition occurs not earlier than at 84 MPa, i.e., by 37 MPa higher than in a pure sample. It seems that with increasing temperature the range of pressures in which the rotator phase exists becomes broader. It is in contrast to pure alkanes where that range reduces, and for n-nonadecane the rotator phase disappears at 348 K and 220 MPa [11]. In our measurements the
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Fig. 9. n-Nonadecane. The number of counts registered in the delay range 2.1–6 ns (long-lived component range), as shown on the spectrum in the inset in right bottom corner, as a function of time. Pressure 40 MPa, temperature 298 K. The zero of time scale means the moment of pressure application.
TEMPERATURE, K Fig. 7. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane at 18 MPa as a function of temperature. Full circles mean the first measurement at given temperature, open symbols – repeated measurement, 6 h later. Vertical broken line shows the transition point from rigid to rotator phase.
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Fig. 10. Ortho-Ps lifetime in argon as a function of pressure at 300 K.
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Fig. 8. Ortho-Ps lifetime and intensity in argon intercalated nheneicosane at 18 MPa as a function of temperature. Full circles mean the first measurement at given temperature, open symbols – second measurement, 6 h later. Vertical scale in this figure is the same as in Fig. 7.
transition is preceded by a slight decrease of s3 lifetime and growth of the intensity of the fourth (argon) component, and then, at 88 MPa the whole long-lived part of the spectrum reduces to one component living about 5 ns, i.e., like for gaseous argon at these pressures. It means that practically all positronium escapes to the outside. Several spectra were taken with decreasing pressure. The data shown in Fig. 11 indicate that the spectra return roughly to the same shape as in the series with rising pressure, except one point, p = 80 MPa, which may indicate hysteresis.
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methods. Also the nature of large defects characteristic of that phase should be explained. The temperature of transition to the rigid phase after intercalation of argon is shifted toward higher values; that shift is particularly large in n-nonadecane at 306 K. At this temperature and pressures above 88 MPa all positronium escapes from the samples to argon surrounding. It is interesting that relatively large free volumes producing the o-Ps component with s3 3.3 ns show no tendency to reduce even at pressures as high as 90 MPa. The rate of s3 decrease with pressure in the range 50–80 MPa is os3/op = 4 · 10 3 ns/MPa, which, according to the pick-off model [6], corresponds to a relative volume decrease 1.4 · 10 3 per MPa. Without intercalation the shortening of s3 with pressure is evident (Fig. 1), os3/op being in that case almost by two orders of the magnitude larger. Pressure lowering restores the shape of PALS spectrum.
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Fig. 11. Ortho-Ps lifetime and intensity in argon intercalated nnonadecane as a function of pressure at 306 K (dots). The intensity of ‘‘argon component’’ is shown at the bottom of figure. Full symbols – pressure up run, open circles – pressure down; diamond relates to the spectrum taken at 309 K. An arrow indicates the expected phase transition point rigid – rotator in nonintercalated samples.
4. Conclusions A general tendency to increase the free volume in n-alkanes after argon intercalation is observed. The effect of s3 and I3 increase is particularly strong at about 12 MPa in n-heptadecane (292.5 K) and in n-nonadecane (302 K). Such a negative compressibility of free volumes at these temperatures can be attributed to the creation of a new variant of the rotator phase, characterized by large size of free volumes, in n-heptadecane and n-nonadecane much larger than in the phase without argon intercalation. It seems that free volume created near the kinked chain of alkane molecule is not sufficient to explain the size of defects appearing in the discussed phase. The existence of a new phase has to be confirmed by other, independent
The authors thank Dr. M. Mardarowicz (Faculty of Chemistry UMCS) for GCMS tests of our samples. The assistance by R. Zaleski in data processing is gratefully acknowledged.
References [1] Y.C. Jean, P.E. Mallon, D.M. Schrader (Eds.), Positron and Positronium Chemistry, World Scientific, Singapore, 2003. [2] O.E. Mogensen, Positron Annihilation in Chemistry, SpringerVerlag, Berlin, 1995. [3] J. Doucet, I. Denicolo`, A. Craievich, J. Chem. Phys. 75 (1981) 1523. [4] A.F. Craievich, I. Denicolo`, J. Doucet, Phys. Rev. B30 (1984) 4782. [5] M. Maroncelli, Song Ping Qi, H.L. Strauss, R.G. Snyder, J. Am. Chem. Soc. 104 (1982) 6237. [6] B. Jasin´ska, A.E. Koziol, T. Goworek, J. Radioanal. Nucl. Chem. 210 (1996) 617. [7] T. Goworek, K. Ciesielski, B. Jasin´ska, J. Wawryszczuk, Chem. Phys. 230 (1998) 305. [8] E.B. Sirota, D.M. Singer, H.E. King Jr., J. Chem. Phys. 100 (1994) 1542. [9] T. Goworek, J. Wawryszczuk, R. Zaleski, Chem. Phys. Lett. 402 (2005) 367. [10] A. Wu¨rflinger, G.M. Schneider, Ber. Bunsenges. Phys. Chem. 77 (1973) 121. [11] H. Forsman, P. Anderson, J. Chem. Phys. 80 (1984) 2804. [12] J. Kansy, Nucl. Instrum. Meth. A 374 (1996) 235. [13] T. Goworek, R. Zaleski, J. Wawryszczuk, Chem. Phys. 295 (2003) 243.