13914
J. Phys. Chem. B 2007, 111, 13914-13918
Free Volume in C60 Modified PPO Polymer Membranes by Positron Annihilation Lifetime Spectroscopy Jan Kruse,† Klaus Ra1 tzke,*,† Franz Faupel,† Dana M. Sterescu,‡ Dimitrios F. Stamatialis,‡ and Matthias Wessling‡ Lehrstuhl fu¨r MaterialVerbunde, Technische Fakulta¨t der Christian-Albrechts-UniVersita¨t zu Kiel, Kaiserstrasse 2, 24143 Kiel, Germany, and Faculty of Science and Technology, Membrane Technology Group, UniVersity of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands ReceiVed: June 26, 2007; In Final Form: October 12, 2007
PPO (poly(2,6-dimethyl-1,4-phenylene oxide)) is a well-known membrane material showing good gas separation properties. The incorporation of nanoparticles can enhance or deteriorate the performance of composite membranes, sometimes depending only on the way of the composite preparation. We have modified the PPO polymer with C60 fullerenes up to a content of 2 wt %. Previous investigations showed a strong dependence of permeability on whether the C60 is simply dispersed in the polymer or chemically bonded to the polymer chains. Free volume effects were suggested as an explanation but not experimentally confirmed. Here, we present free volume studies by positron annihilation lifetime spectroscopy. An additional long positron lifetime shows the increased free volume of composite samples, while the high electron affinity of C60 helps to indicate the homogeneity of the samples. Combining the presented results with permeability measurements refines the understanding of this promising membrane material.
Introduction Industrial gas separation has become a wide field of applications for polymeric membranes. Synthetic membranes are developed with the aim to achieve high permeabilities for one sort of molecule, whereas another undesired species is to be retained. The permeability of a membrane is the product of the solubility, S, and the diffusivity, D, of the diffusing species in the membrane:
P)D×S
(1)
For separation applications, the permeabilities of the gases or vapors to be separated must be different; the efficiency of the separation of two species a and b is given by the selectivity:
R ) Pa/Pb
(2)
The aim of membrane development is to achieve high values in both permeability and selectivity, in order to reduce membrane area and obtain high purity gases. However, it is a common observation that most of the polymers investigated show the general trend that highly permeable polymers possess rather low selectivity (permeability/selectivity trade off relationship). This tradeoff relation between permeability and selectivity was named as the Robeson upper boundary.1 For gas molecules, glassy polymers tend to outperform rubbers by an order of magnitude in selectivity; yet, the existence of an upper bound has been proposed on the basis of kinetic diameters of the penetrants.2 A promising attempt to overcome the tradeoff between permeability and selectivity is the modification of well-known * Corresponding author. Phone: +49-431-880-6227. Fax: +49-431-8806229. E-mail:
[email protected]. † Technische Fakulta ¨ t der Christian-Albrechts-Universita¨t zu Kiel. ‡ University of Twente.
polymer membrane materials with nanoscale fillers.3 Although the classical Maxwell theory of diffusion in composites predicts a decrease in permeability in case of the addition of impermeable filler particles to the membranes,4 various investigations have demonstrated that an improvement in the combination of permeability and selectivity can be achieved for membranes with silica nanoparticles mixed into the polymer.5,6 It has been suggested that the improved membrane performance correlates with an increase in free volume.7 In a recent study, the present authors and others have dispersed Boltorn H40 hyperbranched polymer molecules in poly(2,6-dimethyl-1,4-phenylene oxide) (PPO),8 which is one of the few polymers actually used in industrial membrane applications. A strong increase in gas permeabilities with hardly any compromise in ideal selectivity was found for low H40 concentrations (1 wt %). However, phase separation occurred at higher concentrations leading to lower permeabilities than in pure PPO. For the present study, the same membrane polymer PPO was modified with very small, impermeable nanoparticles, that is, C60, so-called, “buckyballs”. The focus of our study is directed toward a relation between the change in permeability and the free volume. Polotskaya et al. have measured the macroscopic free volume in such composites with dispersed C609,10 and concluded from increased density a decrease in free volume. They attribute this to a strong complex binding between C60 and polymer. The results of their gas permeation experiments show a decrease in permeability with increasing C60 content for all gases under investigation. On the other hand, a slight but significant increase in selectivity is emphasized, opening up a perspective toward highly permeable membranes. In a recent study, some of the present authors have modified the preparation of PPO-C60 composite membranes by covalently linking the C60 to the polymer chain.11 For comparison, both types of membranes with covalently bonded C60 and with simply dispersed C60 were prepared and characterized with equal
10.1021/jp074966+ CCC: $37.00 © 2007 American Chemical Society Published on Web 11/29/2007
C60 Modified PPO Polymer Membranes
J. Phys. Chem. B, Vol. 111, No. 50, 2007 13915 Eldrup.13,14 In this model, the positronium is assumed to be confined in a sphere and a potential well with infinite wall height. For such a problem, the Schro¨dinger equation can be formulated and solved analytically. Furthermore, the model postulates an electron layer at the pore wall, with which the ortho-positronium can interact and decay. Calculation of the overlap integral of the positronium probability density function with this electron layer yields a direct relation between positronium lifetime and the hole radius:
(
τo-Ps ) λ-1 0 1-
Figure 1. Permeability of PPO membranes with covalently bonded (closed symbols) and dispersed (open symbols) C60 for N2, O2, and CO2 (taken from ref 12). All values are normalized with the results of pure PPO. For the bonded C60, an increase in permeability without significant compromise in selectivity is achieved, while the dispersed C60 reduces permeability.
C60 content for concentrations up to 2 wt %. At higher concentrations, the polymer becomes insoluble and difficult to process. The results of the permeation experiments reveal a strong increase in permeability for PPO-C60 bonded composites, without compromise in selectivity. Figure 1 shows the permeabilities of the PPO-C60 membranes of both preparation routes for oxygen, nitrogen, and carbon dioxide gas (see experimental details in ref 12). The increase in permeability is restricted to membranes with bonded C60; dispersed C60 in PPO reduces the gas permeability. For the PPO-C60 bonded membranes, further experiments led to indications of an increase of free volume. For the PPO-C60 dispersed membranes, the C60 form clusters. These clusters seem to induce polymer crystallinity, and they are probably aligned along the film plane creating an extra barrier for gas permeation. The present study aims to investigate in detail the structure of the PPO-C60 composites using positron annihilation lifetime spectroscopy (PALS). Specific attention will be given to the free volume changes of the composites in comparison to pure PPO as well as the distribution of C60 within the polymer. PALS is a particularly sensitive experimental technique for the investigation of open volume defects in metals, semiconductors, and insulators, as positrons probe, to a first approach, the electron density distribution. A positron can be obtained from radioactive decay of isotopes with proton excess, such as 22Na. If a positron is injected into a polymer, it will annihilate with an electron from inside the polymer. If a free electron from its ionization track is available, a hydrogen like bound state called positronium can be formed. All decay spectra can be decomposed as a sum of exponentials, where the reciprocal of the decay rates are the corresponding lifetimes τi. The shortest one, τ1, stems from the singlet state para-positronium and does not provide information about free volume. The second short lifetime τ2 is produced by those positrons which did not find a free electron for positronium formation and decay as “free” positrons. The information about free volume is provided by the third decay mode, the triplet state ortho-positronium (oPs). Its decay is influenced by electrons in the surrounding media. By being dependent on the local electron density, the ortho-positronium thus probes the size of the cavity it is residing in. The larger the free volume hole is, the less is the interaction with surrounding electrons and hence the longer the lifetime. A successful quantum mechanical model for the calculation of free volume hole sizes has been developed by Tao and
Rh 2πRh 1 + sin Rh + δR 2π Rh + δR
)
-1
(3)
This formula includes the reciprocal ortho-positronium decay rate τo-Ps, the spin averaged decay rate in the electron layer λ0, the hole radius Rh, and the thickness of the electron layer δR, which has been calibrated using substances with known pore sizes.15 For large holes, the intrinsic o-Ps annihilation rate λ0T ) 0.8 × 107 s-1 cannot be neglected and will be taken into account by simple addition. The relative intensity of the ortho-positronium against other decay processes is often interpreted as a measure for the number or concentration of free volume holes. However, generally, the intensity I has to be recognized as the product of free volume hole concentration CV and positronium formation probability PPs,
I ) CVPPs
(4)
Thus, the relative intensity also depends on the availability of free electrons and can be strongly influenced by the presence of electron scavengers.16 Isolated C60 has been reported to have a very high electron affinity of 2.6-2.8 eV17 resulting in a low PPs. Indeed, PALS results and positron density calculations in solid C60 crystals have shown that the annihilation takes place in the interstices, not inside the carbon cages.18 These experiments show, in particular, that no ortho-positronium is formed when abundant C60 molecules are available. Changes in the o-Ps lifetime and intensity have also been observed for C60 in solution.19 Strongly reduced Ps formation was observed in polymers in the presence of fullerene containing phenyl-[6,6]C61-buteric acid methyl ester (PCBM) molecules.20 Positron annihilation inside C60 in K6C60 has been reported by Ito et al.;21 however, the electronic structure inside the cage leads to an even shorter lifetime below 200 ps. Free volume measurements in pure PPO from positron lifetime spectroscopy have already been reported in the literature22,23 and are used for comparison here. In the present study, we performed positron lifetime measurements in the PPO-C60 composites and calculated the corresponding free volume by the standard model. Apparently, regions of high local free volume are introduced by the C60 incorporation. The inhibition of positronium formation by C60 is clearly visible and will be discussed with respect to the homogeneity of the distribution of C60 in the samples. Experimental Section Membrane Preparation. The PPO-C60 bonded polymer was prepared in a three-step reaction:11 (1) bromination of PPO to PPO-Br, (2) conversion of PPO-Br into PPO-N3, and (3) conversion of PPO-N3 into PPO-C60. Free radical bromination of the PPO was chosen to provide bromination of the methylene side groups only.24 The bromomethylation of PPO was con-
13916 J. Phys. Chem. B, Vol. 111, No. 50, 2007 firmed by 1H NMR spectroscopy (using a Varian Unity INOVA 300 MHz spectrometer). Membranes of pure PPO as well as of PPO-C60 bonded and PPO-C60 dispersed in concentrations of 0.5, 1, 1.5, and 2 wt % were prepared. Besides the pure PPO polymer and the final bonded PPO-C60 composite, membranes of the intermediate steps of sample preparation PPO-Br and PPO-N3 were also available. These were investigated in order to exclude an interfering influence of functional groups not replaced by C60 on positronium formation.16 The number concentration of functionalized groups in the intermediate synthetic steps was equivalent to 1 wt % of C60. All membranes were cast from solutions in chlorobenzene. The films of thickness around 80 µm were dried in a vacuum oven at 30 °C for several weeks until the solvent was completely removed. PALS Measurements. The dried polymer films were cut to square plates of 8 × 8 mm2 using a scalpel. Na-22 encapsuled in Kapton foil was used as a positron source. To ensure that all emitted positrons annihilate in the sample, the source was placed between two film stacks of 800 µm thickness each, and this “sandwich” was finally covered in aluminum foil. Measurements were performed in a vacuum equipped sample holder at 10-2 mbar to avoid artifacts due to moisture and residual gas sorption. The temperature was kept constant at T ) 30 °C. The positron lifetime spectrometer consists of a fast-fast coincidence setup with plastic scintillators. The instrument resolution is approximately 280 ps. Each lifetime spectrum consists of 107 annihilation events, distributed over 3200 channels of 25.3 ps width. PAL spectra were evaluated using the program LT9.0.25 Since the PPO polymer is partly amorphous, we have allowed distribution of the ortho-positronium lifetimes. When another constituent is added to the polymer, another intermediate or longer lifetime might appear in the spectra. If this is the case, the fit algorithm will give bad results if only three lifetime components are expected. Moreover, if a log-normal distribution on a single ortho-positronium lifetime is applied for modeling the distribution in lifetime and free volume size distribution, the fit algorithm, which approximates a least-squares fit to the experimental data, can result in an extremely high width of distribution of log τ. This width is calculated as the standard deviation of the lifetime probability density function and is referred to as dispersion in LT9.0. In our opinion, if the standard deviation of τ exceeds the mean value of the lifetime τ itself, this is a strong argument for two long lifetimes instead of a broad distribution.
Kruse et al. TABLE 1: Overview over Ortho-Positronium Lifetimes from Measurements and Hole Radii Calculated Thereof, Using Eq 1 where Data in PPO-C60 for High C60 Concentration are Unreliable and Hence in Parentheses (See Text for Details) C60 content (wt %) 0
τ3 [ns]
R [nm]
3.1
0.37
τ4 [ns]
R [nm]
0.5 1 1.5 2
PPO-C60 dispersed 2.9 0.36 2.7 0.34 2.7 0.34 2.8 0.35
9.6 9.6 9.6 9.8
0.64 0.64 0.64 0.65
0.5 1 1.5 2
PPO-C60 bonded 2.5 0.33 2.6 0.34 2.1 0.3 1.9 0.28
9.2 9.4 (5.5) (4.8)
0.63 0.64 (0.5) (0.47)
o-Ps lifetimes). This increase in lifetime and the very wide dispersion in lifetimes is, for a mixed system, an indication of a second long lifetime due to the incorporation of C60, whereas one long lifetime component is not suitable to reveal the information included in the spectra. Accordingly, the evaluation of spectra for all C60 containing samples was performed with four lifetime components. Now, the lower o-Ps lifetime component τ3 is only slightly reduced to 2.7-2.8 ns (see Figure 2). A longer lifetime component τ4 of around 10 ns appears which seems to be independent of the C60 concentration. The intensity of both components is affected by some scattering and seems to be slightly decreasing. The sum of both intensities (∼13%) is slightly lower than the o-Ps intensity in pure PPO. The hole size (calculated from τ3 via eq 1) which is attributed to the unaffected PPO regions is slightly smaller than that in the pure PPO. This might be due to the filling of larger holes of PPO by C60. The intensities I3 and I4 as well as the long lifetime τ4 for the dispersed C60 samples depend little on the C60 concentration.
Results and Discussion The pure PPO cast from chlorobenzene exhibits an o-Ps lifetime τ3 of 3.1 ns with an intensity contribution to the spectrum of 21% (see Table 1). A low fit variance could be achieved with a dispersion σ3 of 1.3 ns; thus, there was no indication of a second long lifetime component. This is in good accordance with other studies.22,23 Similar results have been obtained for pure PPO cast from chloroform. The orthopositronium lifetimes of all measurements were converted to free volume hole sizes according to eq 3 (see Table 1). PPO-C60 Dispersed. The spectra of PPO-C60 dispersed were first evaluated with three lifetime components. All samples show an increase in ortho-positronium lifetime to values above 5 ns; simultaneously, the fit requires a dispersion of the third lifetime of approximately 7 ns (throughout the paper the word “dispersion” is either used for dispersion of C60 particles or for dispersion in size of free volume reflected in the dispersion of
Figure 2. Positron lifetime data versus concentration for PPO-C60 dispersed. Squares indicate the o-Ps lifetime components (left axis); circles show the relative o-Ps intensities. For pure PPO, slightly shifted to the left for the sake of clarity, the results of the three component evaluations are given for comparison.
C60 Modified PPO Polymer Membranes
Figure 3. Positron lifetime data versus concentration for PPO-C60 chemically bonded. Squares indicate the o-Ps lifetime components (left axis); circles show the relative o-Ps intensities. For pure PPO, slightly shifted to the left for the sake of clarity, the results of the three component evaluations are given for comparison.
For the interpretation, we assume that the C60 molecules form agglomerates, not necessarily perfectly ordered clusters. It is known that C60 inhibits positronium formation, reflected in a decrease in I3 and I4 compared with those of pure PPO. As these quantities do not decrease with increasing C60 concentration, the C60 seems to be not homogeneously distributed into the polymer, in contrast to chemically bonded C60 (see below). Hence, the addition of more C60 molecules mainly increases the size, not the number of the agglomerates. This interpretation is in good accordance with previous results.12 The detected free volume is not inside the C60 molecule,18,21 but must be located in the vicinity of the C60, where the PPO structure is more disordered. Apparently, there is a discrepancy between microscopic free volume and a decreased macroscopic free volume derived from density measurements by Polotskaya et al.10 However, a decrease in macroscopic free volume, which does not include information on its local distribution, does not contradict the observation of large local free volume elements. A possible connection of these quantities might be a lower hole concentration CV; however, its determination would be superimposed by the Ps inhibition effect of the C60. The gas permeability through the PPO-C60 dispersed membranes is lower than that for the pure PPO (see Figure 112). This is in accordance with our results, which indicate that, although some additional free volume has been created close to or within the C60 agglomerates, the detrimental effects of agglomeration (longer diffusion pathways for the gas molecules, increase of crystallinity12) dominate, resulting in lower gas permeability. PPO-C60 Bonded. The samples with C60 chemically bonded to the PPO polymer exhibit qualitatively the same behavior as PPO + C60 dispersed when evaluated with three lifetime components, resulting in an unrealistic wide dispersion of lifetimes. Also here, a four component analysis needs to be performed. Figure 3 shows the two long lifetimes and their
J. Phys. Chem. B, Vol. 111, No. 50, 2007 13917 respective intensities versus the bonded C60 concentration. For low concentrations, the general behavior is similar to the dispersed samples. The lifetime τ3 is slightly lower (∼2.5 ns); the longest component τ4 reaches values of 9.2 ns (at 0.5 wt %) and 9.4 ns (at 1 wt %; Figure 3b). However, the intensities of both components are lower and strongly decrease with increasing C60 concentration (Figure 3a). At higher C60 concentrations of 1.5 and 2 wt %, the intensity of both components has decreased below 2%. Fixing the lifetime τ4 to 9 ns in the evaluation program is not useful due to the low intensity and the background. At such low intensities, the detection of long lifetimes becomes unreliable, especially for such long lifetimes of almost 10 ns, which suffer from the superposition of the spectrum background and noise. Hence, we put the values in parentheses in Table 1. The strong decrease in ortho-positronium intensity of the PPO-C60 bonded composites created special interest in the intermediate steps of the PPO-C60 synthesis, PPO-Br and PPO-N3. Depending on the positronium formation probability, the o-Ps intensity is known to be sensitive to chemical modifications of the investigated substance.26 To exclude artifacts, for example, from residual functional groups not converted in the next synthesis step, the PALS measurements of the PPO-Br and PPO-N3 were also performed. Indeed, the o-Ps intensity of PPO-Br decreases from 21% (pure PPO) to 12%. However, after replacing the Br by azide groups, the o-Ps intensity in the PPO-N3 polymer is 20% again. Thus, positronium inhibition artifacts by the PPO-C60 preparation route would not be expected, keeping in mind that the cumulative intensity of both o-Ps components in the PPO-C60 with the corresponding amount of C60 functionalizations is only 4.1%. Related to the presence of C60, the reduced intensity of the long lifetime components can be explained according to the established theory of positronium formation and inhibition. Positronium formation depends on the availability of free electrons from the ionization track. C60 is a very efficient electron scavenger with a very high electron affinity,17 thus reducing the positronium formation probability strongly. This interpretation is supported by the intensity data of the PPO with chemically bonded C60, where doubling the concentration from 0.5 wt % to 1 wt % leads to an intensity decrease by almost a factor of 2, continuing for higher concentrations. Conversely, this indicates a homogeneous distribution of C60 in the samples and a respectively much higher extra free volume caused by C60. However, this positronium inhibition effect hampers the direct interpretation of ortho-positronium lifetime and intensity with respect to free volume according to eqs 3 and 4. The membranes with C60 chemically bonded to the PPO show a strongly enhanced permeability to these gases, without the common compromise in selectivity.1,2,12 We have found the presence of high local free volume regions linked to the incorporation of C60, and simultaneously the very effective inhibition of positronium formation has verified the fine dispersion of C60, as was already indicated by the absence of a distinct contrast in the X-ray diffraction pattern.12 The result is apparently a higher diffusivity for faster permeation without obstacles in the membranes. The macroscopic density has also been measured for the PPObonded C60.11 The increase in density is significantly larger than the weighted sum of the PPO and C60 constituents. This decrease in specific volume apparently corresponds to a reduced macroscopic free volume. This demonstrates that for the nanocomposite membranes under investigation the macroscopic free
13918 J. Phys. Chem. B, Vol. 111, No. 50, 2007 volume is not reliable to predict permeabilities, whereas PALS can to some extent access the microscopic structure of the material. Conclusions Although the present experiments are hampered by positronium inhibition, we have shown that positron lifetime spectroscopy can be applied to microscopic free volume investigations in PPO-C60 nanocomposites. The results of free volume measurements have been used to discuss existing permeability measurements in the corresponding membranes. Simply dispersed C60 apparently tends to agglomerate, leading to only a minor increase in free volume and large tortuosity, hence, reduced permeabilities. Chemically bonded C60 is homogeneously distributed and creates large additional free volume sites in the polymer microstructure. All of these results are in good accordance with our permeability measurements. The comparison with density measurements indicates the importance of a detailed study of the microscopic distribution of the free volume. Acknowledgment. D.M.S., D.F.S., and M.W. would like to thank the Netherlands Organization for Scientific Research (STW-NWO) for the financial support (Project No. TPC.5776). References and Notes (1) Robeson, L. M. J. Membr. Sci. 1991, 62, 165-185. (2) Freeman, B. D. Macromolecules 1999, 32, 375-380. (3) Merkel, T. C.; Freeman, B. D.; Spontak, R. J.; He, Z.; Pinnau, I.; Meakin, P.; Hill, A. J. Science 2002, 296, 519-522. (4) Maxwell, J. C. A Treatise on Electricity and Magnetism; Clarendon Press: Oxford, 1873. (5) Hill, R. Phys. ReV. Lett. 2006, 96, 216001. (6) Gomes, D.; Nunes, S.; Peinemann, K.-V. J. Membr. Sci. 2005, 246, 13-25.
Kruse et al. (7) Merkel, T. C.; Freeman, B. D.; Spontak, R. J.; He, Z.; Pinnau, I.; Meakin, P.; Hill, A. J. Chem. Mater. 2003, 15, 109-123. (8) Sterescu, D. M.; Stamatialis, D. F.; Mendes, E.; Kruse, J.; Ra¨tzke, K.; Faupel, F.; Wessling, M. Macromolecules 2007, 40, 5400-5410. (9) Polotskaya, G. A.; Andreeva, D. V.; El’yashevich, G. K. Tech. Phys. Lett. 1999, 25, 555-557. (10) Polotskaya, G. A.; Penkova, A. V.; Toikka, A. M.; Pientka, Z.; Brozova, L.; Bleha, M. Sep. Sci. Tech. 2007, 42, 333-347 (11) Sterescu, D. M.; Bolhuis-Versteeg, L.; van der Vegt, N. F. A.; Stamatialis, D. F.; Wessling, M. Macromol. Rapid Commun. 2004, 25, 1674-1678. (12) Sterescu, D. M.; Stamatialis, D. F.; Mendes, E.; Wubbenhorst, M.; Wessling, M. Macromolecules 2006, 39, 9234-9242. (13) Tao, S. J. J. Chem. Phys. 1972, 56, 5499-5510. (14) Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51-58. (15) Jean, Y. C. Microchem. J. 1990, 42, 72-102. (16) Ito, Y. Mater. Sci. Forum 1995, 175-178, 627-634. (17) Yang, S. H.; Pettiette, C. L.; Conceicao, J.; Cheshnovsky, O.; Smalley, R. E. Chem. Phys. Lett. 1987, 139, 233-238. (18) Jean, Y. C.; Lu, X.; Lou, Y.; Bharathi, A.; Sundar, C. S.; Lyu, Y.; Hor, P. H.; Chu, C. W. Phys. ReV. B 1992, 45, 12126-12129. (19) Sundar, C. S.; Bharathi, A.; Premila, M.; Gopalan, P.; Hariharan, Y. Mater. Sci. Forum 1997, 255-257, 199. (20) Osiele, O. M.; Britton, D. T.; Harting, M.; Sperr, P.; Topic, M.; Shaheen, S. E.; Branz, H. M. J. Non-Cryst. Solids 2004, 338-340, 612616. (21) Ito, Y.; Iwasa, Y.; Tuan, N. M.; Moriyama, S. J. Chem. Phys. 2001, 115, 4787-4790. (22) Nagasaka, B.; Eguchi, T.; Nakayama, H.; Nakamura, N.; Ito, Y. Radiat. Phys. Chem. 2000, 58, 581-585. (23) Hagiwara, K.; Ougizawa, T.; Inoue, T.; Hirata, K.; Kobayashi, Y. Radiat. Phys. Chem. 2000, 58, 525-530. (24) Cabasso, I.; Jagur-Grodzinski, J.; Vofsi, D. J. Appl. Polym. Sci. 1974, 18, 1969-1986. (25) Kansy, J. Nucl. Instrum. Methods Phys. Res., Sect. A 1996, 374, 235-244. (26) Mogensen, O. E. Positron Annihilation in Chemistry; Springer: Berlin, 1995.
