Article pubs.acs.org/JPCC

Positronium Production in Engineered Porous Silica Rafael Ferragut,*,†,‡ Stefano Aghion,†,‡ and Gaia Tosi† †

LNESS and CNISM, Dipartimento di Fisica, Politecnico di Milano, Via Anzani 42, 22100, Como, Italy Istituto Nazionale di Fisica Nucleare, via Celoria 16, 20133 Milano, Italy

‡

Giovanni Consolati‡,§ and Fiorenza Quasso§ §

Department of Aerospace Science and Technology, Politecnico di Milano, via La Masa 34, 20156, Milano, Italy

Mariangela Longhi∥ ∥

Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133, Milano, Italy

Anne Galarneau⊥ and Francesco Di Renzo⊥ ⊥

Institut Charles Gerhardt Montpellier, UMR 5253 CNRS-UM2-ENSCM-UM1, ENSCM, 8 Rue Ecole Normale, 34296, Montpellier, France S Supporting Information *

ABSTRACT: Positronium (Ps) has been the subject of several experimental and theoretical investigations due to its many scientific applications. In this work high positronium yield was found in engineered porous silica. The studied materials were pellets of swollen MCM-41 and of commercial Davicat 1700, obtained by different compression pressures, with mesopores characterized by different structural and chemical features. The measurements were performed with a variable energy positron beam at room temperature. An estimation of the Ps mean diffusion length was obtained by measuring capped samples. A selected swollen MCM-41 sample (0.39 g/cm3) was measured also at cryogenic temperature (8 K). In this material both the Ps yield and the Ps diffusion length are found to be independent of temperature. The pore surface of the swollen MCM-41 samples is very interesting in comparison to commercial silica as it possesses hydrophobic patches to avoid ice formation at low temperature. Positron lifetime measurements show a high Ps survival time inside the mesoporous materials (∼110 ns), which promotes a high Ps mobility during cooling inside the pores favoring diffusion lengths up to 1 μm for swollen MCM-41 materials. Besides, it was possible to estimate the total Ps yield coming up outside the sample at high implantation energies and the time between the implantation of positrons and the Ps release.

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INTRODUCTION Positronium (Ps) is the lightest element, about 10−3 times lighter than hydrogen, and exists in the ground state in two sublevels: singlet (para-Ps, p-Ps) and triplet (ortho-Ps, o-Ps), according to the spins of the electron and positron (antiparallel or parallel, respectively). In a vacuum, their lifetimes are very different, 0.125 and 142 ns for p-Ps and o-Ps, respectively. Also, annihilation features in a vacuum are different: p-Ps annihilates with emission of two γ rays (511 keV each), while o-Ps annihilates by emitting three γ rays, producing a continuous energy distribution for each photon between 0 and 511 keV, where the energy sum of the three photons of the o-Ps annihilation is 1022 keV. When o-Ps is formed inside a porous material, the three γ annihilation probability is reduced by the pick-off effect, that is, the positron of the o-Ps annihilates with © 2013 American Chemical Society

an electron of the porous surface, rather than the o-Ps electron, in a relative singlet state with emission of two γ rays instead of three. Considerable attention has been given to the production of Ps for scientific applications: as a pathfinder inside porous materials (mesopores, zeolites, low-k insulators or semiconductors, polymers, etc.) to study open or closed porosities, their morphology, size, tortuosity, and so on.1 Another potential use is for high density Ps physics, for instance, to form molecular positronium (Ps2)2 and for creating BoseEinstein condensates of Ps. To this last purpose, the production Received: October 15, 2013 Revised: November 26, 2013 Published: November 28, 2013 26703

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of a very high density of positronium (1018 cm−3) is necessary. In this condition the development of a γ ray laser could be possible.3 Another very interesting use is the development of an energy-tunable Ps beam using photodetachment of the positronium negative ion (a bound state of one positron and two electrons) that is expected to be a powerful tool for the investigations of atoms, molecules, and solid surface structures.4 On the other hand, Ps is used for basic studies of antimatter. Indeed, some fundamental questions of modern physics relevant to unification of gravity with the other fundamental interactions, models involving vector and scalar gravitons, matter−antimatter symmetry can be enlightened via experiments with antimatter.5 In this respect, the main goal of the AEgIS (antihydrogen experiment: gravity, interferometry, spectroscopy) collaboration at CERN is to measure for the first time the gravitational interaction between antimatter and matter.6,7 The aim is to produce cold antihydrogen (at about 0.1 K) by means of a charge exchange reaction8 between cold antiprotons and Ps previously excited in a Rydberg state (with 20 ≤ n ≤ 35) by means of two laser pulses.9 Therefore, to obtain a high Ps yield as cold as possible is a critical point for the success of the experiment. Silica-based mesoporous materials are extensively investigated since a high fraction of the implanted positrons form Ps inside them,10 which can be emitted in the pore with kinetic energy of 1−3 eV.11 o-Ps loses its kinetic energy and cools down by means of collisions with the walls of the pore. Another interesting characteristic of porous silica is that, as a consequence of a low pick-off decay rate, o-Ps has a high survival time before annihilation, comparable with the Ps lifetime in vacuum. The long o-Ps lifetime allows a high diffusivity during scattering and ensures o-Ps escape into vacuum, even if it has been produced in depth with positrons implanted at energies higher than 5 keV. In general, for the purposes outlined above it is fundamental to produce cold o-Ps outside a silica porous material; however, only few papers report studies on Ps formation below room temperature.10 The interest of the present work is related mainly to the AEgIS experiment. An efficient formation of cooled positronium atoms is a requisite for the production of antihydrogen (H̅ ) in the AEgIS experiment. The AEgIS experiment will be performed at cryogenic temperatures (∼100 mK). At these temperatures, even in ultrahigh vacuum conditions, water is present among the residual gases inside the chamber, and the formation of ice inside the mesoporous surface of the silica is certain. Indeed, it is known that silica is intrinsically hydrophilic, for this reason, it is extensively used as a liquid sorbent or humidity sensors.12 It is possible to practically eliminate water by means of a baking of the vacuum chamber. However, when delicate electronic instruments are involved in the chamber and when the chamber is connected to an extended line of particles, that is the case of the AEgIS at the antiproton decelerator (AD) facility at CERN, an efficient baking is not feasible. In this context, it is important to test the properties of locally hydrophobic silica porous materials such as MCM-41, able to prevent cryogenic water adsorption. In fact, MCM-41 possesses hydrophobic patches due to the presence of siloxane groups at the corner of the pores13,14 and swollen MCM-41 (obtained by addition of trimethybenzene in the micelles) possesses additional hydrophobic patches on the surface on the pores.15 An advanced characterization of engineered silica porous samples as swollen MCM-41 and Davicat with different

densities by means of positron annihilation techniques and physical adsorption of gas molecules is presented in this work. These materials have a high Ps yield, high survival Ps lifetime, and a high Ps mobility during cooling. Besides, by using a classical diffusion model, in particular for MCM-41 with a density of 0.39 g cm−3, our results and calculations indicate that an important fraction of Ps escapes into the vacuum in tens of nanoseconds also for high positron implantation energies.

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EXPERIMENTAL SECTION Two swollen MCM-4115−17 samples, named thereafter MCM41, were prepared in autoclave at 388 K by using cetyltrimethylammonium bromide (CTAB), 1,3,5-trimethylbenzene (TMB) as swelling agent, pyrogenic silica (Aerosil 200 Degussa), sodium hydroxide, and deionized water in molar ratios 1 SiO2/0.26 NaOH/0.035 NaAlO2/0.1 CTAB/20 H2O/ 1.3 TMB. The resulting samples were dried at 353 K and calcined in air at 773 K for 8 h. For the sake of comparison, another sample was prepared using commercial silica Davicat SI 1700 (purchased from Grace-Davison). The MCM-41 and Davicat samples were compressed to form pellets with a thickness of 5−6 mm and a diameter of 13 mm. The pressure used to form the pellets is critical for the stability of the material. The mechanical stability of MCM-41 depends on their pore size and the thickness of the silica walls between the pores. In the case of swollen MCM-41, it has been shown that, while the pore size is retained for pressure as high as 160 MPa, 20% of the pore volume is already lost after a compression to 80 MPa.18 The swollen MCM-41 samples used in this work were compressed at 7 and 30 MPa. The densities of the samples were, respectively, 0.21 and 0.39 g cm−3, and both samples presented mesoporous volume of 1.84 cm3 g−1 (Figure S1, Table S1). The Davicat sample was compressed at 73 MPa in order to decrease the macropore volume. It presented a density of 0.60 g cm−3 with a mesoporous volume of 1.32 cm3 g−1 (Figure S1, Table S1). One face of each sample was capped with an Al film having a thickness of about 120 nm. The capping layers were deposited by molecular beam epitaxy. Ps formation measurements were performed by means of a variable energy positron beam, with energy up to 18 keV, using the well-known “3γ method” and detecting the γ rays with a high purity germanium detector.19−21 These measurements were carried out in a high vacuum condition (about 10−8 mbar), at two different temperatures: cryogenic temperature (8 K) and room temperature (295 K). Lifetime measurements were performed with a fast−fast timing coincidence system with a time range of about 800 ns (8192 channels, 0.1 ns by channel) and a resolution (fwhm) of 260 ps. A 10 μCi source of 22NaCl deposited between two thin Kapton foil (7.5 μm each) was sandwiched between one porous sample and a tungsten sheet. For each sample, three measurements were carried out; each spectrum contained about 2 × 106 counts. Each sample was inserted in a glass vial and evacuated by a turbo pump; the measurements started after the vacuum level was better than 2 × 10−5 mbar. Spectra were analyzed using the LT program in four components.22 Surface area, pore volume, and mesopore size were determined from N2 adsorption/desorption isotherms at 77 K using a Tristar II 3020 Micromeritics apparatus. Before each measurement, samples were outgassed under vacuum at 523 K for 12 h. Surface area was calculated by the BET method, the pore volume was calculated at the end of mesopore filling, and mesopore diameter was determined by the Broekhoff and de 26704

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Table 1. Lifetimes, Intensities, and Radii Resulting from the Time Annihilation Spectra of the Samples MCM-41 (A and B) and Davicat (C) Measured at Room Temperature sample

τ1 (ns)

I1 (%)

τ2 (ns)

I2 (%)

τ3 (ns)

R3 (nm)

I3 (%)

τ4 (ns)

R4 (nm)

I4 (%)

A (0.21 g cm−3) B (0.39 g cm−3) C (0.60 g cm−3)

0.21(3) 0.22(3) 0.24(3)

43(3) 48(3) 44(3)

0.57(3) 0.60(3) 0.59(3)

41(3) 34(3) 44(3)

2.6(2) 3.1(2) 3.2(2)

0.34(1) 0.37(1) 0.38(1)

4.9(4) 3.9(4) 4.1(4)

109(4) 106(4) 111(4)

6.1(5) 5.8(5) 6.2(5)

11.0(6) 13.3(6) 8.2(6)

Boer method using a cylindrical geometry of pores and demonstrated as one of the more accurate methods to evaluate mesopore size of silica materials.17

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RESULTS AND DISCUSSION Positron lifetime measurements were carried out in the three mesoporous silica samples with different densities: 0.21 g cm−3 (sample A, MCM-41), 0.39 g cm−3 (sample B, MCM-41), and 0.60 g cm−3 (sample C, Davicat). Since only one sample was available for each density, the positron source was inserted between a sample and a tungsten sheet, where Ps is not formed, in order to annihilate all the emitted positrons. Indeed, the goal was to determine Ps lifetime. The results are shown in Table 1. The two shorter lifetime components are ascribed to free positrons, which annihilate in the bulk and in the defects as well as to p-Ps, whose component, having faint intensity, cannot be distinguished from the others. The lifetime of the third component (a few ns) probably comes from o-Ps annihilating in structural defects of the samples. The fourth component (∼100 ns) is the most interesting one, because it can be attributed to o-Ps annihilations into the pores. It is possible to relate such a lifetime to the pore size through a quantum mechanical model originally proposed by Tao and further worked out by Eldrup et al.23,24 In the case of lifetimes of the order of 100 ns or more, as in our samples, to take into account possible excited states into the pores it is necessary to use the so-called extended Tao−Eldrup model.25,26 The radii shown in Table 1, near the corresponding lifetimes, were obtained by using the Tao−Eldrup model in spherical geometry for the third component, or the extended Tao−Eldrup model in cylindrical geometry for the longest component. Due to the presence of the tungsten layer, it is not significant to discuss the intensity of the various components. In spite of the different densities, the o-Ps lifetimes in the three investigated samples are very similar, within the experimental uncertainties, which means that the pore structures are practically the same. There is only a decrease of the intensity I4 in sample C (Davicat) with respect to the samples A and B (MCM-41), that is correlated to a lower pore density. In particular, mesopore diameters obtained by the extended Tao−Eldrup model in cylindrical geometry (∼12 nm) are in accordance with N2 physisorption measurements, giving average diameters in the range of 9−15 nm, with a surface area of about 830 m2 g−1 for samples A and B and 390 m2 g−1 for sample C (Figure S1, Table S1). These pore diameters are in the range of optimum values for o-Ps thermalization.27,28 Investigation of o-Ps formed in the pores near the surface of MCM-41 and Davicat samples (A−C) was carried out by sending a beam of monoenergetic positrons on each sample; positron implantation energy was variable between 1 and 18 keV. Measurements were performed at 8 and 295 K. Figure 1 shows high o-Ps yield as a function of the implantation energy for the studied samples. The maximum positronium fraction F3γ in Figure 1 is about 55, 53, and 49% in samples A, B, and C, respectively. According to the high survival time, the produced o-Ps thermalizes by means of thousands of collisions with the

Figure 1. Positronium 3γ fraction F3γ as a function of the positron implantation energy in uncapped and capped swollen MCM-41 (samples A, 0.21 g cm−3; and sample B, 0.39 g cm−3) and Davicat (sample C, 0.60 g cm−3) measured at room temperature and at 8 K in the case of sample B. The continuous lines used for capped samples are the result of the VEPFIT model and the dashed lines are only a visual guide. Error bars are only shown for one point in each evolution.

pore walls (see τ4 in Table 1). The comparison between sample B (MCM-41) evolutions taken at 8 and 295 K demonstrates that the positronium yield does not depend on temperature for any implantation energy (see also ref 29), as also previously observed by Crivelli et al. for ordered mesoporous silica films.28 Sferlazzo et al. have shown that in crystalline SiO2 the physisorbed o-Ps emitted from the surface depends on the temperature, but the o-Ps produced in the SiO2 bulk is independent of the temperature.30 The observed temperature independence in MCM-41 samples indicates that o-Ps might be produced only into the silica bulk. Another possibility would be that the MCM-41 surface modification with the introduction of hydrophobic patches might have changed the temperature dependence and the o-Ps surface component still exists. The decrease of F3γ observed at low energy in Figure 1 (uncapped samples) is due to the o-Ps emission into vacuum, which implies a decrease of the o-Ps detection efficiency. In these samples, o-Ps yield is remarkably high for any implantation energy in comparison to the thin mesoporous films where it is possible to obtain high yields only at low energies.27,28 High yield at high implantation energies requires rather thick samples (at least of tens of micrometers), a condition easily met with homogeneous and robust pellets. These results are very promising for further work, which will be performed on these materials in the AEgIS experiment at very low temperatures, around 0.1 K. In fact, as outlined in the introduction water vapor absorption by SiO2 at temperatures below 150 K was ascertained even in ultrahigh vacuum conditions.31,32 However, swollen MCM-41 possesses intrinsically hydrophobic patches on their porous structure.13−15 Our results indicate that the effect of gas adsorption or condensation 26705

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at low temperature does not influence the o-Ps yield for MCM41. When the porosity is very high and the pores are interconnected, o-Ps diffuses during cooling. In order to obtain the positronium diffusion length LPs and to prevent o-Ps escape into the vacuum, the mesoporous samples were capped by an Al film. The room temperature results are shown in Figure 1 for MCM-41 and Davicat samples of different densities. Sample B (MCM-41) was measured also at low temperature (8 K) and the results show that the distribution does not depend on temperature. Ps formation is almost zero for implantation energies of about 2 keV; indeed, all the incident positrons annihilate in the metallic layer where no Ps formation is expected. At lower energies (<1.5 keV), a fraction of the positrons form Ps at the Al surface. The results of the positronium fraction as a function of the positron incident energy obtained in the capped porous samples were analyzed by means of a semilinear fitting procedure using the VEPFIT program.33 This program extracts relevant parameters from positron measurements on layered structures. In the present case our attention is focused on the Ps diffusion length. The experimental data were fitted using a model, which considers three layers: surface, an aluminum layer, an interface, and a semi-infinite layer of the mesoporous material. The positrons transport after implantation and thermalization in a solid is approximated by the diffusion theory. According to the fitting of the results the positron diffusion length after thermalization is much lower than the Ps diffusion length. Indeed, the positron diffusion length in the studied materials is about 10 nm and the o-Ps diffusion length, as it will be seen, is of the order of 103 nm. In this condition it is possible to assume that the diffusion equation holds only for Ps. The interface between Al and the porous material used in the analysis model takes into account a possible contamination effect of few nanometres on the porous material with Al during evaporation. It was observed that the positrons implanted at the interface do not influence the calculated profiles. The adopted model is based on the classical assumption that the diffusion coefficient does not depend on the o-Ps temperature during its cooling as is considered by other authors.34 Thus, the diffusion coefficients DPs (DPs = LPs2/τ, calculated using the fourth lifetime o-Ps component, see Tables 1 and 2) are 0.10(1) cm2/s, 0.087(9) cm2/s, and 0.003(1) cm2/

emission from the material, even for high positron implantation energies. The results indicate that the samples with low density and high porous volume favor the Ps diffusion and the Ps yield. Table 2 shows that F3γ slowly decreases as a function of the density, instead the Ps diffusion length decreases abruptly for sample C (Davicat). Taking into account that the lifetime results presented in Table 1 indicate that the pore dimensions of samples A, B, and C are very similar, the explanation of the higher Ps diffusion length obtained in MCM-41 samples (A and B) is certainly related to structural features: both an increased mesoporous volume (1.84 cm3 g−1) and a larger surface area (830 m2 g−1) compared to the Davicat sample (1.32 cm3 g−1 and 390 m2 g−1, respectively). It is well-known that o-Ps formed inside various porous materials is emitted into vacuum with high efficiency. With the aim to calculate the total yield of Ps in vacuum and the time dependent o-Ps emission rate Cassidy et al. recently have proposed a model to solve the classical diffusion equation for positronium where the Ps atoms are created after implantation of positron into a porous sample according to a modified Makhov profile and then diffuse into the porous material.34 Applying this model the total yield of Ps in vacuum per initially formed Ps atom Y(z)̅ for a given positron implantation energy or positron mean implantation depth z̅ is 2⎞ ⎡ ⎤ ⎛ ⎧ ⎡ z z ⎫ z ⎤ Y (z ̅ ) = ⎢1 − ̅ exp⎜⎜π −1⎨ ̅ ⎬ ⎟⎟ erfc⎢π −1/2 ̅ ⎥⎥ ⎢ L Ps L Ps ⎦⎥⎦ ⎣ ⎝ ⎩ L Ps ⎭ ⎠ ⎣

(1)

where the positron mean implantation depth z̅ depends on the kinetic energy E of the implanted positrons into the porous material of density ρ according to

z ̅ = A ρ− 1 E α

with α = 1.6 and A = 40 nm g cm−3 keV−1.6. Y(z)̅ represents the fraction of Ps that reaches the samples surface and diffuses into the vacuum for each Ps atom formed at a certain z.̅ Figure 2a shows the calculations of Y(z)̅ × 100% into the porous MCM41 and Davicat samples as a function of the positron implantation energy. The results refer to the population that encompasses both thermalized and nonthermalized o-Ps atoms. The Ps total yield Y(z)̅ depends on the o-Ps diffusion length LPs (that takes into account indirectly the structural features of the pores, as mentioned before) and on the sample density ρ. As a rule of thumb, Ps total yield at fixed positron implantation energy increases as the Ps atoms mobility and the sample density increase. If o-Ps is created at high implantation energy, that is, deeply into the sample, it has a high probability to annihilate before going out. Figure 2a shows that sample B (MCM-41) allows the highest number of Ps atoms to escape from its surface for all implantation energies. Indeed, this sample has similar diffusion coefficient but higher density than the sample A. Instead, sample C (Davicat) is characterized by a much lower diffusion coefficient despite the higher density. Figure 2b reports the Ps yield outside the sample B. The upper scale represents the positron mean implantation depth and the right scale was obtained by taking the maximum F3γ (about 53%, see Figure 1) in this sample. It is possible to compare the calculation of the Ps yield outside the sample B (Figure 2b) with the experimental results presented in Figure 1 for the same sample (when the

Table 2. Ps Diffusion Length in MCM-41 and Davicat Samples Obtained by Means of VEPFIT Modela T (K)

sample −3

A (0.21 g cm ) B (0.39 g cm−3) B (0.39 g cm−3) C (0.60 g cm−3)

295 295 8 295

F3γ (%) 55 53 53 49

± ± ± ±

1 1 1 1

ZAl (nm) 118 120 120 118

± ± ± ±

6 5 5 7

Zint

LPs (nm)

5F 5±2 5F 5F

1050 ± 50 960 ± 50 1010 ± 50 190 ± 50

(2)

a

The thicknesses Z of the Al capping layer and the interface between Al and the porous materials are also included. The value indicated with F is a fixed parameter.

s, for samples A, B, and C, respectively. As mentioned before, sample B results do not depend on temperature. The diffusion length is almost the same at 8 and 295 K, within the experimental uncertainties; therefore, the Ps diffusivity is not limited by thermal effects. The values found for the diffusion length, which are rather high, are consistent with the high o-Ps 26706

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By using the model mentioned before, it is also possible to estimate when Ps will be emitted into vacuum after the implantation of the positrons. Figure 3 reports the Ps emission

Figure 3. Normalized emission rate and normalized yield for two positron implantation energies (see ref 34) calculated for sample B (MCM-41). It is possible to estimate the time at which half of the total amount of the Ps is emitted (50% of the normalized yield): ∼12 and ∼40 ns for 3 and 6 keV, respectively.

Figure 2. (a) Total yield of Ps in vacuum per initial Ps atom Y(z)̅ as a function of the positron implantation energy E calculated according to eq 1 for samples MCM-41 (A, B) and Davicat (C). (b) The total yield of Ps is reproduced as a function of the mean implantation depth z̅ only for sample B (MCM-41). The Ps yield per incident positron in vacuum is presented on the right-hand for this sample.

rate and the Ps yield both normalized to 100% as a function of time for the sample B calculated also with the model presented in ref 34. These plots give an idea of the dispersion in time of the emitted Ps. It is possible to observe that within 12 and 40 ns half of the Ps escapes from the sample when implanted at 3 and 6 keV, respectively. At the above-mentioned times, the Ps emission rates are, respectively, about 30 and 45% for these energies (see vertical dashed lines in Figure 3). At 6 keV, it is expected mainly thermal or low energy Ps emission.

mesoporous material was capped with an Al film to prevent oPs escape into the vacuum). In Figure 1 at about 6 keV in sample B 50% of the produced o-Ps takes contact with the Al capping layer and is quenched by pick-off annihilating in two γ rays. If the capping layer would not be present the Ps atoms would reach the vacuum. For this comparison it is necessary to subtract to the implantation energies, the implantation energy to overcome the Al foil, thus, is estimated the positron mean implantation depth z1/2 for which one-half of o-Ps overcome the vacuum. This z1/2 value is about one-half of the o-Ps diffusion length for each material (z 1/2 ≈ 1/2 L Ps ), corresponding to positrons implanted at about or less than 3 keV in sample B. In this case, it is possible to obtain only an approximated value because the implantation profile after the subtraction of the Al contribution would be different to the used to calculate the results of Figure 2b. Figure 2b shows that at 3 keV 57% of o-Ps overcome the vacuum (about 30% of the implanted positrons F3γ) for about the same depth estimated previously (z1/2). Within the used approximation for this comparison the accordance between the results of Figures 1 and 2b is good and reveals that the model proposed by Cassidy et al.34 is realistic. The calculated results reported in Figure 2b show that at 6 keV about 22.5% of o-Ps are emitted into the vacuum, which corresponds to 12% of the positron implanted (F3γ). It is clear that a balance must be reached between efficient o-Ps thermalization, which requires deep positron implantation and high o-Ps yield into vacuum, which is favored by not large implantation depths in comparison with the o-Ps diffusion length.

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CONCLUSIONS

The optimum characteristics of a Ps converter at cryogenic temperature depends of morphological, structural, and chemical features of the mesopores. The results obtained in the studied engineered mesoporous silica samples indicate that a swollen MCM-41 is very promising. This material contains ordered domains (powder grains) compressed forming pellet with open mesopores with a mean diameter of about 10 nm, a mass density of 0.39 g cm−3, a mesoporous volume 1.84 cm3 g−1, a surface area of 830 m2 g−1 and possess hydrophobic patches at the porous surface. The demonstrated good characteristics as a Ps converter for the AEgIS experiment are related to the following aspects: high Ps yield at high positron implantation energy (>5 keV), independently on the temperature and on the effect of gas adsorption at low temperature, long survival time of Ps inside the pores, and very high Ps mobility. The obtained results and calculations indicate that Ps escape into vacuum is consistent with the literature data in homogeneous silica porous materials where thermalized Ps overcome the interface with the vacuum.35−37 26707

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ASSOCIATED CONTENT

S Supporting Information *

Swollen MCM-41 (samples A and B) compressed at 7 and 30 MPa, respectively, feature the same nitrogen adsorption isotherm (Figure S1) as the uncompressed swollen MCM-41. Similarly Davicat silica sample compressed at 73 MPa (sample C) feature the same nitrogen adsorption isotherm (Figure S1) as the uncompressed Davicat silica. Porosity characteristic determined by nitrogen adsorption−desorption isotherm as given in Table S1. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +39 031 332 7338. Fax +39 031 332 7617. Notes

The authors declare no competing financial interest.

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REFERENCES

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