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Positron Lifetime in Mesoporous Silica of MCM-41 Type Jan Wawryszczuk,† Jacek Goworek,‡ Radoslaw Zaleski,† and Tomasz Goworek*,† Institute of Physics and Department of Adsorption, Faculty of Chemistry, Maria Curie-Sklodowska University, 20-031 Lublin, Poland Received March 21, 2002. In Final Form: July 29, 2002 Positron lifetime spectra in ordered mesoporous silica were measured. In the raw material (still containing the template) the voids in micellae reaching 1 nm in size were observed. Ortho-positronium (o-Ps) lifetime was found to be very sensitive to the carbon deposits left in pores after pyrolysis. In highly dispersed materials the relation between the pore diameter and positronium lifetime is shadowed by o-Ps escape from the pores to extragranular spaces. A very slow thermalization of o-Ps and increased lifetime of free positrons in low-density bulk were also observed.
Introduction The discovery of ordered mesoporous M41S materials in 1992 disclosed a new family of porous materials with numerous applications in the fields of catalysis, sorption, chromatography, and electronic technology.1,2 The most commonly studied member of this family is MCM-41 mesoporous silica which contains hexagonally ordered mesopores from 1.0 to over 10 nm in diameter. The pores are cylindrically shaped and uniform in size. The channel diameter of MCM-41 can be controlled by using templates with alkyl chains of different length. MCM-41 silicas are synthesized by the templating technique1 using quaternary ammonium surfactants CnH2n+1(CH3)3NBr with n from 8 to 20. Although the structural properties of these mesoporous silicas were extensively studied over the past years, the topology of MCM-41 type materials on a molecular level has not been satisfactorily recognized yet. On a microscale the unifromity of cylindrical channels may be questionable due to the presence of defects in the silica skeleton, possible irregularities, and the presence of carbon deposites formed during pyrolysis of the organic matrix. In most studies concerning the pore structure of MCM-41 the capillary condensation theory3 was applied to determination of pore size distribution. However, besides the classic methods of porosity investigation, some new methods can be useful in throwing light on some properties of the media under study. Recently the positron annihilation lifetime spectroscopy (PALS) has gained rising popularity as a tool in the study of mesoporous media. In this paper we want to discuss the applicability of the positron lifetime method in the case of ordered silica. Positron Annihilation Method The PALS idea consists of measurements of the average ortho-positronium (o-Ps) lifetime. Positron, slowed in the * Corresponding author. Fax: +48 815376191. E-mail: goworek@ tytan.umcs.lublin.pl. † Institute of Physics. ‡ Department of Adsorption, Faculty of Chemistry. (1) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-W.; Olson, P. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (2) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710. (3) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: New York, 1982.
medium, can form positronium, i.e., a bound state with one of the electrons. Such a bound state can exist in two substates depending on mutual spin orientation of the involved particles. Singlet substate (para-Ps) is a shortlived species (0.125 ns), while triplet one (o-Ps), living in a vacuum 142 ns, can inside the medium survive the time depending on the size of free (electron-less) volume in which it is trapped.4 Shortening the o-Ps lifetime in the medium is mainly due to the pick-off process, i.e., annihilation of the positron bound in o-Ps with one of the electrons from the medium of reverse spin orientation instead with its “own” electron. Intrinsic decay of o-Ps occurs with emission of 3 gamma quanta, while in the pick-off process, 2 quanta. The PALS technique has been applied so far to study the sub-nanometer voids in polymers, using the lifetimevolume relation described by the Tao-Eldrup model.5 In 1997 we showed that the method could be extended toward larger free volumes by taking into account the o-Ps annihilation from the excited levels in the potential well in which it is trapped.6 The model was then modified in relation to cylindrical capillaries.7 After the next modification done by Gidley et al.,8 consisting of the assumption of simplified rectangular geometry, the PALS method found application, e.g., to thin porous films being prospective insulators for ULSI circuits.9 The o-Ps decay rate (reciprocal of mean lifetime) λo-Ps is an average over populated states:
λo-Ps )
∑λnmgm exp(-Enm/kT) ∑gm exp(-Enm/kT)
(1)
where λnm, gm, Enm, k, and T are the decay rate from particular nm state, the statistical weight, the energy of (4) Mogensen, O. E. Positron Annihilation in Chemistry; SpringerVerlag: Berlin, 1995. (5) Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51. (6) Goworek, T.; Ciesielski, K.; Jasin´ska, B.; Wawryszczuk, J. Chem. Phys. Lett. 1997, 272, 91. (7) Ciesielski, K.; Dawidowicz, A. L.; Goworek, T.; Jasin´ska, B.; Wawryszczuk, J. Chem. Phys. Lett. 1998, 289, 41. (8) Gidley, D. W.; Frieze, W. E.; Dull, T. L.; Yee, A. F.; Ryan, E. T.; Ho, H.-M. Phys. Rev. B 1999, 60, R5157. (9) Gidley, D. W.; Lynn, K. G.; Petkov, M. P.; Weber, M. H.; Sun, J. N.; Yee, A. F. In New Directions in Antimatter Chemistry and Physics; Surko, C. M., Gianturco, F. A., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001; pp 151-171.
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that state, the Boltzmann constant, and the temperature, respectively. The decay rate λnm is given as
λnm ) λbPnm + (1 - Pnm)λT
(2)
where Pnm is the probability of finding o-Ps in the state labeled nm outside the electron-free void, λb is the hypotetical o-Ps decay rate in the bulk, usually assumed to be 2 ns-1, λT is the o-Ps decay rate in a vacuum, λT ) 0.007 ns-1. The whole lifetime dependence on void size is contained in Pnm; eq 1 introduces also the dependence on temperature. Due to a honeycomb structure of the ordered silica pore system, the most appropriate pore geometry for Pnm calculation seems to be the cylindrical one (infinite cylinder length); in that case we have7
Pnm )
∫ZZ
nm
nmR/(R+∆)
∫0 Z
Jm2(r)r dr/
nm
Jm2(r)r dr
(3)
where Jm(r), Znm, and R are the Bessel cylindrical function, the n-th zero crossing point of that function, and the cylinder radius, respectively; ∆ is an empirical parameter related to the penetration depth of the o-Ps wave function into the bulk. Our estimate for ∆ is 0.19 nm.7 As a rule, the higher the energy level the shorter is the lifetime of o-Ps located in it. In the case of ordered silica we expect only one value of o-Ps lifetime corresponding to a well-defined radius of capillaries. A few attempts to measure the PALS spectra in MCM-41 type materials were rather disappointingsa broad (continuous) distribution of long lifetimes was observed.10 In the paper by Ito et al.,11 the spectrum was processed as a sum of discrete components; thus, instead of a continuous λ spectrum, a series of exponential components was found. However, the data on the composition, structure, and preparation of samples are not given, which makes the discussion of the results difficult (two longest components are surprisingly weak). One of the factors leading to distortion of the spectrum is a slow thermalization of o-Ps. At the moment of trapping the kinetic energy of the positronium atom is equal to the depth of the trapping potential, and then Ps is thermalized due to collisions with the walls. In quantum approach this can be described as cascading down through the series of excited levels. Finally, o-Ps reaches equilibrium with the medium populating the low-lying levels according to the Boltzmann law; eq 1 is valid for the equilibrium state only. However, that initial lack of equilibrium is only one of the possible sources distorting the expected lifetimevolume relation. This and other factors will be the subject of study here. Experimental Section Materials and Sample Characterization. Synthesis of MCM-41 was accomplished using the procedure described in ref 12. n-Hexadecylpyridinium (HDP) chloride was selected as the templating surfactant. Tetraetoxysilane (TEOS) was used as a silica source. Prior to the experiments the sample was heated to 820 K for 5 h (template removal), and next kept at this temperature in oxygen flow during a predetermined time to remove the residual carbon located inside the channels. Ap(10) Goworek T.; Ciesielski, K.; Jasin´ska, B.; Wawryszczuk, J. Mater. Sci. Forum 1997, 255-257, 296. (11) Ito, K.; Yagi, Y.; Hirano, S.; Miyayama, M.; Kudo, T.; Kishimoto, A.; Ujihira, Y. J. Ceram. Soc. Jpn. 1999, 107, 123. (12) Gru¨n, M.; Unger, K. K.; Matsumoto, A.; Tsutsumi, K. In Characterization of Porous Solids, COPS IV; McEnaney, B., Mays, T. J., Roquerol, J., Rodriguez-Reinoso, F., Sing, K. S. W., Unger, K. K., Eds.; The Royal Society of Chemistry: Cambridge, U.K., 1997; p 81.
plication of HDP surfactant guarantees a better structural longrange ordering of the obtained silica in comparison to n-hexadecyltrimethylammonium (HDTMA) bromide template.12 Some supplementary PALS measurements were performed also for MCM-41 material with another length of the alkyl chain (n-octadecyltrimethylammonium bromide template, ODTMA). For short, these two materials, HDP and ODTMA based, will be denoted below, according to the chain length, as C16P and C18. Adsorption-desorption isotherms were measured at liquid nitrogen temperature (77 K), using a Micromeritics ASAP 2010 apparatus. Pore size distribution was calculated from desorption isotherms using the Barrett-Joyner-Halenda (BJH) method.13 The specific surface area SBET was calculated from the BrunauerEmmett-Teller (BET) method over the range of relative pressure between 0.05 and 0.25, taking the cross-sectional area of the nitrogen molecule to be 0.162 nm2. The total pore volume Vp was estimated from a single point adsorption at a relative pressure of 0.985. The carbon content in the sample was estimated using a CHN analyzer (Perkin-Elmer CHN 2400). PAL Spectrometer. The 22Na isotope decaying to 22Ne served as a source of positrons. Since the energy of positrons is high, up to 500 keV, they easily penetrate into the sample and are able to reach closed free volumes inaccessible in the adsorption methods. In PALS measurements the 22Na positron source sealed in a Kapton envelope was placed between two layers of the powder sample, pressed together by a screwed cap inside a small brass container. The container was fixed atop of a copper rod with a heating coil just below the sample holder. The rod served also as a coldfinger of a cryostat, so the sample temperature could be regulated from 93 to over 500 K. The whole sample/source sandwich was kept at a low pressure ≈ 0.5 Pa to avoid conversion of o-Ps into p-Ps on paramagnetic oxygen molecules from the air. Between the chamber and pump there was a liquid nitrogen trap freezing out the vapors. The PALS measurements were performed at 283 K, if not stated otherwise. The positron lifetime spectrometer was a conventional fastslow setup4 with pulse pile-up inspection; scintillators were BaF2 crystals in the geometry excluding the possibility of summing effects. In the time measuring system the start signal was produced by 1274 keV γ-ray following the decay of 22Na, i.e., the positron birth; the stop signal was produced by one of annihilation photons. In porous media an essential number of o-Ps atoms decay into 3 gamma quanta. Their energy spectrum is continuous, extending from 0 to 511 keV; thus, to improve the efficiency of counting the stop energy window in the spectrometer was widely open (80% of the energy range). At such a setting the resolution time was 0.31 ns. The time base of the PALS spectrometer was 2 µs (8000 channels). The number of events collected per spectrum was (5-12) × 106. Data Processing. The time spectrum should contain at least three components: the shortest-lived belonging to p-Ps decay, an intermediate one (less than 1 ns) due to annihilation of free positrons, and the long-lived component belonging to o-Ps. The channel width 0.230 ns makes difficult the separation of the first two components; on the other hand, the long-lived one can be of a complex structure: the o-Ps decay curve is usually not exponential, which corresponds to the distribution of lifetimes s(λ). In our case the spectra were analyzed using the LT program,14 in which the log-Gaussian shape of the decay rate distribution can be assumed:
[
s(λ) ∝ exp -
]
ln2(τpλ) 2σ2
(4)
where τp is the lifetime at the peak of distribution, σ is the distribution width (σ ) 0 for a discrete component). Each component is characterized by three parameters: lifetime, distribution width, and relative intensity. Sometimes it is convenient to describe s(λ) by other parameters: average lifetime τav instead of τp, second-order moment of distribution (variance) (13) Barrett, E. P.; Joyner, L. G.; Halenda, P. H. J. Am. Chem. Soc. 1951, 73, 373. (14) Kansy, J. Nucl. Instrum. Methods Phys. Res., Sect. A 1996, 374, 235.
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σs instead of σ. Respective relations are
τav ) τp exp(σ2/2);
σs2 ) τav2[exp(σ2) - 1]
(5)
If not stated otherwise, in data processing we have assumed the existence of three componentsstwo short-lived were discrete, and the longest-lived one was with lifetime distribution. In some cases the long-lived part was approximated as a sum of two logGaussian distributions (when very long lifetimes appeared). Correction for positron absorption in the Kapton envelope was applied.
Results and Discussion Free Volumes before Pyrolysis. The PALS spectra for raw MCM material still filled with organic template showed characteristic features: the presence of a component with the lifetime of several nanoseconds and the another of a very long lifetime. In C16P that short component had 3.4 ns lifetime and 10% intensity, while in C18 the lifetime was 4.0 ns and intensity of 14%. The longest lived component in both cases had 123 ns lifetime, but the intensity was 4.2% in C16P and 11% in C18. The first of the components mentioned above had the lifetime longer than usually observed in organic solids, defected crystals or polymers. The respective diameter of the free volume in which o-Ps is trapped in C18 reached 0.9 nm. Such voids can be the result of errors in stacking the micellar structure, or they are left after water evaporation. Note that the void diameter is near one-third of the inner diameter of the silica skeleton. When the template is not removed, there are no pores and the longest-lived component can be ascribed to the o-Ps emitted from the bulk to intergrain spaces, owing to a large total external surface of grains (140 m2/g in C18). The size of free intergrain spaces in the maximum of their distribution found by liquid nitrogen desorption measurements was 32 nm. According to the pick-off model in Gidley’s version,7 assuming the positronium free path similar to that in a cube, one receives the expected lifetime of about 127 ns, which is fully consistent with the experimental value. Short-Lived Components. After pyrolysis of the template, the 3-4 ns component (as well as the 123 ns one) disappeared and the only short-lived components were those belonging to p-Ps and to annihilation of free positrons in silica. Free positrons had the lifetime of ≈ 0.66 ns in C16P and ≈ 0.67 ns in C18, longer than that observed in porous silica of comparable specific pore volume (0.480.50 ns).15 The lifetime of free positrons should be roughly inversely proportional to the density of the material of a definite chemical composition; thus such a lifetime lengthening can be evidence of a loose structure of silica skeleton. If inverse proportionality is assumed, the lifetime found in our experiment gives a rough estimate of the density of silica skeleton of about 1.6 g/cm2, similar to that reported by Floquet et al.16 using sorption capacity and neutron diffraction methods. In the skeleton still filled with template (as in the previous section) the observed lifetime of free positrons was shorter, 0.46 ns, as it was an average over the skeleton and organic interior (typical free positron lifetime in organic solids is 0.30-0.35 ns). In classic amorphous silica also a component of a lifetime ≈1.5 ns appears (see e.g. ref 17); it belongs to o-Ps located (15) Huang, Y. M.; Qin, G. G.; Yu, W. Z.; Xiong J. J. Mater. Sci. Forum 1995, 175-178, 391; also the measurements by authors of this paper. (16) Floquet, N.; Coulomb, J. P.; Giorgio, S.; Grillet, Y.; Llewellyn, P. L. Stud. Surf. Sci. Catal. 1998, 117, 583. (17) Hugenschmidt, C.; Holzwarth, U.; Jansen, M.; Kohn, S.; Maier, K. J. Non-Cryst. Solids 1997, 217, 72.
Figure 1. Adsorption/desorption isotherms of nitrogen at 77 K: (circles) C16P decarbonized; (diamonds) “as produced”; (open symbols) desorption; (full symbols) adsorption.
Figure 2. Pore diameter distribution curves for C16P determined by liquid nitrogen sorption method: (dashed line) “as produced” sample; (solid line) decarbonized sample.
in small structural imperfections, about 0.46 nm in diameter (average). In the case of MCM-41 structures, such a component was not detectable. At a wall thickness of ≈1 nm, typical for this kind of material, the defects analogous to those in bulk silica are open to the outside, being rather concavities not able to trap Ps, or are located so close to the surface that positronium, even if initially trapped, escapes to capillaries. Carbon Contamination. The “as produced” material has characteristic brownish hue induced by the presence of residual carbon left in the sample after pyrolysis of the organic template. That carbon can be removed by oxygen flow at high temperatures; as a result a white product is obtained. From the viewpoint of the porosity there are no big differences between white and brown samples. Figure 1 shows adsorption/desorption isotherms of nitrogen at 77 K (the quantity of adsorbed gas is expressed as its volume at standard temperature and pressure (STP)) for C16P samples: as produced and decarbonized. Figure 2 shows pore size distribution curves for the same samples. The results of adsorption/desorption measurements are collected in Table 1. The surface area of the as produced sample was 12% smaller than in the decarbonized one, i.e., still remained large. The pore diameters at the peak
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Table 1. Parameters Characterizing the Pore Structure of Silicas Investigated: Specific Surface Area SBET, Volume of Regular Mesopores Vp, and Pore Radius at the Maximum of Pore Size Distribution Rp sample
SBET, m2/g
Vp, cm3/g
Rp, nm
C16P after pyrolysis C16P decarbonized C18 after pyrolysis C18 decarbonized
1240 1400 1130 1190
0.96 1.18 0.86 0.88
1.24 1.19 1.52 1.52
of distrubution for white and brown samples are very similar. The diameter for the decarbonized sample was found to be even slightly smaller, but one should remember that the error of surface determination is about 10%; moreover, small shrinking during thermal treatment is also possible.18,19 Contrary to adsorption abilities, the PALS method reveals that the lifetime spectrum is very sensitive to the carbon content; the o-Ps part of the lifetime spectrum in “brown” samples was shorter-lived and far from the exponential shape expected for definite R if the pick-off process determines the decay rate. Three examples of such spectra are shown in Figure 3. A systematic study of the spectrum dependence on the carbon content in C16P was undertaken. The burnt-off product was kept in oxygen flow at 770 K during 3 h, 6 h, etc., and the PALS spectra were measured at 283 K. The content of carbon in each sample was determined with a CHN analyzer. A certain initial content of nitrogen (1.9%) was also detected, disappearing after 9 h of treatment. The result of PALS measurements is shown in Figure 4 together with the data on the carbon content. The o-Ps lifetime spectrum shifts toward larger values with the decrease of carbon content and, after ∼16 h of oxygen treatment, transforms into a long-lived discrete component, τo-Ps ) 108 ( 1 ns, supplemented by a low intensity distribution (∼3%) of shorter lifetimes being the result of the o-Ps annihilation events before thermalization. Continuation of oxygen treatment leads to stabilization of the carbon content at the level of about 0.4 ( 0.1%. That part of carbon could not be eliminated. Interaction of o-Ps with carbon deposits leads to its destruction and in effect to shortening the lifetime (quenching). The quenching rate per 1% of carbon can be evaluated as λq1 ) 3.5 × 10-2 ns-1. Note that even at the carbon content of 1% the rate of quenching is by the order of magnitude larger than the intrinsic 3γ annihilation rate λT. The plot of total λq vs carbon content c was linear, but crossing abcissa at c ) 0.4%, thus that nonremovable part of carbon looked as though it was not participating in the processes involving o-Ps. In a conducting medium Ps formation is not energetically favorable; thus, in our case it was formed in silica skeleton and ejected to the pore (or to outside). The pore surface, after template removal, was at least 10 times larger than the external surface of particles; thus the process of Ps emission through the grain surface, dominant in the raw material (with organic template retained), in the final product was of secondary importance. The presence of carbon reduced also the intensity of the o-Ps component. That intensity should be proportional to the fraction of the area uncovered with carbon deposit, and at total carbon covering the intensity of o-Ps should be reduced to nil. (18) Kleitz, F.; Schmidt, W.; Schu¨th, F. Microporous Mesoporous Mater. 2001, 44-45, 95. (19) Di Renzo, F.; Desplantier, D.; Galarneau, A.; Fajula, F. Catal. Today 2001, 66, 75.
Figure 3. Shape of positron lifetime spectra in C16P: (a) “as produced”; (b) after 6 h of oxygen treatment; (c) after 16 h (and more). Background of random coincidences subtracted.
Figure 4. Carbon content and PALS spectrum parameters for C16P sample (o-Ps lifetime, width of the lifetime distribution, relative intensity) as a function of oxygen treatment duration. The spectra for 0, 3, and 6 h decomposed into three components; for 6 h and more, into four components ((dashed lines) third component; (solid lines) fourth component).
Destructive action of conducting deposits, evident in the case of carbon, can also play a certain role in pore capping in thin films8,9,20 by sputtering Al, Ti, and Au. When the pore diameters are of the order of 2-20 nm, the sputtered metal can be sedimented also inside the interconnected pores and shorten the lifetime of o-Ps diffusing along the channels. Continuous change of the lifetime and intensity of o-Ps with carbon removal is an argument supporting the (20) Petkov, M. P.; Weber, M. H.; Lynn, K. G.; Rodbell, K. P. Appl. Phys. Lett. 2000, 77, 2470.
Positron Lifetime in MCM-41 Type Mesoporous Silica
dispersed deposition of carbon. If carbon was localized in the form of a single cluster, one should expect the o-Ps time spectrum with two components only: for carbonless pores and with carbon. For the carbonless free volume we expect 108 ns lifetime (as mentioned above); thus, one can try to analyze the spectrum introducing an additional component with the lifetime fixed at 108 ns. For the samples decarbonated during less than 9 h, nothing longlived can be fitted. Total disappearance of the long-lived component, which was previously seen in the samples containing the template (the intensity over 10%) and originating from the emission of o-Ps to the extragranular spaces, means that carbon after pyrolysis settles also on the external surfaces of grains. Smooth transition from short to long lifetimes correlates with the observation by Gun’ko et al.21 who have found that after pyrolysis carbon is distributed in the form of spots over the whole pore length. Thermalization of o-Ps. Even after thorough removal of carbon the long-lived part of the spectrum was not exactly exponential. This can be the result of distribution of pore radii or lack of thermal equilibrium Ps - bulk (lack of thermalization). In ordered silica there should be no distribution of radii and the effect should be ascribed to incomplete thermalization. The presence of “hot” ortho-positronium can be detected by the method proposed by Fox and Canter.22 It consists of analyzing the long-lived part of the spectrum only and changing the initial point of the analyzed range. We have analyzed the tail of the spectrum as one component with the distribution of λ. As long as this part of the spectrum contained the decays of nonthermalized positronium, a surplus of counts appeared in the small delay region and the LT program fitted the distorted exponential with nonzero σ. The initial point D of the analyzed part (spectrum cutoff point) was shifted toward larger delays, and the average lifetime and σ were determined. At a sufficiently large D the width σ reached zero; i.e., one discrete component only was observed (at very long lifetimes the τ dependence on radius is very weak and σ close to 0 can be observed even when there is a moderate distribution of radii). The delay D0 at which the spectrum becomes exponential (σ ) 0) is a measure of thermalization time.23 The lower the temperature, the longer is the delay time to observe the discrete component. With moving the beginning of the analyzed range D forward, and hence deterioration of the signal-to-background ratio, the value σs becomes very sensitive to the background estimate and is therefore not precisely reproducible from sample to sample. However, the tendency of changes with temperature and the time scale of the thermalization process was in all cases the same (the lifetime value did not show such sensitivity). An example of σs vs D dependence for three distinctly different temperatures is shown in Figure 5 for the case of C16P. At 93 K the decrease of σs in the reticular structure of MCM-41 occurred very slowly; D0 was ≈160 ns. In C18 it was still longer; in that case the processing of the whole spectrum (assuming four components) gave also the longest-lived component with nonzero σ. That correlates (21) Gun’ko, V. M.; Leboda, R.; Skubiszewska-Zie¸ ba, T.; Turov, V. V.; Kowalczyk, P. Langmuir 2001, 17, 3148. (22) Fox, R. A.; Canter, K. F. J. Phys. B 1978, 11, L255. (23) This definition of thermalization time is specific for the method applied here and does not coincide with the definitions used by: Dauwe, C.; Consolati, G.; Van Heocke, T.; Segers, D. Nucl. Instrum. Methods Phys. Res., Sect. A 1996, 371, 497 (the rate of transition from initial to final value of λ for long-lived component). Or by: Chang T.; Xu, M.; Zeng, X. Phys. Lett. A 1987, 126, 189 (time of decrease of the Ps energy below 0.1 eV).
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Figure 5. Width of lifetime distribution σs in C16P fitted by LT program as a function of spectrum cutoff point at various temperatures: (a) 93 K; (b) 283 K; (c) 473 K.
Figure 6. o-Ps lifetime vs radius of cylindrical pore at 283 K, calculated from eqs 1-3. Vertical dashed line indicates the pore radius from LN adsorption measurement for C16P sample. In the calculations the 50 lowest energy levels of Ps in the potential well are taken into account.
with the observation by Mills et al.,24 who found that only 2% of Ps escaping from ultrafine SiO2 powder at 4.2 K was thermalized. o-Ps Lifetime in Ordered Silica. In the decarbonized sample the lifetimes of the long-lived component at 283 K were found to be 116 and 108 ns, for C18 and C16P, respectively. The expected lifetimes can be calculated from the pick-off model for cylindrical pore structure (eqs 1-3), assuming the radii determined in LN adsorption measurements. In the case of our MCM-41 with rather narrow pores, at temperatures near 300 K it is sufficient to perform summation in (1) over several lowest states; the population of others is negligible. Figure 6 shows the τ vs R curve for 283 K. It is seen that the calculated lifetimes τo-Ps are drastically different from those observed in the experiment. Elongation of the average lifetime was observed in thin porous films8,9,20 as a result of the escape of o-Ps atoms from the pores to outside. If migration to the outside occurs, (24) Mills, A. P., Jr.; Shaw, E. D.; Chichester, R. J.; Zuckerman, D. M. Phys. Rev. B 1989, 40, 2045.
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and the reverse (return to the grains) can be neglected, one can apply the well-known two-state model.25 According to that model the splitting into two components should be observed: for positrons annihilating in the pores and outside of them. The decay rate λin for o-Ps in the pores is
λin ) λo-Ps + K(t)
(6)
where K is the rate of transition from pore to extragranular free volume. If K was constant, the eq 6 would mean only the shortening of the lifetime; time dependent K leads to nonexponential decay (average lifetime is also shorter than expected from the pick-off models). The value of λout in extragranular spaces is determined by the size of voids between the grains and does not depend on pore dimensions. The rate λout should be equal to that observed in raw material with the skeleton still filled with organic molecules, i.e., 123 ns. In the case of our decarbonized C16P and C18 samples, practically only one long-lived component was found; its lifetime was as given above 108 and 116 ns, respectively. The lifetimes were slightly shorter than those observed in raw material, but small modification of the particle sizes is possible during pyrolysis and drying, and thence also of the spaces between them. The sizes of porous particles can be estimated in our case as 50-120 nm, while, according to the measurements by Jun Xu et al.,26 o-Ps can escape from the depths up to ≈1 µm so practically entirely diffuses to the outside. The intensity of that component was about 44% of all annihilation events (see Figure 4), very high as compared to raw samples; it means that Ps is really formed inside pores and then migrates out. The effect of Ps escape is not visible in classic porous media due to the much greater length of pores produced, e.g., by etching relatively big grains. In Vycor glass even at short etching time (20 min) in cold acidic batch one obtains the etched channel length ≈25 µm.27 To collect more information on the longest component, the temperature dependence of its lifetime was observed. The spectra were measured from 98 to 473 K; the lifetime at large delays (from 90 ns upward) is shown in Figure 7. The values for two samples from separate production batches were identical. The decrease of lifetime at temperatures above 270 K corresponds rather well to that calculated for a cube with a side ≈ 30 nm; however, at low temperatures it tended to a saturation. If the discussed component is produced by o-Ps outside the grains, there should be distribution of void sizes and hence also of lifetime, while the experiment gave σ ) 0. The two latter effects still need explanation. Following the practice by Gidley et al.8,9 and others28 we tried to close the outlets of pores in order to reduce the fraction of o-Ps escaping to the outside. Well-decarbonized MCM-41 was covered with Sephadex G200 resin (molecular weight 2000-100 000; production Pharmacia Fine Chemicals AB) from water solution. The samples were dried 3 h at ≈370 K, and drying was continued inside a PALS chamber under vacuum. Some positrons annihilated in the resin layer; however, the e+ lifetime spectrum in Sephadex G200 contained a 1.66 ns component as the (25) Eldrup, M.; Pedersen, N. J.; Sherwood, J. N. Phys. Rev. Lett. 1979, 43, 1407. (26) Jun Xu; Moxom, J.; Shu Yang; Suzuki, R.; Ohdaira, T. Submitted for publication in Chem. Phys. Lett. (27) Jasinska, B.; Dawidowicz, A. L.; Goworek, T. Radiat. Phys. Chem. 2000, 58, 723. (28) Uedono, A.; Zhi Quan Chen; Suzuki, R.; Ohdaira, T.; Mikado, T.; Fukui, S.; Shiota, A.; Kimura, S. J. Appl. Phys. 2001, 90, 2498.
Figure 7. Temperature dependence of the longest lifetime in C16P sample. The size of the symbols corresponds to the limits of uncertainity.
longest-lived one, thus not disturbing the spectrum part related to the pores. The only effect was reduction of the total long-lived part intensity (the mass of resin layer was about one-fourth that of silica). The PALS spectra of such samples showed that the covering was by far incomplete as a quite strong long-lived component still existed. The lifetime of that component was almost identical with the components for uncovered samples. This can be the result of evaporation of water, which was initially present in the pores, and then going out can reopen some of them. Also the thickness of the resin layer can be far from uniform, leaving some fragments uncovered. A new component appeared in such a spectrum; its intensity was approximately 85% that of the longest lived. Its average lifetime in C16P was 35.4 ( 0.6 ns, variance 31.2 ( 0.6 ns. The average lifetime was very close to that expected for o-Ps in the pores (the cylindrical model gives 35.6 ns), but the width of distribution was very large. Even if o-Ps resides in the pores, there are still further factors which influence the observed lifetimes. It cannot be excluded that some pores still contain water molecules. The walls separating the pores can contain imperfections, openings allowing o-Ps transitions from pore to pore. de Broglie wavelength of thermalized Ps is larger than silica skeleton thickness, allowing tunneling between the pores. Baugher et al.29 have shown that, even in high porosity media, the tunneling is strongly reduced due to mismatching the energy levels in potential wells differing in radius. This blocking of tunneling, obvious in the media with broad distribution of pore radii, does not work in ordered silica, where all pore channels are essentially identical. Conclusions The positron annihilation methods were successfully applied to the study of such porous materials as liquated and etched Vycor glass, porogen loaded thin films, and silica gels. The experiments performed in this work indicate that in the case of ordered silica in the form of sub-micrometer grains the situation is much more complex. One of the most important factors distorting the positron lifetime spectrum is residual carbon left in the sample when the template is removed by pyrolitic method. (29) Baugher, A. H.; Kossler, W. J.; Petzinger, K. G. Macromolecules 1996, 29, 7280.
Positron Lifetime in MCM-41 Type Mesoporous Silica
At least 16 h of oxygen treatment at 770 K is needed to obtain stable and reproducible spectrum parameters; higher temperature can cause partial loss of structural ordering.18 Positronium destruction on conducting surfaces can thus have a certain influence also on the lifetimes when the pores are capped by metal sputtering. Carbon deposits can be easily detected by PALS, while classic sorption methods are practically insensitive to its presence. Slow thermalization effects can be minimized by analyzing only a part of the o-Ps spectrum at large delays and performing the measurements at a relatively high temperature. In highly dispersed porous media like MCM-41 in the form of sub-micrometer grains the relation between the pore size and o-Ps lifetime cannot be described by simple pick-off models. The dominant effect is o-Ps escape to the outside due to small pore length. The PALS technique could give quantitative information on pore diameters if the materials were prepared in larger blocks or layers of
Langmuir, Vol. 19, No. 7, 2003 2605
parallel tubes on a substrate; the grain sizes have to exceed the expected path of o-Ps migration. The temperature dependence of the longest lifetime does not always follow the predictions. The mechanism of the spread of lifetimes in the pores closed by the insulating Sephadex layer is unknown to us. The lifetime of free positrons in the MCM-41 type material is longer than usually observed in porous silica, which allows one to make a rough estimate of the density of silica skeleton. Acknowledgment. The authors wish to thank MSc. Ryszard Kusak for preparation of the sample technology and production and Dr. Antoni Hoffman for carbon content measurements. This work was partly supported by Polish KBN Grant 7 T09A 055 21. LA020280R
