Annihilation pores

PALS is based on the injection of positrons into investigated sample and measurement of their lifetimes before annihilation with the electrons in the sample. After entering the sample, positron thermalizes in very short time, approx. 10"12 s, and in process of diffusion it can either directly annihilate with an electron in the sample or form positronium (para-positronium, p-Ps or orto-positronium, o-Ps, with vacuum lifetimes of 125 ps and 142 ns, respectively) if available space permits. In the porous materials, such as zeolites or their gel precursors, ort/zo-positronium can be localized in the pore and have interactions with the electrons on the pore surface leading to annihilation in two gamma rays in pick-off process, with the lifetime which depends on the pore size. In the simple quantum mechanical model of spherical holes, developed by Tao and Eldrup [18,19], these pick-off lifetimes, up to approx. 10 ns, can be connected with the hole size by the relation ... 

Several versions of positronium annihilation measurements are sensitive to the differences between open and closed porosity. The detection geometry, the annihilation types and the lifetime change when closed pores with no... 

The 3-to-2 photon ratio technique observes the ratio of 3 versus 2 photon annihilations of positronium (and positrons). In vacuum positronium will annihilate via 3-photon decays only. Trapped inside closed pores, both annihilation paths are possible. This change can be used to detect the onset of open porosity as shown in Figure 7.2. A change in slope (the slope is shown as a solid line) occurs at about 23% porogen load, indicative of an increased likelihood for positronium to escape from the sample. 

The ratio of 3-to-2 photon annihilations is not only a measure for open porosity it also changes with the concentration of pores and their size. A typical ratio measurement can be performed in several seconds on standard... 

Roughly speaking, 3-to-2 photon annihilation ratio measurements can be considered as a BET technique, which is sensitive to both open and closed pores. Positronium can be considered as the smallest atom possible. No pore will be too small. Positrons are implanted rather than adsorbed and forms positronium. Positronium annihilates into 2 or 3 photons from within pores, or into 3 photons only after escape (desorption) out of the sample through open porosity. In addition, depth dependent information can be provided. 

Positronium can pick-off an electron during a collision with a pore wall and annihilate into two photons. Between collisions, only three photon annihilations occur, just as in vacuum. Quantum mechanically, the overlap with the wall-electron wave functions decreases with the distance from the wall and pick-off (two photons) becomes less likely. With increasing pore size collisions become less frequent. The ratio of 3 photon annihilations to 2 photons probes the combination of pore size and total pore volume as well as their link to the sample surface, and can be measured by examining the energy distribution of annihilation photons. This 3-to-2 photon ratio can be calibrated to absolute fractions of positronium in the annihilation spectrum [16, 17]. 

Figure 7.5 3-to-2 photon ratio when considering the diffusion length, the formation probability and the increased chance for three-photon annihilation in larger pores. 

It turns out that the positronium signal from the pores is very small and quite comparable to MSSQ with less than 10% porogen. Either positronium rarely forms and traps the pores, or the positronium-wall interaction is much stronger and causing pick-off annihilation within a few bounces, rather than thousands of bounces as in the case of MSSQ. 

As can be seen in Figure 7.15 very different lifetimes occur and each dataset shows different lifetimes. In principle the sample material and the size distribution of pores and the open porosity component each generate an annihilation rate (f ) with some relative intensity (I ). The spectrum is then convoluted with the experimental response function (R). Random statistical noise and a certain background (B) level are added. The measured time spectmm M(t)... 

The 2 dominant components are due to the annihilation of positrons in the sample MSSQ material independent of pores ( 0.5 ns) para-positronium (-0.1 ns). Ortho-positronium annihilations in the MSSQ cage structure occur with a -4 ns lifetime. Lifetimes of 10 ns and greater are due to positronium in pores and tend to increase with increasing porogen load. Open porosity is associated with a lifetime of -100 ns (80% case, dashed line). 

Figure 7.20 Lifetime results versus porogen load shown on three separate time scales. The shortest lifetimes on the bottom frame are due to annihilations of positrons and positronium in the MSSQ material. The middle frame shows the positronium annihilations from closed pores and from open pores in the top frame. Statistical errors are shown or smaller than the symbols. See text.

Figure 7.21 Intensities corresponding to the lifetimes shown in figure 7.20. The intensities associated with positrons and positronium annihilation in the MSSQ matrix are shown in the bottom panel and the positronium annihilations (ortho positronium) from pores and open porosity in the top panel. The line-and-star in the bottom panel indicates 1/3 of the sum of all ortho positronium annihilations. Statistical errors are shown or smaller than the symbols. See text.

The 3-to-2 photon technique, simple counting setups and, possibly mean lifetime measurements could fulfill these criteria. A simple setup, shown schematically in Figure 7.28, is suitable for the first two applications. Positrons are implanted into the sample. Focusing into micron-sized areas is possible. Positronium forms, traps in pores and annihilates in closed pores or escapes through open porosity. Two detectors, one behind the sample and a second with an aperture on the side, observe all positronium (and positron) annihilations and only those from within the sample, respectively. The former detector is also set up to provide 3-to-2 photon ratios. 

For future high-speed microelectronic devices, copper interconnection with low dielectric constant (low-k) interlayer films is required to decrease RC (R interconnect resistance, C interlayer dielectric capacitance) delay. Recently, porous Si02 and silica-based films, developed for low-k films, have been extensively studied by positron annihilation spectroscopy [28], [29], [19]. Since Ps formation occurs with high probability, and the o-Ps annihilate via pick-off process in Si02-based materials, positron annihilation spectroscopy (especially PALS) gives useful information on the size of the pores. 

Positronium formation and annihilation behavior in Si and Si02 thin films are reviewed. Positronium is highly sensitive to pore (or void) sizes, surface properties of pores, defects near pore surfaces, etc., in various Si and Si02 samples. Therefore, not only positron annihilation spectroscopy but also positronium annihilation spectroscopy is useful for characterization of Si and Si02 materials. 

Suzuki, R., Ohdaira, T., Shioya, Y. and Ishimaru, T. (2001) Pore characteristics of low-dielectric-constant films grown by plasma-enhanced chemical vapor deposition studied by positron annihilation lifetime spectroscopy , Jpn. J. Appl. Phys. 40, L414. 

Pore dimensions can be determined also by positron annihilation lifetime spectroscopy (PALS). Positron in a solid can create a bound structure with an electron, called positronium (Ps). Its triplet state (ortho-Ps) has an intrinsic lifetime in vacuum 142 ns, but when trapped in a free volume, like a pore, it lives shorter. The o-Ps lifetime is... 

This technique, firstly applied to metals and ceramics, has become a popular tool in polymers science for the determination of free volume [4,6-8] and starts to be applied to carbonaceous materials [9-12], Positron studies of porous materials have been predominantly oriented towards the chemical interaction of positrons with gases filling the porosity or with molecular layers adsorbed on the pore surface. Few studies have focused in the relation between annihilation characteristics with pore size and pore size distribution. Only in same cases, the annihilation time and the pore size have been directly related, and most of these studies have been carried out with silica gels [5,13,14], although other materials like porous resins (XADS) [15] have also been studied. In all these studies, it has been observed that the lifetime of positrons (t) increases with pore width. 

In the present work, positron annihilation lifetime spectroscopy has been applied to characterize the porosity of activated carbons fibers. These materials are essentially microporous [16], with slit shaped pores and with a homogeneous pore size distribution. Because of that, they seem to be the most appropriate materials to analyze the application of PALS technique to the characterization of porous carbon materials. 

Regarding the intensity, the higher value corresponds to the intermediate component, ti, which represents approximately the 90% of the total intensity. This agrees with the results obtained in previous studies carried out with porous carbons [12] and carbon fibers from mesophase pitch [11]. In the first study [12] only the intermediate component (ti) was found from the lifetime spectrum. These results indicate that, in carbon materials with high surface area, most of the positron annihilation takes place on the surface of the porosity. In the second case [11], i.e., PALS in carbon fibers, two components in the lifetime spectrum were found. The first component with high intensity (97%) and lifetime of 367 ps was attributed to positron annihilation in pores. The second one with a lifetime of 1130 ps corresponds to the annihilation of positronium atoms (i e., o-Ps). 

Almost a linear dependence between pore size and positrons lifetime can be observed which was not clearly obtained in previous studies. This relationship is expected because when the pores are wider the probability of interaction between the positrons and the surface electron density in the pore walls decreases. This results in a lower rate of positrons annihilation with the surrounding electrons and then a higher lifetime. A simple model for the annihilation process can be constructed assuming that the positron is trapped in a spherical pore of radius R of constant potential. The resolution of the Schroedinger equation shows that the lifetime of positrons is a function of R [5]. 

Activated carbon fibers essentially microporous and with well-developed porosity have been used to asses the suitability of PALS to characterize microporous carbons. The lifetime spectra of the ACFs present two components. The first one with lifetime Ti = 375-395 ps corresponds to the annihilation of positrons with electrons at the surface of the pores. The second component with lifetime T2 = 1200-1900 ps corresponds to the annihilation of o-Ps. 

Good correlations have been found between this new technique and others typically used to characterize porous materials (i e., SAXS and gas adsorption). The results obtained show a direct relationship between positrons lifetime and pore size. An increase of pore size produces an increase in the positron lifetime Additionally, PALS is sensitive to structural changes produced during CO2 and steam activation. Thus, the annihilation mechanism which is favoured with increasing the burn-off is different depending on the activating agent... 

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