Positronium annihilation lifetime

The progress in the determination of porosity of various types of materials has arisen over the past ten years from advances in application of new spectroscopy techniques. In the present paper the application of small angle X-ray scattering (SAXS), positronium annihilation lifetime spectroscopy (PALS) and low temperature nitrogen adsorption methods to the characterization of mesoporosity is reviewed using different types of silica gels with chemically modified surface. The results from the three methods are compared and discussed. 

Kilburn, D., Wawryszczuk, J., Dlubek, G., Pionteck, J., Hassler, R., and Alam, M. A., Temperature and pressure dependence of the free volume in poly isobutylene from positron lifetime and pressure-volume-temperarnreexperiments,Macromol. Chem. Phys., 207,721-734(2006b). Kim, S. H., Chung, J. W., Kang, T. J., Kwak, S.-Y, and Suzuki, T., Determination of the glass transition temperature of polymer/layered silicate nanocomposites from positronium annihilation lifetime measurements. Polymer, 48, 4271-4277 (2007). 

Positronium Annihilation Lifetime Spectroscopy. Positron annihilation lifetime spectroscopy (pals) is primarily viewed as techniqne to parameterize the imoccnpied volnme, or so-called free volume, of amorphous polymers. In vacuo, the ortho-positronium (o-Ps) has a well-defined lifetime T3 of 142 ns. This lifetime is cut short when o-Ps is embedded in condensed matter via the pick-oflT mechanism whereby o-Ps prematurely annihilates with one of the surroimding boimd electrons. The quantum mechanical probability of o-Ps pick-off annihilation depends on the electron density of the medium, or the size of the heterogeneity. Typically the heterogeneity is assiuned to be a spherical cavity (164,165) so that T3 can be easily related to an average radius R (Ro = R -i- AR) of the nanopore ... 

Free volume or hole volume is ostensibly measured experimentally by positronium-annihilation-lifetime spectroscopy (PALS). In organic glasses, including amorphous polymers, the ortho-positronium (o-Ps) bound state of a positron has a strong tendency to localize in heterogeneous regions of low electron density. In vacuo, an... 

The positronium annihilation lifetime spectroscopy was successfiilly applied to the study of pore structure of the as-synthesized sample of MCM-41. The PALS technique can supply information about imperfections in the template structure as well as silica walls of MCM-41. The interior of cylindrical micelles encaged in the silica skeleton exhibits the presence of some kind of defects which disappear when pressure of argon increases. Howeva-, small voids present in the walls of silica network are resistant to compression and their dimensions are independent of pressure. Under mechanical pressure one can observe total destruction of interparticle pores at about 140 MPa. However, small voids in the sample are present up to 450 MPa. Temperature treatment leads to quite different effects than those observed for pressure experiment. 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

Since the earliest work with positronium by Deutsch and coworkers (e.g. Deutsch, 1951 Deutsch and Brown, 1952) its annihilation lifetimes, or decay rates, have been studied both theoretically and experimentally. 

The p-Ps has a shorter lifetime than o-Ps and it annihilates into two photons, while o-Ps annihilates into three photons. The intrinsic lifetime is 0.125 ns and 142 ns for the free p-Ps and o-Ps, respectively. In ordinary molecular media, the electron density is low enough so that Ps can pick off electrons from the media that have anti-parallel spin to that of the positron, and undergo two-photon annihilation. This is called the pick-off annihilation of Ps. The pick-off annihilation of o-Ps not only occurs in the form of two-photon annihilation, it also shortens the o-Ps lifetime from 142 ns (free o-Ps) to a few ns. The pick-off annihilation lifetime of o-Ps in molecular systems is about one order of magnitude greater than in crystalline or metallic media. Experimental determination of o-Ps lifetime is one of the most useful methods for positron and positronium chemistry. This is because o-Ps lifetime contains information about electron density, which governs the basic properties of chemical bonding in molecules. It is also controlled by the physical structure of molecules. 

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 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 aim of this chapter is to introduce the reader to the application of positron annihilation techniques to polymers. An extensive review of the large volume of publications related to positron studies in polymers will not be presented. Rather it is intented to introduce the reader to the theory and techniques used in polymer studies and indicate the types of information that can be obtained about different polymer systems. The main focus of this chapter will be on the use of positron annihilation lifetime spectroscopy (PAL) in polymer studies. Chapter 11 discusses the use of monoenergetic slow positron beams used to study polymers surfaces. One of the interesting new developments in the application of positron annihilation techniques in polymers is the positron age-momentum correlation technique (AMOC). This technique promises to shed new light on the mechanisms of positronium formation and annihilation in polymer systems. A more detailed discussion of this technique can be found elswhere in this text. 

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... 

Dlubek, G., Eichler, S., Hiibner, Ch., and NageL Ch., Reasons for the deviation of Iff and x from the expected lifetime parameters of positronium annihilation in polymers, Nucl. Instrum. Methods Phys. Res. B, 149, 501-513 (1999a). 

Two series of cellulose samples, Avicel and Whatman CFll cellulose ball-milled powders with different crystallinity are studied below Tg temperature by using positron annihilation lifetime spectroscopy. A good correlation is found between ortho-positronium formation probability and crystallinity as measured by Fourier transform -infrared spectroscopy. Sub-nanometer hole distributions are found to be narrowed as a function of milling time. These are interpreted in terms of microstructural changes of cellulose. 

In recent years, positron annihilation lifetime (PAL) spectroscopy has been demonstrated to be a special sub-nanometer probe to determine the free-volume hole size, fraction and distribution in a variety of polymers (4-9). In this technique, measured lifetimes and relative intensities of the positron and positronium, Ps (a bound atom which consists of an electron and a positron), are related to the size and fraction of sub-nanometer holes in polymeric materials. Because of the positive-charge nature, the positron and Ps are repelled by the ion core of polymer molecules and trapped in open spaces, such as holes, free volumes, and voids. The observed... 

Reaction of a positron with an electron gives a metastable positronium (Ps) particle, which may have antiparallel spins (para-positronium, p-Ps) or parallel spins (ort/jo-positronium, o-Ps). Within a polymer, the longer lifetimes of o-Ps may be related to the size, concentration and distribution of free volume elements. There have been a number of studies of PIM-1 by positron annihilation lifetime spectroscopy (PALS) [33-36]. 

Positron annihilation lifetime spectroscopy (PALS) studies the lifetime spectrum of ortho-positrons after being injected into the sample [3,4]. This lifetime depends on the probability of the ortho-positronium (o-Ps) particle (a hydrogen-like bound state formed by a positron-electron pair) to be quenched and annihilate. This probabihty is higher in condensed matter than in vacuum. Of all the probe methods PALS is nowadays probably the most versatile one and the most widely used. The o-Ps particle is the smallest probe available and can thus detect the smallest free volume elements furthermore, the method furnishes information on the average free volume size and on the FV size distribution. 

A certain fraction of these positrons, however, may enter the bound state of the positronium (Ps), by combining with an electron. Ps can be formed in two ground states either in the triplet or ortho state, with parallel spin orientation and an intrinsic average annihilation lifetime of 1.4 x 10" s, or in the singlet or para state with antiparallel spin orientation, which has an intrinsic average lifetime of 1.25 x 10"l s (Fig. 3). 

Positron Annihilation Lifetime Spectroscopy (PALS) provides a measure of free volume holes or voids, free volume, and free volume distribution, at an atomic scale. The technique exploits the fact that the positively charged positron (e" ), the antiparticle to the electron, preferentially samples regions of low positive charge density. When injected in a polymer matrix, thermalized positrons can combine with an electron to form a bound state, known as positronium (Ps). This species can only exist in a void and it rapidly annihilates on contact with the electron cloud of a molecule. For polymer studies using PALS, it is ortho-positronium (oPs, a triplet state) which is of interest. The oPs spin exchanges with electrons of opposite spin on the walls of the cavity and it is annihilated. Thus, the oPs lifetime, 13, gives a measure of the mean free volume cavity radius, whereas the relative intensity of... 

Positron annihilation lifetime spectroscopy (PALS) is normally applied to determine the free volume properties of a cured thermoset. The theory and methodology of PALS [27, 28] is briefly described next. The positron, an antiparticle of an electron, is used to investigate the free volume between polymer chains. The birth of the positron can be detected by the release of a gamma ray of characteristic energy. This occurs approximately 3 ps after positron emission when the Na decays to Ne. Once inside the polymer material, the positron forms one of the two possible types of positroniums, an ort o-positronium or a p(3 ra-positronium, obtained by pairing with an electron abstracted from the polymer environment. The decay spectra are obtained by the death event of the positron, pi ra-positronium or ort o-positronium species. By appropriate curve fitting, the lifetimes of the various species and their intensity can be determined. The lifetime of an ort o-positronium (Xj) and intensity (I3) have been found to be indicative of the free volume in a polymer system because this is where the relevant species become localised. X3 is related to the size of the free volume sites and I3 to their number concentration. The free volume properties of difunctional and multifunctional epoxies are shown in Table 3.5. The data clearly... 

The positron annihilation lifetime spectroscopy provides the information on free volume size and their concentration in porous solids independently if they are open and closed inaccesible for odsorptives. Ortho-positronium (o-Ps) forms in free volumes and its pick-off annihilation probability depends on free volume size. o-Ps lifetimes are related to free volume size in the way described by the extended Tao-Eldrup model (ETE) [11). The intensities of respective spectrum components depend on free volume concentration. 

For investigated MCM-41 samples with polymer coating there can be found three ortho-positronium components, which can be identified as positronium annihilation in the polymer structure (lifetimes 2.5 ns, short spectrum component, SSC), inside the pores (20-40 ns, medium spectrum component, MSC) and outside the grains (100-110 ns, long spectrum... 

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