Positronium lifetime spectroscopy

For subnanometer free volumes, the Tao-Eldrup model [33] is conventionally used to relate positron lifetime to free-volume size. For nanometer pores as studied here, Gidley s model [23, 24] was used to relate the positron lifetimes to pore sizes. The 47-ns lifetime for the F88 copolymer-generated porous film yields a diameter pore size of 3.7 nm if the pores are assumed to be a closed sphere, while the 54-ns lifetime for the PI03 copolymer-generated film corresponds to a diameter pore size of 4.3 nm. It is pointed out that future work is needed to relate positronium lifetimes and pore sizes, especially for uncapped films, since positronium lifetimes of those samples include contributions from both closed and open pores. 

Porogen Molecular Mass PEO mass fraction (%) Lps (nm) x0.Ps(ns) Uncapped D (nm) Xo-Ps (ns) Capped 

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Positronium lifetime spectroscopy is particularly well suited for stud)hng defects in crystals and structural fluctuations in amorphous materials and can give an estimate of free volumes in condensed matter [116]. It is a useful technique to estimate the free volume of polymeric membranes [117]. In a study on silica gels, the decay lifetime has been found (Fig. 4.16) to be proportional to the pore diameters (measured by N2 adsorption) between 30 and 100 A [118]. Information on pore size distribution and surface area may also be obtained by means of calibration curves. 

Positron annihilation spectroscopy (PAS) was first applied to investigate [Fe(phen)2(NCS)2] [77]. The most important chemical information provided by the technique relates to the ortho-positronium lifetime as determined by the electron density in the medium. It has been demonstrated that PAS can be used to detect changes in electron density accompanying ST or a thermally induced lattice deformation, which could actually trigger a ST [78]. 

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. 

In this chapter we consider the physics of the positronium atom and what is known, both theoretically and experimentally, of its interactions with other atomic and molecular species. The basic properties of positronium have been briefly mentioned in subsection 1.2.2 and will not be repeated here. Similarly, positronium production in the collisions of positrons with gases, and within and at the surface of solids, has been reviewed in section 1.5 and in Chapter 4. Some of the experimental methods, e.g. lifetime spectroscopy and angular correlation studies of the annihilation radiation, which are used to derive information on positronium interactions, have also been described previously. These will be of most relevance to the discussion in sections 7.3-7.5 on annihilation, slowing down and bound states. Techniques for the production of beams of positronium atoms were introduced in section 1.5. We describe here in more detail the method which has allowed measurements of positronium scattering cross sections to be made over a range of kinetic energies, typically from a few eV up to 100-200 eV, and the first such studies are summarized in section 7.6. 

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. 

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. 

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... 

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. 

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. 

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... 

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 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 investigation of pores in solids, the positron annihilation lifetime spectroscopy (PALS) uses a very small probe - the positronium atom, which is a boxmd state of positron and electron. The lifetime of the positronium triplet state (ortho-positronium, o-Ps) in the matter is... 

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. 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

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