Positron annihilation spectroscopy theory

Reaction with a polymerizable mixture, giving nanofibers covalently attached to the polymer, has also been studied [155]. Different techniques, including dynamic mechanical analysis and positron annihilation spectroscopy show that interaction at the nanofiber-polymer interface produces radical changes in the glass transition of the material. The effect of the addition of cellulose nanocrystals on the properties of a polyurethane matrix are theoretically described by the free volume theory. 

Apart from the theoretical approaches, electronic energy spectra of carbides and nitrides have been studied using a variety of experimental techniques X-ray emission and photoelectron spectrosopy, optical and Auger spectroscopy, electron energy loss and positron annihilation spectroscopy, etc. However, interpretation of the results obtained requires, as a rule, use of the computational methods of the band theory of solids and quantum chemistry. Moreover, the data provided by theoretical methods are important by themselves, because they give much more detailed information on the electron states and chemical bonding than any of the experimental methods. They also allow us to model theoretically... 

In particular, the most powerful method for studing lattice defects, due to the high sensitivity of positrons to open volume defects such as vacancies, vacancy clusters, voids, dislocations, grain boundaries, etc., is positron annihilation spectroscopy (PAS). A diagram illustrating the applicability of PAS and other techniques as a function of defect size and density versus depth in material is shown in Figure 4.25. Thus, PAS represents a non-local experimental technique that is sensitive to microstructural defects at the atomic scale. A well-established theory of positron annihilation phenomena is currently available. Especially for metallic materials, it is possible to perform ab initio calculations of positron parameters for various defects and atomic arrangements [72,73]. 

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. 

Consolati, G., Quasso, R, Simha, R., and Olson, G. B., On the relation betwen positron annihilation lifetime spectroscopy and lattice-hole-theory free volume, J. Polym. Sci. B, 43, 2225-2229 (2005). 

The free-volume concept dates back to the Clausius [1880] equation of state. The need for postulating the presence of occupied and free space in a material has been imposed by the fluid behavior. Only recently has positron annihilation lifetime spectroscopy (PALS see Chapters 10 to 12) provided direct evidence of free-volume presence. Chapter 6 traces the evolution of equations of state up to derivation of the configurational hole-cell theory [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971], in which the lattice hole fraction, h, a measure of the free-volume content, is given explicitly. Extracted from the pressure-volume-temperature PVT) data, the dependence, h = h T, P), has been used successfully for the interpretation of a plethora of physical phenomena under thermodynamic equilibria as well as in nonequilibrium dynamic systems. 

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... 

Free volume present in nanocomposite systems plays a major role in determining the overall performance of the membranes. Positron annihilation lifetime spectroscopy (PALS) is an efficient technique used for the analysis of free volume. The diffusion of permeant through polymeric membranes can be described by two theories, namely, molecular and free-volume theories. According to the free-volume theory, the diffusion is not a thermally activated process as in the molecular model, but it is assumed to be the result of random redistributions of free-volume voids within a polymer matrix. Cohen and Turnbull developed the free-volume models that describe the diffusion process when a molecule moves into a void larger than a critical size, Vc- Voids are formed during the statistical redistribution of free volume within the polymer. It is found that the relative fractional free volume of unfilled polymer decreases on the addition of layered silicates. The decrease is attributed to the interaction between layered silicate and polymer because of the platelet structure and high aspect ratio of layered silicates. The decrease is explained to the restricted mobility of the chain segments in the presence of layered silicates. This results in reduced free-volume concentration or relative fractional free volume [49]. 

---