Encyclopedia of Membranes

2016 Edition
| Editors: Enrico Drioli, Lidietta Giorno

Free Volume Element

  • Yuri Yampolskii
Reference work entry
DOI: https://doi.org/10.1007/978-3-662-44324-8_251

Free volume element (FVE) (synonyms: microcavity, hole) is a conditional notion used for description of free volume in polymers (mainly in glassy polymers). Thus, in the positron annihilation lifetime spectroscopy (PALS) (Shrader and Jean 1988; Bartos 2000), it is defined as a sphere with the diameter R estimated using the Tao-Eldrup equation (Tao 1972; Eldrup et al. 1981) via the o-positronium lifetimes τi. In this approach it is conceived that polymer can be considered as a continuous matrix with uniformly distributed in it spheres with the size 4/3(πR3). It was also assumed that cylindrical shape of FVE is a more realistic representation, so corresponding equation for calculation of the volume of FVE was proposed (Goworek et al. 2000). The PALS method permits an estimation of the mean concentration of FVE or hole number density N (Dlubek et al. 2003). In all the polymers, the N values are limited within relatively narrow range of (2–8) 1020 cm−3 at the glass transition temperature T

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of SciencesMoscowRussia