Encyclopedia of Membranes

2016 Edition
| Editors: Enrico Drioli, Lidietta Giorno

Free Volume Distribution

Reference work entry
DOI: https://doi.org/10.1007/978-3-662-44324-8_250
Size distribution of free volume in glassy membrane materials is accessible to estimation by computer simulations ( molecular dynamics, MD) and to experimental studies by the probe methods. In low permeable and highly selective conventional glassy polymers like polyimides, size distribution of free volume elements (microcavities), according to MD, is located within the range of microcavity radius 1–5 Å and can be represented by the Gauss function (Heuchel et al. 2004) (see Fig. 1). For polymers with greater gas permeability such as poly(trimethylsilyl propyne) (PTMSP) or amorphous Teflon AF, according to MD, it is much wider and extends up to microcavity radius 10–12 Å (Hofmann et al. 2003) (see Fig. 2). Positron annihilation lifetime spectroscopy (PALS) also indicates widely distributed sizes of free volume in highly permeable polymers. However, there are two interpretations of wide size distribution. According to Shantarovich et al. ( 1993) and Consolati et al. ( 1996), lifetime...
This is a preview of subscription content, log in to check access.


  1. Consolati TG, Genco I, Pegoraro M, Zandeighi L (1996) J Polym Sci: Part B: Polym Phys 34:357–367CrossRefGoogle Scholar
  2. Dlubek G (2008) Positron annihilation spectroscopy. In: Seidel A (ed) Encyclopedia of polymer science and technology. Wiley, HobokenGoogle Scholar
  3. Heuchel M, Hofmann D, Pullumbi P (2004) Macromolecules 37:201–214CrossRefGoogle Scholar
  4. Hofmann D, Heuchel M, Yampolskii Y, Khotimskii V, Shantarovich V (2002) Macromolecules 35:2129–2140CrossRefGoogle Scholar
  5. Hofmann D, Entrialgo-Castano M, Lerbret A, Heuchel M, Yampolskii Y (2003) Macromolecules 36:8528–8538CrossRefGoogle Scholar
  6. Yampolskii Y, Shantaovich V, Chernyakovskii F, Kornilov A, Plate N (1993) J Appl Polym Sci 47:85–92CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

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