Encyclopedia of Membranes

2016 Edition
| Editors: Enrico Drioli, Lidietta Giorno

Free Volume Estimation

  • Yuri Yampolskii
Reference work entry
DOI: https://doi.org/10.1007/978-3-662-44324-8_252

Originally, free volume was interpreted (H. Fujita, M.H. Cohen and D. Turnbull, J.S. Vrentas and J.L. Duda) as an abstract parameter that fits the equation of free volume model. The methods for quantitative determination of free volume were proposed by S. Sugden and later by A. Bondi (1968). According to the latter, free volume Vf (cc/g) can be estimated as the difference: Vf = Vsp – Vocc, where the specific volume is defined as Vsp = 1/ρ (ρ is the polymer density), while occupied volume Vocc can be found as 1.3 Vw, where Vw is the van der Waals volume of the repeat unit of the polymer. The Vw value can be estimated from the increments tabulated for various groups (Van Krevelen and te Nijenhuis 2009). The factor 1.3 is taken from the packing density of molecular crystal at 0 K (accounting for inaccessible volume). Bondi’s formula was criticized: the factor 1.3 might not be a universal constant, applicable in all cases; Vwof repeat units cannot be considered as the sum of increments...

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  1. Bondi A (1968) Physical properties of molecular crystals, liquids and gases. Wiley, New YorkGoogle Scholar
  2. Dlubek G (2008) Positron annihilation spectroscopy. In: Seidel A (ed) Encyclopedia of polymer science and technology. Wiley, HobokenGoogle Scholar
  3. Van Krevelen DW, te Nijenhuis K (2009) Properties of polymers. Their correlation with chemical structure, their numerical estimation and prediction from additive group contributions. Elsevier, AmsterdamGoogle Scholar
  4. Yampolskii Y (2007) Methods for investigation of free volume in polymers. Russ Chem Rev 76:59–78CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

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