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...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bondi A (1968) Physical properties of molecular crystals, liquids and gases. Wiley, New York
Dlubek G (2008) Positron annihilation spectroscopy. In: Seidel A (ed) Encyclopedia of polymer science and technology. Wiley, Hoboken
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, Amsterdam
Yampolskii Y (2007) Methods for investigation of free volume in polymers. Russ Chem Rev 76:59–78
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Yampolskii, Y. (2016). Free Volume Estimation. In: Drioli, E., Giorno, L. (eds) Encyclopedia of Membranes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44324-8_252
Download citation
DOI: https://doi.org/10.1007/978-3-662-44324-8_252
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44323-1
Online ISBN: 978-3-662-44324-8
eBook Packages: Chemistry and Materials ScienceReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics