Encyclopedia of Membranes

2016 Edition
| Editors: Enrico Drioli, Lidietta Giorno

Free Volume Model

Reference work entry
DOI: https://doi.org/10.1007/978-3-662-44324-8_253

The concept of free volume is extensively used in respect of various properties of condensed phases. Regarding nonporous polymeric membranes, it is quite useful in the description of diffusion phenomena. The model proposed by Cohen and Turnbull (1959) for transport in liquids and amorphous glasses considers a matrix consisting from hard molecules. It gives the following equation for the diffusion coefficient as a function of average free volume per molecule \( {\mathrm{v}}_{\mathrm{f}}:\mathrm{D}=\mathrm{A}\ \exp \left(-\upgamma {\mathrm{v}}^{*}/{\mathrm{v}}_{\mathrm{f}}\right) \)

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References

  1. Cohen MH, Turnbull D (1959) J Phys Chem 31:1164–1169CrossRefGoogle Scholar
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  4. Vrentas JS, Duda JL (1977) J Polym Sci Polym Phys Ed 15:403–417; J Appl Polym Sci 21(1977):1715–1728Google 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