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2003 | 1 | 4 | 402-426

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Methods for the calculation of occupied volumes in glassy polymers: The lattice integration and the monte carlo methods


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A new model for characterizing the free volume of a glassy polymer-gas systems is proposed. An improved method for the calculation of occupied volume per monomer unit was developed within the limits of this model. The model assumptions, error estimates and algorithm efficiencies are described. Using the example of polyvinyltrimethylsilane, it is shown that linear dependences of logarithms of the diffusion and the permeability coefficients on specific accessible volume for inert gases exist.










Physical description


1 - 12 - 2003
1 - 12 - 2003


  • A.N.Nesemeyanov Institute of Elementoorganic Compounds, Russian Academy of Sciences, Moscow, Russia
  • A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, Russia
  • A.N.Nesemeyanov Institute of Elementoorganic Compounds, Russian Academy of Sciences, Moscow, Russia


  • [1] J. Frenkel: Kinetic Theory of Liquids, Dover, New York, 1946.
  • [2] M.H. Cohen, D. Turnbull: “Molecular transport in liquids and gases”, Journal of Chemical Physics, Vol. 31, (1959), pp. 1164–1169. http://dx.doi.org/10.1063/1.1730566[Crossref]
  • [3] R. Simha, R.F. Boyer: “On a general relation involving the glass temperature and coefficients of expansion pf polymers”, Journal of Chemical Physics, Vol. 37, (1962), pp. 1003–1007. http://dx.doi.org/10.1063/1.1733201[Crossref]
  • [4] A. Bondi: Physical properties of molecular crystals, liquid, and gases, Wiley, New York, 1968
  • [5] Y. Hirayama, T. Yoshinaga, Y. Kusuki, K. Nonomiya, T. Sakakibara, T. Tamari: “Relation of gas permeability with structure of aromatic polyimides”, Journal of Membrane Science, Vol. 111, (1996), pp. 169–192. http://dx.doi.org/10.1016/0376-7388(95)00172-7[Crossref]
  • [6] D.N. Theodorou: “Molecular Simulations of Sorption and Diffusion in Amorphous Polymers”, In: P. Neogi (Ed.): Diffusion in Polymers, Decker, New York, 1996, p. 67
  • [7] D. Hofmann, L. Fritz, J. Ulbricht, C. Shepers, M. Boehning: “Detailed-atomistic molecular modeling of small molecule diffusion and solution processes in polymeric membrane materials”, Macromolecular Theory and Simulations, Vol. 6, (2000), pp. 293–327. http://dx.doi.org/10.1002/1521-3919(20000701)9:6<293::AID-MATS293>3.0.CO;2-1[Crossref]
  • [8] J.G. Victor, J.M. Torkelson: “On measuring the distribution of local free volume in glassy polymers by photochromic and fluorescence techniques”, Macromolecules, Vol. 20, (1987), pp. 2241–2250. http://dx.doi.org/10.1021/ma00175a032[Crossref]
  • [9] V.P. Shantarovich, I.B. Kevdina, Yu.P. Yampolskii, A.Yu. Alentiev: “Positron Annihilation Lifetime Study of High and Low Free Volume Glassy Polymers: Effects of Free Volume Sizes on the Permeability and Permselectivity”, Macromolecules, Vol. 33, (2000), pp. 7453–7466. http://dx.doi.org/10.1021/ma000551+[Crossref]
  • [10] N.A. Plate, Yu.P. Yampolskii: “Relationships between Structure and Transport Properties for High Free Volume Polymeric Materials”, In: D.R. Paul, Yu.P. Yampolskii (Eds.): Polymeric Gas Separation Membranes, CRC Press, Boca Raton, 1993, p.155.
  • [11] A.A. Askadskii, V.I. Kondraschenko: Computer-Based Materiology of Polymers, Scientific World, Moscow, 1999.
  • [12] M.J.S. Dewar, E.F. Zoebisch, E.F. Healy, J.J. Stewart: “Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model”, Journal of the American Chemical Society, Vol. 107, (1985), pp. 3902–3909. http://dx.doi.org/10.1021/ja00299a024[Crossref]
  • [13] I.A. Ronova, E.M. Rozhkov, A.Yu. Alentiev, Yu.P. Yampolskii: “Occupied and accessible volumes in glassy polymers and their relation with gas permeation parameters”, Macromolecular Theory and Simulations, [in print].
  • [14] D. Hudson: Statistics, CERN, Geneva, 1964.
  • [15] N.A. Plate, S.G. Drugaryan, V.S. Khotimskii, V.V. Teplyakov, Yu.P. Yampolskii: “Novel poly(silicon olefins) for gas separations”, Journal of Membrane Science, Vol. 52, (1990), pp. 289–304. http://dx.doi.org/10.1016/S0376-7388(00)85133-9[Crossref]
  • [16] Yu.P. Yampolskii, V.V. Volkov: “Studies in gas permeability and membrane gas separation in the Soviet Union”, Journal of Membrane Science, Vol. 64, (1991), pp. 191–228 http://dx.doi.org/10.1016/0376-7388(91)80092-K[Crossref]
  • [17] V.V. Tepljakov: Molecular and phase structure of polymers and its gas separation properties, (dissertation), IPS, Moscow, 1992.
  • [18] A.Yu. Alentiev and Yu.P. Yampolskii: “Meares equation and the role of cohesion energy density in diffusion in polymers”, Journal of Membrane Science, Vol. 206, (2002), pp. 291–306. http://dx.doi.org/10.1016/S0376-7388(01)00777-3[Crossref]
  • [19] C. Nagel, K. Guenther-Schade, D. Fritsch, T. Strunskus, and F. Faupel: “Free Volume and Transport Properties in Highly Selective Polymer Membranes”, Macromolecules, Vol. 35, (2002), pp. 2071–2077. http://dx.doi.org/10.1021/ma011028d[Crossref]
  • [20] J.S. Vrentas and J.L. Duda: “Diffusion in Polymer-Solvent Systems”, Journal of polymer Science, Polymer Physics Edition, Vol. 15, (1977), pp. 403–439. http://dx.doi.org/10.1002/pol.1977.180150302[Crossref]
  • [21] T. Miyamoto and K. Shibayama, Journal Of Applied Physics, Vol. 44, (1973), p. 5372. http://dx.doi.org/10.1063/1.1662158[Crossref]
  • [22] D.R. Paul, Yu.P. Yampolskii (Eds.): Polymeric Gas Separation Membranes, CRC Press, Boca Raton, 1993.

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