Molecular Simulation of Gas and Vapor Transport in Highly Permeable Polymers

Materials Science of Membranes for Gas and Vapor Separation

Volumn , Issue , 2006, Pages 95-136

  Fried, Joel R ^a  

^a UNIVERSITY OF CINCINNATI   (United States)

Author keywords

COMPASS (COndensed phase optimized Molecular Potentials for Atomistic Simulation Studies); Computational methods; Equilibrium molecular dynamics method Class II force fields; Fractional free volume; Gas and vapor transport molecular simulation; Gas sorption isotherms and grand canonical monte carlo (GCMC) method; Membrane transport fundamentals; Polymer studies; Transition state theory (TST) method

Indexed keywords

EID: 33847416924     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/047002903X.ch3     Document Type: Chapter

References (253)

1. H. L. Frisch, 'Sorption and transport in glassy polymers -a review', Polym. Eng. Sci., 20, 2-13 (1980).
2. S. A. Stern and H. L. Frisch, 'The selective permeation of gases through polymers', Annu. Rev. Mater. Sci., 11, 523-550 (1981).
3. H. L. Frisch and S. A. Stern, 'Diffusion of small molecules in polymers', Crit. Rev. Solid State Mater. Sci., 11, 123-187 (1983).
4. S. A. Stern and S. Trohalaki, 'Fundamentals of gas diffusion in rubbery and glassy polymers', in Barrier Polymers and Structures, W. J. Koros (Ed.), American Chemical Society, Washington, DC, USA, pp. 22-59 (1990).
5. W. J. Koros, M. R. Coleman and D. R. B.Walker, 'Controlled permeability polymer membranes', Annu. Rev. Mater. Sci., 22, 47-89 (1992).
6. S. A. Stern, 'Polymers for gas separations: the next decade', J. Membr. Sci., 94, 1-65 (1994).
7. W. J. Koros and G. K. Fleming, 'Membrane-based gas separation', J. Membr. Sci., 83, 1-80 (1993).
8. J. H. Petropoulos, 'Mechanisms and theories for sorption and diffusion of gases in polymers', in Polymeric Gas Separation Membranes, D. R. Paul and Y. P. Yampol'skii (Eds), CRC Press, Boca Raton, FL, USA, pp. 17-81 (1994).
9. T. Aoki, 'Macromolecular design of permselective membranes', Prog. Polym. Sci., 24, 951-993 (1999).
10. D. R. Paul, 'Transport properties of polymers', in Applied Polymer Science, R. W. Tess and G. W. Poehlein (Eds), American Chemical Society, Washington, DC, USA, pp. 253-275 (1985).
11. H. B. Hopfenberg and V. Stannet, 'The diffusion and sorption of gases and vapours in glassy polymers', in The Physics of Glassy Polymers, R. N. Haward (Ed.), John Wiley & Sons, Inc., New York, NY, USA, pp. 504-547 (1973).
12. G. K. Fleming and W. J. Koros, 'Dilation of polymers by sorption of carbon dioxide at elevated pressures. 1. Silicone rubber and unconditioned polycarbonate', Macromolecules, 19, 2285-2291 (1986).
13. R. M. Barrer, 'Permeation, diffusion and solution of gases in organic polymers', Trans. Faraday Soc., 35, 629-643 (1939).
14. W. R. Vieth, J. M. Howell and J. H. Hsieh, 'Dual sorption theory', J.Membr. Sci., 1, 177-220 (1976).
15. K. Toi, G. Morel and D. R. Paul, 'Gas sorption and transport in poly(phenylene oxide) and comparisons with other glassy polymers', J. Appl. Polym. Sci., 27, 1997-2005 (1982).
16. V. Teplyakov and P. Meares, 'Correlation aspects of the selective gas permeabilities of polymeric materials and membranes', Gas Sep. Purif., 4, 66-74 (1990).
17. H. L. Frisch, 'The time lag in diffusion', J. Phys. Chem., 61, 93-95 (1957).
18. D. R. Paul and W. J. Koros, 'Effect of partially immobilizing sorption on permeability and the diffusion time lag', J. Polym. Sci. Part B: Polym. Phys. Ed., 14, 675-685 (1976).
19. J. Crank and G. S. Parks, Diffusion in Polymers, Academic Press, London, UK (1968).
20. P. Meares, 'The diffusion of gases through polyvinyl acetate', J. Am. Chem. Soc., 76, 3415-3422 (1954).
21. S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes, McGraw-Hill, New York, NY, USA (1941).
22. F. Bueche, Physical Properties of Polymers, John Wiley & Sons, Inc., New York, NY, USA (1962).
23. L. M. Robeson, 'Correlation of separation factor versus permeability for polymeric membranes', J. Membr. Sci., 62, 165-185 (1991).
24. L. M. Robeson, W. F. Burgoyne, M. Langsam, A. C. Savoca and C. F. Tien, 'High performance polymers for membrane separation', Polymer, 35, 4970-4978 (1994).
25. B. D. Freeman, 'Basis of permeability/selectivity tradeoff relations in polymeric gas separation membranes', Macromolecules, 32, 375-380 (1999).
26. C.-L. Lee, H. L. Chapman, M. E. Cifiuentes, K. M. Lee, L. D. Merrill, K. L. Ulman and K. Venkataraman, 'Effects of polymer structure on the gas permeability of silicone membranes', J. Membr. Sci., 38, 55-70 (1988).
27. M.W. Hellums,W. J. Koros, G. R. Husk and D. R. Paul, 'Fluorinated polycarbonates for gas separation applications', J. Membr. Sci., 46, 93-112 (1989).
28. A. Bondi, 'van der Waals volumes and radii', J. Phys. Chem., 68, 441-451 (1964).
29. S. Sugden, 'Molecular volumes at absolute zero. Part. II. Zero volumes and chemical composition', J. Chem. Soc., 1786-1798 (1927).
30. K. Hagiwara, T. Ougizawa, T. Inoue, K. Hirata and Y. Kobayashi, 'Studies on the free volume and the volume expansion behavior of amorphous polymers', Rad. Phys. Chem., 58, 525-530 (2000).
31. W. W. Lee, 'Selection of barrier materials from molecular structure', Polym. Eng. Sci., 20, 65-69 (1980).
32. L. A. Pilato, L. M. Litz, B. Hargitay, R. C. Osborne, A. G. Farnham, J. H. K. E. Fritze and J. E. McGrath, 'Polymers for permselective membrane gas separations', Polym. Prepr., 16, 41-46 (1975).
33. A. A. Askadskii, Physical Properties of Polymers: Prediction and Control, Gordon and Breach, Amsterdam, The Netherlands (1996).
34. I. Pinnau, C. G. Casillas, A. Morisato and B. D. Freeman, 'Long-term permeation properties of poly(1-trimethylsilyl-1-propyne) membranes in hydrocarbon-vapor environment', J. Polym. Sci. Part B: Polym. Phys. Ed., 35, 1483-1490 (1997).
35. Y. C. Jean, 'Characterizing free volumes and holes in polymers by positron annihilation spectroscopy', paper presented at the NATO Advanced Research Workshop, Varenna, Italy, July 16-17 (1993).
36. R. A. Pethrick, 'Positron annihilation -a probe for nanoscale voids and free volume', Prog. Polym. Sci., 22, 1-47 (1997).
37. G. Dlubek, D. Kilburn, V. Bondarenko, J. Pionteck, R. Krause-Rehberg and M. A. Alam, 'Positron annihilation: a unique method for studying polymers', Macromol. Symp., 210, 11-20 (2004).
38. A. Y. Alentiev, V. P. Shantarovich, T. C. Merkel, V. I. Bondar, B. D. Freeman and Y. P. Yampolskii, 'Gas and vapor sorption, permeation and diffusion in glassy amorphous Teflon AF1600', Macromolecules, 35, 9513-9522 (2002).
39. G. Golemme, J. B. Nagy, A. Fonseca, C. Algieri and Y. Yampolskii, '129Xe NMR study of free volume in amorphous perfluorinated polymers: comparison with other methods', Polymer, 44, 5039-5045 (2003).
40. J. G. Victor and J. M. Torkelson, 'On measuring the distribution of local free volume in glassy polymers by photochromic and fluorescence techniques', Macromolecules, 20, 2241-2250 (1987).
41. J. S. Royal and J. M. Torkelson, 'Photochromic and fluorescent probe studies in glassy polymer matrices. 5. Effects of physical aging on bisphenol-A polycarbonate and poly(vinyl acetate) as sensed by a size distribution of photochromic probes', Macromolecules, 25, 4792-4796 (1992).
42. Y. P. Yampol'skii, M. V. Motyakin, A. M. Wasserman, T. Masuda, M. Teraguchi, V. S. Khotimskii and B. D. Freeman, 'Study of high permeability polymers by means of the spin probe technique', Polymer, 40, 1745-1752 (1999).
43. Y. Kobayashi, K. Haraya, S. Hattori and T. Sasuga, 'Evaluation of polymer free volume by positron annihilation and gas diffusivity measurements', Polymer, 35, 925-928 (1994).
44. Y. C. Jean, J.-P. Yuan, J. Liu, Q. Deng and H. Yang, 'Correlations between gas permeation and free-volume hole properties probed by positron annihillation spectroscopy', J. Polym. Sci. Part B: Polym. Phys. Ed., 33, 2365-2371 (1995).
45. Z. Yu, J. D. McGervey, A. M. Jamieson and R. Simha, 'Can positron annihilation lifetime spectroscopy measure the free-volume hole size distribution in amorphous polymers?', Macromolecules, 28, 6268-6272 (1995).
46. Y. C. Jean, 'Comments on the paper''Can positron annihilation lifetime spectroscopy measure the free-volume hole size distribution in amorphous polymers?' Macromolecules, 26, 5461-5757 (1996).
47. K. Suvegh, M. Kapper, A. Domjan and A. Vertes, 'Comparison of simulated and measured free volume distributions in polymers', Rad. Phys. Chem., 58, 539-543 (2000).
48. M. H. Cohen and D. Turnbull, 'Molecular transport in liquids and glasses', J. Phys. Chem., 31, 1164-1169 (1959).
49. H. Fujita, 'Diffusion in polymer-diluent systems', Fortschr. Hochpolym.-Forsch., 3, 1-47 (1961).
50. K. Haraya and S.-T. Hwang, 'Permeation of oxygen, argon and nitrogen through polymer membranes', J. Membr. Sci., 71, 13-27 (1992).
51. R. K. Bharadwaj and R. H. Boyd, 'Small molecule penetrant diffusion in aromatic polyesters: a molecular dynamics simulation study', Polymer, 40, 4229-4236 (1999).
52. H. Takeuchi and K. Okazaki, 'Molecular dynamics simulation of diffusion of simple gas molecules in a short chain polymer', J. Chem. Phys., 92, 5643-5652 (1990).
53. C. Nagel, E. Schmidtke, K. Gunther-Schade, D. Hofmann, D. Fritsch, T. Strunskus and F. Faupel, 'Free volume distributions in glassy polymer membranes: comparison between molecular modeling and experiments', Macromolecules, 33, 2242-2248 (2000).
54. D. R. B. Walker and W. J. Koros, 'Transport characterization of a polypyrrole for gas separations', J. Membr. Sci., 55, 99-117 (1991).
55. T.-H. Kim, W. J. Koros and G. R. Husk, 'Advanced separation membrane materials: rigid aromatic polyimides', Sep. Sci. Technol., 23, 1611-1626 (1988).
56. E. R. Hensema, M. H. V. Mulder and C. A. Smolders, 'On the mechanism of gas transport in rigid polymer membranes', J. Appl. Polym. Sci., 49, 2081-2090 (1993).
57. A. Shimazu, T. Miyazaki and K. Ikeda, 'Interpretation of d-spacing determined by wide-angle X-ray scattering in 6FDA-based polyimide by molecular modeling', J. Membr. Sci., 166, 113-118 (2000).
58. A. C. Puleo, D. R. Paul and P. K. Wong, 'Gas sorption and transport in semicrystalline poly(4-methyl-1-pentene)', Polymer, 30, 1357-1366 (1989).
59. J. A. Horas and M. G. Rizzotto, 'On the diffusion of gases in partially crystalline polymers', J. Polym. Sci. Part B: Polym. Phys. Ed., 27, 175-187 (1989).
60. A. A. Gusev, F. Müller-Plathe, W. F. van Gunsteren and U. W. Suter, 'Dynamics of small molecules in bulk polymers', Adv. Polym. Sci., 116, 207-247 (1994).
61. F. Müller-Plathe, 'Permeation of polymers -a computational approach', Acta Polym., 45, 259-293 (1994).
62. D. N. Theodorou, 'Molecular simulations of sorption and diffusion in amorphous polymers', in Diffusion in Polymers, P. Neogi (Ed.), Marcel Dekker, New York, NY, USA, pp. 67-142 (1996).
63. A. A. Gusev and U.W. Suter, 'Dynamics of small molecules in dense polymers subject to thermal motion', J. Chem. Phys., 99, 2228-2234 (1993).
64. R. L. June, A. T. Bell and D. N. Theorodorou, 'Transition-state studies of xenon and SF6 diffusion in silicalite', J. Phys. Chem., 95, 8866-8878 (1991).
65. R. Q. Snurr, A. T. Bell and D. N. Theodorou, 'Investigation of the dynamics of benzene in silicalite using transition-state theory', J. Phys. Chem., 98, 11948-11962 (1994).
66. A. Gusev and U.W. Suter, 'A model for transport of diatomic molecules through elastic solids', J. Comp.-Aided Mater. Des., 1, 63-73 (1993).
67. A. A.Gray-Weale, R.H. Henchman, R.G. Gilbert, M. L. Greenfield and D. N. Theodorou, 'Transition-state theory model for the diffusion coefficients of small penetrants in glassy polymers', Macromolecules, 30, 7296-7306 (1997).
68. D. Hofmann, L. Fritz, J. Ulbrich and D. Paul, 'Molecular modelling of amorphous membrane polymers', Polymer, 38, 6145-6155 (1997).
69. D. Hofmann, L. Fritz, J. Ulbrich and D. Paul, 'Molecular simulation of small molecules diffusion and solution in dense amorphous polysiloxanes and polyimides', Comp. Theor. Polym. Sci., 10, 419-436 (2000).
70. M. Heuchel and D. Hofmann, 'Molecular modelling of polyimide membranes for gas separation', Desalination, 144, 67-72 (2002).
71. M. Heuchel, D. Hofmann and P. Pullumbi, 'Molecular modeling of small-molecule permeation in polyimides and its correlation to free-volume distributions', Macromolecules, 37, 201-214 (2004).
72. A. A. Gusev, S. Arizzi, U. W. Suter and D. J. Moll, 'Dynamics of light gases in rigid matrices of dense polymers', J. Chem. Phys., 99, 2221-2227 (1993).
73. A. A. Gusev, U. W. Suter and D. J. Moll, 'Relationship between helium transport and molecular motions in glassy polycarbonate', Macromolecules, 28, 2582-2584 (1995).
74. M. Lopez-Gonzalez, E. Saiz, J. Guzman and E. Riande, 'Experimental and simulation studies on the transport of gaseous diatomic molecules in polycarbonate membranes', J. Chem. Phys., 115, 6728-6736 (2001).
75. M. Lopez-Gonzalez, E. Saiz, J. Guzman and E. Riande, 'Experimental and simulation studies on the transport of argon in polycarbonate pembranes', Macromolecules, 34, 4999-5004 (2001).
76. M. Lopez-Gonzalez, E. Saiz, E. Riande and J. Guzman, 'Transport of helium in polycarbonate membranes', Polymer, 43, 409-413 (2002).
77. M. L. Greenfield and D. N. Theodorou, 'Molecular modeling of methane diffusion in glassy atactic polypropylene via multidimensional transition state theory', Macromolecules, 31, 7068-7090 (1998).
78. B. Widom, 'Some topics in the theory of fluids', J. Chem. Phys., 39, 2808-2812 (1963).
79. D. M. Razmus and C. K. Hall, 'Prediction of gas adsorption in 5A ° zeolites using Monte Carlo simulation', AIChE J., 37, 769-779 (1991).
80. K. S. Schweizer and J. G. Curro, 'PRISM theory of the structure, thermodynamics and phase transitions of polymer liquids and alloys', in Atomistic Modeling of Physical Properties, L. Monnerie and U. W. Suter (Eds), Springer-Verlag, Berlin, Germany, pp. 319-377 (1994).
81. J. G. Curro, K. G. Honnell and J. D. McCoy, 'Theory for the solubility of gases in polymers: application to monatomic solutes', Macromolecules, 30, 145-152 (1997).
82. J. L. Budzien, J. D. MCoy, D. H.Weinkauf, R. A. LaViolette and E. S. Peterson, 'Solubility of gases in amorphous polyethylene', Macromolecules, 31, 3368-3371 (1998).
83. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, 'Equation of state calculations by fast computing machines', J. Chem. Phys., 21, 1087-1092 (1953).
84. S. Trohalaki, A. Kloczkowski, J. E. Mark, D. Rigby and R. J. Roe, 'Estimation of diffusion coefficients for small molecular penetrants in amorphous polyethylene', in Computer Simulation of Polymers, R. J. Roe (Ed.), Prentice Hall, Englewood Cliffs, NJ, USA, pp. 220-232 (1991).
85. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press, New York, NY, USA (1987).
86. R. Chitra and S. Yashonath, 'Estimation of error in the diffusion coefficient from molecular dynamics simulations', J. Phys. Chem. B, 101, 5437-5445 (1997).
87. S. Trohalaki, A. Kloczkowski, J. E. Mark, R. J. Roe and D. Rigby, 'Molecular-dynamics simulations of small molecule diffusion in polyethylene', Comp. Theor. Polym. Sci., 2, 147-151 (1992).
88. L. S. Darken, 'Diffusion, mobility, and their interrelation through free energy in binary metallic systems', Trans. AIMME, 175, 184-201 (1948).
89. S. Sunderrajan, C. K. Hall and B. D. Freeman, 'Estimation of mutual diffusion coefficients in polymer/penetrant systems using nonequilibrium molecular dynamics simulations', J. Chem. Phys., 105, 1621-1632 (1996).
90. R. M. Barrer, 'Nature of the diffusion process in rubber', Nature, 140, 106-107 (1937).
91. R. H. Gee and R. H. Boyd, 'Small penetrant diffusion in polybutadiene: a molecular dynamics simulation study', Polymer, 36, 1435-1440 (1995).
92. J. Han and R. H. Boyd, 'Molecular packing and small-penetrant diffusion in polystyrene: a molecular dynamics simulation study', Polymer, 38, 1797-1804 (1996).
93. P. T. Cummings and D. J. Evans, 'Nonequilibrium molecular dynamics approaches to transport properties and non-Newtonian fluid rheology', Ind. Eng. Chem. Res., 31, 1237-1252 (1992).
94. G. S. Heffelfinger and F. van Swol, 'Diffusion in Lennard-Jones fluids using dual control volume grand canonical molecular dynamics simulation (DCV-GCMD)', J. Chem. Phys., 100, 7548-7552 (1994).
95. A. Thompson and G. S. Heffelfinger, 'Direct molecular simulation of gradient-driven diffusion of large molecules using constant pressure', J. Chem. Phys., 110, 10693-10705 (1999).
96. J. M. D. MacElroy, 'Nonequilibrium molecular dynamics simulation of diffusion and flow in thin microporous membranes', J. Chem. Phys., 101, 5274-5280 (1994).
97. S.-i. Furukawa, T. Shigeta and T. Nitta, 'Nonequilibrium molecular dynamics for simulating permeation of gas mixtures through nanoporous carbon membranes', J. Chem. Eng. Jpn, 29, 725-727 (1996).
98. S.-i. Furukawa and T. Nitta, 'Computer simulation studies on gas permeation through nanoporous carbon membranes by non-equilibrium molecular dynamics', J. Chem. Eng. Jpn, 30, 116-122 (1997).
99. L. Xu, M. G. Sedigh, M. Sahimi and T. T. Tsotsis, 'Nonequilibrium molecular dynamics simulation of transport of gas mixtures in nanopores', Phys. Rev. Lett., 80, 3511-3514 (1998).
100. S.-i. Furukawa and T. Nitta, 'Non-equilibrium molecular dynamics simulation studies on gas permeation across carbon membrane with different pore shape composed of micrographite crystallites', J. Membr. Sci., 178, 107-119 (2000).
101. T. Duren, F. J. Keil and N. A. Seaton, 'Composition dependent transport diffusion coefficients of CH4/CF4 mixtures in carbon nanotubes by nonequilibrium molecular dynamics simulations', Chem. Eng. Sci., 57, 1343-1354 (2002).
102. P. I. Pohl and G. S. Heffelfinger, 'Massively parallel molecular dynamics simulation of gas permeation across porous silica membranes', J. Membr. Sci., 155, 1-7 (1999).
103. M. G. Martin and A. P. Thompson, 'Effect of pressure, membrane thickness, and placement of control volumes on the flux of methane through thin silicalite membranes: a dual control volume grand canonical molecular dynamics study', J. Chem. Phys., 114, 7174-7181 (2001).
104. Q. Zhang, J. Zheng, A. Shevade, L. Zhang, S. H. Gehrke, G. S. Heffelfinger and S. Jiang, 'Transport diffusion of liquid water and methanol through membranes', J. Chem. Phys., 117, 808-818 (2002).
105. H. Kikuchi, S. Kuwajima and M. Fuluda, 'Permeability of gases in rubbery polymer membrane: application of pseudo-nonequilibrium simulation', Chem. Phys. Lett., 358, 466-472 (2002).
106. C. Tunca and D. F. Ford, 'Coarse-grained nonequilibrium approach to the molecular mnodeling of permeation through microporous membranes', J. Chem. Phys., 120, 10763-10767 (2004).
107. F. Mü ller-Plathe, 'Gas sorption and transport in polyisobutylene: equilibrium and nonequilibrium molecular dynamics simulations', J. Chem. Phys., 98, 9895-9904 (1993).
108. W. Brostow, J.-P. Dussault and B. L. Fox, 'Construction of Voronoi polyhedra', J. Comp. Chem., 29, 81-92 (1978).
109. M. Tanemura, T. Ogawa and N. Ogita, 'A new algorithm for three-dimensional Voronoi tesselation', J. Comp. Phys., 51, 191-207 (1983).
110. R. Voorintholt, M. T. Kosters, G. Vegter, G. Vriend and W. G. J. Hol, 'A very fast program for visualizing proteins surfaces, channels and cavities', J. Mol. Graphics, 7, 243-245 (1989).
111. S. Lee and W. L. Mattice, 'A ''phantom bubble'' model for the distribution of free volume in polymers', Comp. Theor. Polym. Sci., 9, 57-61 (1999).
112. D. Rigby and R. J. Roe, 'Molecular dynamics simulation of polymer liquid and glass. 4. Freevolume distribution', Macromolecules, 23, 5312-5319 (1990).
113. T. Zheng, Masters Thesis, Department of Chemical Engineering, University of Cincinnati, OH, USA (2000).
114. V. M. Shah, S. A. Stern and P. J. Ludovice, 'Estimation of the free volume in polymers by means of a Monte Carlo technique', Macromolecules, 22, 4660-4662 (1989).
115. F. T. Gentile, S. Arizzi, U. W. Suter and P. J. Ludovice, 'Structural characterization of polycarbonates for membrane applications by atomic level simulation', Ind. Eng. Chem. Res., 34, 4193-4201 (1995).
116. J. S. Yang, K. Choi andW. H. Jo, 'Comparison of gas diffusion in poly [1-(trimethylsilyl)-1-propyne] and polydimethylsiloxane by atomistic modeling', Macromol. Theor. Simul., 9, 287-291 (2000).
117. B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan and M. Karpus, 'CHARMM: a program for macromolecular energy, minimization, and dynamics calculations', J. Comp. Chem., 4, 187-217 (1983).
118. S. L. Mayo, B. D. Olafson and W. A. Goddard, 'DREIDING: A generic force field for molecular simulation', J. Phys. Chem., 94, 8897-8909 (1990).
119. H. J. C. Berendsen, D. van de Spoel and R. van Drunen, 'GROMACS: A message-passing parallel molecular dynamics implementation', Comp. Phys. Commun., 91, 43-56 (1995).
120. H. Sun, S. J. Mumby, J. R. Maple and A. T. Hagler, 'An ab initio CFF93 all-atom force field for polycarbonates', J. Am. Chem. Soc., 116, 2978-2987 (1994).
121. A. T. Hagler, S. Lifson and P. Dauber, 'Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 2. A benchmark for the objective comparison of alternative force fields', J. Am. Chem. Soc., 101, 5122-5130 (1979).
122. H. Sun, 'COMPASS: An ab initio force-field optimized for condensed-phase applications -overview with details on alkane and benzene compounds', J. Phys. Chem. B, 102, 7338-7364 (1998).
123. H. Sun, P. Ren and J. R. Fried, 'The COMPASS force field: parameterization and validation for phosphazenes', Comp. Theor. Polym. Sci., 8, 229-246 (1998).
124. J. Yang, Y. Ren, A.-m. Tian and H. Sun, 'COMPASS force field for 14 inorganic molecules, He, Ne, Ar, Kr, Xe, H2, O2, N2, NO, CO, CO2, NO2, CS2 and SO2, in liquid phases', J. Phys. Chem. B, 104, 4951-4957 (2000).
125. D. Hofmann, M. Entrialgo-Castano, A. Lerbret, M. Heuchel and Y. Yampolskii, 'Molecular modeling investigation of free volume distributions in stiff chain polymers with conventional and ultrahigh free volume: comparison between molecular modeling and positron lifetime studies', Macromolecules, 36, 8528-8538 (2003).
126. A. J. Schultz, C. K. Hall and J. Genzer, 'Box search algorithm for molecular simulation of systems containing periodic structures', J. Chem. Phys., 120, 2049-2055 (2004).
127. R. Auhl, R. Everaers, G. S. Grest, K. Kremer and S. J. Plimpton, 'Equilibration of long chain polymer melts in computer simulations', J. Chem. Phys., 119, 12718-12728 (2003).
128. F. Mü ller-Plathe, S. C. Rogers and W. F. van Gunsteren, 'Diffusion coefficients of penetrant gases in polyisobutylene can be calculated correctly by molecular dynamics simulations', Macromolecules, 25, 6722-6724 (1992).
129. T. R. Cuthbert, N. J. Wagner, M. E. Paulaitis, G. Murgia and B. D'Aguanno, 'Molecular dynamics simulation of penetrant diffusion in amorphous polypropylene: diffusion mechanisms and simulation size effects', Macromolecules, 32, 5017-5028 (1999).
130. S. Neyertz and D. Brown, 'Influence of system size in molecular dynamics simulation of gas permeation in glassy polymers', Macromolecules, 37, 10109-10122 (2004).
131. T. R. Cuthbert, N. J. Wagner and M. E. Paulaitis, 'Molecular simulation of glassy polystyrene: size effects on gas solubilities', Macromolecules, 30, 3058-3065 (1997).
132. M. Amini, M. Forsyth, S. Gruenhut, P. Meakin and D. R. MacFarlane, 'Equilibrium strategies in molecular dynamics', Electrochim. Acta, 43, 1381-1386 (1998).
133. K. Choi and W. H. Jo, 'Effect of chain flexibility on selectivity in the gas separation process: molecular dynamics simulation', Macromolecules, 28, 8598-8603 (1995).
134. F. Jagodic, B. Borstnik and A. Azman, 'Model calculation of the gas diffusion through polymer bulk', Makromol. Chem., 173, 221-231 (1973).
135. H. Takeuchi, 'A jump motion of small molecules in glassy polymers: a molecular dynamics simulation', J. Chem. Phys., 93, 2062-2067 (1990).
136. F. Müller-Plathe, 'Diffusion of penetrants in amorphous polymers: a molecular dynamics study', J. Chem. Phys., 94, 3192-3199 (1991).
137. P. V. K. Pant and R. H. Boyd, 'Simulation of diffusion of small-molecule penetrants in polymers', Macromolecules, 25, 494-495 (1992).
138. S. Trohalaki, A. Kloczkowski, J. E. Mark, R. J. Roe and D. Rigby, 'Molecular dynamics simulations of small molecule diffusion in polyethylene', Comp. Theor. Polym. Sci., 2, 147-151 (1992).
139. P. V. K. Pant and R. H. Boyd, 'Molecular dynamics simulation of diffusion of small penetrants in polymers', Macromolecules, 26, 679-686 (1993).
140. R. H. Boyd and P. V. K. Pant, 'Molecular packing and diffusion in polyisobutylene', Macromolecules, 24, 6325-6331 (1991).
141. F. Müller-Plathe, S. C. Rogers and W. F. van Gunsteren, 'Computational evidence for anomalous diffusion of small molecules in amorphous polymers', Chem. Phys. Lett., 199, 237-243 (1992).
142. F. Mü ller-Plathe, L. Laaksonen and W. F. van Gunsteren, 'Cooperative effects in the transport of small molecules through an amorphous polymer matrix', J. Mol. Graphics, 11, 118-126 (1993).
143. F. Müller-Plathe, 'Molecular dynamics simulation of gas transport in amorphous polypropylene', J. Chem. Phys., 96, 3200-3205 (1992).
144. J. Han and R. H. Boyd, 'Small-molecule penetrant diffusion in hydrocarbon polymers as studied by molecular dynamics simulation', Macromolecules, 27, 5365-5370 (1994).
145. H. Qariouh, R. Schue, F. Schue and C. Bailly, 'Sorption, diffusion and pervaporation of water/ ethanol mixtures in polyetherimide membranes', Polym. Int., 48, 171-180 (1999).
146. S. Y. Lim, T. T. Tsotsis and M. Sahimi, 'Molecular simulation of diffusion and sorption of gases in an amorphous polymer', J. Chem. Phys., 119, 496-504 (2003).
147. D. N. Theodorou and U. W. Suter, 'Detailed molecular structure of a vinyl polymer glass', Macromolecules, 18, 2467-2478 (1985).
148. M. B. Moe,W. J. Koros and D. R. Paul, 'Effects of molecular structure and thermal annealing on gas transport in two tetramethyl bisphenol-A polymers', J. Polym. Sci. Part B: Polym. Phys. Ed., 26, 1931-1945 (1988).
149. M. Aguilar-Vega and D. R. Paul, 'Gas transport properties of polycarbonates and polysulfones with aromatic substituents on the bisphenol connect group', J. Polym. Sci. Part B: Polym. Phys. Ed., 31, 1599-1610 (1993).
150. C. L. Aitken, W. J. Koros and D. R. Paul, 'Gas transport properties of bisphenol polysulfones', Macromolecules, 25, 3651-3658 (1992).
151. C. L. Aitken,W. J. Koros and D. R. Paul, 'Effects of structural symmetry on gas transport properties of polysulfones', Macromolecules, 25, 3224-3434 (1992).
152. K. Ghosal, R. T. Chern, B. D. Freeman, W. H. Daly and I. I. Negulescu, 'Effect of basic substituents on gas sorption and permeation in polysulfone', Macromolecules, 29, 4360-4369 (1996).
153. J. S. McHattie, W. J. Koros and D. R. Paul, 'Gas transport properties of polysulphones: 2. Effect of bisphenol connector groups', Polymer, 32, 2618-2625 (1991).
154. S. Niemela, J. Lappanen and F. Sundholm, 'Structural effects on free volume distribution in glassy polysulfones: molecular modelling of gas permeability', Polymer, 37, 4155-4165 (1996).
155. J. C. Schmidhauser and K. L. Longley, 'The effect of bisphenol-A monomer structure on the gas permeability of aromatic polycrabonates', J. Appl. Polym. Sci., 39, 2083-2096 (1990).
156. J. S. McHattie,W. J. Koros and D. R. Paul, 'Effect of isopropylidene replacement on gas transport properties of polycarbonates', J. Polym. Sci. Part B: Polym. Phys. Ed., 29, 731-746 (1991).
157. W. J. Koros and D. R. B.Walker, 'Gas separation membrane material selection criteria: weakly and strongly interacting feed component situations', Polym. J., 23, 481-490 (1991).
158. M.-B. Hagg,W. J. Koros and J. C. Schmidhauser, 'Gas sorption and transport properties of bisphenol-1-polycarbonate', J. Polym. Sci. Part B: Polym. Phys. Ed., 32, 1625-1633 (1994).
159. L. M. Costello and W. J. Koros, 'Effect of structure on the temperature dependence of gas transport and sorption in a series of polycarbonates', J. Polym. Sci. Part B: Polym. Phys. Ed., 32, 701-713 (1994).
160. W. J. Koros, A. H. Chan and D. R. Paul, 'Sorption and transport of various gases in polycarbonate', J. Membr. Sci., 2, 165-190 (1977).
161. S. Arizzi, P. H. Mott and U. W. Suter, 'Space available to small diffusants in polymeric glasses: analysis of unoccupied space and its connectivity', J. Polym. Sci. Part B: Polym. Phys. Ed., 30, 415-426 (1992).
162. M. Aguilar-Vega and D. R. Paul, 'Gas transport properties of polyphenylene ethers', J. Polym. Sci. Part B: Polym. Phys. Ed., 31, 1577-1589 (1993).
163. A. Alentiev, E. Drioli, M. Gokzhaev, G. Golemme, O. Ilinich, A. Lapkin, V. Volkov and Y. Yampolskii, 'Gas permeation properties of phenylene oxide polymers', J. Membr. Sci., 138, 99-107 (1998).
164. J. R. Fried, M. Sadat-Akhavi and J. E. Mark, 'Molecular simulation of gas permeability: poly(2,6-dimethyl-1,4-phenylene oxide)', J.Membr. Sci., 149, 115-126 (1998).
165. P. P. Ewald, 'Die Berechnung optischer und electrostatischer Gitterpotentiale', Ann. Phys. (Leipsig), 64, 253-287 (1921).
166. K. Toi, H. Tsuzumi and T. Ito, 'Substitution group effects in gas separation with polyimides', Polym. Polym. Compos., 7, 45-51 (1999).
167. D. Ayala, A. E. Lozano, J. d. Abajo, C. Garcia-Perez, J. G. d. l. Campa, K.-V. Peinemann, B. D. Freeman and R. Prabhakar, 'Gas separation properties of aromatic polyimides', J. Membr. Sci., 215, 61-73 (2003).
168. T. H. Kim, W. J. Koros, G. R. Husk and K. C. O'Brien, 'Relationship between gas separation properties and chemical structure in a series of aromatic polyimides', J. Membr. Sci., 37, 45-62 (1988).
169. S. A. Stern, Y. Mi, H. Yamamoto and A. K. S. Clair, 'Structure/permeability relationships of polyimide membranes. Applications to the separation of gas mixtures', J. Polym. Sci. Part B: Polym. Phys. Ed., 27, 1887-1909 (1989).
170. Y.-C. Wang, S.-H. Huang, C.-C. Hu, C.-L. Li, K.-R. Lee, D.-J. Liaw and J.-Y. Lai, 'Sorption and transport properties of gases in aromatic polyimide membranes', J. Membr. Sci., 248, 15-25 (2005).
171. E. Smit, M. H. V. Mulder, C. A. Smolders, H. Karrenbeld, J. van Eerden and D. Feil, 'Modelling of the diffusion of carbon dioxide in polyimide matrices by computer simulation', J. Membr. Sci., 73, 247-257 (1992).
172. R. Zhang andW. L. Mattice, 'Atomistic modeling of the diffusion of small penetrant molecules in the bulk amorphous polyimide of 3,30,4,40-benzophenonetetracarboxylic dianhydride and 2,2-dimethyl-1,3-(4-aminophenoxy)propane', J. Membr. Sci., 108, 15-23 (1995).
173. D. Hofmann, J. Ulbrich, D. Fritsch and D. Paul, 'Molecular modelling simulation of gas transport in amorphous polyimide and poly(amide imide) membrane materials', Polymer, 37, 4773-4785 (1996).
174. C. S. Ewig, T. S. Thacher and A. T. Hagler, 'Derivation of class II force fields. 7. Nonbonded force field parameters', J. Phys. Chem. B, 103, 6889-7014 (1999).
175. M. Clark, R. D. Cramer and N. V. Opdenbosch, 'Validation of the general purpose Tripos 5.2 force field', J. Comp. Chem., 10, 982-1012 (1991).
176. E. Pinel, D. Brown, C. Bas, R. Mercier, N. D. Alberola and S. Neyertz, 'Chemical influence of the dianhydride and the diamine structure on a series of copolyimides studies by molecular dynamics simulations', Macromolecules, 35, 10198-10209 (2002).
177. K. Mizoguchi, Y. Kamiya and T. Hirose, 'Gas transport in poly [bis(trifluoroethoxy)phosphazene] above the T(1) transition', J. Polym. Sci. Part B: Polym. Phys. Ed., 29, 695-703 (1991).
178. T. Hirose and K. Mizoguchi, 'Gas transport in poly(alkoxyphosphazene)', J. Appl. Polym. Sci., 43, 891-900 (1991).
179. H. R. Allcock, C. J. Nelson, W. D. Coggio, I. Manners, W. J. Koros, D. R. B. Walker and L. A. Pessan, 'Gas permeation and selectivity of poly(organophosphazene) membranes', Macromolecules, 26, 1493-1502 (1993).
180. L. E. Starannikova, D. R. Tur, V. V. Teplyakov and N. A. Plate, 'Gas separation properties of poly [bis(trifluoroethoxy)phosphazene]', Polym. Sci., 36, 1610-1615 (1994).
181. C. J. Orme, J. R. Klaehn and F. F. Stewart, 'Gas permeability and ideal selectivity of poly [bis-(4-tert-butylphenoxy)phosphazene]', J. Membr. Sci., 238, 47-55 (2004).
182. J. R. Fried and P. Ren, 'The atomistic simulation of the gas permeability of poly(organophosphazenes). Part 1. Poly(dibutoxyphosphazenes)', Comp. Theor. Polym. Sci., 10, 447-463 (2000).
183. J. R. Fried and N. Hu, 'The molecular basis of CO2 interaction with polymers containing fluorinated groups: computational chemistry of model compounds and molecular simulation of poly [bis(2,2,2-trifluoroethoxy)phosphazene]', Polymer, 44, 4363-4372 (2003).
184. N. Hu and J. R. Fried, 'The atomistic simulation of the gas permeability of poly(organophosphazenes): 2. poly [bis(2,2,2-trifluoroethoxy)phosphazene]', Polymer, 46, 4330-4343 (2005).
185. J. R. Fried and P. Ren, 'Molecular simulation of the glass transition of polyphosphazenes', Comp. Theor. Polym. Sci., 9, 111-116 (1999).
186. T. Hirose, Y. Kamiya and K. Mizoguchi, 'Gas transport in poly [bis(trifluoroethoxy)phosphazene]', J. Appl. Polym. Sci., 38, 809-820 (1989).
187. Y. P. Yampol'skii, N. B. Bespalova, E. S. Finkel'-shtein, V. I. Bondar and A. V. Popov, 'Synthesis, gas permeability, and gas sorption properties of fluorine-containing norbornene polymers', Macromolecules, 27, 2872-2878 (1994).
188. S. A. Stern, V. M. Shah and B. J. Hardy, 'Structure-permeability relationships in silicone polymers', J. Polym. Sci. Part B: Polym. Phys. Ed., 25, 1263-1298 (1987).
189. Y. Tsujita, 'Gas sorption, diffusion and permeation of ordered polymeric membranes', Chin. J. Polym. Sci., 18, 301-307 (2000).
190. V. M. Shah, B. J. Hardy and S. A. Stern, 'Solubility of carbon dioxide, methane and propane in silicone polymers. Effect of polymer backbone chains', J. Polym. Sci. Part B: Polym. Phys. Ed., 31, 313-317 (1993).
191. J. E. Mark, 'Overview of siloxane polymers', in Silicones and Silicone-Modified Materials, S. J. Clarson, J. J. Fitzgerald, M. J. Owen and S. D. Smith (Eds), American Chemical Society, Washington, DC, USA, pp. 1-10 (2000).
192. A. C. M. Kuo, 'Poly(dimethylsiloxane)', in Polymer Data Handbook, J. E. Mark (Ed.), Oxford University Press, New York, NY, USA, pp. 411-435 (1999).
193. R. M. Sok, H. J. C. Berendsen and W. F. V. Gunsteren, 'Molecular dynamics simulation of the transport of small molecules across a polymer membrane', J. Chem. Phys., 96, 4699-4704 (1992).
194. S. G. Charati and S. A. Stern, 'Diffusion of gases in silicone polymers: molecular dynamics simulations', Macromolecules, 31, 5529-5535 (1998).
195. V. P. Shantarovich, I. B. Kevdina, Y. P. Yampolskii and A. Y. Alentiev, 'Positron annihilation lifetime study of high and low free volume glassy polymers: effects of free volume sizes on the permeability and permselectivity', Macromolecules, 33, 7453-7466 (2000).
196. S. Trohalaki, L. C. DeBolt, J. E. Mark and H. L. Frisch, 'Estimation of free volume for gaseous penetrants in elastomeric membranes by Monte Carlo simulations', Macromolecules, 23, 813-816 (1990).
197. L. Fritz and D. Hofmann, 'Molecular dynamics simulations of the transport of water-ethanol mixtures through polydimethylsiloxane membranes', Polymer, 38, 1035-1045 (1997).
198. J. E. Mark, 'Silicon-containing polymers', in Silicon-Based Polymer Science: A Comprehensive Resource, J. M. Ziegler and F. W. G. Fearon (Eds), American Chemical Society, Washington, DC, USA, pp. 48-68 (1990).
199. J. R. Fried and B. Li, 'Molecular simulation of gas sorption and diffusion in silicon-based polymers', in Advanced Materials for Membrane Separations, I. Pinnau and B. D. Freeman (Eds), American Chemical Society, Washington, DC, USA, pp. 24-38 (2004).
200. V. E. Raptis, I. G. Economou, D. N. Theodorou, J. Petrou and J. H. Petropoulos, 'Molecular dynamics simulation of structure and thermodynamic properties of poly(dimethylsilamethylene) and hydrocarbon solubility therein: toward the development of novel membrane materials for hydrocarbon separation', Macromolecules, 37, 1102-1112 (2004).
201. S. A. Solov'ev, Y. P. Yampolski, I. G. Economou, N. V. Ushahov and E. S. Finkel'shstein, 'Thermodynamic parameters of hydrocarbon sorption by poly(silmethylenes)', Polym. Sci. Ser. A, 44, 293-300 (2002).
202. A. Alentiev, I. G. Economou, E. Finkelshstein, J. Petrou, V. E. Raptis, M. Sanopoulou, S. Soloviev, N. Ushakov and Y. Yampolskii, 'Transport properties of silmethylene homo-polymers and random copolymers: experimental measurements and molecular simulation', Polymer, 45, 6933-6944 (2004).
203. T. Higashimura, T. Masuda and M. Okada, 'Gas permeability of polyacetylenes with bulky substituents', Polym. Bull., 10, 114-117 (1983).
204. K. Takada, H. Matsuya, T. Masuda and T. Higashimura, 'Gas permeability of polyacetylenes carrying substituents', J. Appl. Polym. Sci., 30, 1605-1616 (1985).
205. Y. Ichiraku, S. A. Stern and T. Nakagawa, 'An investigation of the high gas permeability of poly(1-trimethylsilyl-1-propyne)', J. Membr. Sci., 34, 5-18 (1987).
206. T. Nakagawa, T. Saito, S. Asakawa and Y. Saito, 'Polyacetylene derivatives as membranes for gas separations', Gas Sep. Purif., 2, 3-8 (1988).
207. T. Masuda, Y. Iguchi, B.-Z. Tang and T. Higashimura, 'Diffusion and solution of gases in substituted polyacetylene membranes', Polymer, 29, 2041-2049 (1988).
208. N. A. Plate, A. K. Bokarev, N. E. Kaliuzhnyi, E. G. Litvinova, V. S. Khotimskii, V. V. Volkov and Y. P. Yampol'skii, 'Gas and vapor permeation and sorption in poly(trimethylsilylpropyne)', J. Membr. Sci., 60, 13-24 (1991).
209. A. C. Savoca, A. D. Surnamer and C.-f. Tien, 'Gas transport in poly(silylpropynes): the chemical structure point of view', Macromolecules, 26, 6211-6216 (1993).
210. A. Morisato, H. C. Shen, S. S. Sankar, B. D. Freeman, I. Pinnau and C. G. Casillas, 'Polymer characterization and gas permeability of poly(1-trimethylsilyl-1-propyne) [PTMSP], poly(1-phenyl-1-propyne) [PPP] and PTMSP/PPP blends', J. Polym. Sci. Part B: Polym. Phys. Ed., 34, 2209-2222 (1996).
211. L. E. Starannikova and V. V. Teplyakov, 'Gas permeability of poly [1-(trimethylsilyl)-1-propyne]: evaluation of experimental data and calculation methods',Polym. Sci.Ser.A,39,1142-1147(1997).
212. T. C. Merkel, V. Bondar, K. Nagai and B. D. Freeman, 'Hydrocarbon and perfluorocarbon gas sorption in poly(dimethylsiloxane), poly(1-trimethylsilyl-1-propyne) and copolymers of tetrafluoroethylene and 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole', Macromolecules, 32, 370-374 (1999).
213. T. Masuda, E. Isobe and T. Higashimura, 'Poly [1-(trimethylsilyl)-1-propyne]: a new high polymer synthesized with transition-metal catalysts and characterized by extremely high gas permeability', J. Am. Chem. Soc., 103, 7473-7474 (1983).
214. K. Nagai, T. Masuda and T. Nakagawa, 'Poly [1-(trimethylsilyl)-1-propyne] and related polymers: synthesis, properties, and functions', Prog. Polym. Sci., 26, 721-798 (2001).
215. Y. P. Yampol'skii, S. M. Shishatskii, V. P. Shantorovich, E. M. Antipov, N. N. Kuzmin, S. V. Rykov, V. L. Khodjaeva and N. A. Plate, 'Transport characteristics and other physicochemical properties of aged poly(1-(trimethylsily)-1-propyne)', J. Appl. Polym. Sci., 48, 1935-1944 (1993).
216. K. Ishihara, Y. Nagasse and K. Matsui, 'Pervaporation of alcohol/water mixtures through poly [1-(trimethylsilyl)-1-propyne] mixtures', Makromol. Chem., Rapid Commun., 7, 43-46 (1986).
217. T. Masuda, B.-Z. Tang and T. Higashimura, 'Ethanol-water separation by pervaporation through substituted-polyacetylene membranes', Polym. J., 18, 565-567 (1986).
218. M. Langsam and L. M. Robeson, 'Substituted propyne polymers -Part II. Effects of aging on the gas permeability properties of poly [1-(trimethylsilyl) propyne] for gas separation membranes', Polym. Eng. Sci., 29, 44-54 (1989).
219. K. Nagai, M. Mori, T. Watanabe and T. Nakagawa, 'Gas permeation properties of blend and copolymer membranes composed of 1-trimethylsilyl-1-propyne and 1-phenyl-1-propyne structures', J. Polym. Sci. Part B: Polym. Phys. Ed., 35, 119-131 (1997).
220. T. Nakagawa, S. Fujisaki, H. Nakano and A. Higuchi, 'Physical modification of poly [1-(trimethylsilyl)-1-propyne] membranes for gas separation', J. Membr. Sci., 94, 183-193 (1994).
221. R. S. Prabhakar, T. C. Merkel, B. D. Freeman, T. Imizu and A. Higuchi, 'Sorption and transport properties of propane and perfluoropropane in poly(dimethylsiloxane) and poly(1-trimethylsilyl-1-propyne)', Macromolecules, 38, 1899-1910 (2005).
222. L. C. Witchey-Lakshmanan, H. B. Hopfenberg and R. T. Chern, 'Sorption and transport of organic vapors in poly [1-(trimethylsilyl)-1-propyne]', J. Membr. Sci., 48, 321-331 (1990).
223. K. Nagai, A. Higuchi and T. Nakagawa, 'Bromination and gas permeability of poly(1-trimethylsilyl-1-propyne) membrane', J. Appl. Polym. Sci., 54, 1207-1217 (1994).
224. I. Pinnau and L. G. Toy, 'Transport of organic vapors through poly(1-trimethylsily-1-propyne)', J. Membr. Sci., 116, 199-209 (1996).
225. B. Freeman and I. Pinnau, 'Separation of gases using solubility-selective polymers', TRIP, 5, 167-173 (1997).
226. V. V. Teplyakov, D. Roizard, E. Favre and V. S. Khotimsky, 'Investigations on the peculiar permeation properties of volatile organic compounds and permanent gases through PTMSP', J. Membr. Sci., 220, 165-175 (2003).
227. Y. P. Yampol'skii, V. P. Shantorovich, F. P. Chernyakovskii, A. I. Kornilov and N. A. Plate, 'Estimation of free volume of poly(trimethylsilyl propyne) by positron annihilation and electrochromism methods', J. Appl. Polym. Sci., 47, 85-92 (1993).
228. G. Consolati, I. Genco, M. Pegoraro and L. Zanderighi, 'Positron annihilation lifetime (PAL) in poly [1-(trimethylsilyl)propyne] (PTMSP): free volume determination and time dependence of permeabilty', J. Polym. Sci. Part B: Polym. Phys. Ed., 34, 357-367 (1996).
229. R. Srinivasan, S. R. Auvil and P. M. Burban, 'Elucidating the mechanism(s) of gas transport in poly [1-(trimethylsilyl)-1-propyne] (PTMSP) membranes', J. Membr. Sci., 86, 67-86 (1994).
230. Y. P. Yampol'skii and V. P. Shantarovich, 'Chemica structure, free volume of glassy polymers, and prediction of their membrane properties', Polym. Sci., Ser. C, 43, 2329-2349 (2001).
231. S. B. Clough, X. F. Sun, S. K. Tripathy and G. L. Baker, 'Molecular dynamics smulalation of substituted polyacetylene', Macromolecules, 24, 4264-4269 (1991).
232. M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, 'AM1: a new general purpose quantum mechanical molecular model', J. Am. Chem. Soc., 107, 3902-3909 (1985).
233. J. R. Fried and D. K. Goyal, 'Molecular simulation of gas transport in poly [1-(trimethylsilyl)-1-propyne]', J. Polym. Sci. Part B: Polym. Phys. Ed., 36, 519-536 (1998).
234. S. V. Dixon-Garrett, K. Nagai and B. D. Freeman, 'Sorption, diffusion, and permeation of ethylbenzene in poly(1-trimethylsilyl-1-propyne)', J. Polym. Sci. Part B: Polym. Phys. Ed., 38, 1078-1089 (2000).
235. T. Zheng and J. R. Fried, 'Monte Carlo simulation of the sorption of pure and mixed alkanes in poly [1-(trimethylsilyl)-1-propyne]', Sep. Sci. Technol., 36, 959-973 (2001).
236. T. C. Merkel, V. Bondar, K. Nagai and B. D. Freeman, 'Sorption and transport of hydrocarbon and perfluorocarbon gases in poly(1-trimethylsilyl-1-propyne)', J. Polym. Sci. Part B: Polym. Phys. Ed., 38, 273-296 (2000).
237. T. M. Madkour, 'Development of the molecular design rules of ultra-permeable poly [1-(trimethylsilyl)-1-propyne]', Polymer, 41, 7489-7497 (2000).
238. D. Hofmann, M. Heuchel, Y. Yampolskii, V. Khotimskii and V. Shantarovich, 'Free volume distributions in ultrahigh and lower free volume polymers: comparison between molecular modeling and positron lifetime studies', Macromolecules, 35, 2129-2140 (2002).
239. A. M. Polyakov, L. E. Starannikova and Y. P. Yampolskii, 'Amorphous Teflons AF as organophilic pervaporation materials. Separation of mixtures of chloromethanes', J. Membr. Sci., 238, 21-32 (2004).
240. Y. Wang, P. T. Inglefield and A. A. Jones, 'NMR characterization of penetrants in high permeability polymers', Polymer, 43, 1867-1872 (2002).
241. T. C. Merkel, Z. He, I. Pinnau, B. D. Freeman, P. Meakin and A. J. Hill, 'Sorption and transport in poly(2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole-co-tetrafluoroethylene)',Macromolecules, 36, 8406-8414 (2003).
242. X.-Y. Wang, K. M. Lee, Y. Lu, M. T. Stone, I. C. Sanchez and B. D. Freeman, 'Cavity size distributions in high free volume glass polymes by molecular simulation', Polymer, 45, 3907-3912 (2004).
243. P. J. Veld, M. T. Stone, T. M. Trunskett and I. C. Sanchez, 'Liquid structure via cavity size distributions', J. Phys. Chem. B, 104, 12028-12034 (2000).
244. M. J. Hwang, T. P. Stockfisch and A. T. Hagler, 'Derivation of class II force fields. 2. Derivation and characterization of a class II force field, CFF93, for the alkyl functional group and alkane molecules', J. Am. Chem. Soc., 116, 2515-2525 (1994).
245. J. A. Maple, M. J. Hwang, T. P. Stockfisch, U. Dinur, M.Waldman, C. S. Ewig and A. T. Hagler, 'Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules', J. Comp. Chem., 15, 162-182 (1994).
246. M. A. LaPack, J. C. Tou, V. L. McGuffin and C. G. Enke, 'The correlation of membrane permeabillity with Hildebrand solubility parameters', J. Membr. Sci., 86, 263-280 (1994).
247. C.-C. Hu, C.-S. Chang, R.-C. Ruaan and J.-Y. Lai, 'Effect of free volume and sorption on membrane gas transport', J. Membr. Sci., 226, 51-61 (2003).
248. K. Tanaka, T. Kawai, H. Kita, K.-i. Okamoto and Y. Ito, 'Correlation between gas diffusion coefficient and positron annihilation lifetime in polymers with rigid polymer chains', Macromolecules, 33, 5513-5517 (2000).
249. A. Morisato and I. Pinnau, 'Synthesis and gas permeation properties of poly(4-methyl-2-pentyne)', J. Membr. Sci., 121, 243-250 (1996).
250. W. J. Koros, G. K. Fleming, S. M. Jordan, T. H. Kim and H. H. Hoehn, 'Polymeric membrane materials for solution-diffusion based permeation separations', Prog. Polym. Sci., 13, 339-401 (1988).
251. Y. Tamai, H. Tanaka and K. Nakanishi, 'Molecular simulation of permeation of small penetrants through membranes. 1. Diffusion coefficients', Macromolecules, 27, 4498-4508 (1994).
252. D. Hofmann, L. Fritz, J. Ulbrich, C. Schepers and M. Bohning, 'Detailed-atomistic molecular modeling of small molecule diffusion and solution processes in polymeric membrane materials', Macromol. Theory Simul., 9, 293-327 (2000).
253. T. C. Merkel, V. I. Bondar, K. Nagai, B. D. Freeman and I. Pinnau, 'Gas sorption, diffusion and permeation in poly(dimethylsiloxane)', J. Polym. Sci. Part B: Polym. Phys. Ed., 38, 415-433 (2000).