Some pitfalls in the use of the Knudsen equation in modelling diffusion in nanoporous materials

Chemical Engineering Science

Volumn 66, Issue 3, 2011, Pages 284-293

  Bhatia, Suresh K ^a   Nicholson, David ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Adsorption; Diffusion; Diffusion in membranes; Knudsen flow; Mass transfer; Transport processes

Indexed keywords

ADSORPTION EFFECT; ADSORPTION EQUILIBRIUM CONSTANTS; COMMONLY USED; CORRELATED RANDOM WALKS; DIFFUSIVITIES; EFFECTIVE MEDIUM THEORIES; EXPERIMENTAL EVIDENCE; KNUDSEN; KNUDSEN DIFFUSIVITY; KNUDSEN FLOW; LOW PRESSURES; MACROPORES; MESOPORE; MESOPOROUS CARBON; MODEL-BASED; NANOPOROUS CARBONS; NANOPOROUS MATERIALS; OSCILLATOR MODEL; PORE NETWORKS; POROUS MEDIUM; SHORT CIRCUITING; TRANSPORT PROCESS; VAN DER WAALS INTERACTIONS;

ADSORPTION; EQUILIBRIUM CONSTANTS; PORE SIZE; POROUS MATERIALS; SILICA; VAN DER WAALS FORCES;

DIFFUSION;

EID: 78650712935     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2010.10.038     Document Type: Article

References (60)

1. Alsyouri H.M., Lin J.Y.S. Gas diffusion and microstructural properties of ordered mesoporous silica fibers. J. Phys. Chem. B 2005, 109:13623-13629.
2. Argönül A., Keil F.J. An alternative procedure for modelling of Knudsen flow and surface diffusion. Chem. Eng. 2008, 52:37-55.
3. Bhatia S.K. Stochastic theory of transport in inhomogeneous media. Chem. Eng. Sci. 1986, 41:1311-1324.
4. Bhatia S.K. Modeling pure gas permeation in nanoporous materials and membranes. Langmuir 2010, 26:8373-8385.
5. Bhatia S.K., Chen H., Sholl D.S. Comparisons of diffusive and viscous contributions to transport coefficients of light gases in single-walled carbon nanotubes. Mol. Simul. 2005, 31:643-649.
6. Bhatia S.K., Jepps O.G., Nicholson D. Tractable molecular theory of transport of Lennard-Jones fluids in nanopores. J. Chem. Phys. 2004, 120:4472-4485.
7. Bhatia S.K., Nicholson D. Transport of simple fluids in nanopores: theory and simulation. AIChE J. 2006, 52:29-38.
8. Bhatia S.K, Nicholson D. Modeling mixture transport in nanopores: departure from existing paradigms. Phys. Rev. Lett. 2008, 100:236103.
9. Bhatia S.K., Nicholson D. Friction based modeling of multi-component transport at the nanoscale. J. Chem. Phys. 2008, 129:164709.
10. Bhatia S.K., Nicholson D., Comments on "Diffusion in a mesoporous silica membrane: validity of the Knudsen diffusion model". Chem. Eng. Sci. 2010, 65:4519-4520.
11. Bhatia S.K., Sonwane C.G. Capillary coexistence and criticality in mesopores: modification of the Kelvin theory. Langmuir 1998, 14:1521-1524.
12. Burggraaf A.J. Single gas permeation of thin zeolite (MFI) membranes: theory and analysis of experimental observations. J. Membr. Sci. 1989, 155:45-65.
13. Cavalacante C.L., Silva N.M., Souza-Aguiar E.F., Sobhrinho E.V. Diffusion of paraffins in dealuminated Y mesoporous molecular sieve. Adsorption 2003, 9:205-212.
14. Chen H., Sholl D.S. Rapid diffusion of CH4/H2 mixtures in singlewalled carbon nanotubes. J. Am. Chem. Soc. 2004, 126:7778-7779.
15. Cunningham R.E., Williams R.J.J. Diffusion in Gases and Porous Media 1980, Plenum Press, New York.
16. Davis M.E. Ordered porous materials for emerging applications. Nature 2002, 417:813-821.
17. Deepak P.D., Bhatia S.K. Transport in capillary network models of porous media theory and simulation. Chem. Eng. Sci. 1994, 49:245-257.
18. Dvoyashkin M., Valiullin R., Kärger J., Einike W-D., Gläser R. Direct assessment of transport properties of supercritical fluids confined to nanopores. J. Am. Chem. Soc. 2007, 129:10344-10345.
19. Evans R.B., Mason G.M., Watson E.A. Gaseous diffusion in porous media. 2. Effect of pressure gradients. J. Chem. Phys. 1961, 35:2076-2083.
20. Evans R.B., Mason G.M., Watson E.A. Gaseous diffusion in porous media. 2. Effect of pressure gradients. J. Chem. Phys. 1962, 36:1894-1902.
21. Gruener S., Huber P. Knudsen diffusion in silicon nanochannels. Phys. Rev. Lett. 2008, 100:064502.
22. Higgins S., DeSisto W., Ruthven D.M. Diffusive transport through mesoporous silica membranes. Microp. Mesop. Mater. 2009, 117:268-277.
23. Hollewand M.P., Gladden L.F. Modelling of diffusion and reaction in porous catalysts using a random 3-dimensional network model. Chem. Eng. Sci. 1992, 47:1761-1770.
24. Ismadji S., Bhatia S.K. The use of liquid phase adsorption isotherms for characterization of activated carbons. J. Colloid Interface Sci. 2001, 244:319-335.
25. Jackson R. Transport in Porous Catalysts 1977, Elsevier, Amsterdam.
26. Jakobtorweihen S., Lowe C.P., Keil F.J., Smit B. Diffusion of chain molecules in carbon nanotubes: the effect of host lattice flexibility and theory of diffusion in the Knudsen regime. J. Chem. Phys. 2007, 127:024904.
27. Jepps O., Bhatia S.K., Searles D.J. Wall mediated transport in confined spaces: exact theory for low density. Phys. Rev. Lett. 2003, 91:0126102.
28. Jepps O., Bhatia S.K., Searles D.J. Modeling diffusion transport in slit pores. J. Chem. Phys. 2004, 120:5396-5406.
29. Keil F.J. Temperature and pore size effects on diffusion in single-wall carbon nanotubes. J. Univ. Chem. Technol. Metall. 2010, 45:161-168.
30. Kerkhof P.J.A.M., Geboers M.A.M. Toward a unified theory of isotropic molecular transport phenomena. AIChE J. 2005, 51:79-121.
31. Kirkpatrick S. Percolation and conduction. Rev. Mod. Phys. 1973, 45:574-588.
32. Knudsen M. The laws of the molecular current and the internal friction current of gases by channels. Ann. Phys. (Leipzig) 1909, 29:75-130.
33. Knudsen M., Fisher W.J. The molecular and the frictional flow of gases in tubes. Phys. Rev. 1910, 31:586-588.
34. Kresge C.T., Leonowicz M.E., Roth W.J., Vartuli J.C., Beck J.S. Ordered mesoporous molecular-sieves synthesized by a liquid-crystal template mechanism. Nature 1992, 359:710-772.
35. Krishna R, van Baten J.M. An investigation of the characteristics of the Maxwell-Stefan diffusivities of binary mixtures in silica nanopores. Chem. Eng. Sci. 2009, 64:870-882.
36. Kärger J., Freunde D. Mass transfer in micro- and mesoporous materials. Chem. Eng. Technol. 2002, 25:769-778.
37. Kärger J., Stallmach F., Vasenov S. Structure mobility relations of molecular diffusion in nanoporous materials. Magn. Reson. Imaging 2003, 21:185-191.
38. Markovic A., Stoltenberg D., Enke D., Schlünder E.-U., Seidel-Morgenstern A. Gas permeation through porous glass membranes Part I. Mesoporous glasses-effect of pore diameter and surface properties. Microp. Mesop. Mater. 2009, 36:17-31.
39. Malek K., Coppens M-O. Effects of surface roughness on self- and transport diffusion in porous media in the Knudsen regime. Phys. Rev. Lett. 2001, 87:125505.
40. Mason E.A., Malinauskas A.P., Evans R.B. Flow and diffusion of gases is porous media. J. Chem. Phys. 1967, 46:3199-3216.
41. Mayo S.L., Olafson B.D., Goddard W.A. DREIDING: a generic force field for molecular simulations. J. Phys. Chem. 1990, 94:8897-8909.
42. Neimark A.V., Ravikovitch P.I., Grun M., Schuth F., Unger K.K. Pore size analysis of MCM-41 type adsorbents by means of nitrogen and argon adsorption. J. Colloid Interface Sci. 1998, 207:159-169.
43. Nicholson D, Petropoulos J.H. A fundamental approach to molecular flow in pore spaces. Berichte der Bunsen-Gesseschaft 1975, 79:796-798.
44. Nguyen T.X., Bae J.-S., Wang Y., Bhatia S.K. On the strength of the hydrogen-carbon interaction as deduced from physisorption. Langmuir 2009, 25:4314-4319.
45. Papadopoulos G.K., Theodorou D.N., Vasenkov S., Kärger J. Mesoscopic simulations of the diffusivity of ethane in beds of NaX zeolite crystals: Comparison with pulsed field gradient NMR measurements. J. Chem. Phys. 2007, 126:094702.
46. Qiao S., Bhatia S.K. Diffusion of linear paraffins in nanoporous silica. Ind. Eng. Chem. Res. 2005, 44:6477-6484.
47. Qiao S., Bhatia S.K. Diffusion of n-decane in nanoporous MCM-41 silica. Microp. Mesop. Mater. 2005, 86:112-123.
48. Ruthven D.M. Response to comments from S.K. Bhatia and D. Nicholson. Chem. Eng. Sci. 2010, 65:4521-4522.
49. Ruthven D.M., DeSisto W.J., Higgins S. Diffusion in a mesoporous silica membrane: validity of the Knudsen diffusion model. Chem. Eng. Sci. 2009, 64:3201-3203.
50. Selvam P., Bhatia S.K., Sonwane C.G. Recent advances in processing and characterization of periodic mesoporous mcm-41 silicate molecular sieves. Ind. Eng. Chem. Res. 2001, 40:3237-3261.
51. Skoulidas A.I., Ackerman D.M., Johnson J.K., Sholl D.S. Rapid transport of gases in carbon nanotubes. Phys. Rev. Lett. 2002, 89:185901.
52. Sokhan V.P., Nicholson D., Quirke N. Fluid flow in nanopores: accurate boundary conditions for carbon nanotubes. J. Chem. Phys. 2002, 117:8531-8539.
53. Sonwane C.G., Bhatia S.K. Structural characterization of MCM-41 over a wide range of length scales. Langmuir 1999, 15:2809-2816.
54. Szekely J., Evans J.W., Sohn H.Y. Gas-Solid Reactions 1976, Academic Press, New York.
55. Tjatjopoulos G.J., Feke D.L., Mann J.A. Molecule micropore interaction potentials. J. Phys. Chem. 1988, 92:4006-4007.
56. Uhlhorn R.J.R., Keizer K., Burgraaf A.J. Gas and surface diffusion in modified γ-alumina systems. J. Membr. Sci. 1989, 46:225-241.
57. Xiao J., Wei J. Diffusion mechanism of hydrocarbons in zeolites-I. Theory. Chem. Eng. Sci. 1992, 47:1123-1141.
58. Yang R.T. Gas Separation by Adsorption Processes 1987, Butterworth-Heinemann, Boston.
59. Yoshimune M., Yamamoto T., Nakaiwa M., Haraya K. Preparation of highly mesoporous carbon membranes via a sol-gel process using resorcinol and formaldehyde. Carbon 2008, 46:1031-1036.
60. Zalc M., Reyes S.C., Iglesia E. The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures. Chem. Eng. Sci. 2004, 59:2947-2960.