Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-07T20:32:25.990Z Has data issue: false hasContentIssue false
  • English
  • Français

Dipolar Energy Transfer and Knudsen Diffusion Inside Disordered Porous Media: Interfacial Geometry and Chord Distributions.

Published online by Cambridge University Press:  15 February 2011

P. Levitz
P. Levitz*
Affiliation:
CRMD-CNRS, 1B Rue De La Ferollerie, Orldans La Source, 45071 Cedex2, France.
Get access

Abstract

The interfacial geometry of a disordered porous medium strongly influences Knudsen diffusion of gases and interfacial dipolar energy transfer. Some interesting comparison can be made between these two transport processes, involving statistical properties of chords belonging either to the solid matrix or to the pore network. A quantitative analysis of these two mechanisms is proposed, based on a chord distribution model. In a first part, we discuss how chord distribution functions contribute to the stastistical characterization of a porous medium. We show that a direct connection between imaging techniques and small angle scattering provides, in many cases, a reliable description of theses functions. In a second part, interfacial direct energy transfer is analyzed. This one step excitation transfer strongly relies on the interfacial autocorrelation function φ2s(r). An analytic expression of φ2s(r) is given and theoretical predictions compared with available experiments. In a third part and following the seminal work of Derjaguin on the Knudsen diffusion, we critically examine how the self diffusion coefficient can be related to the two first moments of the pore chord distribution. A direct comparison with experimental results and numerical simulations is presented in the case of a model porous medium: the random packing of hard spheres. Finally, we analyze a trapping reaction where an excited gas molecule, diffusing in the Knudsen regime, relaxes primarily by wall effects. We show how the chord distribution of the pore network permits to compute the survival probability of the tagged molecules. Two situations are more closely analyzed: the strong and the very weak wall quenching efficiency.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 290: Symposium N – Dynamics in Small Confining Systems , 1992 , 197
Copyright
Copyright © Materials Research Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ciccariello, S., Cocco, G., Benedetti, A. Enzo, A.,S., Phys Rev B 23, 6474 (1981)Google Scholar
[2] Mering, J., Tchoubar, D., J.Appl.Cryst. 1, 153 (1968)Google Scholar
[3] Levitz, P., Tchoubar, D., J.Phys. I 2, 771 (1992)Google Scholar
[4] Levitz, P., Ehret, G., Sinha, S.K., Drake, J.M., J.Chem.Phys 95,6151 (1991)Google Scholar
[5] Drake, J.M., Klafter, J., Levitz, P., Science 251,1574(1991)Google Scholar
[6] Klafter, J., Blumen, A., J.Chem.Phys. 80, 875 (1985)Google Scholar
[7] Levitz, P., Drake, J.M., Klafter, J., J.Chem.Phys, 89, 5224 (1988)Google Scholar
[8] Levitz, P., Drake, J.M.,J.Klafter,Chem.Phys.Lett. 148, 557 (1988)Google Scholar
[9] Blumen, A., J.Chem.Phys. 74, 6926 (1981)Google Scholar
[10] Blumen, A., Klafter, J., Zumofen, G., J.Chem.Phys. 84,1397 (1986)Google Scholar
[11] Crowley, T.L., PhD Thesis, Oxford University, 1984 Google Scholar
[12] Teubner, M., J.Chem.Phys. 92, 4501 (1990)Google Scholar
[13] Onuki, A., Phys.Rev. A, 45, R3384 (1992)Google Scholar
[14] Valleau, J.P., Diestler, D.J., Cushman, J.H., Schoen, M., Hertzner, A.W., Riley, M.E., J.Chem.Phys. 95, 6194(1991)Google Scholar
[15] Huizenga, D.G., Smith, D.M., AIChE Journal, 32, 1(1986)Google Scholar
[16] Derjaguin, B., Comptes rendus de l'academie des sciences de l'URSS. 7, 623 (1948)Google Scholar
[17] Streider, W.C., Prager, S., Phys. Fluids. 11, 2544 (1968)Google Scholar
[18] Dixmier, A., J Phys (Paris) 39, 873 (1978)Google Scholar
[19] Pavlovitch, A., Jullien, R., Meakin, P., Physica A 176, 206 (1991)Google Scholar
[20] Adler, B.J., Wainwright, T.E., J.Chem.Phys. 33,1439.(1960)Google Scholar
[21] Woodcock, L.V., J.Chem.Soc.Faraday.Trans.2 74, 1667.(1976)Google Scholar
[22] Zumofen, G., Blumen, A., Klafter, J., J.Chem.Phys. 82, 3198 (1985)Google Scholar
[23] De Gennes, P.G., C.R.Acad.Sci.Ser 2 295, 1061.(1982)Google Scholar
[24] Blumen, A., Zumofen, G., J.Chem.Phys. 77, 5127.(1982)Google Scholar