The effect of pore surface roughness on Knudsen diffusion in nanoporous media is investigated by dynamic Monte Carlo simulations and analytical calculations. A conceptual difference is found between the roughness dependence of the macroscopic, transport diffusivity and the microscopic, self-diffusivity, which is reminiscent of diffusion in zeolites, where a similar difference arises due to adsorption effects and intermolecular interactions. Because of the dependence of the self-diffusivity on molecular residence times, self-diffusion may be roughness dependent, while transport diffusion is not. Detailed proofs are given. The differences become significant when the pore surface is rough down to molecular scales, as is the case, e.g., for many common sol–gel materials. Simulations are in good agreement with analytical calculations for several tested rough, fractal pore structures. These results are important for the interpretation of experimental diffusion measurements and for the study of diffusion-reaction processes in nanoporous catalysts with a rough internal surface.

1.
P. M. Adler, Porous Media: Geometry and Transport (Butterworth-Heinemann, Stoneham, MA, 1992).
2.
The CRC Handbook of Solid State Electrochemistry, edited by P. J. Gellings and H. J. M. Bouwmeester (CRC, Boca Raton, FL, 1997).
3.
M.
Sahimi
,
G. R.
Gavalas
, and
T. T.
Tsotsis
,
Chem. Eng. Sci.
45
,
1443
(
1990
).
4.
R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts (Clarendon, Oxford, 1975), Vol. 1.
5.
F. J.
Keil
,
Catal. Today
53
,
245
(
1999
).
6.
M. P.
Hollewand
and
L. F.
Gladden
,
Chem. Eng. Sci.
47
,
2757
(
1992
).
7.
A.
Burghardt
,
J.
Rogut
, and
J.
Gotkowska
,
Chem. Eng. Sci.
43
,
2463
(
1988
).
8.
L.
Zhang
and
N. A.
Seaton
,
Chem. Eng. Sci.
49
,
41
(
1994
).
9.
S.
Arbabi
and
M.
Sahimi
,
Chem. Eng. Sci.
46
,
1749
(
1991
).
10.
G. F. Froment and K. B. Bischoff, Chemical Reactor Analysis and Design, 2nd ed. (Wiley, New York, 1990).
11.
C. K.
Lee
and
S. L.
Lee
,
Surf. Sci.
339
,
171
(
1995
).
12.
C.
McGreavy
,
J. S.
Andrade
, and
K.
Rajagopal
,
Chem. Eng. Sci.
47
,
2751
(
1992
).
13.
M.
Sahimi
,
Rev. Mod. Phys.
65
,
1393
(
1993
).
14.
Y.
Nakano
,
S.
Iwamoto
,
I.
Yoshinaga
, and
J. W.
Evans
,
Chem. Eng. Sci.
42
,
1577
(
1987
).
15.
M. H.
Abbasi
,
J. W.
Evans
, and
I. S.
Abramson
,
AIChE J.
29
,
617
(
1983
).
16.
V. N.
Burganos
and
S. V.
Sotirchos
,
Chem. Eng. Sci.
44
,
2451
(
1989
).
17.
Physical and Chemical Aspects of Adsorption and Catalysts, edited by B. G. Linsen (Academic, London, 1970).
18.
D. H.
Davis
,
J. Appl. Phys.
31
,
1169
(
1960
).
19.
D.
Avnir
,
D.
Farin
, and
P.
Pfeifer
,
Nature (London)
308
,
261
(
1984
).
20.
M.-O.
Coppens
,
Colloids Surf., A
187–188
,
257
(
2001
).
21.
M.
von Smoluchowski
,
Ann. Phys. (Leipzig)
4F
,
1559
(
1910
).
22.
M.-O.
Coppens
and
G. F.
Froment
,
Fractals
3
,
807
(
1995
).
23.
M.-O.
Coppens
and
G. F.
Froment
,
Chem. Eng. Sci.
50
,
1013
(
1995
).
24.
S. B.
Santra
and
B.
Sapoval
,
Phys. Rev. E
57
,
6888
(
1998
).
25.
D. G.
Huizenga
and
D. M.
Smith
,
AIChE J.
32
,
1
(
1986
).
26.
O.
Geier
,
S.
Vasenkov
, and
J.
Kärger
,
J. Chem. Phys.
117
,
1935
(
2002
).
27.
K.
Malek
and
M.-O.
Coppens
,
Phys. Rev. Lett.
87
,
125505
(
2001
).
28.
K.
Malek
and
M.-O.
Coppens
,
Colloids Surf., A
206
,
335
(
2002
).
29.
M.-O. Coppens and K. Malek, Chem. Eng. Sci. (in press).
30.
P.
Clausing
,
Ann. Phys. (Leipzig)
5F
,
567
(
1930
).
31.
M.-O.
Coppens
and
G. F.
Froment
,
Chem. Eng. Sci.
50
,
1027
(
1995
).
32.
J. Kärger and D. M. Ruthven, Diffusion in Zeolites and other Microporous Solids (Wiley, New York, 1992).
33.
D. N. Theodorou, R. Q. Snurr, and A. T. Bell, Comprehensive Supramolecular Chemistry; Molecular Dynamics and Diffusion in Microporous Materials (Pergamon, Berlin, 1996).
34.
D. M.
Ruthven
,
R. I.
Derrah
, and
K. F.
Loughlin
,
Can. J. Chem.
51
,
3514
(
1973
).
35.
D. T.
Hayhurst
and
A. R.
Paravar
,
Zeolites
8
,
27
(
1988
).
36.
N.
Van-Den-Begin
,
L. V. C.
Rees
,
J.
Caro
, and
M.
Bülow
,
Zeolites
9
,
287
(
1989
).
37.
U.
Schemmert
,
J.
Kärger
, and
J.
Weitkamp
,
Microporous Mater.
32
,
101
(
1999
).
38.
H.
Jobic
,
J.
Kärger
, and
M.
Bee
,
Phys. Rev. Lett.
82
,
4260
(
1999
).
39.
F.
Müller-Plathe
,
S. C.
Rogers
, and
W. F.
van Gunsteren
,
J. Chem. Phys.
98
,
9895
(
1993
).
40.
T.
Düren
,
S.
Jakobtorweithen
,
F. J.
Keil
, and
N. A.
Seaton
,
Phys. Chem. Chem. Phys.
5
,
369
(
2003
).
41.
M. R.
Schure
,
R. S.
Maier
,
D. M.
Kroll
, and
H. T.
Davis
,
Anal. Chem.
74
,
6006
(
2002
).
42.
M.-O. Coppens, in Fractals in Engineering, 2nd ed., edited by J. Lévy-Vehel, E. Lutton, and C. Tricot (Springer, Berlin, 1997), p. 336.
43.
B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
44.
J. M. D.
MacElroy
and
S.-H.
Suh
,
J. Chem. Phys.
106
,
8595
(
1997
).
45.
L. A.
Pozhar
,
Phys. Rev. E
61
,
1432
(
2000
).
46.
L. F.
Xu
,
M.
Sahimi
, and
T. T.
Tsotsis
,
Phys. Rev. E
62
,
6942
(
2000
).
47.
M.
Knudsen
,
Ann. Phys. (Leipzig)
4F
,
75
(
1909
).
48.
J.
Klafter
,
M. F.
Shlesinger
, and
G.
Zumofen
,
Phys. Today
49
,
33
(
1996
).
49.
J.
Kärger
and
D.
Freude
,
Chem. Eng. Technol.
25
,
769
(
2002
).
50.
S. K.
Bhatia
and
J. S.
Gupta
,
Rev. Chem. Eng.
8
,
177
(
1992
).
51.
J. W.
Evans
,
M. H.
Abbasi
, and
A.
Sarin
,
J. Chem. Phys.
72
,
2967
(
1980
).
52.
V. N.
Burganos
and
S. V.
Sotirchos
,
Chem. Eng. Sci.
44
,
2451
(
1989
).
53.
S. M.
Auerbach
,
Int. Rev. Phys. Chem.
19
,
155
(
2000
).
54.
C.
Uebing
and
R.
Gomer
,
J. Chem. Phys.
100
,
7759
(
1994
).
55.
D. S.
Sholl
,
Ind. Eng. Chem. Res.
39
,
3747
(
2000
).
56.
C. H.
Mak
,
H. C.
Andersen
, and
S. M.
George
,
J. Chem. Phys.
88
,
4052
(
1988
).
57.
M.-O.
Coppens
,
A. T.
Bell
, and
A. K.
Chakraborty
,
Chem. Eng. Sci.
53
,
2053
(
1998
).
58.
D. S.
Sholl
and
K. A.
Fichthorn
,
Phys. Rev. Lett.
79
,
3569
(
1997
).
59.
E. J.
Maginn
,
A. T.
Bell
, and
D. N.
Theodorou
,
J. Phys. Chem.
97
,
4173
(
1993
).
60.
S. C.
Reyes
,
J. H.
Sinfelt
, and
G. J.
DeMartin
,
J. Phys. Chem. B
104
,
5750
(
2000
).
61.
A. I.
Skoulidas
and
D. S.
Sholl
,
J. Phys. Chem.
106
,
5058
(
2002
).
62.
F. J.
Keil
,
R.
Krishna
, and
M.-O.
Coppens
,
Rev. Chem. Eng.
16
,
71
(
2000
).
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