Gaussian random fields; mesoporous materials; SBA15
Abstract :
[en] Clipping a Gaussian random field at a level that is position-dependent yields statistically non-homogeneous morphologies, relevant to many ordered nanostructured materials. The 1-point and 2-point probability functions of the morphology are derived, as well as a general relation between the specific surface area and the gradient of the clipping function. The general results are particularized for the comprehensive analysis of small-angle x-ray scattering and nitrogen adsorption of SBA-15 ordered mesoporous silica.
Research Center/Unit :
Departement de Chimie Appliquée, ULiège
Disciplines :
Physics Materials science & engineering
Author, co-author :
Gommes, Cédric ; Université de Liège - ULiège > Département de chimie appliquée > Génie chimique - Génie catalytique
Pirard, Jean-Paul ; Université de Liège - ULiège > Département de chimie appliquée > Génie chimique - Génie catalytique
Language :
English
Title :
Morphological models of complex ordered materials based on inhomogeneously clipped Gaussian fields
Publication date :
December 2009
Journal title :
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
ISSN :
1539-3755
eISSN :
1550-2376
Publisher :
American Physical Society, College Park, United States - Maryland
Volume :
80
Pages :
061401
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
G. Matheron, Elements Pour Une Théorie des Milieux Poreux (Masson, Paris, 1967).
S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer, New York, 2001).
A. P. Roberts and E. J. Garboczi, Proc. R. Soc. London, Ser. A 458, 1033 (2002). 10.1098/rspa.2001.0900
C. H. Arns, M. A. Knackstedt, and K. R. Mecke, Phys. Rev. Lett. 91, 215506 (2003). 10.1103/PhysRevLett.91.215506
E. Roduner, Chem. Soc. Rev. 35, 583 (2006). 10.1039/b502142c
J. W. Cahn, J. Chem. Phys. 42, 93 (1965). 10.1063/1.1695731
J. A. Quiblier, J. Colloid Interface Sci. 98, 84 (1984). 10.1016/0021-9797(84)90481-8
N. F. Berk, Phys. Rev. Lett. 58, 2718 (1987). 10.1103/PhysRevLett.58.2718
M. Teubner and R. Strey, J. Chem. Phys. 87, 3195 (1987). 10.1063/1.453006
N. F. Berk, Phys. Rev. A 44, 5069 (1991). 10.1103/PhysRevA.44.5069
S. H. Chen, D. D. Lee, K. Kimishima, H. Jinnai, and T. Hashimoto, Phys. Rev. E 54, 6526 (1996). 10.1103/PhysRevE.54.6526
F. Bron and D. Jeulin, Image Anal. Stereol. 23, 33 (2004).
P. Levitz, Adv. Colloid Interface Sci. 76-77, 71 (1998). 10.1016/S0001-8686(98)00042-6
A. P. Roberts, Phys. Rev. E 55, R1286 (1997). 10.1103/PhysRevE.55.R1286
C. J. Gommes and A. P. Roberts, Phys. Rev. E 77, 041409 (2008). 10.1103/PhysRevE.77.041409
A. P. Roberts, Phys. Rev. E 56, 3203 (1997). 10.1103/PhysRevE.56.3203
D. J. Nott and R. J. Wilson, Signal Process. 80, 125 (2000). 10.1016/S0165-1684(99)00116-4
V. De Oliveira, Comput. Stat. Data Anal. 34, 299 (2000). 10.1016/S0167-9473(99)00103-6
J. A. Quintanilla and W. M. Jones, Phys. Rev. E 75, 046709 (2007). 10.1103/PhysRevE.75.046709
M. Grigoriu, J. Appl. Phys. 94, 3762 (2003). 10.1063/1.1600827
Y. Yin and A. P. Alivisatos, Nature (London) 437, 664 (2005). 10.1038/nature04165
I. W. Hamley, Angew. Chem., Int. Ed. 42, 1692 (2003). 10.1002/anie.200200546
J. Quintanilla and S. Torquato, Phys. Rev. E 55, 1558 (1997). 10.1103/PhysRevE.55.1558
A. P. Roberts and M. A. Knackstedt, Phys. Rev. E 54, 2313 (1996). 10.1103/PhysRevE.54.2313
P. Debye, H. R. Anderson, and H. Brumberger, J. Appl. Phys. 28, 679 (1957). 10.1063/1.1722830
J. G. Berryman, J. Math. Phys. 28, 244 (1987). 10.1063/1.527804
A. D. McNaught, and A. Wilkinson, Compendium of Chemical Terminology (Blackwell Scientific, Oxford, 1997).
D. Zhao, J. Feng, Q. Huo, N. Melosh, G. H. Fredrickson, B. F. Chmelka, and G. D. Stucky, Science 279, 548 (1998). 10.1126/science.279.5350.548
J. R. A. Sietsma, J. D. Meeldijk, J. P. den Breejen, M. Versluijs-Helder, A. J van Dillen, P. E. de Jongh, and K. P. de Jong, Angew. Chem., Int. Ed. 46, 4547 (2007). 10.1002/anie.200700608
F. Gao, Q. Lu, X. Liu, Y. Yan, and D. Zhao, Nano Lett. 1, 743 (2001). 10.1021/nl0156383
G. Dosseh, X. Yongde, and C. Alba-Simionesco, J. Phys. Chem. B 107, 6445 (2003). 10.1021/jp034003k
J. Prass, D. Müter, P. Fratzl, and O. Paris, Appl. Phys. Lett. 95, 083121 (2009). 10.1063/1.3213564
C. J. Gommes, H. Friedrich, M. Wolters, P. E. de Jongh, and K. P. de Jong, Chem. Mater. 21, 1311 (2009). 10.1021/cm803092c
H. Friedrich, P. E. de Jongh, A. J. Verkleij, and K. P. de Jong, Chem. Rev. (Washington, D.C.) 109, 1613 (2009). 10.1021/cr800434t
M. Kruk, M. Jaroniec, C. H. Ko, and R. Ryoo, Chem. Mater. 12, 1961 (2000). 10.1021/cm000164e
Z. Liu, O. Terasaki, T. Ohsuna, K. Hiraga, H. J. Shin, and R. Ryoo, ChemPhysChem 2, 229 (2001). 10.1002/1439-7641(20010417)2:4<229::AID- CPHC229>3.0.CO;2-G
S. Ciccariello, G. Cocco, A. Benedetti, and S. Enzo, Phys. Rev. B 23, 6474 (1981). 10.1103/PhysRevB.23.6474
O. Glatter and K. Kratky, Small-Angle X-ray Scattering (Academic, London, 1982).
S. Förster, A. Timmann, M. Konrad, C. Schellbach, A. Meyer, S. S. Funari, P. Mulvaney, and R. Knott, J. Phys. Chem. B 109, 1347 (2005). 10.1021/jp0467494
See EPAPS Document No. E-PLEEE8-80-014912 for the derivation of the relation between 2-point function and specific surface area for inhomogeneous morphologies, as well as for the details of calculations leading to Eq.. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.