title: Scale-dependent diffusion anisotropy in nanoporous silicon.
abstract: Nanoporous silicon produced by electrochemical etching of highly B-doped p-type silicon wafers can be prepared with tubular pores imbedded in a silicon matrix. Such materials have found many technological applications and provide a useful model system for studying phase transitions under confinement. This paper reports a joint experimental and simulation study of diffusion in such materials, covering displacements from molecular dimensions up to tens of micrometers with carefully selected probe molecules. In addition to mass transfer through the channels, diffusion (at much smaller rates) is also found to occur in directions perpendicular to the channels, thus providing clear evidence of connectivity. With increasing displacements, propagation in both axial and transversal directions is progressively retarded, suggesting a scale-dependent, hierarchical distribution of transport resistances ("constrictions" in the channels) and of shortcuts (connecting "bridges") between adjacent channels. The experimental evidence from these studies is confirmed by molecular dynamics (MD) simulation in the range of atomistic displacements and rationalized with a simple model of statistically distributed "constrictions" and "bridges" for displacements in the micrometer range via dynamic Monte Carlo (DMC) simulation. Both ranges are demonstrated to be mutually transferrable by DMC simulations based on the pore space topology determined by electron tomography.
authors.affiliation: University of Leipzig, Faculty of Physics and Earth Sciences, Linnéstraße 5, D-04103 Leipzig, Germany.|University of Gießen, Institute of Theoretical Physics, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany.
authors.forename: Daria
authors.initials: D
authors.lastname: Kondrashova
authors.affiliation: University of Leipzig, Faculty of Physics and Earth Sciences, Linnéstraße 5, D-04103 Leipzig, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Lauerer
authors.affiliation: University of Leipzig, Faculty of Physics and Earth Sciences, Linnéstraße 5, D-04103 Leipzig, Germany.
authors.forename: Dirk
authors.initials: D
authors.lastname: Mehlhorn
authors.affiliation: Institut de Recherches sur la Catalyse et l'Environnement - CNRS 2, Avenue Albert-Einstein, F-69626 Villeurbanne Cedex, France.
authors.forename: Hervé
authors.initials: H
authors.lastname: Jobic
authors.affiliation: Leibniz University Hannover, Institute of Physical Chemistry and Electrochemistry, Callinstr. 3-3A, D-30167 Hannover, Germany.
authors.forename: Armin
authors.initials: A
authors.lastname: Feldhoff
authors.affiliation: Quantachrome Ins., 1900 Corporate Drive, Boynton Beach, Florida 33426, USA.
authors.forename: Matthias
authors.initials: M
authors.lastname: Thommes
authors.affiliation: Indian Institute of Science Education &Research Mohali, Sec 81, SAS Nagar, Manauli - 140306, Punjab, India.
authors.forename: Dipanjan
authors.initials: D
authors.lastname: Chakraborty
authors.affiliation: Utrecht University, Department of Inorganic Chemistry and Catalysis, Sorbonnelaan 16, NL-3584 CA Utrecht, The Netherlands.
authors.forename: Cedric
authors.initials: C
authors.lastname: Gommes
authors.affiliation: Utrecht University, Department of Inorganic Chemistry and Catalysis, Sorbonnelaan 16, NL-3584 CA Utrecht, The Netherlands.
authors.forename: Jovana
authors.initials: J
authors.lastname: Zecevic
authors.affiliation: Utrecht University, Department of Inorganic Chemistry and Catalysis, Sorbonnelaan 16, NL-3584 CA Utrecht, The Netherlands.
authors.forename: Petra
authors.initials: P
authors.lastname: de Jongh
authors.affiliation: University of Gießen, Institute of Theoretical Physics, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany.
authors.forename: Armin
authors.initials: A
authors.lastname: Bunde
authors.affiliation: University of Leipzig, Faculty of Physics and Earth Sciences, Linnéstraße 5, D-04103 Leipzig, Germany.
authors.forename: Jörg
authors.initials: J
authors.lastname: Kärger
authors.affiliation: University of Leipzig, Faculty of Physics and Earth Sciences, Linnéstraße 5, D-04103 Leipzig, Germany.
authors.forename: Rustem
authors.initials: R
authors.lastname: Valiullin