Surface Permeabilities DOI: 10.1002/anie.200804785 Assessing Surface Permeabilities from Transient Guest Profiles in Nanoporous Host Materials** Despina Tzoulaki, Lars Heinke, Hyuna Lim, Jing Li, David Olson, Jürgen Caro, Rajamani Krishna, Christian Chmelik, and Jörg Kärger* The rate of mass exchange with the surroundings is essential for the technological performance of nanoporous materi- als [1–3] and depends on both the diffusion coefficients within the porous material and the surface permeabilities. [4] While diffusion within porous materials has been in the focus of numerous publications, [5–8] to date the surface permeability, which is important in nanotechnology and in life sciences [9] and medicine, [10] has not been considered quantitatively. With the introduction of interference microscopy, [8, 11] this defi- ciency may now be overcome. To date, the observation of transient concentration profiles in most of the nanoporous materials revealed substantial deviations from their ideal behavior. [12, 13] Moreover, repeating adsorption–desorption cycles often lead to dramatic changes in the observed concentration patterns. [14] Only very recently, crystals of the metal–organic framework (MOF) Zn(tbip) [15] (H 2 tbip = 5-tert-butyl isophthalic acid) proved to be stable enough to allow the essentially unlimited repetition of adsorption– desorption runs with complete reproducibility. This extra- ordinary quality allowed the measurement of surface perme- abilities under variation of guest sizes, guest concentrations, and the type of experiment (equilibrium and non-equilibri- um). Agreement between the concentration dependence of the surface permeabilities and the diffusion coefficients provides first insight into the nature of the surface resistances of these systems. Molecular exchange between the host system and the surrounding space is described by Ficks 2nd law implemented with a boundary condition [Eqs. (1)and (2)]. D, j(x=0), a, and c eq denote the diffusion coefficient in the host system, flux through the surface, surface permeability, and guest concen- tration in equilibrium with the external atmosphere, respec- tively. @cðx; tÞ @t ¼ @ @x D @cðx; tÞ @x ð1Þ jðx ¼ 0Þ¼ D @cðx; tÞ @x     x¼0 ¼ aðcðx ¼ 0Þ c eq Þ ð2Þ Following Equation (1), the diffusion coefficient may be determined from the spatial–temporal dependence of the concentration profile. [8, 11] Surface permeabilities, however, are directly accessible only at the crystal surface and, generally, have been determined by the best fit to the experimental data. [11, 16] While diffusion coefficients depend on the guest concentration, surface permeation is correlated with a whole range of concentrations, from the actual boundary concentration (c(x=0) = c surf ) to the equilibrium concentration c eq . We have explored the surface permeability as a function of these two limiting concentrations. Since surface permeabilities are expected to vary between different crystals, their concentration dependence must be determined with one crystal. Measurements of this type require a high degree of reproducibility which was feasible in the case of Zn(tbip). [15] Zn(tbip) crystals have an elongated, hexagonally pris- matic form with lengths of hundreds micrometers and diameters of tens of micrometers and are traversed by one- dimensional pores (Figure 1a) along their long axis. Their synthesis is described in Ref. [15] and Figure 1b,c show typical crystals. Samples were activated for 1.5 h under evacuation at 393 K. We selected ethane, propane, and n-butane as guest molecules. Sorption was initiated by varying the gas pressure in the surrounding atmosphere. The time constants of equilibration in the crystal were between 8.5–12 min for ethane and 30 h for n-butane. After equilibration with the surrounding gas phase, tracer-exchange experiments were started by replacing the molecules in the gas phase by their isotopes. All measurements were performed at room temper- ature. Concentration profiles were recorded by interference microscopy [8, 11, 16] and IR micro-imaging [17] (see the Support- ing Information for details). Figure 2 shows the permeability data obtained for one crystal from a large number of adsorption and desorption [*] D. Tzoulaki, L. Heinke, Dr. C. Chmelik, Prof.Dr. J. Kärger Department of Experimental Physics I, University of Leipzig Linnestrasse 5, 04103, Leipzig (Germany) Fax: (+ 49) 341-973-2549 E-mail: kaerger@physik.uni-leipzig.de H. Lim, Prof. Dr. J. Li, Prof. Dr. D. Olson Department of Chemistry and Chemical Biology, Rutgers University 610 Taylor Road, Piscataway, NJ 08854 (USA) Prof. Dr. J. Caro Department of Physical Chemistry and Electrochemistry Leibniz University of Hanover Callinstrasse 3a, 30167 Hanover (Germany) Prof. Dr. R. Krishna Van’t Hoff Institute for Molecular Sciences University of Amsterdam, Nieuwe Achtergracht 166 1018 WV Amsterdam (The Netherlands) [**] We thank German Research Foundation (DFG), INDENS Marie Curie Program, Studienstiftung des deutschen Volkes, Department of Energy (DOE) (Grant No. DE-FG02-08ER46491) for the financial support. Dr. J. M. van Baten is acknowledged for providing the snapshots of the channels. Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/anie.200804785. Angewandte Chemie 3525 Angew. Chem. Int. Ed. 2009, 48, 3525 –3528  2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim