Assessing Guest Diffusivities in Porous Hosts from Transient Concentration Proﬁles Lars Heinke, 1 Despina Tzoulaki, 1 Christian Chmelik, 1 Florian Hibbe, 1 Jasper M. van Baten, 2 Hyuna Lim, 3 Jing Li, 3 Rajamani Krishna, 2 and Jo ¨rg Ka ¨rger 1 1 Faculty of Physics and Geosciences, Department of Interface Physics, University of Leipzig, Linne ´strasse 5, 04103 Leipzig, Germany 2 Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands 3 Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, New Jersey 08854, USA (Received 22 September 2008; published 11 February 2009) Using the short-chain-length alkanes from ethane to n-butane as guest molecules, transient concen- tration proﬁles during uptake or release (via interference microscopy) and tracer exchange (via IR microimaging) in Zn(tbip), a particularly stable representative of a novel family of nanoporous materials (the metal organic frameworks), were recorded. Analyzing the spatiotemporal dependence of the proﬁles provides immediate access to the transport diffusivities and self-diffusivities, yielding a data basis of unprecedented reliability for mass transfer in nanoporous materials. As a particular feature of the system, self- and transport diffusivities may be combined to estimate the rate of mutual passages of the guest molecules in the chains of pore segments, thus quantifying departure from a genuine single-ﬁle system. DOI: 10.1103/PhysRevLett.102.065901 PACS numbers: 66.30.je, 66.30.Pa, 68.43.Jk Owing to most recent signiﬁcant developments in ma- terial sciences [1] and driven by the fascinating prospects of technical application [2], the diversity of nanoporous materials is continuously increasing [3]. Diffusion is among those processes which may decide about the technological performance of these materials [4–6]. Simultaneously, it is one of the most fundamental phe- nomena and the investigation of diffusion under conﬁne- ment [7,8] is among the hot topics of current fundamental research. Thus, diffusion in nanoporous materials is ad- dressed in numerous publications, with many of them developing theoretical concepts for the explanation of experimental data [9–12]. However, beginning with the application of the pulsed ﬁeld gradient nuclear magnetic resonance to diffusion studies with zeolites [5,13,14], the experimental determination of reliable diffusivities in nanoporous host-guest systems proved to be far from triv- ial. In fact, in numerous cases ‘‘real’’ specimens of nano- porous material turned out to notably deviate from the ideal textbook structure, with the possibility that these devia- tions (pore blockage, cracks), rather than diffusion in the genuine pore space, become rate determining for the ob- served transport phenomena [15,16]. This constraint is of immediate impact on molecular modeling, since it is the experimental evidence which has to serve as the ultimate criterion of its validity. Among the numerous techniques applied to diffusion measurement in nanoporous materials [5,6,14,17], only the recently introduced methods of interference microscopy [16,18–20] and IR microimaging [16] [supplementary ma- terial (SM) 1 and 2 [21] ] are able to monitor transient concentration proﬁles and, hence, diffusion ﬂuxes directly in the interior of individual nanoporous crystallites. To our knowledge, never before in any type of matter could diffusion-driven transient concentration proﬁles be ob- served with a similar wealth of information [22,23]. Moreover, by following tracer exchange, IR microimaging is also able to operate under (quasi-) equilibrium condi- tions. The virtue of these techniques, namely, to focus on a particular, isolated crystal, raises the problem that the number of adsorption or desorption cycles which could be performed with an individual crystal remained rather limited due to sample instabilities. Though to different extents, for most of the investigated specimens the trans- port parameters were eventually found to change with increasing cycle numbers. With the advent of Zn(tbip) (H 2 tbip ¼ 5-tert-butyl isophthalic acid) [24], a highly sta- ble representative of the family of microporous metal organic frameworks (MOFs), we dispose of a nanoporous host system for which an essentially unlimited reproduc- ibility in subsequent adsorption-desorption cycles could be observed. Zn(tbip) (see Fig. 1 and SM 4) is traversed by an array of parallel chains of pore segments in the direction of longitudinal crystal extension. The resulting one- dimensionality of diffusion and structural stability make MOFs of type Zn(tbip) excellent candidates for a system- atic, experimentally founded investigation of the key fea- tures of mass transfer in nanoporous materials. Altogether, more than 60 different adsorption and de- sorption runs with three different guest molecules (ethane, propane, and n-butane) and three runs of tracer exchange (between propane and deuterated propane at two different loadings) have been performed. All measurements were carried out at room temperature (298 K). The adsorption and desorption experiments were initiated by a stepwise variation of the pressure in the surrounding gas atmosphere which can be assumed to occur essentially instantaneously. For observing tracer exchange, after equilibration with the host system, the molecules in the surrounding atmosphere were replaced by their isotopes. Examples of the evolution PRL 102, 065901 (2009) PHYSICAL REVIEW LETTERS week ending 13 FEBRUARY 2009 0031-9007= 09=102(6)=065901(4) 065901-1 Ó 2009 The American Physical Society