For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact relations for the means to describe the thermodynamics of the model under consideration.
The interaction of mesoporous chromium(III) terephthalate [Cr 3 O(C 8 H 4 O 4 ) 3 F(H 2 O) 2 ](MIL 101) with an aqueous solution of the anionic cluster [Re 4 S 4 F 12 ] 4-({Re 4 }) afforded a novel hybrid material {Re 4 }@MIL 101. According to the elemental analysis data, one cavity of the nanoporous framework contains up to two three tetranuclear rhenium clusters. The hybrid sorbent obtained reversibly absorbs up to 3.7 wt.% hydrogen at 77 K and 30 atm.Metal organic frameworks (coordination polymers) form regular structures consisting of metal cations bridged by organic ligands. 1,2 Recently porous coordination poly mers attract great attention due to their possible use in separation, sorption, and storage of gases, first of all, hy drogen. 3-12 The metal organic framework materials with specific H 2 uptakes of ~7.5 wt.% at Т = 77 K and mod erate pressure were prepared. 8 The optimum sorbents for H 2 storage are considered 13 to have narrow (to 1 nm) channels and coordinatively unsaturated polar sites (metal cations), which more strongly hold H 2 molecules on the sorbent surface. For these reasons, the mesoporous struc tures with a pore size of 2-50 nm are not promising sor bents capable of absorbing large amounts of hydrogen, because in these frameworks a considerable part of the structure is not filled by H 2 molecules. We propose the approach to increasing the sorption characteristics of me soporous metal organic frameworks with respect to hy drogen based on the occlusion of polar fluoride metal clus ters in large nanocavities, which decreases the free space in frameworks and provides an additional polarization of the surface inside the new hybrid structure.The present work describes the preparation and study of the characteristics of the hybrid sorbent of the new type {Re 4 }@MIL 101 ({Re 4 } ([Re 4 S 4 F 12 ] 4-, MIL 101, chrom ium(III) terephthalate [Cr 3 O(C 8 H 4 O 4 ) 3 F(H 2 O) 2 ]) and the examination of the hydrogen uptake on this sorbent.
Results and DiscussionThe methods for the preparation of the unique com pound MIL 101 with the zeolite like topology of the met al organic framework have recently been developed. 14 In the porous structure of such a material, regular nanosized cavities of two types with diameters of 3.0 and 3.8 nm are interconnected by windows 1.1 and 1.5 nm in size (Fig. 1). Simplicity of preparation and high thermal and hydrolytic stabilities of the MIL 101 framework are its unambiguous advantages over other mesoporous coordination polymers. The sorption properties of these nanostructures with re spect to hydrogen were reported. 15 The capacity with re spect to hydrogen for MIL 101 at 77 K and 8 MPa is 6.1 wt.% and does not exceed the best parameters for the microporous metal organic coordination polymers under similar conditions. In addition, the heterogeneous cata lysts of the new type were obtained 14,16 on the basis of MIL 101 by the inclusion of catalytically active Keggin polyoxometallates into the framework cavity.In the present work, the tetranuclear rhenium fluoride clus...
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