Phase diagram of softly repulsive systems: the Gaussian and inverse-power-law potentials

We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.     

Unprecedented Electron‐Poor Octahedral Ta6 Clusters in a Solid‐State Compound: Synthesis,Characterisations and Theoretical Investigations of Cs2BaTa6Br15O3

The crystal structure of Cs₂BaTa₆Br₁₅O₃ has been elucidated by using synchrotron X‐ray powder diffraction and absorption experiments. It is built from edge‐bridged octahedral [(Ta₆${{\rm Br}{{{\rm i}\hfill \atop 9\hfill}}}$ ${{\rm O}{{{\rm i}\hfill \atop 3\hfill}}}$ )${{\rm Br}{{{\rm a}\hfill \atop 6\hfill}}}$ ]^4? cluster units with a singular poor metallic electron (ME) count equal to thirteen. This leads to a paramagnetic behaviour related to one unpaired electron. The arrangement of the Ta₆ clusters is similar to that of Cs₂LaTa₆Br₁₅O₃ exhibiting 14‐MEs per [(Ta₆${{\rm Br}{{{\rm i}\hfill \atop 9\hfill}}}$ ${{\rm O}{{{\rm i}\hfill \atop 3\hfill}}}$ )${{\rm Br}{{{\rm a}\hfill \atop 6\hfill}}}$ ]^5? motif. The poorer electron‐count cluster presents longer metal–metal distances as foreseen according to the electronic structure of edge‐bridged hexanuclear cluster. Density functional theory (DFT) calculations on molecular models were used to rationalise the structural properties of 13‐ and 14‐ME clusters. Periodic DFT calculations demonstrate that the electronic structure of these solid‐state compounds is related to those of the discrete octahedral units. Oxygen–barium interactions seem to prevent the geometry of the octahedral cluster to strongly distort, allowing stabilisation of this unprecedented electron‐poor Ta₆ cluster in the solid state.     

Time‐Resolved,In Situ DRIFTS/EDE/MS Studies on Alumina‐Supported Rhodium Catalysts: Effects of Ceriation and Zirconiation on Rhodium–CO Interactions

The effects of ceria and zirconia on the structure–function properties of supported rhodium catalysts (1.6 and 4 wt % Rh/γ‐Al₂O₃) during CO exposure are described. Ceria and zirconia are introduced through two preparation methods: 1) ceria is deposited on γ‐Al₂O₃ from [Ce(acac)₃] and rhodium metal is subsequently added, and 2) through the controlled surface modification (CSM) technique, which involves the decomposition of [M(acac)_x] (M=Ce, x=3; M=Zr, x=4) on Rh/γ‐Al₂O₃. The structure–function correlations of ceria and/or zirconia‐doped rhodium catalysts are investigated by diffuse reflectance infrared Fourier‐transform spectroscopy/energy‐dispersive extended X‐ray absorption spectroscopy/mass spectrometry (DRIFTS/EDE/MS) under time‐resolved, in situ conditions. CeO_x and ZrO₂ facilitate the protection of Rh particles against extensive oxidation in air and CO. Larger Rh core particles of ceriated and zirconiated Rh catalysts prepared by CSM are observed and compared with Rh/γ‐Al₂O₃ samples, whereas supported Rh particles are easily disrupted by CO forming mononuclear Rh geminal dicarbonyl species. DRIFTS results indicate that, through the interaction of CO with ceriated Rh particles, a significantly larger amount of linear CO species form; this suggests the predominance of a metallic Rh phase.     

Condensation and Crystal Nucleation in a Lattice Gas with a Realistic Phase Diagram

We reconsider model II of Orban et al. (J. Chem. Phys. 1968, 49, 1778–1783), a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: Upon closer inspection, the alleged liquid–vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier relative to crystal nucleation from the “liquid”.     

Statistical Entropy of a Lattice-Gas Model: Multiparticle Correlation Expansion

A formula expressing the statistical entropy of a lattice-gas model as a multiparticle correlation expansion is derived in the grand-canonical and in the canonical ensembles. The differences from the analogous expansion in the continuum case are elucidated. The Ising model in one dimension is discussed as a case study.     

Errata: Statistical Entropy of a Lattice-Gas Model: Multiparticle Correlation Expansion

Journal of Statistical Physics -     

A thermally stable Pt/Y-based metal-organic framework: Exploring the accessibility of the metal centers with spectroscopic methods using H2O, CH3OH, and CH3CN as probes

A metal-organic framework (MOF) based on Pt, Y, and 2,2'-bipyridine-5,5'-dicarboxylate (BPDC), stable up to 400 degrees C, has been synthesized and characterized. In this MOF, the Pt centers are coordinated to Cl and the N atoms of the BPDC unit, giving a local environment similar to that found in a series of Pt-organic complexes with catalytic activity toward C-H bond cleavage of alkanes. This new material is a heterogeneous counterpart to the corresponding metal-organic complex. The structure, determined by single-crystal XRD data, is the repetition of three covalently bonded layers. These layers form a block, which is stacking as an (a)(b)(c) sequence along the crystallographic b-axis. Each layer contains the Pt-organic unit, while Y atoms represent the connection between adjacent layers. No covalent connection is present between layer (a) of a block and layer (c) of an adjacent block. EXAFS (BM29 at the ESRF) analysis supports the XRD data. As this MOF crystallizes under hydrothermal conditions, water acts both as solvent and as a direct ligand of Y. Accessibility to the metal centers is demonstrated by reversible water desorption/readsorption, as determined by TPA/TPD, FTIR, UV-vis, EXAFS, and XANES. Importantly, the results show that the as-synthesized material will not suffer a permanent loss in porosity upon solvent removal. In addition to water, methanol, ethanol, and acetonitrile can also access the internal void of the dehydrated phase.     

Liquid-solid coexistence via the metadynamics approach

The metadynamics method, recently proposed by Laio and Parrinello as a general tool to map multidimensional free-energy landscapes [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)], has been exploited with the aim of illustrating the properties of generalized thermodynamic potentials across a discontinuous phase transition. Virtues and limitations of the method are discussed in the exemplifying case of the freezing of a Lennard-Jones fluid in two dimensions.     

The inconsistency in adsorption properties and powder XRD data of MOF-5 is rationalized by framework interpenetration and the presence of organic and inorganic species in the nanocavities

MOF-5 is the archetype metal-organic framework and has been subjected to numerous studies the past few years. The focal point of this report is the pitfalls related to the MOF-5 phase identification based on powder XRD data. A broad set of conditions and procedures have been reported for MOF-5 synthesis. These variations have led to materials with substantially different adsorption properties (specific surface areas in the range 700 to 3400 m(2)/g). The relatively low weight loss observed for some as synthesized samples upon solvent removal is also indicative of a low pore volume. Regrettably, these materials have all been described as MOF-5 without any further comments. Furthermore, the reported powder XRD patterns hint at structural differences: The variations in surface area are accompanied by peak splitting phenomena and rather pronounced changes in the relative peak intensities in the powder XRD patterns. In this work, we use single-crystal XRD to investigate structural differences between low and high surface area MOF-5. The low surface area MOF-5 sample had two different classes of crystals. For the dominant phase, Zn(OH)2 species partly occupied the cavities. The presence of Zn species makes the hosting cavity and possibly also adjacent cavities inaccessible and thus efficiently reduces the pore volume of the material. Furthermore, the minor phase consisted of doubly interpenetrated MOF-5 networks, which lowers the adsorption capacity. The presence of Zn species and lattice interpenetration changes the symmetry from cubic to trigonal and explains the peak splitting observed in the powder XRD patterns. Pore-filling effects from the Zn species (and partly the solvent molecules) are also responsible for the pronounced variations in powder XRD peak intensities. This latter conclusion is particularly useful for predicting the adsorption properties of a MOF-5-type material from powder XRD.