Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains

We consider the Dirichlet eigenvalue problem for the Laplace operator on a variable nonsmooth domain. We extend a result of Lupo and Micheletti concerning the structure of the set of domain perturbations which leave the multiplicity of an eigenvalue unchanged, and we study the set of perturbations which leave a certain eigenvalue unchanged.     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

A new zirconium inorganic building brick forming metal organic frameworks with exceptional stability

Porous crystals are strategic materials with industrial applications within petrochemistry, catalysis, gas storage, and selective separation. Their unique properties are based on the molecular-scale porous character. However, a principal limitation of zeolites and similar oxide-based materials is the relatively small size of the pores, typically in the range of medium-sized molecules, limiting their use in pharmaceutical and fine chemical applications. Metal organic frameworks (MOFs) provided a breakthrough in this respect. New MOFs appear at a high and an increasing pace, but the appearances of new, stable inorganic building bricks are rare. Here we present a new zirconium-based inorganic building brick that allows the synthesis of very high surface area MOFs with unprecedented stability. The high stability is based on the combination of strong Zr-O bonds and the ability of the inner Zr6-cluster to rearrange reversibly upon removal or addition of mu3-OH groups, without any changes in the connecting carboxylates. The weak thermal, chemical, and mechanical stability of most MOFs is probably the most important property that limits their use in large scale industrial applications. The Zr-MOFs presented in this work have the toughness needed for industrial applications; decomposition temperature above 500 degrees C and resistance to most chemicals, and they remain crystalline even after exposure to 10 tons/cm2 of external pressure.     

Cu+(H2) and Na+(H2) adducts in exchanged ZSM-5 zeolites

Cu(I) ions in Cu-ZSM-5 form Cu+(H2) complexes, stable at room temperature and sub-atmospheric H2 pressure, which do not have any homogeneous analogue except for matrix-isolated [Cu(eta2-H2)Cl]. Comparison with the unstable Na+(H2) adducts formed in the parent Na-ZSM-5 zeolite allow the conclusion that the Cu(I)/H2 bond is governed by sigma-pi overlap forces.     

Phosphido‐diphosphine pincer group 3 complexes as efficient initiators for lactide polymerization

New Group 3 metal complexes of the type [LM(CH₂SiMe₃)₂(THF)_n] supported by tridentate phosphido‐diphosphine ligands [(o‐C₆H₄PR₂) ₂ PH; L1‐H : R = iPr; L2‐H : R = Ph] have been synthesized by reaction of L1‐H and L2‐H with [M(CH₂SiMe₃)₃(THF)₂)] (M = Y and Sc). All the new complexes [(o‐C₆H₄PR₂) ₂ PM(CH₂SiMe₃)₂(THF)_n] [M = Y, R = iPr (1), R = Ph (2); M = Sc, R = iPr (3), R = Ph (4)] were studied as initiators for the ring opening polymerization of lactide. The yttrium complexes ( 1 and 2 ) exhibited high activity and good polymerization control, shown by the linear fits in the plot of number‐averaged molecular weight (M_n) versus the percentage conversion and versus the monomer/initiator ratio and by the low polydispersity index values. Interestingly, very good molar‐mass control was observed even when L ‐Lactide was polymerized in the absence of solvent at 130 °C. A good molar‐mass control but lower activities were observed in the polymerization reaction of lactide promoted by the analogous scandium complexes 3 and 4 . © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1374–1382, 2010     

X-ray absorption spectroscopies: useful tools to understand metallorganic frameworks structure and reactivity

The large unit cells, the enormous flexibility and variation in structural motifs of MOFs represent a big challenge in the characterization of MOF materials, particularly in cases where single crystal diffraction data are not available. In this critical review it is shown that in cases where only powder diffraction data are available additional structural information, particularly regarding local coordination within the inorganic cluster, are often mandatory in order to solve the structure. There are also cases where the inorganic cluster does not follow the symmetry of the overall structure. In such cases diffraction techniques will just "see" an average structure, missing the local structure: a lack that may be critical for understanding the specific properties of the material. In both cases, EXAFS spectroscopy is the tool that provides complementary structural information on the inorganic cluster and the way it binds to the ligand. Selected examples will show how EXAFS will be relevant in: (i) confirming the structure obtained from diffraction refinements; (ii) highlighting that the inorganic cornerstone has a lower symmetry with respect to that of the organic framework; (iii) obtaining the local structure of the inorganic cluster in the desolvated material when desolvation causes a partial loss of long range order; (iv) obtaining the local structure of the inorganic cluster in the desolvated material after coordination of a probe (or reactant) molecule, including cluster deformation upon molecule coordination and metal-molecule binding distance; (v) evidencing the presence of impurities in the form of amorphous extra-phases (339 references).     

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.     

The role of dispersive forces determining the energetics of adsorption in Ti zeolites

Ti‐zeolites are interesting materials because of their key role in partial oxidation reactions, as well as under a fundamental point of view being regarded as single site catalysts. Both experimental and computational approaches have been widely applied to the characterization of their active sites, reaching a level of knowledge unmatchable by most other important catalysts. However, several questions are still open, being a proper energetic simulation of the adsorption process of simple molecules, fitting with the experimental outcomes, still missing. The present work wants to underline the role of dispersive forces in correctly determining the adsorption energies of H₂O and NH₃ in Ti chabazite: first dispersive contributions have been included through an ONIOM scheme, comparing the results from semiempirical Grimme scheme and fully ab initio MP2. Being the key contribution of dispersion proved, a fully periodic, Grimme dispersions inclusive approach has been applied, coming to results close to the experimental values. © 2016 Wiley Periodicals, Inc.