A relative gradient theory for layered materials

It is possible to remedy certain difficulties with the description of short wave length phenomena and interfacial slip in standard models of a laminated material by considering the bending stiffness of the layers. If the couple or moment stresses are assumed to be proportional to the relative deformation gradient, then the bending effect disappears for vanishing interface slip, and the model correctly reduces to an isotropic standard continuum. In earlier Cosserat-type models this was not the case. Laminated materials of the kind considered here occur naturally as layered rock, or at a different scale, in synthetic layered materials and composites. Similarities to the situation in regular dislocation structures with couple stresses, also make these ideas relevant to single slip in crystalline materials. Application of the theory to a one-dimensional model for layered beams demonstrates agreement with exact results at the extremes of zero and infinite interface stiffness. Moreover, comparison with finite element calculations confirm the accuracy of the prediction for intermediate interfacial stiffness.

Pore structure tailoring of pillared clays with cation doping techniques

Techniques and mechanism of doping controlled amounts of various cations into pillared clays without causing precipitation or damages to the pillared layered structures are reviewed and discussed. Transition metals of great interest in catalysis can be doped in the micropores of pillared clay in ionic forms by a two-step process. The micropore structures and surface nature of pillared clays are altered by the introduced cations, and this results in a significant improvement in adsorption properties of the clays. Adsorption of water, air components and organic vapors on cation-doped pillared clays were studied. The effects of the amount and species of cations on the pore structure and adsorption behavior are discussed. It is demonstrated that the presence of doped Ca2+ ions can effectively aides the control of modification of the pillared clays of large pore openings. Controlled cation doping is a simple and powerful tool for improving the adsorption properties of pillared clay.

Controlled doping of transition metal cations in alumina pillared clays

A two-step method of loading controlled amounts of transition metal cations into alumina pillared clays (Al-PILCs) is proposed. First, calcined Al-PILC was dispersed into an aqueous solution of sodium or ammonium ions. Increasing the pH of the dispersion resulted in an increase in the amount of cations loaded into the clay. The ion-doped Al-PILC was then exchanged with an aqueous solution of transition metal salt at a pH of similar to 4.5 to replace Na+ or NH4+ ions by transition metal cations. Analytical techniques such as atomic absorption spectroscopy, X-ray diffraction, diffuse reflectance-ultraviolet-visible spectroscopy, as well as N-2 adsorption were used to characterize the PILC products with and without the loading of metal ions. The introduced transition metal species exist in the forms of hydrated ions in the PILC hosts. The content of transition metal ions in the final product increased with the amount of Na+ or NH4+ loaded in the first step so that by controlling the pH of the dispersion in the first step, one can control the doping amounts of transition metal cations into Al-PILCs. A sample containing 0.125 mmol/g of nickel was thus obtained, which is similar to 3 times of that obtained by directly exchanging Al-PILC with Ni(NO3)(2) solution, while the pillared layered structures of the Al-PILC remained. The porosity analysis using N-2 adsorption data indicated that most of the doped transition metal ions dispersed homogeneously in the micropores of the Al-PILC, significantly affecting the micropore structure.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

Cracks of higher modes in Cosserat continua

Rotational degrees of freedom in Cosserat continua give rise to higher fracture modes. Three new fracture modes correspond to the cracks that are surfaces of discontinuities in the corresponding components of independent Cosserat rotations. We develop a generalisation of J- integral that includes these additional degrees of freedom. The obtained path-independent integrals are used to develop a criterion of crack propagation for a special type of failure in layered materials with sliding layers. This fracture propagates as a progressive bending failure of layers – a “bending crack that is, a crack that can be represented as a distribution of discontinuities in the layer bending. This situation is analysed using a 2D Cosserat continuum model. Semi-infinite bending crack normal to layering is considered. The moment stress concentrates along the line that is a continuation of the crack and has a singularity of the power − 1/4. A model of process zone is proposed for the case when the breakage of layers in the process of bending crack propagation is caused by a crack (microcrack in our description) growing across the layer adjacent to the crack tip. This growth is unstable (in the moment-controlled loading), which results in a typical descending branch of moment stress – rotation discontinuity relationship and hence in emergence of a Barenblatt-type process zone at the tip of the bending crack.

A straightforward wet-chemical route to the nanocomposites of general layered clays and metal sulfides

The nanocomposites of general layered clays and metal sulfides could be produced from reactions of the layered clay aqueous suspensions and water-soluble metal-thiourea complexes. The clay could be saponite, montmorillonite, hectorite and laponite, while the metal sulfide could be cobalt sulfide, nickel sulfide, zinc sulfide, cadmium sulfide, and lead sulfide. In the nanocomposites, the clay could be incorporated with the metal sulfide pillars and metal sulfide nanoparticles. (c) 2006 Elsevier B.V. All rights reserved.

Superconductivity mediated by charge fluctuations in layered molecular crystals

We consider the competition between superconducting, charge ordered, and metallic phases in layered molecular crystals with the theta and beta" structures. Applying slave-boson theory to the relevant extended Hubbard model, we show that the superconductivity is mediated by charge fluctuations and the Cooper pairs have d(xy) symmetry. This is in contrast to the kappa-(BEDT-TTF)(2)X family, for which theoretical calculations give superconductivity mediated by spin fluctuations and with d(x)2(-y)2 symmetry. We predict several materials that should become superconducting under pressure.

On the relationship between the critical temperature and the London penetration depth in layered organic superconductors

We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz–Thouless transition is more than an order of magnitude greater than is found experimentally for some materials. This places constraints on theories of superconductivity in these materials.

Cyclotron effective masses in layered metals

Many layered metals such as quasi-two-dimensional organic molecular crystals show properties consistent with a Fermi-liquid description at low temperatures. The effective masses extracted from the temperature dependence of the magnetic oscillations observed in these materials are in the range, m(c)*/m(e) similar to 1 - 7, suggesting that these systems are strongly correlated. However, the ratio m(c)*/m(e) contains both the renormalization due to the electron-electron interaction and the periodic potential of the lattice. We show that for any quasi-two-dimensional band structure, the cyclotron mass is proportional to the density-of-states at the Fermi energy. Due to Luttinger's theorem, this result is also valid in the presence of interactions. We then evaluate m(c) for several model band structures for the beta, kappa, and theta families of (BEDT-TTF)(2)X, where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene) and X is an anion. We find that for kappa-(BEDT-TTF)(2)X, the cyclotron mass of the beta orbit, m(c)*(beta) is close to 2 m(c)*(alpha), where m(c)*(alpha) is the effective mass of the alpha orbit. This result is fairly insensitive to the band-structure details. For a wide range of materials we compare values of the cyclotron mass deduced from band-structure calculations to values deduced from measurements of magnetic oscillations and the specific-heat coefficient gamma.

Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type

We consider the electronic properties of layered molecular crystals of the type theta -D(2)A where A is an anion and D is a donor molecule such as bis-(ethylenedithia-tetrathiafulvalene) (BEDT-TTF), which is arranged in the theta -type pattern within the layers. We argue that the simplest strongly correlated electron model that can describe the rich phase diagram of these materials is the extended Hubbard model on the square lattice at one-quarter filling. In the limit where the Coulomb repulsion on a single site is large, the nearest-neighbor Coulomb repulsion V plays a crucial role. When V is much larger than the intermolecular hopping integral t the ground state is an insulator with charge ordering. In this phase antiferromagnetism arises due to a novel fourth-order superexchange process around a plaquette on the square lattice. We argue that the charge ordered phase is destroyed below a critical nonzero value V, of the order of t. Slave-boson theory is used to explicitly demonstrate this for the SU(N) generalization of the model, in the large-N limit. We also discuss the relevance of the model to the all-organic family beta-(BEDT-TTF)(2)SF5YSO3 where Y=CH2CF2, CH2, CHF.

Porous clays and pillared clays-based catalysts. Part 2: A review of the catalytic and molecular sieve applications

Metal oxide pillared clay (PILC) possesses several interesting properties, such as large surface area, high pore volume and tunable pore size (from micropore to mesopore), high thermal stability, strong surface acidity and catalytic active substrates/metal oxide pillars. These unique characteristics make PILC an attractive material in catalytic reactions. It can be made either as catalyst support or directly used as catalyst. This paper is a continuous work from Kloprogge's review (J.T. Kloprogge, J. Porous Mater. 5, 5 1998) on the synthesis and properties of smectites and related PILCs and will focus on the diverse applications of clay pillared with different types of metal oxides in the heterogeneous catalysis area and adsorption area. The relation between the performance of the PILC and its physico-chemical features will be addressed.

Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

The synthetic organic compound λ(BETS)2FeCl4 undergoes successive transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe3+ magnetic ions in these phase transition. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. This suggests that the field-induced superconducting state is the same as the zero-field superconducting state which occurs under pressure or when the Fe3+ ions are replaced by non-magnetic Ga3+ ions. We show how Hc can be extracted from the observed splitting of the Shybnikov-de Haas frequencies. Furthermore, we use this method of extracting He to predict the field range for field-induced superconductivity in other materials. We also show that at high fields the spin fluctuations of the localized spins are not important.

Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4 and to the layered organic superconductors kappa-(BEDT-TTF)(2)X (BEDT-TTF bis(ethylene-dithio)tetrathiafulvalene); X anion)

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials K-(BEDT-TTF)(2)X, The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs2CuCl4. We find rich phase diagrams for each model. The Sp(N) :antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite N are also discussed. For parameters relevant to Cs2CuCl4 the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap, A metal-insulator transition occurs at intermediate values of the interaction strength.

Characterization of pore structure and coordination of titanium in TiO2 and SiO2-TiO2 sol-pillared clays

Titania sol-pillared clay (TiO2 PILC) and silica-titania sol-pillared clay (SiO2-TiO2 PILC) were synthesized by the sol-gel method. Supercritical drying (SCD) and treatment with quaternary ammonium surfactants were used to tailor the pore structure of the resulting clay. It was found that SCD approach increased the external surface area of the PILCs dramatically and that treatment with surfactants could be used to tailor pore size because the mesopore formation in the galleries between the clay layers follows the templating mechanism as observed in the synthesis of MCM-41 materials. Highly mesoporous solids were thus obtained. In calcined TiO2 PILC, ultrafine crystallites in anatase phase, which are active for photocatalytic oxidation of organics, were observed. In SiO2-TiO2 PILCs and their derivatives, titanium was highly dispersed in the matrix of silica and no crystal phase was observed. The highly dispersed titanium sites are good catalytic centers for selective oxidation of organic compounds. (C) 2001 Academic Press.

Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

l-(BETS)2FeCl4 undergoes transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe31 magnetic ions in these phase transitions. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. We show how He can be extracted from the observed splitting of the Shubnikov–de Haas frequencies. We predict the field range for field-induced superconductivity in other materials.