Analyzing Anisotropic Exchange in a Pentanuclear Os2Ni3 Complex

Spin Hamiltonian parameters of a pentanuclear Os Ni cyanometallate complex are derived from ab initio wave function based calculations, namely valence-type configuration interaction calculations with a complete active space including spin-orbit interaction (CASOCI) in a single-step procedure. While fits of experimental data performed so far could reproduce the data but the resulting parameters were not satisfactory, the parameters derived in the present work reproduce experimental data and at the same time have a reasonable size. The one-centre parameters (local matrices and single-ion zero field splitting tensors) are within an expected range, the anisotropic exchange parameters obtained in this work for an Os−Ni pair are not exceedingly large but determine the low-T part of the experimental χT curve. Exchange interactions (both isotropic and anisotropic) obtained from CASOCI have to be scaled by a factor of 2.5 to obtain agreement with experiment, a known deficiency of such types of calculation. After scaling the parameters, the isotropic Os−Ni exchange coupling constant is cm⁻¹ and the D parameter of the (nearly axial) anisotropic Os−Ni exchange is ⁻¹, so anisotropic exchange is larger in absolute size than isotropic exchange. The negative value of the isotropic J (indicating antiferromagnetic coupling) seemingly contradicts the large-temperature behaviour of the temperature dependent susceptibility curve, but this is caused by the negative g value of the Os centres. This negative g value is a universal feature of a pseudo-octahedral coordination with configuration and strong spin-orbit interaction. Knowing the size of these exchange interactions is important because Os(CN) is a versatile building block for the synthesis of / magnetic materials.     

An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

Crosslinking of vinyl‐terminated biphenyl and naphthalene side‐chain liquid‐crystalline poly(epichlorohydrin) derivatives

We performed the crosslinking of vinyl‐terminated biphenyl and naphthalene side‐chain liquid‐crystalline polyethers using peroxide‐type initiators with and without the addition of tertiary amine promoters. The crosslinking temperatures were chosen in the range of mesophase stability to allow the mesophase order to be frozen. The biphenyl derivatives, with a high isotropization temperature, were crosslinked to a large extent. This led to anisotropic thermosets. To crosslink naphthalene derivatives, amine promoters were needed, but degrees of crosslinking were lower, and anisotropic elastomers were obtained. Crosslinking processes were studied by differential scanning calorimetry, polarized optical microscopy, and Fourier transform infrared spectroscopy. The nature of the frozen mesophase was confirmed by X‐ray diffraction studies on mechanically oriented samples. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2237–2244, 2002     

Effect of microcrystallite preparation conditions on the formation of colloid crystals of cellulose

Stable colloidal suspensions of cellulose microcrystallites may be prepared from filter paper by sulfuric acid hydrolysis. Above a critical concentration, the suspensions form a chiral nematic ordered phase, or colloid crystal. The preparation conditions govern the properties of the individual cellulose microcrystallites, and hence the liquid crystalline phase separation of the cellulose suspensions. The particle properties and the phase separation of the suspensions were strongly dependent on the hydrolysis temperature and time, and on the intensity of the ultrasonic irradiation used to disperse the particles. The particle size of the microcrystallites was characterized with transmission electron microscopy and photon correlation spectroscopy. The surface charge was determined by conductometric titration. It was possible to fractionate the microcrystallites by size using the partitioning between isotropic and liquid crystalline phases; the longer microcrystallites migrate to the liquid crystalline phase     

[3,4]-annulated pyrroles 1. Polynuclear heterocyclic systems based on pyrrolo[3,4-d]pyrimidine-2,4-dione

The intramolecular electrophilic substitution in 6-functionalized 1,3-dimethyl-1H-pyrrolo[3,4-d]pyrimidine-2,4(3H,6H)-diones was used for the synthesis of pyrimido[4′,5′:3,4]-pyrrolo[1,2-a]quinoxaline-8,10(7H,9H)-dione, pyrimido[4′,5′:3,4]pyrrolo[2,1-c][1,2,4]benzo-triazine-8,10(7H,9H)-dione, and 2H-pyrimido[4′,5′:3,4]pyrrolo[1,2-a]indole-2,4,11(1H, 3H)-trione derivatives. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2180–2185, December, 2006.     

Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two‐dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.     

TMTSF2X Salts. Preparation,Structure and Effect of the Anions

The preparation of the TMTSF molecule and some of its properties are reviewed. The preparation of metallic and superconducting TMTSF X salts is described and some structural aspects are discussed, with emphasis of possible order-disorder transitions when X is a non-centrosymmetric anion. Preliminary results for TMTSF₂ TeF₅ which remain conducting to at least 5 K are presented.     

Shear modulus determination in model hydrogels by means of elongated magnetic nanoprobes

The mechanical characterization of complex soft matter by quasi-static magnetometry using nanoscopic magnetic probes is demonstrated for model hydrogels doped with two types of elongated magnetic nanoparticles. Chemically crosslinked poly(acrylamide) (PAAm) hydrogels serve as the matrix in which nickel nanorods or weakly magnetized hematite (α-Fe₂O₃) ellipsoids are embedded as local probes. We investigated the swelling behavior of the ferrogels in order to verify that their equilibrium swelling degree in water is not influenced by the probes, shows a good correlation with the Frenkel–Flory–Rehner model. The proposed magnetomechanical method relies on a correlation between the shear modulus of the PAAm hydrogel matrix and the coercive fields of the corresponding isotropic ferrogels. By extending the Stoner–Wohlfarth model for single-domain blocked magnetic particles by a term for particle rotation in an elastic matrix, information on the shear modulus of the matrix can be obtained. Comparison of the results with the expected relation from rubber elasticity theory illustrates both the general potential as well as the limits of the approach. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012