Polyethylenimine-Containing Cotton Fabrics

Abstract

Polyethylenimine-containing cotton fabrics were prepared by reaction of 1-epoxyethyl-3, 4-epoxycyclohexane with cotton fabric impregnated with polyethylenimine of a moderately high molecular weight. Fabrics with a high unremovable polyethylenimine content and with a different degree of cross-linking were obtained. Adsorption of several heavy metal salts such as mercuric chloride and cupric sulfate by the fabrics was investigated. Adsorption was controlled by polyethylenimine content of the fabric, extent of cross-linking, and the pH of the solution.     

Low temperature magnetic properties of trimeric clusters

The degeneracy in the Heisenberg model of the three chromium clusters having D₃ symmetry is split by the antisymmetric exchange interaction. Based on this new energy level scheme, the low temperature behavior of the specific heat and magnetic susceptibility are reexamined.     

A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.     

Condensing generalized polynomials

An extension of geometric programming to includegeneralized polynomials, and not onlyPositive polynomials, is described, together with an algorithm and a numerical example.     

Effects of the three-spin interactions on the magnetic properties of a simple cubic Ising ferromagnet

For a spin one-half simple cubic Ising ferromagnet, the three-spin interaction are shown to have significant effects on the Curie temperature, the magnetization and the magnetic specific heat based on a calculation by the Bethe-Peierls theory.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Poly?thylenimin enthaltende Baumwollegewebe

Ohne Zusammenfassung     

Numerical computation of second-order system response with variable parameters

Zusammenfassung Die im Aufsatz vorgeschlagene Methode erlaubt die numerische Berechnung des dynamischen Verhaltens von Systemen zweiter Ordnung mit veränderlichen Parametern. Dazu wird das System in zwei Teilsysteme erster Ordnung aufgespalten, die in Reihe wirken. Ihr Verhalten in aufeinanderfolgenden kurzen Zeitintervallen ist dann leicht zu berechnen. Als Beispiele für die Anwendung der Methode wurden Systeme mit veränderlicher hydraulischer Dämpfung gewählt. Eine Erweiterung auf andere Dämpfungsarten und auf Fälle veränderlicher Eigenfrequenz, wie auch auf Systeme höherer Ordnung, ist ohne weiteres möglich.