Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

A novel trilinear decomposition algorithm： Three-dimension non-negative matrix factorization

Non-negative matrix factorization(NMF)is a technique for dimensionality reduction by placing non-negativity constraints onthe matrix.Based on the PARAFAC model,NMF was extended for three-dimension data decomposition.The three-dimension non-negative matrix factorization(NMF3)algorithm,which was concise and easy to implement,was given in this paper.The NMF3algorithm implementation was based on elements but not on vectors.It could decompose a data array directly without unfolding,which was not similar to that the traditional algorithms do.It has been applied to the simulated data array decomposition andobtained reasonable results.It showed that NMF3 could be introduced for curve resolution in chemometrics.     

Theoretical prediction of the contact distance dependence of the electron transfer reactivity of the ClO/ClO− coupling system

On the basis of the structures and properties of the ClO/ClO^? system obtained at the density functional theory (DFT) (UB3LYP) level, employing the 6‐311+G(3df) standard basis set, the electron transfer reactivity of this system is investigated. The results indicate that there are five possible stable coupling complexes that correspond to the generous minima on the global potential energy surfaces (PES). The most stable coupling complex is planar EC4, in which there is a O? O linkage with two trans‐Cl atoms. Their stabilization energies are calculated to be 20.57 (EC1: C₁), 20.54 (EC2: C₂, ²B), 20.69 (EC3: C₁), 20.70 (EC4: C_s, ²A′), and 20.69 (EC.5: C_2h, ²B_u) kcal/mol at the B3LYP/6‐311+G(3df) level; with the correction of the basis set superposition error (BSSE), the stability order of these encounter complexes is EC4 > EC.5 > EC3 > EC1 > EC2. Based on the five encounter complexes, five coupling modes are designed for the study of the electron transfer reactivity of this system. The dissociation energy curves at the activated states and the corresponding activation energies of these five coupling modes are obtained and are compared at the B3LYP/6‐311+G(3df) and MP2/6‐311+G* levels. The inapplicability of DFT methods has also been discussed in this article in predicting the energy curves, especially with a long contact distance, in which DFT methods give the abnormal behavior for the dissociations of the complexes caused by the “inverse symmetry breaking” problem. On the basis of the golden rule of the time‐dependent perturbation theory, the electron transfer reactivity and the contact distance dependence of the various electron transfer kinetics parameters (e.g., activation energy, coupling matrix element) have been analyzed at the UMP2(full)/6‐311+G* level. The electron transfer can take place over a range of contact distances, but the most effective coupling distance corresponds to only a small range. The coupling orientation analyses also indicate that the most favorable coupling mode to the electron transfer does not always correspond to the most stable encounter complex mechanism. Some highly energetic coupling modes are more favorable for the electron transfer. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the calculation of expectation values and transition matrix elements by coupled cluster method

Summary Finite order expressions are derived for expectation values and transition matrix elements within the framework of the coupled cluster method.     

Metallic Particles from Complexing Microcapsules Dispersed in a Silica Gel

A new process to control the distribution of metal nanoparticles is proposed. It involves the use of complexing microcapsules obtained by interfacial polycondensation. The latter are hollow spheres constituted of a polymer membrane, containing an insoluble active ingredient, such as a polyacrylic acid, which can complex Co²⁺ ions. These capsules are dispersed in a silica sol followed by thermal treatments and reduction under H₂ which results in metallic Co nanoparticles confined in the capsules domains. The particles do not diffuse in the matrix.     

Separating Ag, B, Cd, Dy, Eu, and Sm in a Gd matrix using 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester extraction chromatography for ICP-AES analysis

The separation procedure for Ag, B, Cd, Dy, Eu and Sm as impurities in Gd matrix using ICP-AES technique with an extraction chromatographic column has been developed. The spectral interference of the Gd matrix on the elements was eliminated using a chromatography technique with 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (PC-88A) as the mobile phase and XAD-16 resin as the stationary phase. Ag⁺, B₄O₇²⁻, and Cd²⁺ were eluted with 0.1 M HNO₃, while rare earth ions were not. The best eluent for separating Eu and Sm in the Gd matrix was 0.3 M HNO₃. The limit of quantitation for these elements was 0.6-3.0 ng mL⁻¹. The recovery of Ag, B, and Cd was 90-104% using 0.1 M HNO₃ as the eluent, while that of Eu, Gd, and Sm ranged from 100 to 102% with 0.3 M HNO₃. Dy was recovered quantitatively with 4 M HNO₃. The relative standard deviation of the methods for a set of three replicates was between 1.0 and 15.4% for the synthetic and standard Gd solutions. The proposed separation procedure was used to measure Ag, B, Cd, Dy, Eu, and Sm in a standard Gd solution.     

Photo-initiated base-formation in a polymer matrix

It was found that amines were formed efficiently by the photolysis of O-acyloximes followed by hydrolysis in polystyrene films and the relationship between structures of O-acyloximes and yields of amines were investigated. O-phenylacetyl acetophenone oxime (PaApO), O-pivaloyl acetophenone oxime (PApO), and O-benzoyl acetophenone oxime (BApO) as monofunctional O-acyloximes and O,O′-succinyl diacetophenone oxime (SDApO) and O,O′-glutaryl diacetophenone oxime (GDApO) as bifunctional O-acyloximes were examined. The yields of amines for PaApO and SDApO under N₂ were ca. 70%, which was the highest among O-acyloximes examined in this experiment. On the other hand, the yields for PApO, BApO, and GDApO were less than 15% and it was verified that the hydrogen abstraction by imino radicals via 6-membered cyclic intermediates resulted in the lowering of yields. Although the effect of oxygen under photolysis on the yields of amine for PaApO was negligible under 50% conversion of PaApO, the yield decreased with further increase in the conversion and was 50% at 90% conversion. © 1994 John Wiley & Sons, Inc.     

PREPARATION OF POLY（METHYL METHACRYLATE）/LAYERED DOUBLE HYDROXIDES NANOCOMPOSITES via in situ SOLUTION POLYMERIZATION

An exfoliated layered double hydroxides/poly(methyl methacrylate)(LDHs/PMMA)nanocomposite was prepared by in situ solution polymerization of methyl methacrylate(MMA)in the presence of 4-vinylbenzenesulfonate intercalated LDHs(MgAl-VBS LDHs).MgAl-VBS LDHs was prepared by the ion exchange method,and the structure and composition of the MgA1-VBS LDHs were determined by X-ray diffraction(XRD),infrared spectroscopy and elemental analysis.XRD and transmission electron microscopy(TEM)were employed to examine the structure of LDHs/PMMA nanocomposite.It was indicated that the LDHs layers were well exfoliated and dispersed in the PMMA matrix.The grafting of PMMA onto LDHs was confirmed by the extraction result and the weight fraction of grafted PMMA increased as the weight fraction of LDHs in the nanocomposites increased.     

Ce(IV) ion initiated graft polymerization of glycidylmethacrylate onto a demineralized bone matrix: effect of reaction parameters

Studies on chemical modification of demineralized bone matrix (DBM) have opened new arenas in the field of clinical orthopedics owing to its potential osteoinductivity with desired chemical functionality. To widen its usage to biomolecular delivery, graft polymerization of glycidylmethacrylate onto DBM was carried out by a free-radical initiating process using ceric ammonium nitrate as an initiator. The evidence of the grafting reaction was examined by chemical analysis using Fourier transform IR spectroscopy. The grafting condition was standardized by regulating the reaction parameters such as the concentrations of the backbone, the monomer and the initiator, the polymerization temperature and time. The optimum polymerization temperature and time to have the maximum grafting yield were 40 °C and 3 h, respectively. The percentage of grafting and the percentage of grafting efficiency were determined as a function of the reaction parameters, and both were found to increasing initially and thereafter decrease in most of the cases. The grafting results are discussed in a detailed fashion and a reaction mechanism is proposed.