Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

甾醇边链的化学修饰

本文对近年来甾醇边链结构改造的新方法和新动向--Barton 的Gif系统氧化反应及Breslow的远程功能化反应进行了综述。     

STATISTICS OF A NOVEL CLASS OF LIQUID CRYSTAL POLYMERS

A novel class of the liquid crystal polymers with mesogens laterally attached to flexible main chain backbones has been synthesized recently by us. While the flexible backbones tend to take configuration of maximum entropy the mesogenic side groups tend to orientate because of the anisotropie soft dispersion forces. A mean field theory is presented to describe the competition between these two trends which makes it possible for this class of polymers to show anisotropic (liquid crystal) phase within certain temperature range where the polymer main chains and the side chain mesogens will take approximately parallel arrangement, which is different from the normal side chain liquid crystal polymers. The temperature range of the liquid crystal phase, its ordering and phase transition all depend on the flexibility of the backbone, the strengthof the anisotropic forces of the side groups and the hinge elasticity. The results show that the liquid crystalisotropic phase transition is of the first order. The phase diagram, i. e. the dependence of the transition temperature on the structure of the polymers is also given.     

Propene polymerization using homogeneous MAO-activated metallocene catalysts: Me2Si(Benz[e]Indenyl)2ZrCl2/MAO vs. Me2Si(2-Me-Benz[e]Indenyl)2ZrCl2/MAO

Propene was polymerized at 40°C and 2-bar propene in toluene using methylalumoxane (MAO) activated rac-Me₂Si(Benz[e]Indenyl)₂ZrCl₂ ( BI ) and rac-Me₂Si(2-Me-Benz[e]Indenyl)₂ZrCl₂ ( MBI ). Catalyst BI /MAO polymerizes propene with high activity to afford low molecular weight polypropylene, whereas MBI /MAO is less active and produces high molecular weight polypropylene. Variation of reaction conditions such as propene concentration, temperature, concentration of catalyst components, and addition of hydrogen reveals that the lower molecular weight polypropylene produced with BI /MAO results from chain transfer to propene monomer following a 2,1-insertion. A large fraction of both metallocene catalyst systems is deactivated upon 2,1-insertion. Such dormant sites can be reactivated by H₂-addition, which affords active metallocene hydrides. This effect of H₂-addition is reflected by a decreasing content of head-to-head enchainment and the formation of polypropylene with n-butyl end groups. Both catalysts show a strong dependence of activity on propene concentration that indicates a formal reaction order of 1.7 with respect to propene. MBI /MAO shows a much higher dependence of the activity on temperature than BI /MAO. At elevated temperatures, MBI /MAO polymerizes propene faster than BI /MAO. © 1995 John Wiley & Sons, Inc.     

Neuartige Mäander mit Co3+ und Au3+: Na4[AuCoO5] = Na8 [(O2/2(CoO)O2AuO2/2)2]

Novel meander with Co³⁺ und Au³⁺: Na₄[AuCoO₅] = Na₈ ¹∞ [(O_2/2 (CoO)O₂AuO_2/2)₂] By “reaction with the wall” we obtained for the first time transparent brown single crystals of Na₄[AuCoO₅] while heating intimate mixtures of Co₃O₄, Na₂O₂, and K₂O₂ (Co: Na: K = 1.00:4.91:2.20; 650°C/44d) in a sealed gold-tube: monoclinic, P2₁/m, with a = 555.69(4) pm, b = 1042.11 (8) pm, c = 555.69(4) pm, β = 117.387(5)°, Z = 2. Characteristic features of Na₄[AuCoO₅] are meandric chains [(O_2/2 (CoO)O₂AuO_2/2)₂]. The structure has been determined by four-circle diffractometer data (Siemens AED 2; Mo? Kα , graphite, 881 I₀(hkl), R = 0.0366, R_w = 0.0316), parameters as given in the text. The Madelung Part of Lattice Energy, MAPLE, Effective Coordination Numbers, these via Mean Fictive Ionic Radii, and Charge-distribution, CHARDI, are calculated and discussed.     

Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification

Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.     

Model networks of end-linked polydimethylsiloxane chains

Summary Elastomeric networks of high extensibility were prepared by end-linking mixtures of vinyl-terminated polydimethylsiloxane chains having molecular weights of approximately 600 and 11,000 g mol^–1, with silanes chosen to give junction functionalities ranging from 3 to 8. The resulting bimodal networks were studied in elongation, at 25 °C, to their rupture points, and in swelling equilibrium in benzene at room temperature. The elongation moduli [f ^*] were found to be in satisfactory agreement with previous results obtained by end-linking hydroxyl-terminated polydimethylsiloxane chains. Values of [f ^*] at low and moderate deformations gave relatively low values of the ratio of elasticity constants 2C ₂/2C ₁, which is a measure of the extent to which the elongation changes from approximately affine to nonaffine as the elongation increases. The low values obtained for this ratio are presumably due to diminished interpenetration of configurational domains in the case of very short chains. In spite of its small magnitude, 2C ₂/2C ₁ does show some decrease with increase in , as predicted by the recent molecular theory of rubberlike elasticity developed by Flory. The swelling equilibrium results were also found to be in satisfactory agreement with theory. The elongation moduli increased significantly at high elongations, and the values of the elongation at which the upturn was first discernible were very nearly independent of , This is consistent with the interpretation of this anomalous behaviour in terms of limited chain extensibility. The maximum extensibility generally decreased somewhat with increase in and this caused a decrease in both the ultimate strength and the toughness of the elastomer, as measured by the energy required for rupture.     

Rigid-rod polymers with polysiloxane side chains. I. Synthesis and characterization of rigid-rod polyimides with polysiloxane side chains and their compatibility with linear polysiloxanes

Rigid-rod aromatic polyimdies having polydimethylsiloxane side chains were prepared for the purpose of dispersing rigid-rod molecules in silicone matrices for molecular reinforcement. The polyimides were obtained by imidizing the polyamide-acids bearing the side chains either thermally or chemically, which were synthesized by reacting 4,4′-diaminobiphenyl-terminated polysiloxane macromonomers with pyromellitic dianhydride in THF. The polyamide-acid films obtained by removing the solvent were soluble in THF, but the polyimides were insoluble in any common solvent. The polyimides showed no melting transition below 350°C on DSC analysis, at which temperature the side chain started decomposing. Although all the polyimides were anisotropic as observed by a polarizing microscope, x-ray diffraction analysis suggested the presence of only limited chain organization. Blends with linear polydimethylsiloxanes were prepared by casting the THF solution containing the polyamide-acid and the polydimethylsiloxane, followed by solvent evaporation and thermal imidization. With relatively longer side chains, the polyimides were proved to be compatibilized with polydimethylsiloxanes. © 1994 John Wiley & Sons, Inc.     

Synthesis and Crystal Structure of Two One—dimensional Chain Copper Complexes [Cu（TTA）2（4,4‘’—azpy）] and [Cu（TTA）2（3,3‘’—azpy）

Two copper complexes [Cu(TTA)₂(4,4′‐azpy)] (1) and [Cu‐(TTA)₂(3,3′‐azpy)] (2) (HTTA = 1,1,1‐trifluoro‐3‐(2‐thenoyl)‐acetone, 4,4′‐azpy = 4,4′‐azobispyridine, 3,3′‐azpy = 3,3′‐azobispyridine) were synthesized and characterized. The crystal structures were determined by X‐ray diffraction analysis. The crystal 1 belongs to triclinic with space group P1 , a = 0.8515(2) nm, b = 0.9259(2) nm, c = 0.9468(2) nm, a = 66.126(9)°, β = 79.667(9)°, γ = 90.13(1)°, Z = 1, V = 0.6692(2) nm³, D_c = 3.425 g/cm³, γ = 2.113 mm^?1, F(000) = 694, R₁ = 0.0594, wR₂ = 0.1499. The crystal 2 belongs to monoclinic with space group P2₁/c, a = 1.0661(2) nm, b = 1.4296(3) ran, c = 1.0041(3) nm, β = 114.50(3)°, V = 1.3926(5) nm³, Z = 2, D_c = 1.646 g/ cm³, μ = 1.015 mm^?1, F(000) = 694, R₁, = 0.0535, wR₂ = 0.1113. In the crystals of complexes 1 and 2, the copper atoms have distorted octahedral symmetry. The two compounds possess very similar one‐dimensional linear chains linked through the rodlike 4,4′‐azpy ligands or 3,3′‐azpy ligands.     

Design strategies for controlling the molecular weight and rate using reversible addition–fragmentation chain transfer mediated living radical polymerization

Living radical polymerization has allowed complex polymer architectures to be synthesized in bulk, solution, and water. The most versatile of these techniques is reversible addition–fragmentation chain transfer (RAFT), which allows a wide range of functional and nonfunctional polymers to be made with predictable molecular weight distributions (MWDs), ranging from very narrow to quite broad. The great complexity of the RAFT mechanism and how the kinetic parameters affect the rate of polymerization and MWD are not obvious. Therefore, the aim of this article is to provide useful insights into the important kinetic parameters that control the rate of polymerization and the evolution of the MWD with conversion. We discuss how a change in the chain‐transfer constant can affect the evolution of the MWD. It is shown how we can, in principle, use only one RAFT agent to obtain a polymer with any MWD. Retardation and inhibition are discussed in terms of (1) the leaving R group reactivity and (2) the intermediate radical termination model versus the slow fragmentation model. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3189–3204, 2005