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.     

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.     

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     

Metallocene ethylene-1-octene copolymers: Influence of comonomer content on thermo-mechanical, rheological, and thermo-oxidative behaviours before and after melt processing in an internal mixer

The influence of the comonomer content in a series of metallocene-based ethylene-1-octene copolymers (m-LLDPE) on thermo-mechanical, rheological, and thermo-oxidative behaviours during melt processing were examined using a range of characterisation techniques. The amount of branching was calculated from ¹³C NMR and studies using differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) were employed to determine the effect of short chain branching (SCB, comonomer content) on thermal and mechanical characteristics of the polymer. The effect of melt processing at different temperatures on the thermo-oxidative behaviour of the polymers was investigated by examining the changes in rheological properties, using both melt flow and capillary rheometry, and the evolution of oxidation products during processing using infrared spectroscopy.The results show that the comonomer content and catalyst type greatly affect thermal, mechanical and oxidative behaviour of the polymers. For the metallocene polymer series, it was shown from both DSC and DMA that (i) crystallinity and melting temperatures decreased linearly with comonomer content, (ii) the intensity of the β-transition increased, and (iii) the position of the tan δ_max peak corresponding to the α-transition shifted to lower temperatures, with higher comonomer content. In contrast, a corresponding Ziegler polymer containing the same level of SCB as in one of the m-LLDPE polymers, showed different characteristics due to its more heterogeneous nature: higher elongational viscosity, and a double melting peak with broader intensity that occurred at higher temperature (from DSC endotherm) indicating a much broader short chain branch distribution.The thermo-oxidative behaviour of the polymers after melt processing was similarly influenced by the comonomer content. Rheological characteristics and changes in concentrations of carbonyl and the different unsaturated groups, particularly vinyl, vinylidene and trans-vinylene, during processing of m-LLDPE polymers, showed that polymers with lower levels of SCB gave rise to predominantly crosslinking reactions at all processing temperatures. By contrast, chain scission reactions at higher processing temperatures became more favoured in the higher comonomer-containing polymers. Compared to its metallocene analogue, the Ziegler polymer showed a much higher degree of crosslinking at all temperatures because of the high levels of vinyl unsaturation initially present.     

Traceability of (values carried by) reference materials

 Traceability is a property of the result of a measurement. Since values carried by (reference) materials must also have been obtained, of necessity, by measurement, the definition of traceability also applies to reference materials. It is extremely helpful to give the traceability (of the origin) of a reference material a separate name, i.e. 'trackability'. An analysis of the function of values carried by reference materials, shows that they can fulfill different functions, depending on the intended use. One of the functions located outside the traceability chain – and hence not very relevant for establishing traceability – is evaluating the approximate size of the uncertainty of the measurement of an unknown sample by performing a similar measurement on a reference material, used as a 'simulated sample'. Another function is located inside the traceability chain, where the reference material is used as an added 'internal standard'. Then, the value carried by the reference material is essential for establishing the traceability of the measured value of an unknown sample. In the latter application, the reference material acts as an 'amount standard' (the certified value for amount is used). Received: 11 November 1999 / Accepted: 24 February 2000     

连接基团链长度对季铵盐二聚表面活性剂C12-s-C12·2Br在水溶液中胶团化行为的影响

用电导法、稳态荧光法和粘度法研究了二聚表面活性剂C12-s-C12*2Br分子中的连接基团链长度(s=2, 3, 4, 6)对其在水溶液中聚集行为的影响. 实验发现, C12-s-C12*2Br的胶团生成能力远比其单体C12TABr强得多, 前者cmc值较后者降低一个数量级. 胶团聚集数N随表面活性剂浓度c的增大而增大, 其中当s=2时的N值在c=7.7 mmol/L后开始急剧增大. 计算结果表明, 此时胶团形状发生了明显变化, 形成了椭球形的胶团. 粘度测定结果也证实了这一点.