Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

光学活性甲苄菊酯的合成及其结构与活性关系的研究

本文改进了Goffinet方法,完成了(±)-trans菊酸的拆分;改进了Campbel?方法,只用一种拆分剂(奎宁)完成了对(±)-cis菊酸的拆分。用IR、~1HNMR、旋光度测定等方法确定了各甲苄菊酯光学异构体的结构。生物试验表明结构与活性有如下关系:1,各异构体中以1R-酯的杀虫活性为高,尤其(-)-(1R,3R)-trans甲苄菊酯对全部测试昆虫均显示较高的杀虫活性;2,昆虫不同,各异构体的活性次序也略有差异。     

Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN ₂ of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.

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Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN ₂ des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.

     

Deformation behavior of thin,compliant layers under tensile loading conditions

In this article, a connection is made between the behavior of thin layers of Newtonian liquids under tensile loading conditions and the behavior of highly deformable elastic or viscoelastic solids, which are more commonly used as adhesives. The behavior of Newtonian liquids is understood in the most quantitative detail and serves as a starting point for understanding the origins of fingering and cavitation instabilities that appear when the tensile deformation rates applied to these layers are sufficiently large. Similar instabilities appear in solid systems and can be attributed to common features of the stress distribution for incompressible liquids and solids. A unifying treatment is presented that can be used to understand the overall deformation behavior and adhesive performance of a wide variety of solid and liquid systems that are typically applied as thin layers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4023–4043, 2004     

Refractive Indices, Densities and Excess Molar Volumes of Monoalcohols + Water

The refractive index, n _D , and density, ρ, of binary mixtures of monoalcohols + water, have been measured at a temperature of 298.15,K and atmospheric pressure. The variation of the refractive indices of these solutions has also been determined with temperature in the range T = (278.15 to 338.15) K and atmospheric pressure. A comparative study has been made of the refractive indices obtained experimentally and those calculated by means of the Lorentz-Lorenz [Theory of Electrons, Dover Phoenix (1952)] and Gladstone-Dale relations [Trans. R. Soc. London 148:887–902 (1858)]; in all cases, the Gladstone–Dale equation was seen to afford values similar to those obtained experimentally. Calculations have been made of the excess molar volumes, V ^E, and the molar refraction deviations, ΔR, of these mixtures and the differences between the experimental values for refractive index and those obtained by means of the Gladstone–Dale equation. Values of V ^E were compared with others in the literature. In all cases the V ^E values were negative, and in all cases, except in the methanol + water, ΔR showed a maximum for x = 0.8.     

2MgO·2B2O3·MgCl2·14H2O-7.8%H3BO3-H2O体系多温相关系研究

研究了2MgO·2B2O3·MgCl2·14H20在不同温度下的7.8%H3BO3水溶液中的相转化产物及其溶解度.IR,XRD,TG及化学分析表明,相转化产物在0～22℃范围内为MgO·2B2O3·9H20;22～68℃为MgO·2B2O3·7.5H20;68～95℃为MgO·2B2O3·7H20;95～98.8℃为MgO·2B2O3·5H20;100～110℃为MgO·B2O3·3H20;110～120℃为2MgO·B2O3·2H20;120～170℃为2MgO·B2O3·1.5H20;170～200℃为2MgO·B2O3·H20.提出了相转化反应原理.     

Phase relations in NaxCrxTi8−xO16 at 1350 °C and crystal structure of hollandite-like Na2Cr2Ti6O16

Phase relations of rutile, freudenbergite, and hollandite structures were examined in the pseudobinary system NaCrO₂-TiO₂ (i.e., Na_xCr_xTi_8−xO₁₆) at 1350 °C. The hollandite structure was obtained in the composition range 1.7?x?2.0. The symmetry of the samples at room temperature was tetragonal for x=1.7 and 1.75, and monoclinic for x=1.8 and above. Single crystals of monoclinic hollandite Na₂Cr₂Ti₆O₁₆ were grown and the structure refinement has been carried out using an X-ray diffraction technique. The space group was I2/m and cell parameters were a=10.2385(11), b=2.9559(9), c=9.9097(11)Å, and β=90.545(9)° with Z=1. The Na ion distribution in the tunnel was markedly deformed from that in the tetragonal form. It was suggested that Cr/Ti ratios were different between the two framework metal sites.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

YIHn: A New Family of Metal‐rich Hydride Halides

The graphite‐like yttrium hydride halides, YIH_n (0.8 ? n ? 1.0), have been prepared in quantitative yields by heating either YI₃, YH₂ (1:2) or stoichiometric YI₃, YH₂, Y mixtures in sealed Ta ampoules at 900°C. A lower limit of the homogeneity range, n ≈ 2/3, has been determined from dehydrogenation experiments. All YIH_n phases adopt the ZrBr‐type heavy‐atom structure. The hydrogen variation is accompanied by a change in the c lattice constant from 31.162(3) to 31.033(1) Å for n = 0.61(3) to 1.02(3). The YIH_n phases reversibly react with hydrogen at 400‐600°C to form the light green transparent compound YIH₂. However, increasing the reaction temperature above 700°C causes decomposition to an unidentified phase being in equilibrium with YH₂ and YI₃. The arrangement of the heavy atoms in YIH₂ (P m1; a = 3.8579(3) Å, c = 10.997(1) Å) corresponds to a four‐layer I‐Y‐Y‐I slab with the stacking sequence (AbaB) as was found by x‐ray powder diffraction data refinement with the Rietveld method. A miscibility gap exists between YIH and YIH₂. Samples YIH_n (n ? 1.0) show metallic conductivity at room temperature, which changes into semiconducting behavior with decreasing temperature as n approaches its lower value ≈ 2/3.     

Kristallstruktur und Pseudosymmetrie einer neuen Modifikation von Kaliumhexachloroniobat(V), KNbCl6. Anmerkungen zur kubischen Phase

Crystal Structure and Pseudosymmetry of a New Modification of Potassium Hexachloroniobate(V), KNbCl₆. Comments on the Cubic Phase Long needles of KNbCl₆ – invariably twinned around [100] – are obtained if the material is crystallized from SOCl₂ solution. The structure has been determined from X-ray data collected with a single-crystal diffractometer at room temperature [space group P2₁/n, Z = 16, a = 6.894(1), b = 22.073(4), c = 23.337(3) Å, β = 91.00(1)°, R = 0.032 for 2 909 unique reflexions, 290 structural parameters]. Distorted NbCl₆^? octahedra and ?interstitial’? K⁺ ions are found to form similar arrangements, each of them corresponding to a closest packing of spheres with the layer sequence ACAB (stacking symbol hc). The resulting asymmetry in coordination by potassium is coupled with a strong off-centre displacement of the Nb atoms in any of the four independent chlorine polyhedra (0.14 Å on average). A pronounced pseudosymmetry accounts for the twinning. Since P2₁/m2₁/n2₁/b (no. 62) is already a good approximation of the real structure, only one formal step of symmetry reduction (index t2) is needed to create both, the observed twin law and the actual space group P1 2₁/n1. Above 180°C a reconstructive phase transition leads to the ‘face-centred cubic’ modification with ～ 10% lower density.