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.

     

Synthesis and structural studies of polynuclear ruthenium clusters derived from reactions of 1,2,3,4-tetraphenyl-1,2,3,4-tetraphospholane with [Ru3(CO)12]

Reactions of 1,2,3,4-tetraphenyl-1,2,3,4-tetraphospholane (I) with triruthenium dodecacarbonyl at different temperatures result in the cleavage of P-P bonds and even P-C bond(s) in I to afford a series of new ruthenium cluster derivatives containing phosphido and phosphinidene ligands: a penta-ruthenium wing-tip bridged butterfly cluster [Ru₅(CO)₁₁(μ₄-PPh)(μ₃-PPh){(μ₄-η²-(PPh)₂CH₂}] (1), a hepta-ruthenium polyhedral (consisting of two fused square pyramids with a co-apex) cluster [Ru₇(CO)₁₅(μ₄-PPh)₂{(μ₂-PPh)₂CH₂}](2), a linked penta-ruthenium cluster [Ru₄(CO)₁₀(μ₄-PPh)(μ₃-PPh)₂(μ₃-η²-PPhCH₂)Ru(CO)₃] (3), and a hepta-nuclear polyhedral (consisting of two fused square pyramids with different apexes) cluster [Ru₇(CO)₁₅(μ₄-PPh)₂{(μ₂-PPh)₂CH₂}](4). Clusters 2 and 4 are isomeric and differ only in the connection of the two square pyramids in the Ru₇ polyhedron. All the newly obtained clusters have been fully characterized by spectroscopic (IR, FABMS, ¹H- and ³¹P-NMR spectroscopy) and analytical techniques, and their molecular structures are established by single crystal X-ray diffraction analysis.     

Molecular Structure of Samarium Dibromide

The molecular structure of samarium dibromide has been studied by electron diffraction at T _exp = 1250(50) K. The molecule has C_2v symmetry; the internuclear distance R_g(Sm–Br) = 274.5(5) pm; _g =131(6)°. The vibration frequencies were estimated from the experimental values of the mean square vibration amplitudes.     

Structure and Dynamics of Methyl-substituted Beryllocene: [Be(C5Me5)2]

In this paper we study theoretically the molecular structure of [Be(C₅Me₅)₂], with special interest in similarities and differences found in the computed geometric parameters, depending on the treatment of the electron correlation used. Given the low energy differences found between the different configurations studied (less than 4 kcal mol⁻¹), and the high fluxionality found in experimental studies for this compound, we analyzed the dynamics of the system by means of first principles molecular dynamics calculations. A complex dynamics is found and analyzed in terms of two molecular rearrangement processes: 1,2-sigmatropic intraring rearrangement and a ring inversion mechanism that interchanges the roles (with regard to their coordination to the central Be atom) of the two rings.Dedicated to Dr. Jeal Paul Malrieu on occasion of his 65th birthday.     

A new class of aromatic polyetheraroylhydrazides. I. Synthesis and chemical–physical characterization

A series of new aromatic polyetheraroylhydrazides incorporating 4-oxybenzoyl units has been synthesized, whose general formula was [CONHNHCO? O? O–(CH₂)_x? O? phenyl O-CONHNHCOO]_n with x values in the range of 2 to 12. The increasing number of methylene units in the backbone gave rise to polymers which melted before the hydrazidic linkage underwent thermal cyclation to oxadiazole. Moreover, many polymers showed multiple endotherms on melting. X-ray diffraction studies confirmed a crystalline organization of polyhydrazides for methylene units above 4. © 1993 John Wiley & Sons, Inc.     

Synthesis, crystal structure and properties of K2Ta2S10: A novel ternary tantalum polysulfide with TaS8 polyhedra forming infinite anionic chains

The new ternary alkali tantalum polysulfide K₂Ta₂S₁₀ has been synthesized by reacting TaS₂ with an in situ formed melt of K₂S₃ and S at 773 K. The compound crystallizes with four formula units in the monoclinic space group P2₁/n (No. 14) with lattice parameters of . The structure contains two different zigzag chain anions [TaS₅]⁻, running parallel to the crystallographic b-axis separated by potassium cations. The two crystallographically independent tantalum atoms are in a distorted bi-capped trigonal prismatic environment of eight sulfur atoms which was never observed before. The TaS₈ polyhedra share three S atoms on each side to form the anionic chains. The compound was characterized with FIR and Raman spectroscopy.     

Structural integration of tellurium oxide into mixed-network-former glasses: connectivity distribution in the system NaPO(3)-TeO(2).

Sodium phosphate tellurite glasses in the system (NaPO(3))(x)(TeO(2))(1-) (x) were prepared and structurally characterized by thermal analysis, vibrational spectroscopy, X-ray photoelectron spectroscopy (XPS) and a variety of complementary solid-state nuclear magnetic resonance (NMR) techniques. Unlike the situation in other mixed-network-former glasses, the interaction between the two network formers tellurium oxide and phosphorus oxide produces no new structural units, and no sharing of the network modifier Na(2)O takes place. The glass structure can be regarded as a network of interlinked metaphosphate-type P(2) tetrahedral and TeO(4/2) antiprismatic units. The combined interpretation of the O 1s XPS data and the (31)P solid-state NMR spectra presents clear quantitative evidence for a nonstatistical connectivity distribution. Rather, the formation of homoatomic P--O--P and Te--O--Te linkages is favored over mixed P--O--Te connectivities. As a consequence of this chemical segregation effect, the spatial sodium distribution is not random, as also indicated by a detailed analysis of (31)P/(23)Na rotational echo double-resonance (REDOR) experiments.     

Syntheses and X-Ray Crystal Structures of 2-Aminoindenes and Aminocymantrenes

Substituted 2-aminoindenes have been synthesized in almost quantitative yields by reactions of amines such as methylpiperazine, trimethylethylenediamine, 1,4-diaza-cycloheptane and N,N′-dimethylethylenediamine with 2-indanone. The 2-aminoindenes can be deprotonated and reacted with BrMn(CO)₃(Py)₂ to produce the respective aminoindenyl-cymantrenes in yields between 55–70%. The X-ray crystal structures of 2-(methylpiperazine)indenyl-cymantrene 5 (P1 , a = 12.667(3) Å, b = 16.630(3) Å, c = 17.382(3) Å, α = 72.70(3)°, β = 74.59(3)°, γ = 88.66(3)°, V = 3364.1(12) Å ³, Z = 8, R1(2σ(I)) = 4.02%, wR2(2σ(I)) = 10.30%) and the HClO₄ adduct of 2-(trimethylethylenediamine)-indenyl-cymantrene 6 (Cc, a = 23.722(5) Å, b = 6.9080 Å, c = 13.264 Å, β = 111.77(3)°, V = 2018.6(7) Å 3, Z = 4, R1(2σ(I)) = 2.94%, wR2(2σ(I)) = 7.90%) were determined. In both complexes the indenyl-carbon bonded to nitrogen displays significantly longer bonds to manganese [223.5(3)–225.8(3) pm] than the other four carbon atoms [213.3(3)–219.1(3) pm]. The short indenyl-nitrogen bonds of 136.2(4) and 137.8(4) pm are indicative of a substantial multiple bond character. The complexation of Zn²⁺ by the nitrogen atoms of 6 results in significant shifts of the CO stretching frequencies.     

Where are the Sn atoms in LaSb2Snx, 0.1?x?∼0.75?

The composition range and (composite modulated) structure of compounds within the wide range non-stoichiometric LaSb₂Sn_x, 0.1?x?0.75, solid solution is carefully investigated via a combined electron diffraction, XRD and electron probe microanalysis study. Evidence for metastability of the LaSb₂Sn_x phase at the low x composition end of the solid solution is presented. Direct evidence is found for a reasonably (although by no means perfectly) well ordered Sn sub-structure which is, in general, mutually incommensurable with respect to a very well ordered underlying LaSb₂ sub-structure along both a and c directions. The overall (3+2)-d superspace group symmetry is given along with a discussion of the consequences as regards the arrangement of the Sn atoms. The Sn sub-structure c-axis cell dimension shows very little variation with composition x providing direct experimental evidence of the importance of Sn-Sn metallic bonding (along one-dimensional [001] Sn strings) for the stability of the phase.     

用θ-2θ型衍射仪测定溶液结构的新方法

叙述了用θ－２θ型Ｘ射线衍射仪精确测定电解质溶液结构的新实验技术。设计制作了具有恒温功能的超厚液体样品池，并建立了样品池窗口强度的校正方法。优化了液体Ｘ射线衍射数据和结构参数精细化的计算机程序，获得了非常令人满意的实验结果。由θ－２θ型Ｘ射线衍射仪精确测定的径向分布函数与θ－θ型衍射仪自由散射比较，表明ＤＲＦ分辨率有所提高。