Elastic moduli and structure of low density polyethylene

Summary Low density polyethylene film is drawn at room temperature four times the original length and subjected to thermal annealing at 60, 80, and 100 °C keeping the film length constant. Long spacing measured by SAXS increased with increasing temperature of annealing; the increase of the long spacing is presumed to be due to the decrease of the number of micelles through relaxation during the annealing. Simultaneous measurement of the changes of the long spacing and the film length by stretching is carried out and stress-extension curves are obtained. The values of the initial moduli of the long spacingE ₁ and the film lengthY are very near to each other. Elastic modulus of the crystal latticeE _c is known to be 235 GN/m² and that of the amorphous regionE _a is found to be 0.15 GN/m². When higher stress is applied than in the case of the initial modulus, the percentage of extension of film is much greater than that of the long spacing. The discrepancy is explained by the increase of the number of micelles through stress crystallization.Dedicated to Professor Dr. K. Ueberreiter on the occasion of his 70th birthday.     

POLYMER NETWORK-POLY(ETHYLENE GLYCOL)COMPLEXES WITH SHAPE MEMORY EFFECT

The complexes of poly(methacrylic acid-co-methyl methacrylate) network with poly(ethylene glycol) stabilized byhydrogen bonds were prepared. By introducing the poly(ethylene glycol), a large difference in storage modulus below andabove the glass transition temperature occurred and the complexes exhibited shape memory behaviors. The morphology ofcomplexes was studied by using DSC, WAXD, and DMA. The results indicate that the fixed phase of this kind of novelshape memory materials is the network, and the reversible phase is the amorphous state of PEG:PMAA complex phase. Theshape recoverability almost reaches 100%. This type of complexes can be regarded as a novel shape memory network.     

Interplay of Electronic Structure and Bulk Properties in 2D and 3D Ternary Carbonitrides from First Principles

The changes in electronic structure and hardness as inferred from the bulk modulus are investigated for model structures of ternary compounds XC₃N₃ (X = B, Al, P, As, Ga) within the framework of density functional theory (DFT). The optimisations of the proposed two‐ (2D) and three‐dimensional (3D) structures and the calculations of the bulk moduli are performed by a pseudo potential method. The electronic structures are calculated with the augmented sphere wave method (ASW). The obtained hardness for 2D BC₃N₃ system (B₀ ～ 220 GPa) points to a magnitude close to that of graphitic C₃N₄. For heavier X atoms it decreases rapidly. This is equally observed for the 3D systems examined in the β‐C₃N₄ structure for which B₀(β‐BC₃N₃) amounts to ～330 GPa. Within the magnitude of the well known hard material cubic BN, the BC₃N₃ phases can be predicted as candidates for ultra hard materials. The electronic effect induced by the chemical nature of the X substitutional was examined according to its position in the periodic table i.e. X_III or X_V. Both, band structures and the electron localisation function (ELF) were used for this analysis. The ELF plots show a decreasing covalency with heavier X‐atoms. Potential applications of the devised systems are proposed such as dopings with atoms (Li, rare gas) and molecules (N₂).     

Aging effect on the mechanical properties of hybrid gels

Sol-gel derived unsupported films and thin rods have been obtained from co-hydrolysis of triethoxysilane and methyldiethoxysilane. The materials are flexible, dense and transparent. Films and rods have been aged for different periods of time in air at room temperature. The elastic modulus has been measured by means of tensile or flexural tests. Measurements showed an increase of elastic modulus with aging time and showed different values for films and rods. The observed evolution of mechanical properties has been related to a corresponding structural modification as highlighted mainly by MAS-NMR studies. Analyses pointed out the crucial role of condensation processes and showed that the stiffness increase arises from the formation of relatively few bonds which link and constrain pre-existing mobile network regions.     

Quantitative evaluation of stress distribution in bulk polymer samples through the comparison of mechanical behaviors between giant single‐crystal and semicrystalline samples of poly(trans‐1,4‐diethyl muconate)

The Raman shift and crystallite modulus were measured under the application of tensile force for a giant single crystal and a series of uniaxially oriented semicrystalline samples of poly(trans‐1,4‐diethyl muconate) (polyEMU). The apparent Raman shift factor α^app or a vibrational frequency shift per 1 GPa tensile stress was higher for the semicrystalline samples with lower crystallinity or lower bulk modulus. The apparent crystallite modulus E or Young's modulus along the chain axis in the crystalline region was not constant but varied remarkably between the giant single crystal and semicrystalline samples. A systematic change in α^app and E among the polyEMU samples with different preparation history could be interpreted quantitatively on the basis of a mechanical series parallel model consisting of crystalline and amorphous phases. The origin of different E and α^app was speculated to be a stress concentration on the taut‐tie chain contained as a parallel crystalline component in the mechanical model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 444–453, 2003     

General analysis of the measurements of the lateral crystal lattice moduli of semicrystalline polymers by x-ray diffraction and the application to nylon 6

A mathematical representation based on a linear elastic theory is proposed by which one may investigate the dependences of molecular orientation and crystallinity on the crystal lattice moduli and linear thermal expansion coefficients in the direction perpendicular to the chain axis as commonly measured by x-ray diffraction. In the theoretical calculation, a previously introduced model was employed in which oriented crystalline phase is surrounded by oriented amorphous phase and the strains of the two phases at the boundary are identical. The mathematical analysis indicated that the lateral crystal lattice moduli and linear thermal coefficients as measured by x-ray diffraction may be different from the intrinsic crystal moduli and linear thermal coefficients of a crystal unit cell, depending on the structure of the polymer solid. The numerical calculation was applied to nylon 6. As a result, it may be confirmed that the lateral crystal lattice moduli measured by x-ray diffraction are sensitive to the morphology of the bulk speciments and close to the intrinsic crystal moduli if the morphology of the test specimen can be represented by a parallel model with respect to the original stretching longitudinal direction.     

Aging Process Effects on the Characteristics of Vacuum Residue Oxidation Products with the Addition of Crumb Rubber

This paper considers the effect of aging processes on viscoelastic characteristics of vacuum residue oxidation products modified with crumb rubber. Viscoelastic properties were compared to original bitumen raw material-vacuum residue and vacuum residue oxidation products during short-term and long-term aging. The complex shear modulus of the vacuum residue and its oxidation products decreased with an increase in temperature. Short-term aging resulted in increased shear modulus for all samples.The vacuum residue oxidation product modified with crumb rubber had the maximum values of the rutting parameter and fatigue parameter. There was an expansion of the temperature range of plasticity: for the vacuum residue oxidation product with crumb rubber, its value was 67.2 °C. The curves of the black diagram of the modified vacuum residue oxidation product are shifted towards smaller phase angles with the increase in the shear modulus, which indicates the increase in the stiffness and elasticity of the rubber bitumen binders. The vacuum residue oxidation product modified with crumb rubber corresponded to the rubber bitumen binder of the grade RBB 60/90, according to its physical and mechanical indicators.     

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).     

激光干涉法测量弹性模量

从光的干涉原理出发，讨论了金属丝弹性模量的光电测量方法．设计了激光干涉法测量长度微变量的测量装置，并介绍了测量原理，给出了动镜移动方向判别电路．     

The construction and approximation of feedforward neural network with hyp erb olic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.