Electrochemical studies on polymer electrolytes based on poly(methyl methacrylate)-grafted natural rubber for lithium polymer battery

MG30 is natural rubber grafted with 30% poly(methyl methacrylate). Gel polymer electrolytes containing MG30–LiCF₃SO₃–X (X = propylene carbonate, ethylene carbonate) are prepared by solution casting technique. The polymer–salt complexes were investigated using Fourier-transformed infrared. The ionic conductivity of the electrolytes are determined by the ac impedance studies over the temperature range of 303–383 K and is observed to obey the Vogel–Tamman–Fulcher (VTF) rule. The Li⁺ transference number obtained using the Bruce and Vincent method is <0.3. The Li/Li⁺ interface stability is established and the electrolytes were found to be able to withstand a voltage of more than 4.2 V.     

Structure of vinylester networks: A rubber elasticity study

Five networks based on a diglycidylether of bisphenol A-dimethacrylate prepolymer of molar mass 1100 g· mol^?1 crosslinked with 35%, 40%, 45%, 50%, and 55% styrene mass fractions were characterized by Fourier transform infrared spectroscopy, cross-polarization/magic-angle spinning, nuclear magnetic resonance spectroscopy, styrene extraction, and rubber elasticity measurements. Various structural models were built up from the available analytical data, and their crosslink density was compared to the experimental data derived from rubber elastic moduli. Globally, network models based on a purely statistical approach but taking into account the incomplete cure conversion make it possible to predict the trends of modulus variations. The kinetic data on copolymerization show, however, that the material is diphasic, one phase being composed of the vinylester network and the other of practically pure polystyrene. We tried to take this heterogeneity into account in modulus predictions using a simple mixture rule, but the method failed for high styrene mass fractions (s ? 0.45), for which the experimental modulus value is about 50% higher than the predicted one. The results suggest the existence of a morphological transition for a critical styrene weight fraction between 40% and 45%.     

A new basis set for molecular wavefunctions

A new basis set is proposed for molecular self-consistent field and configuration interaction calculations. Expansion functions are proposed in the form sin (r _A · p) exp (-ar_A ²) and cos (r _A · p) exp (-ar _A ²) and it is suggested that they are used as an alternative to the gaussian basis set x_A ⁱy_A ^jz_A ^k exp (-ar _A ²).

It is shown how the new basis can have the same effects, for suitable vectors p, as the gaussian basis. It is further shown that all the one and two-electron integrals in the new basis are evaluable in terms of exponentials, square roots and the complex error function erf (z). First calculations, using the new basis, are presented in LiH, HF and H₂O.     

"甲虫和橡胶带"问题新解

给出“甲虫和橡胶带”问题的一种简便的新解法.     

一维二嵌段高聚物中电荷输运的分子弹性效应

基于扩展SSH(Su-Schrieffer-Heeger)模型并采用动力学方法讨论了一维二嵌段高聚物中分子弹性对电荷输运的影响。我们发现,由于两嵌段高聚物中分子弹性的差异,在其交界处会形成一个载流子跃迁势垒。增大注入电子的动能将有效降低电子隧穿的临界电场,而加大两段高聚物弹性的差别将增大临界电场的强度。     

一维二嵌段高聚物中电荷输运的分子弹性效应

基于扩展SSH(Su-Schrieffer-Heeger)模型并采用动力学方法讨论了一维二嵌段高聚物中分子弹性对电荷输运的影响。我们发现,由于两嵌段高聚物中分子弹性的差异,在其交界处会形成一个载流子跃迁势垒。增大注入电子的动能将有效降低电子隧穿的临界电场,而加大两段高聚物弹性的差别将增大临界电场的强度。     

用纵向振动法测量弹性模量的实验装置

把待测样品制备成细长棒,受到一定拉力时细长棒有一定伸长,这可等效为弹簧,通过测量由细长棒与质量块构成的振子的固有频率可准确测量劲度系数,若测得了其劲度系数即可得该材料的弹性模量.基于以上思路设计了纵向振动法测量弹性模量的实验装置,使弹性模量测量实验既保留了光杠杆法物理概念清晰的优点,又吸取了振动法的长处.     

Longitudinal vibration of cracked nanobeams using nonlocal elasticity theory

The aim of this paper is to study the longitudinal frequency of a cracked nanobeam. The frequency equation of the nanobeam with clamped–clamped and clamped–free boundary conditions is derived based on the nonlocal elasticity theory. According to the equation, it can be found that the effects of the crack parameter, crack location, and nonlocal parameter on the longitudinal frequency of the cracked nanobeam are significant. The frequency decreases with an increase of the crack parameter. However, the increasing nonlocal parameter results in a decrease of the crack effect on the frequency. In addition, when the crack location is near the support, a larger decrease in the frequency can be observed.     

Characteristic of natural rubber composites absorbing X-radiation

Radiopaque polymers can be used in medicine. Conventional protective shields against radiation X contain harmful lead compounds that are heavy and fragile. The aim of this work was to study the check the properties of selected fillers as X-radiation absorbing substance and them use in natural rubber (NR) composites. Fillers and simultaneously active substances were bismuth (III) oxide (Bi₂O₃), gadolinium (III) oxide (Gd₂O₃), tungsten (III) oxide (WO₃) and antimony (III) oxide (Sb₂O₃). The polymeric matrix consisted of NR and sulfuric cross-linking system was applied. The properties of the fillers were determined from zeta potential and particle size measurements. X-ray absorption measurements were carried out using isotopic source ⁵⁷Co (122?keV). The mechanical properties of the thin 1?mm composite plates were examined.     

First-principles calculations of structure and elasticity of hydrous fayalite under high pressure

The structures,elasticities,sound velocities,and electronic properties of anhydrous and hydrous fayalite(Fe_2SiO_4and Fe_(1.75)H_(0.5)SiO_4)under high pressure have been investigated by means of the density functional theory within the generalized gradient approximation(GGA)with the on-site Coulomb energy being taken into account(GGA+U).The optimized results show that H atoms prefer to substitute Fe atoms in the Fe1 site.Compared with the anhydrous fayalite Fe_2SiO_4,the mass density,elastic moduli,and sound velocities of Fe_(1.75)H_(0.5)SiO_4 slightly decrease.According to our data,adding 2.3 wt%water into fayalite leads to reductions of compressional and shear wave velocities(VPand VS)by3.4%–7.5%and 0.3%–3.4%at pressures from 0 GPa to 25 GPa,respectively,which are basically in agreement with the2%–5%reductions of sound velocity obtained by the experimental measurement in the low velocity zones(LVZ).Based on the electronic structure,the valence and conduction bands are slightly broader for hydrous fayalite.However,hydrous fayalite keeps the insulation characteristics under the pressures up to 30 GPa,which indicates that hydration has little effect on its electronic structure.     

基于连续弹性理论分析量子线线宽对应变分布和带隙的影响

基于连续弹性理论分别采用数值方法和格林函数法讨论了量子线的应变分布.格林函数法可以得到应变分布的解析表示式,对规则形状的量子线的应变分布计算比较方便;连续弹性理论采取的是数值解法,结果精度不如格林函数法,但是能方便计算任意形状量子线的应变分布情况, 并可以考虑不同材料的弹性常数的影响.文章还具体讨论了量子线线宽对应变分布和带隙的影响,结果表明：沿线宽方向,应变的绝对值逐渐减小,并随线宽的增加而变大;带隙则随线宽的减小而增大. 关键词： 连续弹性理论 格林函数法 应变 带隙     

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory.Two kinds of completeness of the system of eigenvectors are proven,in terms of those of the compositions of two block operators in the off-diagonal operator matrices.Using these results,the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed.Moreover,we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.     

弹性力学的复变量无网格方法

在移动最小二乘法的基础上，提出了复变量移动最小二乘法.复变量移动最小二乘法的优点是采用一维基函数建立二维问题的逼近函数，所形成的无网格方法计算量小.然后，将复变量移动最小二乘法应用于弹性力学的无网格方法，提出了复变量无网格方法，推导了复变量无网格方法的公式.与传统的无网格方法相比，复变量无网格方法具有计算量小、精度高的优点.最后给出了数值算例. 关键词： 移动最小二乘法 复变量移动最小二乘法 无网格方法 弹性力学 复变量无网格方法     

Vibration analysis of defective graphene sheets using nonlocal elasticity theory

Many papers have studied the free vibration of graphene sheets. However, all this papers assumed their atomic structure free of any defects. Nonetheless, they actually contain some defects including single vacancy, double vacancy and Stone-Wales defects. This paper, therefore, investigates the free vibration of defective graphene sheets, rather than pristine graphene sheets, via nonlocal elasticity theory. Governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defective graphene sheets. Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different defect types are inspected for graphene sheets with clamped or simply-supported boundary conditions on all sides. It is shown that the natural frequencies of graphene sheets decrease by introducing defects to the atomic structure. Furthermore, it is found that the number of missing atoms, shapes and distributions of structural defects play a significant role in the vibrational behavior of graphene. The effect of vacancy defect reconstruction is also discussed in this paper.     

Mechanical and electrical properties of radiation-vulcanized natural rubber latex with waste eggshell powder as bio-fillers

ABSTRACT

This work investigated the mechanical, physical, morphological, and electrical (volume) resistivity properties of radiation-vulcanized natural rubber latex (RVNRL) with additions of waste eggshell (WES) powder, which contained primarily CaCO₃ (calcite). The results showed that increasing gamma irradiation doses from 0 to 30?kGy in 10-kGy increments led to decreases in the swelling ratio and elongation at break but increases in the crosslink density, tensile modulus at 500% elongation, and tensile strength of the composites. The results also suggested that increasing the WES contents from 0 to 2, 4, or 6 parts per hundred parts of rubber by weight (phr) in the composites improved the tensile modulus at 500% elongation, tensile strength, hardness (Shore A), and electrical (volume) resistivity. In addition, after undergoing thermal aging at 70°C for 96?h, the tensile modulus and hardness (Shore A) increased, while the tensile strength and elongation at break decreased. This work also compared the properties of WES/RVNRL with commercial CaCO₃/RVNRL samples at the same 4-phr content. The results indicated that both composites had similar tensile properties, implying possible replacement of commercial CaCO₃ with WES powder as an effective reinforcing filler in RVNRL.     

Theories of surface elasticity for nanoscale objects

The emergence of nanotechnology has driven recent interest in systems having surface atoms as a significant fraction of all atoms present, in particular nano-sheets (ultra-thin slabs), nano-wires, and nano-particles. In these systems, the bulk (i.e. non-surface region or interior) is typically strained in response to the stress of the surface. This elastic strain of the bulk in turn changes the surface lattice constants. Since the bulk and the surface are coupled, the problem must be solved self-consistently. Solving this problem requires a quantitative model of the surface elastic properties which are different from the bulk. In this paper we consider various models that have been proposed for surface elasticity. Our goal is to elucidate the relationship between two contrasting approaches: (1) the Shuttleworth equation which defines a surface stress based on the strain derivative of the surface energy and (2) the Gurtin-Murdoch (GM) theory which considers the surface layer as a membrane with residual strain and with elastic constants different from the bulk. The GM theory is analogous to the 2-D Frenkel-Kontorova (FK) model and can be used to obtain quantitative parameters for the FK model. We present an embedded atom method calculation of the surface elastic constants of Cu(1 1 1) using the GM theory with the surface represented by a membrane one atomic layer thick. This quantitative approach describes the elastic properties of surfaces in a physically appealing way. Just as the bulk elastic constants provide direct information regarding the stress/strain relationship in a bulk material, the surface elastic constants provide similar information for a surface monolayer. This theory will allow elasticity analysis and atomistic calculations of properties of nano-scale objects.     

Magnetic and microwave absorbing properties of magnetite-thermoplastic natural rubber nanocomposites

Magnetic and microwave absorbing properties of thermoplastic natural rubber (TPNR) filled magnetite (Fe₃O₄) nanocomposites were investigated. The TPNR matrix was prepared from polypropylene (PP), natural rubber (NR) and liquid natural rubber (LNR) in the ratio of 70:20:10 with the LNR as the compatibilizer. TPNR-Fe₃O₄ nanocomposites with 4-12 wt% Fe₃O₄ as filler were prepared via a Thermo Haake internal mixer using a melt-blending method. XRD reveals the presence of cubic spinel structure of Fe₃O₄ with the lattice parameter of a=8.395 Å. TEM micrograph shows that the Fe₃O₄ nanoparticles are almost spherical with the size ranging 20-50 nm. The values of saturation magnetization (M_S), remanence (M_R), initial magnetic susceptibility (χ_i) and initial permeability (μ_i) increase, while the coercivity (H_C) decreases with increasing filler content for all compositions. For nanocomposites, the values of the real (ε_r′) and imaginary permittivity (ε_r′′) and imaginary permeability (μ_r′′) increase, while the value of real permeability (μ_r′) decreases as the filler content increases. The absorption or minimum reflection loss (R_L) continuously increases and the dip shifts to a lower frequency region with the increasing of both filler content in nanocomposites and the sample thickness. The R_L is −25.51 dB at 12.65 GHz and the absorbing bandwidth in which the R_L is less than −10 dB is 2.7 GHz when the filler content is 12 wt% at 9 mm sample thickness.     

弹性力学的无单元Galerkin方法的误差估计

基于移动最小二乘法在Sobolev空间W^k,p(Ω)中的误差估计以及弹性力学问题的变分弱形式中出现的双线性形式的连续性和强制性,研究了弹性力学问题的无单元Galerkin方法的误差分析以及数值解的误差和影响域半径之间的关系,给出了弹性力学问题的无单元Galerkin方法在Sobolev空间中的误差估计定理,并证明了当节点和形函数满足一定条件时该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响域半径密切相关.最后,通过算例验证了结论的正确性. 关键词： 无网格方法 无单元Galerkin方法 弹性力学 误差估计     

Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations

In the present work, a three-dimensional (3D) elastic plate model capturing the small scale effects is developed for the free vibration of functionally graded (FG) nanoplates resting on elastic foundations. The theoretical model is formulated employing the nonlocal differential constitutive relations of Eringen in conjunction with the 3D equations of motion of elasticity.The material properties are assumed to vary continuously along the thickness of the nanoplate in accordance with the power law formulation. Through extending the generalized differential quadrature (GDQ) method to the three-dimensional case, the governing equations are simultaneously discretized in every three coordinate directions and are then recast to the standard form of an eigen value problem. Solving the acquired problem, the natural frequencies of the nanoplates with different boundary conditions are calculated. The convergence behavior of the numerical results is checked out and comparison studies are conducted to make sure of the accuracy and reliability of the present model. Finally, the dependence of the vibration behavior of the nanoplate on edge conditions, elastic coefficients of the foundation, scale coefficient, mode number, material and geometric parameters are discussed.     

A new orthogonality relationship for orthotropic thin plate theory and its variational principle

While Hamiltonian system was led to solution of elastic theory a symplectic system-atic methodology for theory of elasticity was established and a symplectic orthogonality relationship was presented[1,2]. For two-dimensional theory of elasticity a new dual vec-tor and a new dual differential matrix were presented by putting the old dual vector[1] in a new order. It was discovered for isotropic materials that the symplectic orthogonality relationship may be decomposed into two independent and s…