Relaxation of residual stress and reentanglement of polymers in spin-coated films

Performing detailed studies of viscoelastic dewetting of thin polystyrene films on solid substrates, we demonstrate the existence of residual stress due to strongly out of equilibrium chain conformations and a reduced entanglement density resulting from film preparation by spin coating. The ratio of stress over elastic modulus was found to increase strongly with decreasing film thickness and increasing chain length. Full equilibration of chain conformations required long times comparable to bulk reptation times. However, for chains longer than about 3000 monomers, the residual stress relaxed faster, at a rate independent of chain length.     

Elastic anomalies at phase transitions in multiferroics

The temperature dependences of the elastic modulus in multiferroics-magnetoelectrics are analyzed, in which magnetic and ferroelectric orderings appear as the result of two successive phase transitions. The analytical relationships for the elastic modulus near the phase transitions to ordered states are obtained for the cases of either linear-quadratic or biquadratic contributions to magneto- and electroelastic coupling. The explicit dependence of the elastic modulus in the multiferroic phase on the magnetoelectric coupling constant was found. It is shown that the characteristic elastic properties in multiferroics can be treated using the Landau theory without taking into account fluctuations. The analysis includes changes in the phase diagrams due to the magneto- and electroelastic coupling.     

The polymorphism of poly(vinylidene fluoride). I. The effect of head-to-head structure

The phenomenon of polymorphism in poly(vinylidene fluoride) has been observed recently by several authors. It has also been reported that high-resolution NMR measurements demonstrate the presence in this polymer of head-to-head linkages, resulting from the “backward” addition of from 5-6% of the monomer units. Since the van der Waals radii of fluorine (1.35 Å) and hydrogen (1.1-1.2 Å) are similar, the cocrystallization in a polymer chain of units that differ only by the substitution of fluorine atoms for hydrogen atoms is not unexpected. The two polymorphic forms of poly(vinylidene fluoride), examined in this investigation, have different chain conformations. Chains in phase I have a planar zigzag conformation, while chains in phase II are assumed to exhibit a 2₁ helical conformation. The incorporation into the polymer chain of small amounts of tetrafluoroethylene or trifluoroethylene comonomer favored the crystallization of phase I. This is in accord with the relative abilities, deduced from consideration of atomic size, of these comonomers to cocrystallize with vinylidene fluoride units in the two indicated chain conformations of the polymer. Since tetrafluoroethylene units are present in the head-to-head structure in the homopolymer, it can be concluded that the elimination of the head-to-head structure will eliminate or restrict crystallization in phase I.     

Effective elastic properties of two-phase composites

Expressions for the effective elastic constants of two-phase composites in the form of series obtained with Fourier transforms have been analyzed. In certain cases, such series are shown to be fully summed up; as a result, one can directly obtain exact expressions for the effective bulk modulus of a composite. It is found that the symmetry of the coefficients in series for the shear modulus and Young’s modulus and the corresponding reciprocal quantities can be used to relate these series to each other. Thus, all well-known exact relations for the effective elastic constants can be derived. A set of equations is proposed to compute the effective constants of a two-dimensional isotropic symmetrical composite with arbitrary properties of its phases.     

Tilt modulus of a lipid monolayer

In addition to the familiar bending and stretching deformations, lipid monolayers and bilayers in their disordered state are often subjected to tilt deformations, occurring for instance in structural rearrangements accompanying membrane fusion, or upon insertion of oblique hydrophobic proteins into lipid bilayers. We study the elastic response of a flat lipid monolayer to a tilt deformation, using the spatial and conformational average of the chain end-to-end vector from the membrane normal to define a macroscopic membrane tilt. The physical origin and magnitude of the corresponding tilt modulus is analyzed using two complementary theoretical approaches. The first is a phenomenological model showing that the tilt and bending deformations are decoupled and the effects of inter-chain correlations on the tilt modulus is small. The second is based on a molecular-level mean-field theory of chain packing, enabling numerical evaluation of the tilt modulus for realistic, multi-conformation, chain models. Both approaches reveal that the tilt modulus involves two major contributions. The first is elastic in origin, arising from the stretching of the hydrocarbon chains upon a tilt deformation and reflecting the loss of chain conformational freedom associated with chain stretching. The second, purely entropic, contribution results from the constraints imposed by a tilt deformation on the fluctuations of chain director orientations. Using the chain-packing theory we compute the two contributions numerically as a function of the cross-sectional area per chain. The elastic and entropic terms are shown to dominate the value of for small and large areas per chain, respectively. For typical cross-sectional areas of lipid chains in biological membranes they areof comparable magnitude, yielding .Received: 12 May 2004, Published online: 3 August 2004PACS: 87.16.-b Subcellular structure and processes - 61.20.Gy Theory and models of liquid structure - 61.30.St Lyotropic phases     

玻璃-橡胶混合颗粒体系的弹性行为研究

废旧橡胶制品颗粒与砂土颗粒混合物作为建筑填充材料具有环保、轻质、减震效果好等特点.软硬组分的混合比例可以调制体系力学性能从而实现兼顾材料柔韧性与强度的需求,但细观层面上材料性能改变的原因尚不明确.本文主要研究玻璃-橡胶混合颗粒体系的弹性行为及其微观机制.利用飞行时间法测量混合材料等效动弹性模量,发现随着橡胶颗粒增加,体系逐渐从类玻璃刚性行为转变为类橡胶柔性行为.离散元模拟结果与实验结果类似.此外,模拟显示低橡胶颗粒占比样品内主要由玻璃颗粒构成主力链结构,而橡胶颗粒基本不参与强力链的构成.当橡胶颗粒占比较大时,玻璃颗粒和橡胶颗粒共同构成主力链网络结构,但颗粒间法向接触力分布相对更为均匀,可视为玻璃颗粒悬浮于橡胶颗粒中.基于上述结果,提出了改进的等效介质理论,用于描述混合颗粒体系的弹性行为.研究认为:橡胶颗粒占比较小时内部颗粒的变形相对均匀,材料近似满足等应变假设,视为并联弹簧模型;橡胶颗粒占比较大时混合材料近似满足等应力假设,视为串联弹簧模型.两种模型得到的结果与模拟结果一致.上述结果有利于从微观角度揭示混合颗粒材料弹性行为的变化机制.     

LF-6及LY-12铝高温凝聚态动力学性质研究──高温剪切模量的测量

 介绍LF-6及LY-12铝合金从常温到400 ℃高温下，在扭转Hopkinson杆上作的动态剪切模量的测试研究，并给出了相应温度范围LF-6铝杨氏模量及泊松比。它们和现有文献中的静态结果比较表明，动态性能普遍高于静态值，在高温下更显著。实验结果表明LF-6和LY-12铝合金，对于温度和加载率都是敏感的，高加载率下相对于静态的温度，敏感性要弱一些。文中给出了剪切模量、弹性模量等与温度的关系式。     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Thermal Expansion and Deformation of Graphene

Taking into consideration short-atomic-range interactions and anharmonic effects,we calculate the thermal expansion coefficients,Gruneisen parameters,the elastic modulus of graphene varying with temperature and the phonon frequency.The anharmonic effects associated with the graphene deformation are also discussed.The results show that the value of thermal expansion coefficient is negative in the moderate temperature range,and it becomes positive when the temperature grows to be higher than a certain value.The change rate of elastic modulus with respect to temperature and pressure are calculated,and phonon frequencies are estimated.In the process of graphene thermal expansion,it is accompanied with the change of bond length and the rotation around the axis normal to the plane.Our results indicate that the effects due to the bond change are more significant than that of the rotation.We also show that if anharmonic effects are ignored,the thermal expansion coefficient and the Gruneisen parameters are zero,and the elastic modulus and the phonon frequency are constant.If anharmonic effects are considered up to the second term,these values will vary with temperature,and become closer to the experimental value.The higher the temperature is,the more significant the anharmonic effects become.     

Effect of heat treatment on the structure and elastic properties of a bulk Pd<Subscript>40</Subscript>Cu<Subscript>30</Subscript>Ni<Subscript>10</Subscript>P<Subscript>20</Subscript> metallic glass

The effect of heat treatment over the range from room temperature to 500°C on the elastic properties of a bulk amorphous Pd₄₀Cu₃₀Ni₁₀P₂₀ alloy was studied. It is shown that the increase in the shear modulus under crystallization of the alloy is two-staged and that the most significant increase in the modulus occurs at the second stage. The obtained results are compared to the x-ray structural data. It is also found that the density characteristics of the as-cast material change very slightly during the transformation from the amorphous to the crystal state, with the density decreasing slightly due to crystallization.     

Characterization of commercial polybutylenes

A series of copolymers and blends based on polybutylene were characterized using ¹³C NMR and thermal analysis. Optical microscopy techniques were used to measure crystallization rates and examine their morphology, and this behavior was related to their composition. As expected, the highest melting and crystallization temperatures, and the fastest crystallization rates were obtained for the polybutylene homopolymer. Copolymerized ethylene randomly distributed along the chain, even at a level of 1%, significantly reduced the melting temperature and crystallization rate. Increasing the ethylene content to 5% results in a polybutylene which crystallizes with difficulty to produce poorly defined spherulites. Four blends based on a polybutylene containing 1% ethylene were studied. A dispersed crystalline phase could be detected in all cases. Two of the blends contained 6-7% ethylene but differed in molar mass. Their melting and crystallization behavior was similar although the spherulite growth rate for the lower molar mass material was a little higher. A second pair of blends contained 5-6% polypropylene and included a “nucleated” and a “nonnucleated” grade. Results for these suggested that the polypropylene itself was acting as a nucleating agent.     

An examination of the longitudinal acoustic mode of polyethylene crystals

Chain lengths have been calculated from the peak positions of the longitudinal acoustic modes (LAM) of polyethylene single crystals grown at several different temperatures. The data are consistent with other experimental results when the crystalline elastic modulus is taken to be 3.6 × 10¹² dyn/cm². However, this is true only if the vibrations of the crystalline chain segments are unaffected by the presence of folds and cilia on the crystal surface. The LAMs of several crystal preparations were also deconvoluted with the first-order LAM of C₉₄H₁₉₀ in order to remove instrumental broadening. The band shapes of the deconvoluted spectra are consistent with the idea that the LAM of polyethylene crystals is composed of two contributions: One due to chain stems in 110 sectors and a second due to chains in 200 sectors.     

Electronic,elastic and dynamical properties of MgSe under pressure: rocksalt and iron silicide phase

The electronic, elastic and dynamical properties of MgSe in the rocksalt (B1) and iron silicide (B28) phase and the effects of pressure on these properties are investigated using first-principles method. The calculated electronic band structure indicates that the B1 phase of MgSe presents an indirect band-gap feature and the band gaps initially increase with pressure and subsequently decrease upon compression. Remarkably, an indirect-to-direct band-gap transition has been observed at the phase transition pressure. The elastic constants, bulk modulus, shear modulus, Young’s modulus, elastic anisotropy and B/G ratio of MgSe in the B1 and B28 phase at high pressure have also been investigated. The bulk modulus, shear modulus and Young’s modulus all increase monotonously with the increasing of pressure for the B1 and B28 phase of MgSe. The calculated phonon frequencies of the B1 phase at zero pressure agree well with available theoretical results. And the transverse acoustic phonon TA(X) mode of this phase completely softening to zero at 82 GPa. The phonon curves of the B28 phase under pressure have also been successfully investigated.     

A density-functional-theory-based finite element model to study the mechanical properties of zigzag phosphorene nanotubes

In this paper, the density functional theory calculations are used to obtain the elastic properties of zigzag phosphorene nanotubes. Besides, based on the similarity between phosphorene nanotubes and a space-frame structure, a three-dimensional finite element model is proposed in which the atomic bonds are simulated by beam elements. The results of density functional theory are employed to compute the properties of the beam elements. Finally, using the proposed finite element model, the elastic modulus of the zigzag phosphorene nanotubes is computed. It is shown that phosphorene nanotubes with larger radii have larger Young's modulus. Comparing the results of finite element model with those of density functional theory, it is concluded that the proposed model can predict the elastic modulus of phosphorene nanotubes with a good accuracy.     

Elastic energy of tilt and bending of fluid membranes

Tilt of hydrocarbon chains of lipid molecules with respect to membrane plane is commonly considered to characterize the internal structure of a membrane in the crystalline state. However, membranes in the liquid state can also exhibit tilt resulting from packing constraints imposed on the lipid molecules in diverse biologically relevant structures such as intermediates of membrane fusion, pores in lipid bilayers and others. We analyze the energetics of tilt in liquid membranes and its coupling with membrane bending. We consider three contributions to the elastic energy: constant tilt, variation of tilt along the membrane surface and membrane bending. The major assumption of the model is that the core of a liquid membrane has the common properties of an elastic continuum. We show that the variation of tilt and membrane bending are additive and that their energy contributions are determined by the same elastic coefficient: the Helfrich bending modulus, the modulus of Gaussian curvature and the spontaneous curvature known from previous studies of pure bending. The energy of a combined deformation of bending and varying tilt is determined by an effective tensor accounting for the two factors. In contrast, the deformation of constant tilt does not couple with bending and its contribution to the elastic energy is determined by an independent elastic constant. While accurate determination of this constant requires additional measurements, we estimate its value using a simplified approach. We discuss the relationships between the obtained elastic Hamiltonian of a membrane and the previous models of membrane elasticity. Received 10 February 2000 and Received in final form 19 June 2000     

二元Ni-Al合金极端条件下的弹性和热力学性能：全电子准谐波近似 cited: 1)

通过在原子尺度上建模来研究Al、NiAl和Ni₃Al合金在极端高温和高压下的点阵常数、弹性常数、弹性模量、泊松比和弹性各向异性因子等性质．计算得到的弹性常数均满足相应的力学稳定条件．由于NiAl和Ni₃Al具有较高的B=G值,在0～30 GPa内都属于延展性材料．通过包含电子热运动对体系吉布斯自由能贡献的全电子准谐近似方法,得到了高温高压下Al、NiAl和Ni₃Al合金的热膨胀系数、体积模量、热容和熵等．计算值与已有的实验值和理论值符合较好     

Magnetoelastic effects in rare-earth vanadates YbVO4 and HoVO4

Magnetoelastic anomalies in the thermal expansion and Young modulus, as well as the ΔE-effect in rare-earth vanadates RVO₄ (R = Ho, Yb), are investigated experimentally and theoretically. A considerable softening of the Young modulus is observed for HoVO₄ and YbVO₄ at T < 70 K and T < 150 K, respectively; this effect is adequately described in the framework of the generalized susceptibility formalism. It is shown that the field dependences of the ΔE-effect and their temperature variation in YbVO₄ can also be described using this approach. To compare with experiment, the magnetoelastic contributions to the Young modulus of an isotropic polycrystal from various elastic modes have been averaged. For the Yb vanadate, considerable magnetoelastic anomalies in the thermal expansion along the tetragonal a and c axes have been discovered. The magnetoelastic contributions are used for determining completely symmetric magnetoelastic coefficients; the role of the completely symmetric quadrupole constant for magnetoelastic effects is analyzed.     

Elastic Behavior of Polymer Chains

在三维非格子模型中研究了高分子链的弹性行为. 使用蒙特卡罗方法在构相空间中对高分子链抽样,每种链都得到了超过109个样本,然后使用类橡胶弹力的非高斯理论对这些样本进行数值分析并进行统计分析. 通过观测链柔性以及伸长量对高分子链的均方末端距、平均能量、平均赫尔姆霍兹自由能、弹力、能量对弹力的贡献和熵对弹力的贡献等性质的影响,发现刚性链比柔性链更加容易被拉伸. 而由于熵的作用,当拉伸长度大到一定程度时,刚性链的拉伸难度会大大增加.     

黏弹性吸声材料复弹性模量优化研究

针对黏弹性材料吸声效率问题,利用分层介质声传播理论和数值算法优化了不同物理条件下材料的复弹性模量。采用参数等效的方法分析了含气泡黏弹性材料的声学特性,并给出了此种材料优化后的弹性模量曲线。根据物理模型计算了一定边界条件下材料复弹性模量等吸声系数曲线,得到了几种背衬条件下黏弹性材料吸声系数大于0.8的弹性模量和损耗因子范围。研究表明调节黏弹性材料的复弹性模量可以有效提高材料的吸声性能,吸声系数大于0.8时其弹性模量和损耗因子范围在不同背衬条件下差异较大,发现一定厚度的钢背衬会降低调控复弹性模量的难度,对含气泡黏弹性材料的计算也可得到类似结果。