The stress tensor in entangled polymers

In entangled polymeric liquids, a subchain connecting two entanglements is an open system which can exchange particles (Kuhn segments) with its neighboring subchains along the polymer chain. We present a calculation of the subchain mechanical behavior as determined from the grand canonical formalism of statistical mechanics, with different subchains in the same chain sharing the same chemical potential. It is shown that the linear monomer density is a constant, as originally inferred by Doi and Edwards, but the tension is generally different from one subchain to another. Accounting for the latter effect leads to a new tensorial strain measure, somewhat different from that proposed by Doi and Edwards.     

Equilibrium statistical distributions for subchains in an entangled polymer melt

In de Gennes-Doi-Edwards theory for entangled polymeric melts, a length scale r₀ is introduced, giving the equilibrium mesh size of the physical network of chains. Each polymer molecule is then represented as a random walk, with a step size r₀ (a “subchain”, made up of n₀ Kuhn segments) dictated by the existence of entanglements. Progressing from this simple picture, an issue that has been constantly overlooked so far, despite its potential relevance, is that of finite-size effects at the de Gennes-Doi-Edwards characteristic length scale. Actually, since a subchain in a melt is a “small”, nonmacroscopic system, fluctuations of both its length and its number of Kuhn segments are certainly nonnegligible. An ad hoc theoretical treatment from nonstandard (nano) statistical mechanics and thermodynamics seems then required, to find the anticipated equilibrium statistical distributions of the subchain population. In this contribution, we carefully discuss this topic. Some predictions from the nonstandard fluctuation-inclusive approach on the statistics of subchains are here obtained, and compared with existing simulations, even down to the atomistic level.     

Dynamic torsion of a two-layer viscoelastic beam

The complex dynamic shear modulus of soft polymeric materials may be determined in principle at low and audio frequencies from torsion pendulum and torsional resonance experiments on metal strips coated with the polymer. In order to determine the polymer shear properties from such experiments, it is necessary to know the torsional rigidity of the two-layer compound beam. This is calculated in the paper by using classical elasticity theory, for the particular case when the metal shear modulus is much greater than that of the soft coating. The theory of dynamic torsion tests is then briefly reviewed and experiments are suggested for determining the polymer dynamic shear properties. A discussion is also given of the effectiveness of polymer coatings as a damping treatment for torsional vibrations.     

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.     

Buckling instability in liquid crystalline physical gels

In a nematic gel we observe a low-energy buckling deformation arising from soft and semisoft elastic modes. We prepare the self-assembled gel by dissolving a coil-side-group liquid-crystalline polymer-coil copolymer in a nematic liquid crystal. The gel has long network strands and a precisely tailored structure, making it ideal for studying nematic rubber elasticity. Under polarized optical microscopy we observe a striped texture that forms when gels uniformly aligned at 35 degrees C are cooled to room temperature. We model the instability using the molecular theory of nematic rubber elasticity, and the theory correctly captures the change in pitch length with sample thickness and polymer concentration. This buckling instability is a clear example of a low-energy deformation that arises in materials where polymer network strains are coupled to the director orientation.     

Stress–Strain Dependence of Cross-Linked Single-Phase Polyether Urethane

Stress–strain dependencies of cross-linked elastomers under stretching are considered. The capabilities to describe stress–strain plots of different types for elastomers, including curves with an inflection, by high-elasticity theories are examined. Limitations in the use of common high-elasticity models in the theoretical calculations of stress–strain plots are revealed. The analysis shows that the stress–strain plots with an inflection can be obtained with appropriate adjustment of the concept of finite chain extensibility. We propose a combined two-parameter model based on this concept and on the theory of high elasticity, taking into account the spatial constraints at the initial stage of stretching of the polymer network. Abilities of the new approach to describe the stress–strain dependencies in an adequate manner are demonstrated for five samples of cross-linked polyurethane over the entire range of strain under stretching.     

Deformation and strength of silica fibers in three-point bending in consideration of nonlinear elasticity of glass

We consider the problem of asymmetric strain and stress distribution in silica fiber under threepoint bending. The parameters of nonlinear elasticity of silica glass under tension and compression are estimated using available data from the literature. It has been found that consideration of the nonlinear elasticity of silica glass leads to a slight increase in the calculated values of strength compared to the data obtained from estimates based on the linear theory of elasticity.     

Piezoelectricity of chiral nematic elastomers

A molecular model of freely jointed chains of chiral monomers is developed to describe the piezoelectric effect in chiral nematic elastomers. The model, an extension of the neo-classical theory of nematic polymer networks, takes into account a chiral biasing of molecular alignment under shear which leads to induced polarisation if the monomers contain a transverse dipole moment. The resulting theory is fully non-linear in elastic deformations, in the spirit of ordinary rubber elasticity. The expansion to the highest order in small strains gives the three linear piezoelectric coefficients predicted by phenomenological models. Received 7 September 1998 and Received in final form 19 October 1998     

Impedance method for measuring shear elasticity of liquids

Experimental results of studying low-frequency (74 kHz) shear elasticity of polymer liquids by the impedance method (analogous to the Mason method) are presented. A free-volume thick liquid layer is placed on the horizontal surface of a piezoelectric quartz crystal with dimensions 34.7 × 12 × 5.5 cm. The latter performs tangential vibrations at resonance frequency. The liquid layer experiences shear strain, and shear waves should propagate in it. From the theory of the method, it follows that, with an increase in the layer thickness, both real and imaginary resonance frequency shifts should exhibit damped oscillations and tend to limiting values. For the liquids under study, the imaginary frequency shift far exceeds the real one, which testifies to the presence of bulk shear elasticity.     

The refined theory of deep rectangular beams based on general solutions of elasticity

The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity.     

Anti-inertial lift in foams: a signature of the elasticity of complex fluids

To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We observe that an asymmetric obstacle (cambered airfoil profile) experiences a downwards lift, opposite to the lift usually known (in a different context) in aerodynamics. Correlations of velocity, deformations, and pressure fields yield a clear explanation of this inverse lift, involving the elasticity of the foam. We argue that such an inverse lift is likely common to complex fluids with elasticity.     

表面弹性对含可溶性活性剂垂直液膜排液的影响

针对含可溶性活性剂的垂直液膜排液过程,在考虑表面弹性作用的基础上,采用润滑理论建立了液膜厚度、表面速度、表面和内部活性剂浓度的演化方程组,通过数值计算分析了表面弹性和活性剂溶解度耦合作用下的液膜演化特征.结果表明：表面弹性是影响可溶性活性剂垂直液膜排液过程中必不可少的因素.排液初期,随表面弹性增加,液膜初始厚度增大,表面更趋于刚性化.随排液进行,弹性不同的液膜呈现不同的典型排液特征：当弹性较小时,液膜上部表面张力高,下部表面张力低,产生正向的马兰戈尼效应,与重力作用相抗衡.当弹性较大时,膜上部表面张力低,下部表面张力高,产生逆向的马兰戈尼效应,促使液膜排液加速,更易发生失稳.活性剂溶解度通过控制液膜表面的活性剂分子吸附量,进而影响表面弹性：当活性剂溶解度较大时,液膜厚度较小,很快发生破断;随溶解度降低,液膜稳定性增加,初始表面弹性也随之增大,并随液膜变薄逐渐接近极限膨胀弹性值.     

Simulation and experimental research on polymer fiber mode selection polished coupler

Multimode dispersion is the main obstacle for high bandwidth in multimode optical fiber （MMF） communication system. Mode selection is an effective method to oppress multimode dispersion. We propose and investigate a kind of polymer optical fiber polished coupler. Beam propagation method （BPM） is employed to calculate the coupling coefficient of transmission modes in MMF coupler, and an output pattern from coupling branch is obtained. Analysis and experiment show that this coupler can select certain modes by changing polished depth, contact area, and intersection angle of two branches, which means that the device can be employed both as a mode selector and a sensor. In addition, simulation shows that five times bandwidth enhancement may be realized by selecting modes with the polymer fiber polished coupler.     

Neumann resonances in linear elasticity for an arbitrary body

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle inR ³ with Neumann boundary conditions. We prove that there exists a sequence of resonances tending rapidly to the real axis.Partly supported by BSF under grant MM 401.     

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。     

高分子锚定的流体膜

将高分子自洽平均场理论和膜弹性理论结合起来研究高分子锚定流体膜体系，得到了高分子链热力学平衡浓度的分布和膜的形状.由于膜对高分子的不可穿透性，造成高分子可以实现的构象受到限制，导致高分子对膜施加不均匀的熵压，从而锚定点附近的膜弯离高分子，这些结果符合前人的理论分析和蒙特卡罗模拟的结果.此外，考察了膜和高分子链段之间的相互作用，高分子链长以及膜的弯曲刚性、张力对膜形变的影响. 关键词： 高分子 流体膜 自洽场理论 Helfrich膜弹性理论     

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。     

Viscoelasticity of a polymer matrix and fracture of heat-resistant fiber composites

This paper reports on the results of investigations into the general regularities of deformation and fracture of fiber composite materials based on new heat-resistant polymer binders. Fiber composites based on these binders can find wide application in various fields of engineering. It is established that an increase in the loss modulus of the polymer matrix decreases the probability of formation of a brittle crack in the matrix at the fiber break and increases the time interval between breakages of adjacent fibers. This leads to retardation of the correlated breakage of the fibers in fiber composite materials under loading, i.e., to an increase in their strength and fracture toughness. The inference is made that the matrix of high-strength heat-resistant fiber composites with a high fracture toughness should possess not only a high elasticity (this has long been known) but also good dissipative properties over the entire temperature range of operation.     

Elasticity of polymer solutions in Couette flow measured by fluorescence resonance energy transfer (FRET)

Polymer solutions are complex fluids that show elasticity and deformation in response to shear flows. A fluorescence resonance energy transfer (FRET) technique has been applied to measure the end-to-end distances of individual polymer molecules in Couette flow, using end-tagged reversible-addition fragmentation chain transfer (RAFT) polymerised poly(methyl methacrylate) (PMMA). Real-time rheofluorescence measurements on these polymers in solution above the critical overlap concentration are reported at several shear rates. The PMMA in Couette flow shows a systematic decrease in fluorescence, corresponding to a reduction in end-to-end distance of the polymer molecules with shear exposure. Full reversibility of the fluorescence signal is observed after the cessation of shear. These results show that polymer solution elasticity arises from compressive deformation of the polymer molecules in Couette flow. At polymer concentrations above the critical overlap, the polymer molecules are restricted by their neighbours and the net hydrodynamic forces are compressive rather than extensive.     

Enhancing near-field photolithography by surface plasmon polaritons excited from negative-refractive-index nanofilms

We report a novel method for enhancing near-field nanophotolithography using negative-refractive-index slabs. In our method, a negative-refractive-index-metal film (NIF) is attached to the plane surface of an aplanatic solid immersion lens (SIL), and the polymer layer is coated on the negative-refractive-index film. The intensity of the transmitted light is enhanced by the surface plasmon polaritons excited in the NIF-polymer composite layer. The numerical results based on the vector diffraction theory show that under the illumination of the SIL-NIF-polymer composite by a sharp focused radially polarized beam, the composite configuration under investigation can substantially increase the spot intensity, suppress the spot expansion along the distance from the interface, and improve the depth of focus, in comparison with conventional focusing systems using bare SILs. In the case where a photoresist film is placed near the composite configuration, a subtle deep-etching pattern with high resolution can be achieved.