Anomalous elasticity of an ordered lamellar liquid foam

We investigate experimentally the linear viscoelastic properties of a lamellar liquid foam as a function of the cell size and spatial organisation. The system consists of multilamellar vesicles generated by a simple shear flow on a lyotropic lamellar phase. The vesicles can be prepared either in an amorphous or a spatially ordered state. Their size is easily tunable in the range R = 0.5-15 μm. Whereas the shear modulus of the amorphous lamellar foam is alike that of usual liquid foams or concentrated emulsions and scales linearly with 1/R, the elastic modulus of the ordered foam is almost independent of the cell size. This result --probably the first describing the elasticity of an ordered foam-like system-- remains unexplained. Received 7 August 2000     

Gels at interfaces

We discuss the adsorption of polymer gels on flat surfaces. Even in cases of complete wetting where the spreading power S is positive and where an equivalent liquid would spread, the elastic stresses due to the gel deformation upon adsorption oppose the spreading. The competition between elasticity characterized by the bulk shear modulus G and capillarity characterized by the spreading power S defines a typical length scale ℓ = S/G for the deformation in the gel. For loose gels ℓ can be of the order of 1 μm. Macroscopic gels larger than ℓ deform only at their edges over a region of size ℓ. Microscopic gels smaller than ℓ show a finite deformation despite the elastic stresses. The elastic stresses limit the spreading of the polymer, but solvent can be sucked out of a swollen gel by wetting the surface. The thin solvent film can extend rather far from the gel edge and carry solvent. We calculate the kinetics of the solvent film formation and of the solvent transfer from a more swollen gel to a less swollen gel. Received 16 July 2001     

Dual mode ultrasonic interferometry in multi-anvil high pressure apparatus using single-crystal olivine as the pressure standard

Acoustic measurements of compressional (P) and shear (S) wave travel times were performed in a 1000-ton uniaxial split-cylinder apparatus (USCA-1000) of the Kawai-type up to 10?GPa at room temperature, using dual mode lithium niobate transducers and ultrasonic interferometry. The cell pressures were calibrated continuously by in-situ measurements of the travel times in a single crystal San-Carlos olivine buffer rod inside the cell assembly. Elastic compressional and shear wave velocities in a dense, fine-grained polycrystalline Al₂O₃ were measured simultaneously to 10?GPa; from these data, the elastic moduli and their pressure derivatives were obtained for the longitudinal modulus {L ₀?=?461(3)?GPa, L ₀′?=?7.0(1)}, the shear modulus {G ₀?=?162(2)?GPa, G ₀′?=?1.9(1)} and the bulk modulus {K ₀?=?245(3)?GPa, K ₀′?=?4.5(1)}.     

Determination of solid materials rigidity modulus by a new nondestructive optical method

We propose a new optical method for the determination of the rigidity modulus G of solid materials. The rigidity modulus is determined by measuring the twisted angle θ as a response of the material sample, depending on the applied force. The measuring of this twisted angle can be carried out by using an adapted polarimetric sensor. The effective measurement of rigidity modulus G for aluminum, Plexiglas and steel was experimentally obtained 1.4464×10¹⁰,0.99417×10⁹ and 1.0395×10¹¹ N m, respectively. The study has demonstrated the effective usefulness of our method for evaluating the rigidity modulus. A good agreement between the theoretical and experimental results was achieved.     

Shear modulus of polydomain, mono-domain and non-mesomorphic side-chain elastomers: Influence of the nematic order

We investigate the behavior of the complex shear modulus of a series of elastomers including mono-domain and poly-domain liquid crystal samples, and a non-mesomorphic sample. We find that the dynamics of the glass transition are strongly modified by the nematic order. This result explains why the truly elastic response of liquid crystal elastomers can only be observed in the isotropic phase at very high temperatures and at very low frequencies. Between the elastic regime and the glassy state, the elastomers have a visco-elastic regime, which is characterized by a Rouse-like behavior for mono-domain and poly-domain samples, and by a Zimm-like behavior for the non-mesomorphic sample. We also show that the mono-domain sample exhibits marked anisotropy of the shear-modulus G ^′. This anisotropy, which is observed for the first time, is a function of frequency and is inverted between low and high frequencies, due to relaxation effects of the orientational order. Received 28 January 2000 and Received in final form 16 October 2000     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). II. Rheological Behavior at the Gel Point

Abstract

Isothermal time evolution measurements at different constant temperatures (170°C, 180°C, and 190°C) over a wide range of frequency for the thermal cross‐linking process of poly(vinyl methyl ether), PVME, have been investigated rheologically. At the onset of cross‐linking (t _onset) the elastic storage modulus, G′, increases abruptly. The magnitude of the elevation in G′ and the value of t _onset were found to be temperature‐dependent. Similar behavior was observed for both the viscous loss modulus, G″ and the complex dynamic viscosity, η*; however, the value of G″ shows a very low sensitivity to the cross‐linking process compared to G′ and η* at the same experimental conditions. The gel point, t _gel, was evaluated from the point of intersection in plots of tan δ vs. curing time for different constant shear frequencies. At the gel point tan δ is no longer frequency‐dependent, and all curves cross‐over, indicating the validity of the Winter–Chambon criterion. The value of t _gel obtained from the coincidence of G′ and G″ was about 10 min longer than that determined from tan δ vs. t, indicating that the crossover of G′ and G″ is not be considered as a general method for evaluation of t _gel. The value of the apparent activation energy of gelation determined from the temperature dependence of t _gel was 74 kJ mol^?1 in good agreement with literature values for other different systems. At the gel point G′ and G″ showed a power law with shear frequency, i.e., G′ ～ G″ ～ ω _n with critical exponents equal to 0.64 and 0.75, respectively, in close agreement with the percolation theory (n = 2/3). The zero shear viscosity, η₀, and the equilibrium shear modulus, G _eq, can also be expressed in power low scaling functions with the relative distance from the gel point, ? i.e., η₀ ～ ?^?k and G _eq ～ ? ^z with k = 1.3 and z = 2.4 in good agreement with the predicted values based on the percolation theory.     

高导无氧铜的高压与高应变率本构模型研究

基于Y/G及G/B为常数的假设,构建了高导无氧铜的七种高压与高应变率本构模型.对于高导无氧铜进行了平面冲击波试验,采用纵向与横向锰铜应力计记录了试件中的纵向与横向应力,从而得到了屈服应力历史.用所构建的七种本构模型进行了数值模拟,并与高导无氧铜的平面冲击波试验结果进行比较.结果表明,平面冲击波载荷下高导无氧铜的屈服强度对于压力、密度、温度以及塑性应变的依赖性是本构描述的关键.而由Hopkinson试验取得的高导无氧铜高应变率本构模型,并不适合描述平面冲击波载荷下的本构特性. 关键词： 本构模型 高导无氧铜 平面冲击波试验 锰铜应力计     

Pressure-induced structural phase transition and elastic properties of rare earth Pr chalcogenides and pnictides

Pressure-induced structural aspects and elastic properties of NaCl-type (B1) to CsCl-type (B2) structure in praseodymium chalcogenides and pnictides are presented. Ground-state properties are numerically computed by considering long-range Coulomb interactions, Hafemeister and Flygare type short-range overlap repulsion, and van der Waals interaction in the interionic potential. From the elastic constants, Poisson's ratio ν, the ratio R_G/B of G (shear modulus) over B (bulk modulus), anisotropy parameter, shear and Young's moduli, Lamé's constant, Kleinman parameter, elastic wave velocity and thermodynamical property such as Debye temperature are calculated. Poisson's ratio ν and the ratio R_G/B indicate that PrX and PrY are brittle in B1 phase and ductile in B2 phase. To our knowledge, this is the first quantitative theoretical prediction of the ductile (brittle) nature of praseodymium chalcogenides and pnictides and still awaits experimental confirmation.     

First-principles calculations of structural stability and mechanical properties of tungsten carbide under high pressure

The structural stability and mechanical properties of WC in WC-, MoC- and NaCl-type structures under high pressure are investigated systematically by first-principles calculations. The calculated equilibrium lattice constants at zero pressure agree well with available experimental and theoretical results. The formation enthalpy indicates that the most stable WC is in WC-type, then MoC-type finally NaCl-type. By the elastic stability criteria, it is predicted that the three structures are all mechanically stable. The elastic constants C_ij, bulk modulus B, shear modulus G, Young?s modulus E and Poisson?s ratio ν of the three structures are studied in the pressure range from 0 to 100 GPa. Furthermore, by analyzing the B/G ratio, the brittle/ductile behavior under high pressure is assessed. Moreover, the elastic anisotropy of the three structures up to 100 GPa is also discussed in detail.     

Theoretical investigations of structural, elastic and thermodynamic properties for PtN2 under high pressure

We have investigated structural and elastic properties of PtN₂ under high pressures using norm-conserving pseudopotentials within the local density approximation (LDA) in the frame of density-functional theory. Calculated results of PtN₂ are in agreement with experimental and available theoretical values. The a/a₀, V/V₀, ductility/brittleness, elastic constants C_ij, shear modulus C′, bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio σ and anisotropy factor A as a function of applied pressure are presented. Through the quasi-harmonic Debye model, we also study thermodynamic properties of PtN₂. The thermal expansion versus temperature and pressure, thermodynamic parameters X (X=Debye temperature or specific heat) with varying pressure P, and heat capacity of PtN₂ at various pressures and temperatures are estimated.     

Effect of interfacial debonding and matrix cracking on mechanical properties of multidirectional composites

In composites, debonding at the fiber–matrix interface and matrix cracking due to loading or residual stresses can effect the mechanical properties. Here three different architectures — 3-directional orthogonal, 3-directional 8-harness satin weave and 4-directional in-plane multidirectional composites — are investigated and their effective properties are determined for different volume fractions using unit cell modeling with appropriate periodic boundary conditions. A cohesive zone model (CZM) has been used to simulate the interfacial debonding, and an octahedral shear stress failure criterion is used for the matrix cracking. The debonding and matrix cracking have significant effect on the mechanical properties of the composite. As strain increases, debonding increases, which produces a significant reduction in all the moduli of the composite. In the presence of residual stresses, debonding and resulting deterioration in properties occurs at much lower strains. Debonding accompanied with matrix cracking leads to further deterioration in the properties. The interfacial strength has a significant effect on debonding initiation and mechanical properties in the absence of residual stresses, whereas, in the presence of residual stresses, there is no effect on mechanical properties. A comparison of predicted results with experimental results shows that, while the tensile moduli E ₁₁, E ₃₃and shear modulus G ₁₂ match well, the predicted shear modulus G ₁₃ is much lower.     

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of ɛ.     

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Elastic properties of metastable crystalline and amorphous gasb-ge semiconductors synthesized under high pressure

We present the systematic study of the elastic shear G and bulk B moduli in amorphous and crystalline metastable ternary solid solutions (GaSb)_1?x Ge_2x . It is found that the moduli of crystalline phases initially decrease with Ge concentration, falling down to minimum values at 20-30% Ge. The minimal values of elastic moduli for amorphous samples are observed at 50-60% Ge. Elastic softness of crystalline solid solutions is assumed to be related to the increase of chemical disorder and, consequently, of static (non-thermal) geometrical disorder in positions of atoms. An additional topological disorder in amorphous solid solutions leads to additional elastic softening.     

Strength and equation of state of molybdenum triboride under 80 GPa pressure,using radial X-ray diffraction

The strength and equation of state of molybdenum triboride have been determined under nonhydrostatic compression up to 80?GPa, using an angle-dispersive radial X-ray diffraction technique in a diamond anvil cell (DAC). The RXD data yield a bulk modulus and its pressure derivative as K_0?=?342(6)?GPa with K₀′?=?2.11(17) at ψ?=?54.7°. Analysis of diffraction data using the strain theory indicates that the ratio of differential stress to shear modulus (t/G) ranges from 0.002 to 0.050 at pressures of 4–80?GPa. Together with theoretical results on the high pressure shear modulus, our results here show that molybdenum triboride sample under uniaxial compression can support a differential stress of ～10?GPa when it started to yield with plastic deformation at ～30?GPa. In addition, we draw a conclusion that MoB₃ is not a superhard material but a hard material.     

First-principles investigations on structural,elastic, electronic properties and Debye temperature of orthorhombic Ni3Ta under pressure

The structural, elastic, electronic properties and Debye temperature of Ni₃Ta under different pressures are investigated using the first-principles method based on density functional theory. Our calculated equilibrium lattice parameters at 0 GPa well agree with the experimental and previous theoretical results. The calculated negative formation enthalpies and elastic constants both indicate that Ni₃Ta is stable under different pressures. The bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν are calculated by the Voigt–Reuss–Hill method. The bigger ratio of B/G indicates Ni₃Ta is ductile and the pressure can improve the ductility of Ni₃Ta. In addition, the results of density of states and the charge density difference show that the stability of Ni₃Ta is improved by the increasing pressure. The Debye temperature Θ _D calculated from elastic modulus increases along with the pressure.     

Rheological Technique as a Sensitive Method to Characterize the Chain Diffusion across the Interface between Polystyrene and Carbon Black Filled Polystyrene

The mutual diffusion process and interphase development taking place at the interface between disks of polystyrene (PS) and carbon black filled polystyrene (CB-PS) in the molten state were investigated by a small-amplitude, oscillatory shear, rheological technique. The rheological method was employed to probe the thermorheological complexity of these polymer disks. It was found that the dynamic complex shear modulus, G*(t), increased with the time of contact in two time regimes at a fixed frequency. The time of transition between the two regimes was observed to be close to the time needed for the transition from the Rouse mode to the reptation mode. The results showed that the content of the carbon black and the temperature affected the slope of the G*(t) – t curve. Scanning electron microscopy revealed the interface disappeared when the diffusion process was complete.     

Supreme shear modulus predicted in the monocarbide system: the Rex W1–x C alloy

The energetic, mechanical and electronic properties as a function of composition for Re_x W_1–x C alloys in the WC structure have been investigated. It has been demonstrated that the shear modulus of WC can be enhanced by alloying with a small amount of Re, to a maximum shear modulus of 311 GPa at x = 0.23. The designed alloy is energetically stable and could be expected to be a potential extremely hard transition‐metal monocarbide, which is attributed to the strong metal–metalloid interaction with modulated valence electron concentration with respect to WC. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropic elastic properties of MB (M = Cr,Mo, W) monoborides: a first-principles investigation

First principles calculations were performed to systematically investigate structure properties, phase stability and mechanical properties of MB (M = Cr, Mo, W) monoborides in orthorhombic and tetragonal structures. The results of equilibrium structures are in good agreement with other available theoretical and experimental data. The elastic properties, including bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by the Voigt-Reuss-Hill approximation. All considered monoborides are mechanically stable. The results of elastic anisotropies show that elastic anisotropy of orthorhombic structure is larger than that of tetragonal structure. Moreover, the minimum thermal conductivities were also estimated using the Cahill’s model, and the results indicate that the minimum thermal conductivities show a dependence on directions.