Comparison of ultrasonic shear wave and dynamic-mechanical measurements in acrylic-type copolymers

An ultrasonic shear wave reflection method was applied to study film formation and temperature dependence of the complex shear modulus (G^*G′ + iG″) in different amorphous films made of aqueous dispersions of acrylic-type copolymers. The data are compared with dynamic-mechanical measurements in the low frequency range. It is shown that the temperature dependence of the storage (G′) and the loss modulus (G″) for both methods can be fitted by the same set of parameters using the Havriliak–Negami function incorporating the Vogel–Fulcher–Tamman–Hesse equation for the temperature dependence of relaxation times. The temperature dependence of the relaxation times obtained from the fits to the ultrasonic shear modulus is compared to the shift factors of the dynamic-mechanical measurements. The agreement between both methods is good. This suggests an almost thermorheological simplicity of the samples for the main glass–rubber relaxation and demonstrates the capacity of the ultrasonic rheometer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1703–1711, 1998     

小形变时杨氏模量等于三倍的剪切模量

尽管高聚物是黏弹性材料,具有时间依赖性和温度依赖性,但在小形变时,弹性理论中的一些假定和定理仍能用来讨论黏弹性高聚物的形变。应力与应变之比是模量,在小形变时,单向拉伸的杨氏模量约等于三倍的剪切模量,E≈3G。     

Electromechanical properties of single domain PZN–12%PT measured by three different methods

In this paper, we compare the electromechanical properties of tetragonal single domain PZN–12%PT single crystals obtained by different methods: resonance–antiresonance method, Brillouin scattering, and resonant ultrasound spectroscopy. The agreement between the different measurements is found satisfactory for many elastic constants within experimental uncertainties. Differences are notable for the elastic constants associated to the propagation of shear waves (c₆₆^E and c₄₄^E). This can be accounted for by imperfections of the sample in acoustic spectroscopy and specific difficulties of shear resonators used for the resonance method. Strong discrepancies are noted for the hardened elastic constant c₃₃^D associated to longitudinal waves propagating along the polarization direction; we suggest this can arise from a frequency dependence of the dielectric constant.     

Network development during epoxy curing: experimental ultrasonic data and theoretical predictions

Ultrasonic waves propagation acts as a dynamic mechanical deformation on a material. When, during ultrasonic wave propagation, chemical or physical changes occurs, the evolution of an elastic modulus can be monitored. Therefore, this technique can be considered a powerful tool for non-destructive cure monitoring with a potential for “in situ” applications. In this work, the isothermal cure of a model epoxy resin cured with an amine is studied using propagation of longitudinal ultrasonic wave. The epoxy to amine ratio is optimized in order to reach full conversion of the amine groups during curing. The relative changes in the ultrasonic velocity and attenuation, measured by the transmission technique, have been applied to the calculation of the longitudinal modulus. The ultrasonic modulus has been compared with the degree of reaction measured using Differential Scanning Calorimetry (DSC). Furthermore a correlation between the ultrasonic modulus and the crosslinking density is presented combining DSC data with the stoichiometry of reactants according with the statistical theory of Miller and Macosko. The plot of the ultrasonic modulus as a function of the crosslinking density suggested that the theory of rubber elasticity can not be applied to the ultrasonic bulk longitudinal modulus as a consequence of the small deformation involved in the propagation of the ultrasonic waves.     

Determination of the complex moduli of viscoelastic materials with the ultrasonic pulse method (part II)

Summary With the aid of an ultrasonic pulse method the velocity and attenuation of longitudinal as well as transverse waves in some polyethylenes were measured in a rather broad temperature range. The density of the polymers studied varied from 0.919 to 0.980 g/cm³ at 23 C. From the measured data the complex elastic moduli, viz.Young's modulusE*, shear modulusG*, bulk modulusK* andPoisson's ratiov* were calculated.     

Ab initio Predictions of Structural and Thermodynamic Properties of Zr2AlC Under High Pressure and High Temperature

The structural and thermodynamic properties of Zr₂AlC at high pressure and high temperature are investigated by first principles density functional theory method. The calculated lattice parameters of Zr₂AlC are in good agreement with the available theoretical data. The pressure dependences of the elastic constants, bulk modulus, shear modulus, Young's modulus, and Vickers hardness of Zr₂AlC are successfully obtained. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. By using the quasiharmonic Debye model, the thermodynamic properties including the Debye temperature, heat capacity, volume thermal expansion coefficient, and Grüneisen parameter at high pressure and temperature are predicted for the first time.     

Brillouin-scattering determination of the acoustic properties and their pressure dependence for three polymeric elastomers

The acoustic properties of three polymer elastomers, a cross-linked poly(dimethylsiloxane) (Sylgard 184), a cross-linked terpolymer poly(ethylene-vinyl acetate-vinyl alcohol), and a segmented thermoplastic poly(ester urethane) copolymer (Estane 5703), have been measured from ambient pressure to approximately 12 GPa by using Brillouin scattering in high-pressure diamond anvil cells. The Brillouin-scattering technique is a powerful tool for aiding in the determination of equations of state for a variety of materials, but to date has not been applied to polymers at pressures exceeding a few kilobars. For the three elastomers, both transverse and longitudinal acoustic modes were observed, though the transverse modes were observed only at elevated pressures (>0.7 GPa) in all cases. From the Brillouin frequency shifts, longitudinal and transverse sound speeds were calculated, as were the C(11) and C(12) elastic constants, bulk, shear, and Young's moduli, and Poisson's ratios, and their respective pressure dependencies. P-V isotherms were then constructed, and fit to several empirical/semiempirical equations of state to extract the isothermal bulk modulus and its pressure derivative for each material. Finally, the lack of shear waves observed for any polymer at ambient pressure, and the pressure dependency of their appearance is discussed with regard to instrumental and material considerations.     

The mechanical moduli of lamellar semicrystalline polymers

Bounds on the elastic constants are derived for semicrystalline polymers whose local morphology is lamellar. Local response matrices (stiffness and compliance) are formulated in three dimensions that simultaneously incorporate uniform in-plane strain and additive forces from layer to layer of crystalline and amorphous phases and uniform stress and additive displacements normal to the lamellar surfaces. Spatial averaging of the stiffness and compliance matrices under the assumption of axially symmetric orientation gives the upper and lower bounds on the longitudinal and transverse tensile moduli and the axial and transverse shear moduli as functions of the separate phase elastic constants, the volume percent crystallinity, and the moments of the orientation 〈cos²θ〉 and 〈cos⁴θ〉. The bounds are much tighter than the Voight upper and Reuss lower bounds that do not recognize phase geometry. Using the known crystal elastic constants of polyethylene, sample calculations on isotropic unoriented materials show that the divergence of bounds at high crystallinity necessitated by the extreme crystal anisotropy shows up only at very high crystallinity. At low temperature the bounds are tight enough to specify G₁, the amorphous modulus, from the measured G and the known crystal elastic constants. At higher temperatures and lower G, the bounds are not tight enough for this purpose but the shear modulus versus crystallinity and temperature data are well fitted by the lamellar lower bound using a temperature-dependent, crystallinity-independent G₁.     

Shear and longitudinal viscosity of non-ionic C12E8 aqueous solutions

We present an extensive set of measurements of steady shear viscosity (eta degrees(s)), longitudinal elastic modulus (M'), and ultrasonic absorption (alpha) in the one-phase isotropic liquid region of the non-ionic surfactant C12E8 aqueous solutions. Within a given temperature interval, this phase extends along the entire surfactant concentration range that could be fully covered in the experiments. In agreement with previous studies, the overall results support the presence of two separated intervals of concentration corresponding to different structural properties. In the surfactant-rich region the temperature dependence of eta degrees(s) follows an equation characteristic of glass-like systems. The ultrasonic absorption spectra show unambiguous evidence of viscoelastic behavior that can be described by a Cole-Cole relaxation formula. In this region, when both the absorption and the frequency are scaled by the static shear viscosity (eta degrees(s)), the scaled attenuation reduces to a single universal curve for all temperatures and concentrations. In the water-rich region the behavior of eta degrees(s), M', and alpha are more complex and reflect the presence of dispersed aggregates whose size increases with temperature and concentration. At these concentrations the ultrasonic spectra are characterized by a multiple decay rate. The high-frequency tail falls in the same frequency range seen at high surfactant content and exhibits similar behaviors. This contribution is ascribed to the mixture of hydrophilic terminations and water present at the micellar interfaces that resembles the condition of a concentrated polymer solution. An additional low-frequency contribution is also observed, which is ascribed to the exchange of water molecules and/or surfactant monomers between the aggregates and the bulk solvent region.     

EuS高压相变发其弹性和热力学性质

采用平面波赝势密度泛函理论,利用第一性原理的方法研究了EuS的晶体结构、高压相变以及弹性性质．计算结果和实验值以及前人利用不同计算模型得到的理论值相吻合．研究了EuS的弹性常数、弹性模量和弹性的各向异性等力学性质随压力变化的趋势．同时研究了泊松比、德拜温度及纵波和横波的弹性波速随压力的变化趋势．基于德拜模型,进而研究了EuS在0-800K和0-60GPa下相变前后的热膨胀系数、热熔、Gruneisen参数等热力学性质．     

Measurement of high frequency linear viscoelastic functions of a nitrile‐butadiene rubber compound by ultrasound spectroscopy

The storage and loss components of the complex wave modulus, M*(ω), measured on a nitrile‐butadiene rubber compound (NBR‐DIN 53538) by ultrasound spectroscopy at a temperature of 293.2 K, were combined with the components of the complex shear modulus, G*(ω), measured on the same sample in a commercial Rheometric Scientific ARES instrument with torsion geometry at different frequencies and temperatures, and superposed in a master plot using the time–temperature superposition principle. From the combined measurements the components of the complex bulk modulus, K*(ω), were obtained by means of the exact formula M*(ω) = K*(ω) + (4/3)G*(ω). Some of the features of the complex bulk modulus reported in the literature for polymeric materials are confirmed for the NBR‐DIN mixture. The maxima in G″(ω) and K″(ω) are separated by more than one order of magnitude in the frequency scale and furthermore, the shapes of the peaks are different. The simple idea, that, for many polymers, the mechanisms for relaxation in shear and in bulk are of the same basic nature appears not to be supported by the present data. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 91–102, 2007     

Structural,elastic, electronic and thermal properties of the cubic perovskite-type BaSnO3

First-principles calculations are performed to investigate the structural, elastic, electronic and thermal properties of the cubic perovskite-type BaSnO₃. The ground-state properties are in agreement with experimental data. The independent elastic constants, C₁₁, C₁₂ and C₄₄, are calculated from direct computation of stresses generated by small strains. A linear pressure dependence of the elastic stiffnesses is found. From the theoretical elastic constants, we have computed the elastic wave velocities along [100], [110] and [111] directions. The shear modulus, Young's modulus, Poisson's ratio, Lamé’s coefficients, average sound velocity and Debye temperature are estimated in the framework of the Voigt-Reuss-Hill approximation for ideal polycrystalline BaSnO₃ aggregate. Using the sX-LDA for the exchange-correlation potential, the calculated indirect fundamental band gap value is in very good agreement with the measured one. The analysis of the site-projected l-decomposed density of states, charge transfer and charge density shows that the bonding is of ionic nature. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the temperature effect on the lattice constant, bulk modulus, thermal expansion coefficient, heat capacity and Debye temperature is calculated.     

Theoretical prediction of the structural,elastic, electronic,optical and thermal properties of the cubic perovskites CsXF3 (X = Ca,Sr and Hg) under pressure effect

Some physical properties of the cubic perovskites CsXF₃ (X = Ca, Sr and Hg) have been investigated using pseudopotential plane-wave method based on the density functional theory. The calculated lattice parameters within GGA and LDA agree reasonably with the available experimental data. The elastic constants and their pressure derivatives are predicted using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé’s constants for ideal polycrystalline aggregates. The analysis of B/G ratio indicates that CsXF₃ (X = Ca, Sr and Hg) are ductile materials. The thermal effect on the volume, bulk modulus, heat capacity and Debye temperature was predicted.     

Film foration and crystallization kinetics of polychloroprene studied by an ultrasonic shear wave reflection method

We report the application of an ultrasonic shear wave reflection technique for the investigation of film formation and crystallization kinetics of one amorphous and two semicrystalline polychloroprene samples with different gel content. Both isothermal and temperature-dependent measurements of the complex dynamic shear modulus (G* = G′ + iG″) have been performed at a frequency of 5.32 MHz. The process of film formation during the evaporation of water is expressed by a stepwise increase of the shear modulus. For the semicrystalline samples a further increase, which is due to crystallization, can be observed. Film formation and crystallization are delayed for the sample with high gel content and its minor final modulus is explained by a lower degree of crystallinity. The time-dependent increase of the shear modulus due to the growth of spherulites has been analyzed by the Avrami equation combined with the Kerner model for the modulus of a two-phase composite (spherulites in an amorphous matrix). The dynamic shear modulus for the spherulites has been estimated by a model introduced by Halpin and Kardos. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2949–2959, 1998     

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

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0～30GPa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．     

Ultrasonic Investigation of the Gelation Process of Poly(Acrylamide) Gels

The time evolution of ultrasonic velocity and attenuation has been investigated in-situ during the gelation process of polyacrylamide (PAAm) hydrogels. Longitudinal ultrasonic pulses were transmitted through the gel samples and continuously recorded to obtain the magnitude and phase of the waves as a function of time and frequency, enabling the attenuation coefficient, α, and phase velocity, v_p, of PAAm gels to be determined. The reaction was characterized by (1) an initial rapid increase in α and v_p, and (2) a subsequent reduction after both quantities passed through a peak associated with the exothermic reaction for the PAAm gelation. The square of v_p is proportional to the longitudinal modulus of the sample and inversely proportional to the density, and the values of v_p for the aged gels were smaller than those before the gelation. The cross-linker concentration dependence was further examined in order to investigate the gelation process accompanied by phase separation.     

The mechanical properties of crystalline cyclopentyl polyhedral oligomeric silsesquioxane

The anisotropic elastic constants of crystalline octacyclopentyl polyhedral oligomeric silsesquioxane (CpPOSS) were determined using molecular dynamics. The force field used for these calculations was shown to model accurately the rhombohedral and triclinic crystal structures of octasilsesquioxane and CpPOSS, respectively, as well as the vibrational frequencies of octasilsesquioxane. The moduli for CpPOSS are anisotropic, with a Reuss-averaged bulk modulus of 7.5 GPa, an isotropic averaged Young's modulus of 11.78 GPa, and an isotropic averaged shear modulus of 4.75 GPa. These isotropic averages or, alternatively, the full anisotropic stiffness tensor of the crystal can be used with micromechanical composite models to calculate the effective elastic properties of polymer nanocomposites that contain crystalline aggregates of CpPOSS.     

Rheology of ethyl cellulose solutions

Steady state flow and dynamic viscoelastic measurements of ethyl cellulose / m-Cresol solutions reveal the existence of an isotropic and anisotropic phase, as well as a biphasic interval. The effect of the applied shear rate is to shift the anisotropic phase to lower concentrations. The anisotropic phase, which is found from 20 wt.-% polymer concentration, is characterized by the following features: A) Three flow regions, pseudoplastic, Newtonian and pseudoplastic, respectively, are observed in $ \eta - \dot \gamma _{21} $ plots but not in η* - ω plots, b) “Grainy” and “thread” textures correspond to regions I and II respectively, c) Activation energies of flow are similar to that of the pure solvent, d) Both dynamic viscoelastic functions G′ and G″ scale with frecuency as ω^0.75, a dependence already observed in complex liquids, like heterogeneous block copolymers. On the other hand, dynamic viscoelastic measurements performed with isotropic systems allow to determine the entanglement modulus and the associated molecular weight between entanglement couplings, M_e⁰=7830.     

Ab initio calculations of the structural and elastic properties of CoSi2

Under GGA, the geometry, energy, electronic structure, and elastic properties of the CoSi₂ have been investigated by using ab initio plane-wave ultrasoft pseudopotential method. The calculated equilibrium lattice parameter a and elastic stiffness constants c ₁₁, c ₁₂, and c ₄₄ are in better agreement with the experimental values than those obtained by both the VAMP and FLAPW with LDA. For engineering and technological applications, the isotropic elastic properties, including the shear modulus G, the bulk modulus B, Young’s modulus E, and Poisson’s ratio , are also calculated for polycrystalline CoSi₂ with Voigt, Reuss, and Hill approximations. The lower Poisson’s ratio of 0.327 means an increase in the volume is associated with the uniaxial tensile deformation and the higher ratio of bulk modulus to shear modulus B/G of 2.56 indicates the ductility of CoSi₂ which is in accordance with the metallic property of CoSi₂ obtained by the density of states.