Determination of elastic shear constants of polyethylene at room temperature by inelastic neutron scattering

The elastic shear constants of both the amorphous and crystalline regions of polyethylene have been measured at room temperature. A newly developed method is used which allows the determination of elastic constants from the coherent inelastic neutron scattering of polycrystals. A deuterated and partially oriented sample is investigated on a triple-axis spectrometer and a time-of-flight instrument. The elastic constants of the crystalline regions of polyethylene are c₄₄ = 2.1 ± 0.3, c₅₅ = 2.2 ± 0.3, c₆₆ = 1.8 ± 0.2, and c′ = 1/4(c₁₁ + c₂₂ ? 2c₁₂) = 0.92 GPa. The shear modulus of the amorphous regions is obtained as G = 0.55 ± 0.03 GPa. In connection with other experimental results the elastic constant matrix is given and compared with theoretical estimates. With simple models, macroscopic moduli are calculated which are in good agreement with published experimental data.     

Elastic moduli of ultradrawn polyethylene

The five independent elastic moduli C₁₁, C₁₂, C₁₃, C₃₃, and C₄₄ of oriented high-density polyethylene with draw ratio λ from 1 to 27 have been determined from ?60 to 100°C by an ultrasonic method at 10 MHz. At low temperature the sharp rise in the axial extensional modulus C₃₃ with increasing λ and the slight changes in the other moduli result from chain alignment and the increase in the number of intercrystalline bridges connecting the crystalline blocks. At high temperature (say, 100°C) the transverse extensional modulus C₁₁, as well as the axial (C₄₄) and transverse (C₆₆) shear moduli, also show substantial increases, reflecting the prominent reinforcing effect of stiff crystalline bridges in this temperature region where the amorphous matrix is rubbery. If the crystalline bridges are regarded as the fiber phase, the mechanical behavior can be understood in terms of the Halpin–Tsai equation for aligned short-fiber composites.     

On the predictability of the high-frequency elastic modulus of semicrystalline polymers as function of crystallinity

The relation of the high-frequency elastic moduli of semicrystalline polymers to volume fraction crystallinity is correctly described by the Hashin-Shtrikman theory, without any disposable constants, as a function of the ratio of the modulus of the amorphous to that of the crystalline phase. Hence the (high-frequency) reduced modulus of semicrystalline polymers is largely a function of the temperature T/T_g. The importance of T/T_m for the modulus of the crystalline phase precludes the existence of a single universal reduced modulus versus temperature curve.     

Ultrasonic measurements of the elastic moduli of ultradrawn polyoxymethylene

We have employed an ultrasonic method to measure from ?40 to 60°C the five independent elastic moduli C₁₁, C₁₃, C₃₃, C₄₄, and C₆₆ of polyoxymethylene with draw ratio λ from 1 to 26 prepared by continuous drawing under microwave heating. The elastic moduli are controlled by three major factors: molecular orientation in the crystalline regions, fraction of noncrystalline taut tie molecules, and void content. The steep rise in the axial extensional modulus C₃₃ and axial Young's modulus E₀ with increasing draw ratio results from the alignment of chains in the crystalline blocks and an increase in the number of disordered taut tie molecules. Below the γ relaxation (located at 0°C at our measurement frequency of 10 MHz), these two factors also give rise to a slight decrease in the transverse extensional modulus C₁₁, Young's modulus E₉₀ and shear modulus C₆₆. At high temperature where the amorphous regions have very low modulus, the stiffening effect of taut tie molecules becomes dominant, leading to an increase in all moduli as λ increases from 1 to 10. At higher λ the void fraction increases appreciably, causing small decreases in E₉₀, C₁₁, and C₆₆ at all temperatures.     

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.     

Elasticity and structure of chemically crosslinked polyurethanes

A combination of electron-microscopy, light-scattering, and stress-birefringence studies on chemically crosslinked polyurethanes point toward the existence of rodlike regions (“bundles”), approximately 3000–8000 Å in length and involving about 5% of the volume, in which molecular orientations are correlated. The elastic behavior of these networks—as indeed that of most rubberlike networks—deviates substantially from the Gaussian behavior. The empirical representation of the data in Mooney-Rivlin plots yields C₁ and C₂ constants which depend on the type of imposed strain. It is thus impossible to identify C₁ with the Gaussian behavior and C₂ with the deviation there-from. Instead, it is found that the elastic behavior can be adequately described if it is assumed that, as a result of the bundle structure, about 5% of the segments of each chain are not free to assume the normal random-walk configurations. The determination of the number of chains in the network from the elastic behavior remains ambiguous, however, and the behavior upon swelling is not (yet) adequately reproduced by the theory. It is conceivable that in many cases deviations from Gaussian elasticity behavior may be caused by an intermolecular structuring effect, rather than by various minor deficiencies in the Gaussian model for the single chain statistics or by anisotropic excluded volume effects, as has been proposed in the past. In the present case, the amount of bundle structure, as well as the C₂/C₁ values, increase with the number of urethane couplings per chain, and this suggests that the interaction of the highly polar urethane couplings is responsible for the structuring. In other networks one often finds a dependence of C₂/C₁ on the previous history of the sample, which suggests that an accidentally trapped order may be responsible for the elastic behavior.     

Structure and dynamics of room temperature ionic liquids with bromide anion: results from 81Br NMR spectroscopy

We report the results of a comprehensive ⁸¹Br NMR spectroscopic study of the structure and dynamics of two room temperature ionic liquids (RTILs), 1‐butyl‐3‐methylimidazolium bromide ([C₄mim]Br) and 1‐butyl‐2,3‐dimethylimidazolium bromide ([C₄C₁mim]Br), in both liquid and crystalline states. NMR parameters in the gas phase are also simulated for stable ion pairs using quantum chemical calculations. The combination of ⁸¹Br spin‐lattice and spin‐spin relaxation measurements in the motionally narrowed region of the stable liquid state provides information on the correlation time of the translational motion of the cation. ⁸¹Br quadrupolar coupling constants (C_Q) of the two RTILs were estimated to be 6.22 and 6.52 MHz in the crystalline state which were reduced by nearly 50% in the liquid state, although in the gas phase, the values are higher and span the range of 7–53 MHz depending on ion pair structure. The C_Q can be correlated with the distance between the cation–anion pairs in all the three states. The ⁸¹Br C_Q values of the bromide anion in the liquid state indicate the presence of some structural order in these RTILs, the degree of which decreases with increasing temperature. On the other hand, the ionicity of these RTILs is estimated from the combined knowledge of the isotropic chemical shift and the appropriate mean energy of the excited state. [C₄C₁mim]Br has higher ionicity than [C₄mim]Br in the gas phase, while the situation is reverse for the liquid and the crystalline states. Copyright © 2015 John Wiley & Sons, Ltd.     

First-principles prediction of metastable niobium and tantalium nitrides M4N5 and M5N6 stoichiometry

A first-principles plane-wave pseudopotential method based on the density functional theory is used to investigate the structural, elastic and electronic properties of M₄N₅ and M₅N₆ (M = a transition metal (TM) Nb, Ta). C₃₃ elastic constant for all compounds is found to be much larger than C₁₁, indicating that a-axis is more compressible than c-axis. Interestingly, we find that C₃₃ and C₁₁ are significantly larger than other elastic constants, resulting in a pronounced elastic anisotropy.     

High‐Temperature Elastic Moduli of Flux‐Grown α‐GeO2 Single Crystal

From high‐precision Brillouin spectroscopy measurements, six elastic constants (C₁₁, C₃₃, C₄₄, C₆₆, C₁₂, and C₁₄) of a flux‐grown GeO₂ single crystal with the α‐quartz‐like structure are obtained in the 298–1273 K temperature range. High‐temperature powder X‐ray diffraction data is collected to determine the temperature dependence of the lattice parameters and the volume thermal expansion coefficients. The temperature dependence of the mass density, ρ, is evaluated and used to estimate the thermal dependence of its refractive indices (ordinary and extraordinary), according to the Lorentz–Lorenz equation. The extraction of the ambient piezoelectric stress contribution, e₁₁, from the C′₁₁–C₁₁ difference gives, for the piezoelectric strain coefficient d₁₁, a value of 5.7(2) pC N^?1, which is more than twice that of α‐quartz. As the quartz structure of α‐GeO₂ remains stable until melting, piezoelectric activity is observed until 1273 K.     

Structural, electronic and elastic properties of MAX phases M2GaN (M = Ti, V and Cr)

Based on first-principles total energy calculations, we have investigated the systematic trends for structural, electronic and elastic properties of the MAX phases M₂GaN depending on the type of M transition metal (M are Ti, V and Cr). The optimized zero pressure geometrical parameters: the two unit cell lengths (a, c), the internal coordinate z and the bulk modulus are calculated. The results for the lattice constants are in agreement with the available experimental data. The band structures show that all studied materials are electrical conductors. The analysis of the site-projected l-decomposed density of states shows that bonding is due to M d-N p and M d-Ga p hybridizations. The elastic constants are calculated using the static finite strain technique. The shear modulus C₄₄, which is directly related to the hardness, reaches its maximum when the valence electron concentration is in the range 10.5–11.0. The isotropic elastic moduli, namely, bulk modulus (B), shear modulus (G), Young's modulus (E) and Poisson's ratio (σ) are calculated in framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline M₂GaN aggregates. We estimated the Debye temperature of M₂GaN from the average sound velocity. This is the first quantitative theoretical prediction of the electronic structures, and elastic constants and related properties for Ti₂GaN, V₂GaN and Cr₂GaN compounds that require experimental confirmation.     

Studies of the effect of orientation on the elastic constants of stretched and hydrostatically extruded polychlorotriflouroethylene: A reorientational model in semicrystalline polymers

A reorientational model of polymer solids is given. The solid is described as a collection of small, orientable units. The elastic constants of the oriented polymer are given as a combination of the elastic constants of the orientable units and of the orientation parameters 〈P₂(cosθ)〉 and 〈P₄(cosθ)〉. The elastic constants of stretched and hydrostatically extruded samples of polychlorotriflouroethylene are obtained with Brillouin light scattering. These are fitted to the model and the orientation parameters are calculated. The elastic constants from the extruded samples are fit well by the model but the fit to the stretched film is less satisfactory. Hydrostatic extrusion in polymers is thus assumed to be a reorientation process in the amorphous phase, but the stretching process is not completely reorientational.     

Periodic DFT approach to benzotrifuroxan crystal

Density Functional Theory (DFT) calculations at the B3LYP/6‐21G* level were performed on crystalline benzotrifuroxan (BTF). The frontier bands are generally quite flat. The energy gap between the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LUCO) is 3.89 eV, indicating that the crystal is an electrical insulator. All the atoms of BTF make up both the lower and the higher energy bands. The projection of density of state (DOS) indicates that there exists no region with much higher reactivity as other explosives, since the coplanar rings of BTF are conjugated. An anisotropic impact on the bulk makes the electron transfer from carbon atoms to nitrogen and oxygen atoms, which lowers the strength of the C–C bond. The crystal lattice energy is predicted to be –47.39 kJ/mol. The elastic constants C₁₁, C₂₂, and C₃₃ are predicted to be 191.48 GPa, 94.39 GPa, and 347.42 GPa, respectively. The large differences of C₁₁, C₂₂, and C₃₃ indicate the anisotropic properties of BTF upon impacting. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Solid-state 13C nuclear magnetic resonance characterization of MDI-based polyurethanes

¹³C solid-state nuclear magnetic resonance (NMR) experiments on linear polyurethanes and poly(ether-urethane) block copolymers demonstrate that ¹³C spin-lattice relaxation experiments in the laboratory [T₁(C)] and rotating [T_1p(C)] frames provide the most information about domain morphology in these microphase-separated polymer systems. T₁(H) TCH, and T_1p(H) data are less useful in a 4,4′-methylene bis(p-phenyl isocyanate)-1,4-butanediol (MDI/BD) hard-segment material, the MDI bridging methylene and the MDI urethane carbonyl T₁(C and T_1p(C) times fall in characteristic ranges for crystalline, amorphous, interfacial, and dissolved species. BD methylene carbons have short T_1p(C) for crystalline and long T_1p(C) for amorphous hard-segment aggregates. The distinct T_1p(C) and T₁(C) fractins observed are attributed to the presence of several crystalline polymorphs. Both T₁(C) results and DSC endotherms indicate that the crystalline polymorphs present in the poly(ether-urethane) are less ordered than the types seen in the pure hard-segment material. © 1993 John Wiley & Sons, Inc.     

Effect of a rigid,non-polar solute on the dielectric anisotropy,the splay and bend elastic constants,and on the rotational viscosity coefficient of 4-4′-n-heptylcyanobiphenyl

The effect of mixing a rigid, non-polar, non-mesogenic solute, biphenyl (C₆H₅-C₆H₅), in the nematic solvent 7CB (4,4′-n-heptylcyanobiphenyl) is investigated. The solute is found to reduce the nematic order and a two-phase region appears. We report measurements of the transition temperatures, dielectric anisotropy, and splay and bend elastic constants, as well as the rotational viscosity coefficient by the method of electric field-induced Fréedericksz transition for biphenyl concentrations up to 8.0%.     

Equilibria of extended-chain polymers exhibiting crystalline and liquid-crystalline phases

The phase diagram of poly(p-benzamide) (PBA) in N,N-dimethylacetamide/LiCl solutions was determined for two PBA samples having weight-average molecular weights of about 10,000. The various equilibria were studied using analytical, viscometric, and optical microscope measurements. The phase diagram at 25°C, taking as variables the concentration of polymer (C_p) and LiCl (C_s), involves several equilibria which can be summarized as follows: solid ? isotropic solution when 0.75 ≤ C_s ≤ 2 g/dl, solid ? anisotropic solution when 2 ≤ C_s ≤ 4 g/dl, isotropic solution ? anisotropic solution when 2 ≤ C_s ≤ 4 g/dl, and C_p > 6 g/dl, and dilute isotropic solution ? gel when C_s > 4 g/dl. In the C_p range in which the isotropic and anisotropic phases coexist, enrichment of the high-molecular-weight component of the polymer in the anisotropic phase becomes more marked as the volume fraction of the latter phase is decreased. The two PBA samples exhibit noticeable differences in solubility, absolute viscosity, and in their viscosity-concentration behavior. The location of the maximum in the latter dependence does not necessarily coincide with the first appearance of the anisotropic phase. In the absence of a flow field, anisotropic solutions exhibit an irreversible increase in viscosity. Inclusion of the equilibria involving the crystalline state furnishes insight into some of the common observations for extended-chain polymers. A diagram illustrates the superposition of the solubility curves for a crystalline polymer and the liquid-crystal regions. This indicates that, for the high melting crystalline polymers, the crystalline phase should be stable relative to the concentrated anisotropic phase of the wide biphasic region.     

Anisotropic properties of poly(ethylene terephthalate) by Brillouin spectroscopy: Anisotropic properties of oriented bulk and nanostructured poly(ethylene terephthalate) determined by Brillouin spectroscopy and birefringence experiments

Using Brillouin spectroscopy (BS), the tensor of the elastic constants of oriented poly(ethylene terephthalate) was determined for a variety of morphologies obtained by different uniaxial drawing procedures. The extreme values of the moduli along the drawing direction at frequencies of a few gigahertz were C₃₃ = 40 GPa and C₄₄ = 1.8 GPa. As a result of the invariants of the single‐phase aggregate model, the oriented state is dominated by the Reuss average even at extreme draw ratios and subsequent to a deformation‐induced crystallization. This is documented in both the BS orientation parameter and the BS mode numbers in comparison with birefringence. Additional spectral lines observed at draw ratios larger than 6 are discussed in relation to the formation of nanostructured phases. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1201–1213, 2002     

Measurement of the orientational elastic constants and the twist viscosity of nematic side chain polymers

Abstract

The temperature dependence of the three elastic constants k _ii (i = 1, 2, 3) and the twist viscosity γ₁ of two nematic side chain polyacrylates and one comparable low molecular weight compound have been measured by means of the Freedericksz effect. The change from the low to the high molecular liquid crystal causes a change of the ratio k ₃₃/k ₁₁ from greater to less than unity, but the order of magnitude of the elastic constants remains the same. In contrast, the twist viscosity of the polymeric liquid crystal is about 1000 times greater in magnitude than that of a comparable low molecular weight liquid crystal. The activation energy for the viscosity of the polymer differs by a factor 3–4 from that of the low molecular weight liquid crystal. The elastic constants as well as the twist viscosity show a quadratic dependence on the order parameter S over a wide temperature range.     

Half-metallicity,magnetism, mechanical,thermal, and phonon properties of FeCrTe and FeCrSe half-Heusler alloys under pressure

The half-metallicity of Heusler alloys is quite sensitive to high pressure and disorder. To understand this phenomenon better, we systematically studied the half-metallic nature, magnetism, phonon, and thermomechanical properties of FeCrTe and FeCrSe Heusler alloys under high pressure using ab initio calculations based on density functional theory. The ground-state lattice constants for FeCrTe and FeCrSe alloys are 5.93 and 5.57 Å, respectively, consistent with available theoretical results. Formation energy, cohesive energy, elastic constants, and phonon dispersion confirmed that both compounds are thermodynamically and mechanically stable. The FeCrTe and FeCrSe alloys showed a half-metallic character with a band gap of 0.68 and 0.58 eV at 0 GPa pressure, respectively, and magnetic moments of 2.01 μ_B for both alloys, using generalized gradient approximation (GGA) approximation. FeCrTe alloy changes from metallic to half-metallic above 30 GPa pressure using GGA + U. The elastic properties were scrutinized, and it was found that, at 0 GPa pressure, FeCrTe is ductile, and FeCrSe is brittle. Under pressure, FeCrSe becomes brittle above 10 GPa pressure. Average sound velocity V_m, Debye temperature Ɵ_D, and heat capacity C_V were predicted under pressure. These outcomes will improve the integration of Fe-based half-Heusler alloys in spintronic devices.     

Brillouin scattering of oriented films of poly(vinylidene fluoride) and poly(vinylidene fluoride) -poly( methyl methacrylate) blends

Temperature dependent Brillouin scattering studies of PVF₂ films stretched to various stretch ratios have been carried out. Elastic constants for unstretched and stretched films have been obtained as functions of temperature. The elastic constant C₃₃ of the stretched films has a greater temperature dependence than that of unstretched films. To elucidate the effect of the surrounding amorphous matrix on the Brillouin spectrum of semicrystalline PVF₂ film, we carried out Brillouin scattering studies of films made from blends of PVF₂ and PMMA.     

Chain transfer with siloxanes during free-radical polymerization

Chain transfer constants (C_s) for a number of substrates containing the silicon-oxygen bond are measured in polymerizing methyl methacrylate. Additionally, a few measurements are run in styrene in order to estimate the influence of polar factors on chain transfer. The methylsiloxanes studied all show very low values of C_s (10^?5 to 10^?6). The chain transfer constants of a number of propylsiloxane derivatives are negligibly influenced by the presence of silicon. Thus, (Me₃SiO)₂MeSiCH₂MeCH(C₆H₅) shows a value of C_s nearly that reported for cumene, and (MeO)₃SiCH₂CH₂CH₂SH shows values of C_s close to those reported for alkyl mercaptans.