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.     

Mechanical relaxations and moduli of oriented nylon 66 and nylon 6

The mechanical relaxations of dry and wet nylon 66 and nylon 6 with draw ratios λ = 1–3 have been studied from ?180 to 160°C and in the frequency range of 1 Hz to 10 MHz. The five independent elastic moduli C_11, C_12, C_13, C_33, and C₄₄ have also been determined by an ultrasonic method at 10 MHz. Wide-angle x-ray diffraction and birefringence measurements reveal that the crystalline orientation rises sharply at low λ and becomes saturated near λ = 3; the amorphous orientation function increases continuously, reaching values of 0.3–0.5 at λ = 3. The alignment of molecular chains and the presence of taut tie molecules in the amorphous regions lead to a lowering of segmental mobility, thereby reducing the magnitude and increasing the peak temperature and activation energy of the α relaxation. Water absorption weakens the interchain bonding and so gives rise to effects opposite to those of drawing. At low temperature, the development of mechanical anisotropy is largely determined by the overall chain orientation, with the c-shear mechanism contributing a small additional effect. However, above the α relaxation, where the amorphous region is rubbery, the stiffening effect of taut tie molecules becomes dominant and leads to increases in all moduli.     

Mechanical and transport properties of highly drawn isotactic polypropylene

Quenched films of isotactic polypropylene were drawn at 110°C up to draw ratio λ = 18. The axial elastic modulus was measured as function of λ up to the highest achieved λ. The sorption and diffusion of CH₂Cl₂ at 25°C in the undrawn and drawn samples were studied. Exclusively transparent samples were used for the measurement of the density and transport properties. This reduces the maximum usable draw ratio to 15. The drawing process is inhomogeneous with neck propagation. In the neck the draw ratio increases by about 6. As a consequence of the increasing fraction of taut tie molecules the axial elastic modulus increases faster than the draw ratio. The transport parameters D, S, and λ indicate that the original lamellar morphology is completely transformed into the microfibrillar structure.     

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.     

Thermal conductivity and thermal expansivity of thermotropic liquid crystalline polymers

The thermal conductivity and thermal expansivity of a thermotropic liquid crystalline copolyesteramide with draw ratio λ from 1.3 to 15 have been measured parallel and perpendicular to the draw direction from 120 to 430 K. The sharp rise in the axial thermal conductivity K_par; and the drastic drop in the axial expansivity α_∥ at low λ, and the saturation of these two quantities at λ > 4 arise from the corresponding increase in the degree of chain orientation revealed by wide-angle x-ray diffraction. In the transverse direction, the thermal conductivity and expansivity exhibit the opposite trends but the changes are relatively small. The draw ratio dependences of the thermal conductivity and expansivity agree reasonably with the predictions of the aggregate model. At high orientation, K_par; of the copolyesteramide is slightly higher than that of polypropylene but one order of magnitude lower than that of polyethylene. In common with other highly oriented polymers such as the lyotropic liquid crystalline polymer, Kevlar 49, and flexible chain polymer, polyethylene, α_par; of the copolyesteramide is negative, with a room temperature value differing from those of Kevlar 49 and polyethylene by less than 50%. Both the axial and transverse expansivity show transitions at about 390 and 270 K, which are associated with large-scale segmental motions of the chains and local motions of the naphthalene units, respectively. ©1995 John Wiley & Sons, Inc.     

Effect of temperature on the dynamic young's and shear moduli of unidirectional carbon fiber-epoxy composite beams

The resonance frequencies of unidirectional carbon fiber reinforced/epoxy composite beams were studied over the temperature range 24–225°C. Longitudinal Young's moduli E₁₁ and longitudinal-transverse shear moduli G₁₂ were computed from the experimental data by the use of Timoshenko beam theory. The effects of transverse shear deformation (a function of E₁₁/G₁₂) were found to increase in importance with increasing temperature. Values of G₁₂ were found to be approximately proportional to the shear modulus G_m of matrix material but were about 30% lower than predicted by the theory of Hashin and Rosen. The anisotropy of the carbon filaments and voids in the composite samples were proposed to account for the discrepancy between theory and experiment.     

Nonlinear relaxation of stress and birefringence in simple extension of 1,2-polybutadiene

Relaxation of stress and birefringence in simple extension has been studied for two samples of 1,2-polybutadiene with 95% and 88% vinyl content and weight-average molecular weight 1.9 and 2.9 × 10⁵, respectively. The extension ratio, λ, ranged from 1.14 to 2.08, temperatures from 0 to 15°C, and times, reduced to 0°C, up to 3 × 10⁵ sec. The stress-optical coefficient C was negative and positive, respectively, for the two samples, the difference being attributable to opposite signs and very different magnitudes of the contributions of the 1,2 and 1,4 moieties to the birefringence. For each polymer, C was independent of time but increased (algebraically) with temperature. For one polymer a very minor dependence of C on λ was observed. At any instant of time, the dependence of both stress and birefringence on λ could be described by equations of the Mooney–Rivlin form with coefficients C₁,C₂ and B₁,B₂, respectively. At short times the contributions of the C₁ and C₂ terms to the stress and of the B₁ and B₂ terms to the birefringence are roughly equal. With increasing time, C₁ and B₁ decrease gradually while C₂ and B₂ remain constant over several decades in time. Finally, C₂ and B₂ decrease rather rapidly. A tentative interpretation of these phenomena in terms of motions of entanglements is given.     

Mechanical properties of ultra-oriented polyethylene

Semicrystalline polymers generally exhibit moduli well below their theoretical limit due to chain folding and to lack of crystal alignment. Modulus increases attainable through standard drawing procedures are limited by sample fracture before large draw ratios are reached. Using an Instron capillary rheometer which allowed a draw ratio of > 300, transparent polyethylene strands of unusually high c-axis orientation have been produced by a combination of pressure and shear. The virtually perfect crystalline orientation and evidence for extended chains confirm that a significant improvement in modulus can be realized by this technique. The dynamic tensile storage modulus was measured by Vibron over the temperature range ?160°C to +120°C. Room-temperature moduli were 7 × 10¹¹ dyne/cm², higher than any reported values for drawn polyethylene. Values also remained above 10¹¹ dyne/cm² even at 120°C. The moduli and morphological data have been related by a model consisting of an extended-chain component in paralled with a conventional drawn morphology. Experimental and calculated moduli are compared and related to available theory.     

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.     

X‐ray diffraction study of the thermal expansion behavior of cellulose triacetate I

Highly crystalline samples of cellulose triacetate I (CTA I) were prepared from highly crystalline algal cellulose by heterogeneous acetylation. X‐ray diffraction of the prepared samples was carried out in a helium atmosphere at temperatures ranging from 20 to 250 °C. Changes in seven d‐spacings were observed with increasing temperature due to thermal expansion of the CTA I crystals. Unit cell parameters at specific temperatures were determined from these d‐spacings by the least squares method, and then thermal expansion coefficients (TECs) were calculated. The linear TECs of the a, b, and c axes were α_a = 19.3 × 10^?5 °C^?1, α_b = 0.3 × 10^?5 °C^?1 (T < 130 °C), α_b = ?2.5 × 10^?5 °C^?1 (T > 130 °C), and α_c = ?1.9 × 10^?5 °C^?1, respectively. The volume TEC was β = 15.6 × 10^?5 °C^?1, which is about 1.4 and 2.2 times greater than that of cellulose I_β and cellulose III_I, respectively. This large thermal expansion could occur because no hydrogen bonding exists in CTA I. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 517–523, 2009     

Elastic modulus and thermal conductivity of ultradrawn polyethylene

The axial and transverse Young's modulus and thermal conductivity of gel and single crystal mat polyethylene with draw ratios λ = 1–350 have been measured from 160 to 360 K. The axial Young's modulus increases sharply with increasing λ, whereas the transverse modulus shows a slight decrease. The thermal conductivity exhibits a similar behavior. At λ = 350, the axial Young's modulus and thermal conductivity are, respectively, 20% and three times higher than those of steel. For this ultradrawn material both the magnitude and the temperature dependence of the axial Young's modulus are close to those of polyethylene crystal. The high values of the axial Young's modulus and thermal conductivity arise from the presence of a large percentage (∼85%) of long needle crystals. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3359–3367, 1999     

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.     

Plastic deformation of polypropylene. IV. Wide-angle x-ray scattering in the neck region

Wide-angle x-ray scattering (WAXS) patterns of two polypropylene samples, a quenched sample drawn at 21°C and an annealed sample drawn at 100°C, were investigated in a range of values of draw ratio λ very closely spaced through the neck region. In both cases, a range of small λ where deformation occurred by spherulite deformation was followed by one of higher λ where microfibrils were formed. The contribution to the WAXS pattern of microfibrils could be clearly distinguished from that of deformed spherulites because of the better orientation parallel to the draw direction of the former as compared to the latter. Additionally, for a drawing temperature of 21°C, microfibrils crystallize in the “smectic” phase as compared to the monoclinic phase for the initial sample and deformed spherulites. At this temperature, plastic deformation proceeds through the spherulite deformation mechanism up to λ = 1.4 accompanied by an increase in chain orientation with increasing λ. For λ > 1.4 plastic deformation appears to occur exclusively through microfibril formation. For drawing at 100°C, spherulite deformation is accompanied by very little change in chain orientation up to λ = 2, where microfibril formation begins. For λ > 2 (T_d = 100°C) plastic deformation is accompanied by both microfibril formation and some spherulite deformation as reflected by changes in both orientation and crystallite size. At this temperature the lateral crystallite size in the microfibrils is related to the long period according to the “equilibrium crystallite shape” previously found for annealed polypropylene.     

Mechanical properties of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A study of the mechanical properties of poly(ferrocenyldimethylsilane) [Fe(η‐C₅H₄)₂SiMe₂]_n, 3 , a novel organometallic polymer, has been performed on thin films of this material. The Young's modulus and Poisson's ratio of film samples (15 × 1 × 1 mm) of 3 were measured in quasi‐static tension using a video extensometer. For 3 , the values of the Young's moduli (E) and Poisson's ratios (ν) were similar between axes in the plane and independent of the splicing direction used during sample preparation. The mean and standard deviation of the Young's modulus and Poisson's ratio were 0.78 ± 0.08 GPa and 0.37 ± 0.06 GPa, respectively. Thermomechanical analysis of 3 revealed a steady decrease of E from a room temperature value of approximately 0.70 GPa. Additionally, it was found that at 150 °C, 3 was unable to support even small stresses, consistent with the onset of a melt transition (ca. 135 °C). A mathematical model based on molecular geometry is developed to describe the results. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2280–2288, 2005     

Lateral thermal expansion of cellulose Iβ and IIII polymorphs

Measurements of the thermal expansion coefficients (TECs) of cellulose crystals in the lateral direction are reported. Oriented films of highly crystalline cellulose I_β and III_I were prepared and then investigated with X‐ray diffraction at specific temperatures from room temperature to 250 °C during the heating process. Cellulose I_β underwent a transition into the high‐temperature phase with the temperature increasing above 220–230 °C; cellulose III_I was transformed into cellulose I_β when the sample was heated above 200 °C. Therefore, the TECs of I_β and III_I below 200 °C were measured. For cellulose I_β, the TEC of the a axis increased linearly from room temperature at α_a = 4.3 × 10^?5 °C^?1 to 200 °C at α_a = 17.0 × 10^?5 °C^?1, but the TEC of the b axis was constant at α_b = 0.5 × 10^?5 °C^?1. Like cellulose I_β, cellulose III_I also showed an anisotropic thermal expansion in the lateral direction. The TECs of the a and b axes were α_a = 7.6 × 10^?5 °C^?1 and α_b = 0.8 × 10^?5 °C^?1. The anisotropic thermal expansion behaviors in the lateral direction for I_β and III_I were closely related to the intermolecular hydrogen‐bonding systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1095–1102, 2002     

Synthesis and characterization of a Cu(II) complex of 2-benzylmercapto-5-methyl-1,3,4-thiadiazole (C10H10N2S2)

A Cu(II) complex of 2-benzylmercapto-5-methyl-1,3,4-thiadiazole was synthesized and characterized. The crystal structure of the copper complex and the free ligand were determined by single-crystal X-ray diffraction at room temperature: {[Cu(C₁₀H₁₀N₂S₂)₂(Cl)₂], P 1 triclinic, a = 8.1450(2) Å, b = 8.1690(2) Å, c = 10.8180(3) Å, α = 97.4040(12)°, β = 101.6270(11)°, γ = 116.1431(14)°; C₁₀H₁₀N₂S₂ ligand, Pbca orthorhombic, a = 8.7938(7) Å, b = 9.6491(7) Å, c = 25.3552(18) Å}. The metal complex framework consists of discrete units that provide crystalline stability through a network of van der Waals contacts. The Cu(II) is coordinated by two chloride ions and two 2-benzylmercapto-5-methyl-1,3,4-thiadiazole monodentate ligands showing a distorted square planar configuration. Both thiadiazole ligands coordinate through the N atom bonded to the benzylthio substituted C atom.

The FTIR spectroscopic data are consistent with this structural model. Analysis of the magnetic susceptibility from 5 K to room temperature indicates the presence of paramagnetic Cu(II), confirmed by the EPR spectrum.     

Reindarstellung,Kristallzüchtung und Kristallstrukturbestimmung von Iodtrioxid

Synthesis, Crystal Growth, and Crystal Structure Determination of Iodine Trioxide For the first time, pure and single crystalline iodine trioxide has been obtained and its identity proven by a crystal structure determination, unambigously. It forms at slow decomposition of orthoperiodic acid in concentrated sulfuric acid at 70°C during 3–6 weeks. The crystal structure (triclinic, P1 ; a = 500.6(2), b = 674.1(3), c = 679.5(3) pm, α = 97.31(3), β = 96.43(3), γ = 105.36(3)°; 1754 independent reflections, R = 0.064) contains one I₄O₁₂ molecule per unit cell. The oxide can be regarded as a mixed anhydride formed by condensation of two molecules H₅IO₆ and HIO₃, each. The axial atoms in an I₂O₁₀ doubleoctahedron are bridged by two IO groups. The pointsymmetry is C_2h. The molecules are connected via short intermolecular oxygen iodine bridges to form twodimensional infinite layers. The crystal structure thus represents an intermediate between molecular and polymeric.     

Volume dependence of thermal conductivity and bulk modulus for poly(propylene glycol)

The thermal conductivity λ and heat capacity per unit volume of poly(propylene glycol) PPG (0.4 and 4.0 kg·mol⁻¹ in number-average molecular weight) have been measured in the temperature range 150–295 K at pressures up to 2 GPa using the transient hot-wire method. At 295 K and atmospheric pressure, λ = 0.147 W m⁻¹K⁻¹ for PPG (0.4 kg·mol⁻¹) and λ = 0.151 W m⁻¹K⁻¹ for PPG (4.0 kg·mol⁻¹). The temperature dependence of λ is less than 4 × 10⁻⁴ W m⁻¹K⁻² for both molecular weights. The bulk modulus has been measured in the temperature range 215–295 K up to 1.1 GPa. At atmospheric pressure, the room temperature bulk moduli are 1.97 GPa for PPG (0.4 kg·mol⁻¹) and 1.75 GPa for PPG (4.0 kg·mol⁻¹). These data were used to calculate the volume dependence of $ \lambda ,g\, = - \left( {\frac{{\partial \lambda /\lambda }}{{\partial V/V}}} \right)_T $. At room temperature and atmospheric pressure (liquid phase) we find g = 2.79 for PPG (0.4 kg·mol⁻¹) and g = 2.15 for PPG (4.0 kg·mol⁻¹). The volume dependence of g, (∂g/∂ log V)_T varies between −19 to −10 for both molecular weights. Under isochoric conditions, g is nearly independent of temperature. The difference in g between the glassy state and liquid phase is small and just outside the inaccuracy of g of about 8%. The theoretical model for λ by Horrocks and McLaughlin yields an overestimate of g by up to 120%. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 345–355, 1998     

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.