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.     

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.     

Orientation behavior of high-modulus polyoxymethylene produced by microwave heating drawing

The orientation behavior of high-modulus polyoxymethylene tapes produced by tensile drawing with microwave heating has been investigated over the draw ratio range 10–29. Young's modulus E increases monotonically with draw ratio λ and reaches 55 GPa. The volume fraction of taut tie molecules (TTMs) in the amorphous phase has been estimated by using a Takayanagi model for oriented tapes. The increase in E at draw ratios of less than 10 is mainly due to the increase in crystalline orientation (crystalline orientation function, 0.00 → 0.99). The increase in E at draw ratios of more than 10 is due to the increase both in crystallinity (volume-fraction crystallinity, 0.84 → 0.95) and in TTM (TTM fraction, 0.14 → 0.40). The maximum Young's modulus obtainable by this method of drawing is estimated to be ca. 72 GPa from the relation between 1/E and 1/λ².     

Mechanical and transport properties of drawn crosslinked low-density polyethylene

The values of drawing dependence of the density ρ, axial elastic modulus E, and maximum draw ratio λ of crosslinked low-density polyethylene (CLPE) rather similar to those obtained with un-crosslinked branched material of similarly low density. Very much the same applies to the equilibrium concentration of sorbed methylene chloride in the amorphous component and the zero-concentration diffusion coefficient D₀. The exponential concentration coefficient γD , however, even at the maximum draw ratio, shows no indication of the rapid increase so characteristic of the completed transformation from the lamellar to the fibrous structure. On the basis of this finding, one can understand the small deviations in the dependence of the mechanical properties between the crosslinked and uncrosslinked branched material. The segments between the crosslinks, much shorter than the free molecules, favor the formation of the interfibrillar tie molecules that limit the drawability of the sample. But since they cannot be extended to the same length as the free molecules, they contribute less to the total fraction of tie molecules per amorphous layer and hence yield a smaller axial elastic modulus.     

Sorption and diffusion of toluene in isotropic and oriented linear polyethylene

Sorption and diffusion of toluene vapor in linear polyethylene with mass-fraction crystallinity between 0.48 and 0.82 and draw ratios λ up to 10 have been studied at 30°C. The sorbed concentration in the amorphous phase C_a is little affected by crystallinity, indicating that the free-volume fraction is roughly the same for all isotropic samples. However, the diffusion path becomes more tortuous with increasing crystalline content, thereby leading to a sixfold drop in the zero-concentration diffusion coefficient D₀. Drawing has more drastic effects, reducing C_a and D₀ by factors of 4 and 60, respectively, as λ increases to 10. These large changes result from the transformation of the initially spherulitic material into a fibrous structure, which is composed of aligned microfibrils with taut tie molecules lying on the outer boundaries. The effects of crystallinity and orientation on the concentration dependence of the diffusion coefficient are also discussed.     

Localized Yielding Around Crack Tips of Double‐Network Gels

Double‐network (DN) gels, a type of interpenetrating polymer network (IPN) consisting of rigid and flexible polymer components, exhibit two outstanding mechanical behaviors: yielding deformation of the entire specimen in tensile tests and quite high fracture energy in tearing tests. In this study, atomic force microscope (AFM) measurements were conducted on DN gels to determine the local Young's moduli immediately below the fracture surfaces E_f and below the usual molded surfaces E_m, and compare the local modulus with bulk Young's moduli measured before and after the yielding deformation, denoted as E_h and E_s, respectively. E_m and E_h are around 0.1 MPa; E_f and E_s, around 0.01 MPa, one order lower than the former two moduli. The order relation indicates that yielding deformation occurred locally around the crack tip of the DN gel during fracture. This supports the basic assumption of phenomenological models recently proposed to explain high fracture energy of DN gels. (H. R. Brown, Macromolecules 2007 , 40, 3815–3818; Y. Tanaka, Europhys. Lett. 2007 , 78, 56005).

     

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     

A structural model for high-modulus polyethylene derived from entanglement concepts

Starting from the concept that the entanglement network is a controlling factor in polymer deformation, a molecularly based model has been constructed for polyethylene, drawn or extruded to high extension ratios λ. It predicts the experimentally observed form of the increase of Young's modulus E with λ: E^?1 = B + Cλ^?2. The model structure consists of imperfect crystalline microfibrils 10-30 nm in diameter and length αλ², about 1 μm at λ = 30. The microfibrils terminate at clusters of entanglements, and are embedded in a matrix of low modulus. This structure is very similar to that derived from solution-grown shish-kebab material. Available melting-point data for highly extended material fit the structural model well.     

Elastic properties of poly(hydroxybutyrate) molecules

Elasticity of various poly(hydroxybutyrate) (PHB) molecules of regular and irregular conformational structure was examined by the molecular mechanics (MM) calculations. Force - distance functions and the Young's moduli E were computed by stretching of PHB molecules. Unwinding of the 2(1) helical conformation H is characterized at small deformations by the Young's modulus E = 1.8 GPa. The H form is transformed on stretching into the highly extended twisted form E, similar to the beta-structure observed earlier by X-ray fiber diffraction. The computations revealed that in contrast to paraffins, the planar all-trans structure of undeformed PHB is bent. Hence, a PHB molecule attains the maximum contour length in highly straightened, but slightly twisted conformations. A dependence of the single-chain moduli of regular and disordered conformations on the chain extension ratio x was found. The computed data were used to analyze elastic response of tie (bridging) molecules in the interlamellar (IL) region of a semi-crystalline PHB. A modification of the chain length distribution function of tie molecules tau(N) due to secondary crystallization of PHB was conjectured. The resulting narrow distribution tau(N) comprises the taut tie molecules of higher chain moduli prone to overstressing. The molecular model outlined is in line with the macroscopically observed increase in the modulus and brittleness of PHB with storage time.     

Tensile yield of isotactic polypropylene in terms of a lamellar‐cluster model

In this study, the structural factors controlling the yield in isotactic polypropylene materials were theoretically investigated. To describe the yielding behavior of spherulitic polypropylenes, we introduced a new structural unit, lamellar clusters, which are several stacked lamellae bound by tie molecules. It was shown that tie molecules between adjacent lamellar clusters produce a concentrated load acting on the cluster surface, leading to the bending deformation of the lamellar clusters. The yielding behavior can be explained if one assumes that the disintegration of the lamellar clusters occurs when the elastic‐strain energy stored by the bending deformation reaches a critical value. By applying the fracture theory of composites to a system consisting of lamellar clusters and tie molecules, we found the yield stress σ_y to be proportional to , in which E_Y is the Young's modulus and U_y is the yield energy. The proportional coefficient between σ_y and depends only on the cluster size and tie‐molecule density, so this proportionality is expected to be true for other spherulitic semicrystalline polymers such as polyethylenes, being independent of temperature and tensile rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1037–1044, 2000     

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     

Molecular orbital studies of polyethylene deformation

Young's modulus E for polyethylene in the chain direction is calculated with molecular orbital theory applied to n-alkanes C₃H₈ through n-C₁₃H₂₈ and analyzed with the cluster-difference method. Semiempirical CNDO, MNDO, and AM1 models and ab initio HF/STO-3G, HF/6-31G, HF/6-31G*, and MP2/6-31G* models are used. Cluster-difference results, when extrapolated to infinite chain length, give E in good agreement with moduli evaluated with molecular cluster or crystal orbital methods, provided minimal basis sets are employed. E decreases from 495 GPa (CNDO) to 336 GPa (MP2/6-31G*) as the level of theory is improved, consistent with established behaviors of the various models. Our calculations do not reproduce earlier molecular cluster or crystal orbital results, which gave E < 330 GPa. The most rigorous MP2/6-31G* model is known to overestimate force constants by ∼ 11%; the scaled modulus E = 299 GPa is in good accord with E = 306 GPa from recent calculations based on experimental vibration frequencies. © 1996 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.     

Pulsed NMR observation of ultradrawn polypropylene

Proton spin-spin relaxation times have been measured as a function of temperature for ultradrawn polypropylene with draw ratios λ up to 24. The three relaxation times T_2a (the longest), T_2i (intermediate), and T_2c (the shortest), observed for all the samples, have been ascribed to the relaxations of the amorphous, constrained amorphous, and crystalline components, respectively. T_2i and T_2a, which reflect the changes in structure and mobility in the noncrystalline regions, decrease with increasing λ; T_2i becomes saturated at λ > 9, whereas T_2a shows a substantial decrease up to λ = 24. The continued decrease in T_2a indicates that the constraint on the amorphous segments keeps increasing up to the highest λ. The associated mass fractions F_a, F_i, and F_c also change with λ. At λ < 9, the increasc in F_i with increasing λ is accompanied by a decrease in F_a, with F_c remaining unchanged. At higher λ, however, F_a is almost constant, and stepwise rises in F_c at about λ = 12 and 24 are accompanied by corresponding drops in F_i. It seems that, in this high draw ratio range, some of the taut molecules are fully extended and are in sufficiently good lateral register to transform into crystalline bridges. This conjecture is supported by the similarity in the λ dependence of F_c and the mass-fraction crystallinity obtained from the heat of fusion.     

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.     

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.     

Quantitative evaluation of stress distribution in bulk polymer samples through the comparison of mechanical behaviors between giant single‐crystal and semicrystalline samples of poly(trans‐1,4‐diethyl muconate)

The Raman shift and crystallite modulus were measured under the application of tensile force for a giant single crystal and a series of uniaxially oriented semicrystalline samples of poly(trans‐1,4‐diethyl muconate) (polyEMU). The apparent Raman shift factor α^app or a vibrational frequency shift per 1 GPa tensile stress was higher for the semicrystalline samples with lower crystallinity or lower bulk modulus. The apparent crystallite modulus E or Young's modulus along the chain axis in the crystalline region was not constant but varied remarkably between the giant single crystal and semicrystalline samples. A systematic change in α^app and E among the polyEMU samples with different preparation history could be interpreted quantitatively on the basis of a mechanical series parallel model consisting of crystalline and amorphous phases. The origin of different E and α^app was speculated to be a stress concentration on the taut‐tie chain contained as a parallel crystalline component in the mechanical model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 444–453, 2003