Elastic Modulus Of Crystalline Regions Research Articles

Surface versus Volume Properties on the Nanoscale: Elastomeric Polypropylene

The difference between the mechanical properties of a material at the surface and in the bulk is an open issue in polymer science. We studied the mechanical surface properties of polypropylene using atomic force microscopy in peak-force tapping mode. The bulk properties were obtained from layer-by-layer measurements of elasticity, adhesion, and dissipation, with the successive layers removed via wet-chemical ablation. The original sample surface revealed nearly similar mechanical properties for the amorphous and crystalline regions due to a thin (∼22 nm) amorphous top layer. However, in the bulk material, the elastic modulus of crystalline regions was greater than that of amorphous regions. We observed nanoscale crystalline inhomogeneities caused by phase separation that can affect the mechanical stability of polypropylene on the macroscopic scale. The combination of force–volume analysis together with successive ablation of the sample layers form the basis of quantitative nanomechanical tomography.

Temperature dependence of the elastic modulus of crystalline regions of polyethylene with different microstructures—explanation with the kinked-chain model

Abstract Temperature dependence of the elastic modulus E 1 of crystalline regions in the direction parallel to the chain axis has been measured by x-ray diffraction for various kinds of polyethylene (PE) with different microstructures. The E 1 value is 235 GPa for all kinds of PE at room temperature. However, in some cases, E 1 began to decrease at a certain temperature, in one case at 50°C and in one at 65°C. The lattice spacing for the (002) plane also decreased with increasing temperature. The thermal expansion coefficient αc changed discontinuously around the temperature range where E 1 began to decrease. This indicates that axial thermal molecular motion (i.e., incoherent thermal motion) is enhanced at high temperature. These phenomena could well be explained with the kinked-chain model where two gauche conformations are incorporated in the all-trans, fully extended conformation. The kinked chain deforms very easily through the change of internal rotation around the C—C bond, which has a small force ...

Studies on the temperature dependence of the elastic modulus of crystalline regions of polymers: 14. Poly(vinyl alcohol) with different tacticities

The temperature dependence of the elastic modulus E 1 of crystalline regions in the direction parallel to the chain axis has been measured by X-ray diffraction for poly (vinyl alcohol) (PVA) with different tacticities. The E 1 value for PVA with 55.4% syndiotactic diads, sPVA (55.4%), decreased above 120°C, which was in accordance with that of atactic PVA. The lattice spacing for the (0 2 0) plane (the fibre axis is b) also decreased with increasing temperature. The thermal expansion coefficient α c changed discontinuously around the temperature range where E 1 began to decrease. These phenomena could be explained using the kinked-chain model, where a small amount of a contracted portion, such as a kink, was incorporated into the chain molecule as in the case of atactic PVA. On the other hand, the El value of sPVA (63.0% ) remained unchanged till 150°C. The value of α c did not change with increasing temperature in this case. Consequently, the molecular motion that is responsible for the decrement of E 1 is considered to be restricted for sPVA (63.0%) because of strong intermolecular hydrogen bonds. Further, increasing the syndiotacticity is considered to be one of the most effective ways to introduce high heat resistance into PVA.

Temperature dependence of the elastic modulus of crystalline regions of isotactic poly(4-methyl-1-pentene)

Abstract The elastic modulus E 1 of crystalline regions of isotactic poly(4-methyl-1-pentene) (P4M1P) in the direction parallel to the chain axis and its temperature dependence were investigated by x-ray diffraction. E 1 values for the (001) and (007) planes of P4M1P agreed well at 4.1 GPa at room temperature. This small E value could be attributed both to the contracted helical conformation (7/2 helix) and to a large cross-sectional area of P4M1P in the crystalline regions. Though the lattice distortion of the first kind increased and partial destruction of crystallites occurred with increasing stress, the stress-strain curve for the crystal lattice was linear up to 80 MPa. However, the E1 value remained unchanged up to 150°C. The lattice spacing for the (007) plane increased monotonously with increasing temperature, with a thermal expansion coefficient of 0.9 × 10−4 K−1. These phenomena were in contrast with the temperature dependence of E 1 values of various polymers previously reported, in which E 1 d...

Elastic modulus of crystalline regions of polyethylene with different microstructures: Experimental proof of homogeneous stress distribution

Abstract Elastic modulus E 1 of crystalline regions in the direction parallel to the chain axis has been measured for various kinds of polyethylene (PE) with different microstructures, such as ultrahigh-modulus PE, linear low-density PE, high-pressure-crystallized PE, and a heat-drawn PE whose crystallite size exceeds its long period, etc., by x-ray diffraction. The E 1 value, which corresponds to the initial slope of stress-strain curve for the crystal lattice, is 235 GPa for all kinds of PE irrespective of the estimation method of the diffraction peak shift for the (002) plane owing to the constant stress applied. This indicates that the assumption of “homogeneous stress distribution,” that is, stress in the crystalline regions was equal to the stress applied to the sample, is proved experimentally at least for PE. The E 1 value at −155°C is obtained as high as 254 GPa. The x-ray diffraction method is considered to be the most proper method to evaluate the E 1 value.

共重合アラミドの結晶弾性率

共重合アラミドの結晶弾性率

Experimental Determination of the Elastic Modulus of Crystalline Regions of Some Aromatic Polyamides, Aromatic Polyesters, and Aromatic Polyether Ketone

Experimental Determination of the Elastic Modulus of Crystalline Regions of Some Aromatic Polyamides, Aromatic Polyesters, and Aromatic Polyether Ketone

Elastic moduli of crystalline regions of poly(ether ether ketone).

Elastic moduli of crystalline regions of poly (ether ether ketone)_??_(PEEK) in the direction parallel (El) and perpendicular (Et) to the chain axis were determined by X-ray diffraction. The observed moduli Et are as follows; (110); Et=5.9 GPa, (200); Et=4.2 GPa, (020); Et=5.0 GPa. The Et value for the (200) plane is nearly equal to that of polyethylene (ca. 4 GPa). This means that there is no especially strong interaction other than dispersion forces in this direction. But Et values for the (020), (110) planes are somewhat large. This is considered to be due to the dipole-dipole interactions between ether (carbonyl) linkages, since these functional groups are superposed upon each other in these directions. On the other hand, different orders of meridional reflections give different El values (31, 57, 71 GPa for (002), (006) and (008) plane, respectively). This phenomena may be due to the increase of the crystallite size by the applied stress. Judging from the similarity to the calculated El value (69 GPa), it seems that the El value for the (008) plane (71 GPa) is valid, from which the force required to stretch a molecule by 1% can be calculated as 1.64×10-5 dyne.

Elastic modulus of crystalline regions of poly (β-trichloromethyl-β-propiolactone) in the direction parallel to the chain axis obtained by solid-state polymerization

Abstract The elastic modulus E1 of crystalline regions of poly(β-trichloromethyl- propiolactone) (PTCPL) in the direction parallel to the chain axis has been measured by the x-ray diffraction method. PTCPL was obtained by solid-state polymerization. The value of E1 for the (014) plane of PTCPL was 25 × 104 kg/cm2, whereas the value of the specimen modulus (Y1) was 10.3 × 10.3 × 104 kg/cm2. The value of Y1 is very low compared with that of E1 from the viewpoint of microstructure. These results are discussed in terms of the molecular conformation in the crystalline regions and the crystal defects.

Elastic modulus of crystalline regions of poly(butylene terephthalate) in the direction parallel to the chain axis

AbstractThe elastic modulus El of crystalline regions of poly(butylene terephthalate) in the direction parallel to the chain axis has been measured by the x‐ray diffraction method. Values of El for the (104) planes of the α‐ and β‐form crystal modifications were 13.5 X 104 and 21.0 X 104 kg/cm2, respectively. These values of El are very low compared with that of polyethylene terephthalate (110 X 104 kg/cm2). The results are discussed in terms of the molecular conformation in the crystalline regions.

Elastic moduli of polymer crystals for the chain axial direction

AbstractSome experiments were carried out to prove the validity of the assumption of a simple series model for the calculation of the elastic modulus of crystalline regions in oriented linear polymers from X‐ray determination of lattice extension. Various specimens such as filaments, fibers, and films were prepared from polyethylene, polyvinyl alcohol, polypropylene, polyoxymethylene and cellulose, stress‐strain curves constructed under the assumption of a simple series model; and calculated values of modulus compared. In spite of the differences of microstructures of these specimens, nearly the same value for the lattice modulus was obtained for each polymer. A large difference of specimen moduli had no effect on the lattice modulus. Lattice moduli of dry and water‐swollen polyvinyl alcohols or cellulose did not differ from each other. These results are a strong support for the above assumption.Extensibility of various polymer molecules was also discussed.

Experimental determination of the elastic modulus of crystalline regions in oriented polymers

AbstractThe elastic modulus of the crystalline regions in some oriented polymers was determined. An x‐ray diffractometer specially constructed for this purpose was used, and the lattice extension in the direction of the fiber axis was measured under application of a direct load. Usually a meridional reflection was used for the measurement of the lattice extension, but in the case where no strong meridional reflection exists a reflection from planes which are almost perpendicular to the fiber axis of the crystallites was used. The elastic modulus was calculated under the assumption of a simple series model. The values found are as follows: polyvinyl alcohol, 255 × 104 kg./cm.2; polyethylene, 240 × 104 kg./cm.2; polypropylene, 42 × 104 kg./cm.2; polyoxymethylene, 54 × 104 kg./cm.2; cellulose, 137 × 104 kg./cm.2; polyvinylidene chloride, 41.5 × 104 kg./cm.2.