Crystal modulus

Surface crack length Fitted constant Fibre diameter Die exit diameter Young s modulus Crystal modulus Modulus of Maxwell element Modulus of Voigt element Strain energy release rate Boltzmann s constant... 

The molecular chain in crystal lattice of the monoclinic a form has a helical conformation with three units per turn to avoid the steric hindrance of the bulky methyl groups and a large cross-section of 0.344 nm. The crystal modulus along molecular chains therefore is low, which is estimated to be 41.2 GPa by X-ray diffraction measurement or 88.2 GPa by Raman spectroscopy. The theoretical tensile strength is calculated to be 18.2 GPa. 

However, the ratios of a maximum modulus attained to the crystal modulus for iPP and polyethylene, are very high, 0.971... 

Keywords iPP fibers and films, high modulus, high strength, crystal modulus, theoretical strength, mechanical properties, drawfing, draw ratio, molecular weight, superstructme, lamella, tie molecule, relaxation transitions, ultrastrong fibers and films. 

For sPP, at a given draw ratio, the modulus was remarkably lower for sPP than for iPP, yet the tensile strengths were not significantly different. The maximum tensile modulus and strength of sPP achieved were 3.0 and 0.33 GPa, respectively. These values were remarkably lower than those (20 and 0.60 GPa, respectively) achieved for an iPP having comparable molecular characteristics, reflecting the low crystal modulus, drawability and crystallinity of sPP compared to those of iPP. 

It has been shown (46) that PTT has a very low theoretical crystal modulus, 2.59 GPa (375, 550 psi), compared to 107 GPa (1.55 x 10 psi) of PET (47) because of PTT s highly contracted helical-like conformation, whereas PET chain is fully extended with trans conformation. When a PTT fiber is stretched in situ in a waxd, the fiber period, measured from the Bragg d-spacing, increases immediately and is proportional to the applied strain up to 4% strain before deviating from affine deformation (48). Up to this critical strain the crystal deformation is reversible. The response of microscopic crystalline chains to macroscopic deformation explains why PTT has the best elastic recovery among the three aromatic polyesters. Further, PTT s elastic recovery and permanent set are nearly the same as nylon-6,6 up to 30% strain (25). 

Yarns spun from solution have a different crystalline stmcture (cellulose II) than natural cellulose (cellulose I). The difference is that cellulose I has two tntermolec-ular hydrogen bonds formed parallel to the glucosidic bond, whereas cellulose II has only one parallel hydrogen bond. The main effect is a large difference in crystal modulus 130-180 GPa for cellulose I, 60-90 GPa for cellulose II. All attempts to produce man-made fibers with a cellulose I structure, and hence an even higher modulus, have remained unsuccessful, however. 

Table 9.4 summarizes properties of various fibers. The tensile strength and modulus of PBO fibers were reported to be 5.8 and 352 GPA, respectively [82, 83]. The mechanical properties of PBO fibers depend on polymer molecular weight, processing and post processing conditions [84, 85]. The modulus of PBO fiber from X-ray diffraction was measured to be in the range of 460-480 GPA [86, 87]. Figure 9.9 shows crystal modulus versus fiber modulus of various high performance fibers. 

Figure 9.9 Comparison between fiber modulus and crystal modulus of different fibers (reprinted from ref. 74 with permission from Wiley).

Young s modulus as a function of draw ratio is shown in Figure 3.21. It can be seen that the modulus, which even at room temperature can reach an appreciable fraction of the crystal modulus, depends only on the final draw ratio and is independent of the relative molecular mass and the initial morphology. Hence an appropriate model appears to he one that depends on the structnre produced during deformation rather than on the starting material. 

The elastic modulus of a polymer crystal provides us with important information on the molecular conformation in the crystal lattice [24]. The elastic modulus (crystal modulus) of the crystalline regions in the direction parallel to the chain axis has been measured for a variety of polymers by X-ray diffraction [25]. Examination of the data so far accumulated enables us to relate the crystal modulus, namely, the extensivity of a polymer molecule, both to the molecular conformation and the mechanism of deformation in the crystal lattice. Furthermore, knowledge of the crystal modulus is of interest in connection with the mechanical properties of the polymer, because the crystal modulus gives the maximum attainable modulus for the specimen modulus of a polymer. 

The initial slope of the stress-strain curve of the crystalline regions gives the crystal modulus, when the changes in the crystal lattice spacing under a constant stress are monitored by X-ray diffraction. 

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