Crystallization modulus, effect

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. 

Stretching a polymer sample tends to orient chain segments and thereby facilitate crystallization. The incorporation of different polymer chains into small patches of crystallinity is equivalent to additional crosslinking and changes the modulus accordingly. Likewise, the presence of finely subdivided solid particles, such as carbon black in rubber, reinforces the polymer in a way that imitates the effect of crystallites. Spontaneous crystal formation and reinforcement... 

In the above, the variable R is the radius between center to center fiber spacing, while r is the fiber radius. The shear modulus (Gm) can be approximated as Em/3. The matrix modulus is effected by the level of crystallinity and it is important that the samples are fully crystallized to ensure reproducibility. The value of (> for 30wt% glass-fiber-reinforced PET has been calculated as 3.15 x 104. Using the mathematical analysis shown above, the orientation function of the glass fiber... 

Spiering et al. (1982) have developed a model where the high-spin and low-spin states of the complex are treated as hard spheres of volume and respectively and the crystal is taken as an isotropic elastic medium characterized by bulk modulus and Poisson constant. The complex is regarded as an inelastic inclusion embedded in spherical volume V. The decrease in the elastic self-energy of the incompressible sphere in an expanding crystal leads to a deviation of the high-spin fraction from the Boltzmann population. Pressure and temperature effects on spin-state transitions in Fe(II) complexes have been explained based on such models (Usha et al., 1985). 

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