Semicrystalline polymers birefringence

By optical microscopy (OM), birefringent structures are observed in semicrystalline polymers, characterized by "Maltese-crosses" under crossed polars as seen in Figure 6. As these structures grow symmetrically in three dimensions... 

Until now we have considered the basic origin of birefringence and some of the general techniques used for determining this optical parameter. It is necessary, however, to discuss certain limitations when interpreting this parameter. Until now no mention has been made of two or multiphase systems such as semicrystalline polymers, amorphous block copolymers or even plasticized or filled polymers. In such systems the measured birefringence can be expressed as... 

One specific area where the procedures discussed above have been applied is to semicrystalline polymers. Here the birefringence is written as... 

Examination of thin sections of semicrystalline polymers reveals that the crystallites themselves are not arranged randomly, but form regular birefringent structures with circular symmetry. These structures, which exhibit a characteristic Maltese cross-optical extinction pattern, are called spherulites. Although spherulites are characteristic of crystalline polymers, they have also been observed to form in low-molar-mass compoimds that are crystallized from highly viscous media. 

This model should apply best to glassy or semicrystalline polymers, e.g. polyethylene. Figure 11.6 shows the experimental birefringence Am plotted against X for a series of drawn samples of low-density polyethylene and Am calculated according to the pseudo-affine deformation scheme. The general features of the curve are fitted, in particular the concavity relative to the A-axis, but the fit is not quantitative. 

The theoretical descriptions of biaxial orientation and the relationships to physical properties are not as well developed as those of uniaxial orientation. In amorphous polymers, birefringence can measure total molecular orientation and can be used to predict properties. For semicrystalline polymers, a more... 

Average-orientation, amorphous-orientation, and crystalline-orientation functions are required to describe the oriented state completely (3,36). This description permits the calculation of amorphous-phase orientation, which is required to relate and predict physical properties. The determination of crystalline orientation requires the more advanced analytical techniques of X-ray diffraction or dichroic ratios from polarized infrared spectroscopy. Average or total orientation functions are measured by birefringence. Amorphous and crystalline orientation functions are separated by measuring the sonic modulus and assuming a molecular model for the semicrystalline polymer (3). 

Birefringence of Semicrystaiiine Poiymers. For semicrystalline polymers the birefringence is the sum of the following terms ... 

The strain-induced birefringence in the amorphous region of a semicrystalline polymer disappears at the glass-transition temperature, as the chains assume isotropic configurations. 

The velocity of sound depends on the modulus, and the velocity of sound is greater when it propagates along than transverse to the chain axis. In a semicrystalline polymer, both the crystals and the amorphous phase contribute in proportion to their relative contents. In that sense, the sonic modulus is similar to birefringence. The following expression relating sonic modulus ( ) and Hermans orientation factor for a semicrystalline polymer was derived by Samuels (1974) ... 

The second method, known as the Kofler method, is used only for semicrystalline polymers. It consists of heating the sample by hot-stage unit mounted under a microscope and viewing it between crossed polarizers. When crystalline material melts, the characteristic double refraction from the crystalline aggregates disappears. The point at which the double refraction or birefringence (typically a rainbow color) completely disappears is taken as the melting point of the polymer. Figure 13-2 shows a commercially available apparatus. The use of a control sample for comparison is particularly helpful in both methods. 

The developments described above presume single-phase materials. For multiple-phase materials, such as semicrystalline polymers, contributions for both phases must be introduced plus form birefringences for uniaxial orientation (58)... 

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