Sonic modulus, polymer chain

Polymers may exhibit a biaxial orientation. The segmental orientation function is in this case a function of two angular variables, i.e. /(, v), as shown in Figure 10.7. The in-plane orientation is different in the zx and zy planes (Figure 10.7). There are several methods commonly used to determine chain orientation in-plane birefringence, wide angle X-ray diffraction, small angle X-ray diffraction, infrared spectroscopy and sonic modulus measurements. In the case of uniaxial orientation there is only... 

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) ... 

Like the velocity of light, the velocity of sound differs in magnitude when measured along the polymer chain axis as compared to a direction transverse to the chain axis. A measurement of the velocity of sound can, therefore, also be used in place of the birefringence. We again assume that the crystalline and amorphous phases contribute in proportion to their relative amounts. Experimental details of this method, which involves a measurement of the sonic modulus, can be found in the hterature, which also describes other methods (such as infrared dichroism) that can be used to determine the amorphous orientation factor [58, 66]. 

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