GENERAL-ANALYSIS OF THE MEASUREMENTS OF THE LATERAL CRYSTAL-LATTICE MODULI OF SEMICRYSTALLINE POLYMERS BY X-RAY-DIFFRACTION AND THE APPLICATION TO NYLON-6

A mathematical representation based on a linear elastic theory is prop osed by which one may investigate the dependences of molecular orienta tion and crystallinity on the crystal lattice moduli and linear therma l expansion coefficients in the direction perpendicular to the chain a xis as commonly measured by x-ray diffraction. In the theoretical calc ulation, a previously introduced model was employed in which oriented crystalline phase is surrounded by oriented amorphous phase and the st rains of the two phases at the boundary are identical. The mathematica l analysis indicated that the lateral crystal lattice moduli and linea r thermal coefficients as measured by x-ray diffraction may be differe nt from the intrinsic crystal moduli and linear thermal coefficients o f a crystal unit cell, depending on the structure of the polymer solid . The numerical calculation was applied to nylon 6. As a result, it ma y be confirmed that the lateral crystal lattice moduli measured by x-r ay diffraction are sensitive to the morphology of the bulk specimens a nd close to the intrinsic crystal moduli if the morphology of the test specimen can be represented by a parallel model with respect to the o riginal stretching longitudinal direction.