X-Ray Line Broadening in Isotactic Polystyrene

Abstract

Wide-angle x-ray line-broadening data from several samples of isotactic polystyrene with different histories of pretreatment have been obtained by diffractometer techniques. These data have been analyzed according to several theories of the separation of the line-broadening effects due to small crystallite size and to lattice distortion; the results obtained from several integral breadth methods and from full line-profile analysis via Fourier transformation are compared. In each instance, annealing produces larger crystallite sizes and smaller degrees of lattice distortion. However, the actual numerical results obtained vary with the method of separation. Some of these variations arise from questionable assumptions in particular theories of size-distortion separation and others occur because different physical quantities are determined. It is possible, for example, to obtain information concerning number-average and weight-average crystallite sizes. For one isotactic polystyrene sample, good correlation of crystallite size from wide-angle diffraction, long period from low-angle diffraction, and x-ray crystallinity is demonstrated. Experimental problems encountered in the collection of line-profile data for polymer systems are also discussed, with particular emphasis on methods of correcting data for the effects of instrumental broadening. It is shown that a simple method based upon a Gaussian approximation to the profile shapes is often adequate to carry out the instrumental broadening correction.