A small angle X-ray scattering study of polyethylene fibres, using the two-dimensional correlation function

Abstract

From the general principles of diffraction theory it follows that Fourier transformation of the function describing the distribution of the diffracted X:ray intensity in reciprocal space leads to a function in direct space representing the autoconvolution of the electron density variations in the diffracting object. As on the one hand this function contains all the information that is hidden in the diffraction pattern, and on the other hand can be more readily interpreted in terms of structural details than the intensity function itself, it is often used in the solution of structures from X-ray diffraction data. In small angle X-ray scattering (SAXS) it is usually scaled to have the value 1 in the origin; it is then called the correlation function. Its general properties have been discussed by Porod (1) and by Debye, Anderson and Brumberger (2); the application of a onedimensional correlation function to the lamellar structures occurring in isotropic semicrystalline polymers was recommended by Vonk and Kortleve (3).In this paper the use of two-dimensional correlation functions in the study of SAXS from fibres of uni-axial symmetry is discussed. Here the situation differs from the one encountered in isotropic polymers in that the basic structure in the isotropic polymers (stacks of alternating crystalline and amorphous layers) might be taken for granted, whereas there is no general agreement on the basic structure occurring in polymer fibres.Many of these substances show a four-point SAXS pattern, which has been explained in different ways, as is to be discussed below. Therefore in the present case the correlation function should in the first place serve in asserting the most appropriate model, and secondly in finding the correct values of the various parameters involved. The potentiality of the correlation function in these respects will be demonstrated in the analysis of the diffraction pattern from a cold drawn and subsequently annealed fibre of low density polyethylene. The approach followed is to compare the 'observed' correlation function, obtained by Fourier transformation of the observed intensity function, with 'calculated' correlation functions, based on the different models that have or can be proposed. Furthermore, also calculated intensity functions were obtained by Fourier transforming the calculated correlation functions; the comparison of these with the original observed intensity functions was however made in a qualitative way only. Experimental and computational detailsThis was a commercial low density polyethylen of the type Stamylan 2800, manufactured by DSM. Its density after compression molding (cooling rate 40 °C/min.), as determined according to method ISO 1183 D, was 0.920; the melt flow index, determined according to method ISO R 292, amounted to 0.30 gr/10 min. From a compression molded sheet dumbbell shaped specimens were made that were drawn at room temperature at a rate of 2.5 cm/min, to fracture at an extension of 700%. Annealing was achieved in conditions where the samples were free...

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