Small-angle X-ray study of sisal fibre using correlation functions

Abstract

Various macromolecular parameters of air-dried Agave sisalana (sisal) fibre are investigated by small-angle X-ray scattering (SAXS) techniques considering it as a densely packed micellar system by applying the theories put forward by Vonk (1973). The authors show that the small-angle X-ray scattering intensities of de-waxed air-dried sisal fibre deviate from Porod's law, establishing that the fibre is non-ideal two-phase structure characterized by continuous variation of electron density at the phase boundary. Therefore the mean square electron density gradient < mod grad eta mod 2> in isotropic structure is proportional to the fourth moment integral s4/(s) ds of the SAXS intensity distribution and to the second derivative of the correlation function at the origin in reciprocal space where s is the radial coordinate in reciprocal space. Since sisal fibre has a two-space structure with unsharp phase boundaries, the above relations are used to find out the thickness E of the transition region. The most general approach to the small-angle X-ray scattering makes use of the correlation functions, which were introduced by Debye and Bueche (1949) and which contain implicitly all the information obtainable from the scattering curve. The scattered intensities and correlation functions are related by Fourier transformations. Other important physical parameters are obtained with the help of one- and three-dimensional correlation functions are D, the average periodicity transverse to the layer, S/V, the specific inner surface phi 1, the volume fraction of matter, phi 2, the volume fraction of void lc, the length of coherence, l1 and l2, the transverse lengths, lr, the range of inhomogeneity, fc, the characteristic number and 2E/D, the volume fraction of transition layer.