The derivation of the cellulose microfibril angle by small-angle X-ray scattering from structurally characterized softwood cell-wall populations

A method is presented for the measurement, using small-angle X-ray scattering (SAXS), of the microfibril angle and the associated standard deviation for the cellulose microfibrils in the S-2 layer of the cell walls of softwood specimens. The length and orientation of over 1000 cell walls in the irradiated volume of the specimen are measured using quantitative image analysis. From these data are calculated the azimuthal variation of the scattered intensity. The calculated values are compared with the measured values. The undetermined parameters in the analysis are the microfibril angle (M) and the standard deviation (sigma(Phi)) of the intensity distribution arising from the wandering of the fibril orientation about the mean value. The two parameters are varied to give the best fit between the calculated and the measured values. Six separate pairs of values are determined for six different values of the angle of incidence of the X-ray beam relative to the normal to the radial direction in the specimen. The results show good agreement. The azimuthal distribution of scattered intensity for the real cell-wall structure is compared with that calculated for an assembly of rectangular cells with the same ratio of transverse to radial cell-wall lengths. Despite the existence of marked differences in the intensity distributions around the zero azimuth angle, the position of the extreme flanks of the distribution is very close for the real and the rectangular cells. This means that useful values of the microfibril angle can be obtained from the curve for the real cells using the Meylan parameter T derived by drawing tangents to the flanks of the intensity distribution and using M = kT. The value of k is M/( M + 2 sigma(Phi)). Since both of these parameters are determined in the work now described, k is also determined. It is also demonstrated that for beta = 45 degrees ( where beta is the angle between the plane face of the wood specimens and the radial direction) the peaks in the azimuthal intensity distribution for the real and the rectangular cells coincide. If this peak position is Phi(45), then the microfibril angle can be determined from the relation M = tan(-1)( tan Phi(45)/ cos45 degrees), which is precise for rectangular cells.