Abstract—The objective of this research is to suggest a regression models on the age-affecting and microfibril angle in Acacia mangium wood. Farther objective is to estimate the optimum age which produce fully crystalline cellulose in Acacia mangium wood. The term microfibril angle (MFA) in wood refers to the angle between the spiralling cellulose fibrils and the long axis of the tracheid cell wall. Acacia mangium wood was chosen for experimental data. In this study, the main MFA of the cell walls were determined for thin samples of thickness 200μm from pith and outwards, for eight ages of Acacia mangium wood. The determination of MFA was based on diffraction pattern arising from cellulose crystal planes of the type 002 generated by x-ray diffraction and recorded using an electronic detector. Age-contributing factors were measured; the diffraction angle (2θ), relative intensity, full width at half maximum (FWHM), the nearest between two neighbouring atoms in the crystalline structure (d-spacing) and the peak height, had been taken into account at different ages, pith and bark of tree. Regressions were done in comparing the microfibril angle, MFA at different ages using the least-square method and cubic-spline interpolation. The latter was able to interpolate a polynomial up to the third order. The range of the optimum angle was found to have benefited foresters in deciding the time for tree cropping and harvesting. The results show that comparisons of linear polynomials for Acacia mangium at different tree ages had shown that the MFA varies according to age with a small mean and variance. Using the LS method, the regression equations of the grain size as corresponds to the regions of the trunk, gave an optimal fit of R2>0.87, indicating a strong positive relationship. It was found that the cellulose crystalline has grown fully at ao about 23.0 ± 0.5 year for completely studied tree age.

Index Terms—Crystallographic factors, regression model, interpolation, microfibril angle, optimum angle.

T. A. Tabet is with the School of International Tropical Forestry, Universiti Malaysia Sabah, 88400, Kota Kinabalu, Sabah, Malaysia, (e-mail: tamertbt@ums.edu.my). F. A. Aziz is with Physics Department, Centre for Defence Foundation Studies, National Defence University of Malaysia (NDUM), Kem Sg. Besi 57000 Kuala Lumpur, Malaysia, (e-mail: afauziah@upnm.edu.my). N. Abdulla is with the Mathematics with Economics Programme, School of Science and Technology , Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah, (e-mail: noraini@ums.edu.my).

Cite: Tamer A. Tabet, Fauziah Abdul Aziz, and Noraini Abdulla, "Modeling Microfibril Angle and Tree Age in Acacia Mangium Wood Using X-Ray Diffraction Technique," International Journal of Applied Physics and Mathematics  vol. 2, no. 5, pp. 338-341, 2012.