Variation in wood shrinkage evaluated by the eigenvalue distribution of the near infrared spectral matrix

Abstract

Wood interactions with water occur at the cell wall, therefore, shrinkage should be closely related to wood density. Nevertheless, woods with almost the same density often show substantially different shrinkage. This study suggests a method to evaluate variation in shrinkage based on an eigenvalue analysis of the near infrared spectral matrix. The set of eigenvalues calculated from the variance-covariance matrix was defined as the Hamiltonian, which represents the energy eigenstate of the wood, and the wood variation is discussed from the viewpoints of thermodynamics and statistical mechanics. To determine the validity of this idea, two sample groups with almost equal wood density values, one showing high shrinkage and the other low, were prepared. The eigenvalues of the high shrinkage samples were widely distributed compared with those of the low shrinkage samples. As a result, the Helmholtz free energy was higher in the high shrinkage samples and entropy was higher in the low shrinkage samples. Hence, the Hamiltonian calculated from the variance-covariance matrix of NIR spectra explained differences in shrinkage between the two groups and was consistent with actual physical images of woods. These results were also supported by optical micrographs and stiffness data. The dimensional changes of wood are complex phenomena involving many factors. The method proposed in this research would be useful for evaluating phenomena in which many factors contribute cooperatively to a system, rather than individually.