Energetics of the distribution of cell wall in wood based on an eigenvalue analysis

Abstract

Abstract Wood is a highly heterogeneous material characterized by a number of properties that vary significantly among samples. Even in woods of the same density, substantial differences in properties show up depending on the distribution pattern of their cell walls. With the aim of deep understanding of the wood variation, we examine this pattern from the physical perspectives using samples of the same density but with significantly different shrinkages. The power spectrum, which represents the regularity of the occurrence of cell walls or lumen, was obtained through Fourier transform processing of micrographs of the transverse sections of wood samples. The set of eigenvalues calculated from the variance–covariance matrix comprising the spectra is identified with a Hamiltonian representing the energy eigenstate of the wood. The cell wall distribution can then be analyzed from within thermodynamics and statistical mechanics. The eigenvalues from the images of latewood were widely distributed compared with those from earlywood. The first eigenvalue is equivalent to the Helmholtz free energy, and thus the high-shrinkage samples showed large Helmholtz free energy because of the high presence of latewood. The Shannon entropy calculated from the probability associated with each energy eigenstate was larger in images of earlywood than latewood. That is, low-shrinkage samples have a more homogeneous structure than high-shrinkage samples. These results were strongly consistent with observations from micrographs and previous knowledge of the physical properties of woods. The physical approaches proposed in this study is independent of the origin of the data and therefore has a wide application.

Keywords

• Fourier spectrum
• Random matrix
• Information statistical physics
• Helmholtz free energy
• Entropy