Thickness Dependence of Optical Transmittance of Transparent Wood: Chemical Modification Effects

Abstract

Transparent wood (TW) is an emerging optical material combining high optical transmittance and haze for structural applications. Unlike nonscattering absorbing media, the thickness dependence of light transmittance for TW is complicated because optical losses are also related to increased photon path length from multiple scattering. In the present study, starting from photon diffusion equation, it is found that the angle-integrated total light transmittance of TW has an exponentially decaying dependence on sample thickness. The expression reveals an attenuation coefficient which depends not only on the absorption coefficient but also on the diffusion coefficient. The total transmittance and thickness were measured for a range of TW samples, from both acetylated and nonacetylated balsa wood templates, and were fitted according to the derived relationship. The fitting gives a lower attenuation coefficient for the acetylated TW compared to the nonacetylated one. The lower attenuation coefficient for the acetylated TW is attributed to its lower scattering coefficient or correspondingly lower haze. The attenuation constant resulted from our model hence can serve as a singular material parameter that facilitates cross-comparison of different sample types, at even different thicknesses, when total optical transmittance is concerned. The model was verified with two other TWs (ash and birch) and is in general applicable to other scattering media.

Keywords: anisotropic scattering; attenuation coefficient; photon diffusion equation; transmittance; transparent wood.

Figure 1

(a) SEM image of the cross-section of balsa wood template, (b) Schematic image illustrating light scattering in TW, (c) light scattering pattern for a beam that has passed through the TW sample.

Figure 2

(a, b) Transmittance spectra of the nonacetylated TW and acetylated TW in the visible range. (c, d) Fitting between the lnT_total and the sample thickness for nonacetylated TW and acetylated TW at wavelength of 550 nm, respectively. The pictures inseted in c and d show both the TW samples with different thicknesses on top of a printed symbol “W”.

Figure 3

(a, b) SEM micrographs of freeze-fractured cross-sections of nonacetylated TW and acetylated TW, the arrows show scattering centers (the red arrows are the interface between PMMA and wood cell wall, greens are the air gaps). (c, d) Possible path and path length in the cell lumen and TW samples, respectively. (e, f) Haze spectra of nonacetylated TW and acetylated TW in the visible range.

Figure 4

(a) Optical transmittances of an acetylated TW with a thickness of 1 cm and nonacetylated TW with a thickness of 0.59 cm. Predicted values are presented together with experimental data. The inserted images show the two types of TW samples on top of a printed symbol “W”. (b) Fitting between total transmittance and the sample thickness of nonacetylated transparent wood made from birch and ash. The transmittance was collected at wavelength of 550 nm.