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Fractal geometry of wood internal surfaces in the hygroscopic range Hao, Bingye

Abstract

The study was aimed at exploring the geometry of the internal surfaces of wood cell walls and/or the sorbed water molecules in the hygroscopic range by using fractal theories for Douglas-fir (Pseudotsuga menziesii (Mirb.) Frano) (heartwood and sapwood) and western red cedar (Thujaplicata Donn.) heartwood (unextracted and extracted). The study was divided into experimental and modelling parts. The experimental studies included two main targets: (1) development of sorption isotherms by using wafer-shaped specimens and (2) examination of the moisture content of the altered volumes of the cubicshaped specimens for Douglas-fir heartwood and unextracted red cedar at a relative vapor pressure of about 0.92. The theoretical studies included: (1) development of two new sorption equations, (2) their evaluation and comparison with the classic BET (using the data from the wafer-shaped specimens), and (3) examination of the mass fractal phenomenon for bound water (using the data from the cubic-shaped specimens). Failure of the classic BET theory to predict moisture sorption of wood at the higher sorption regions (relative vapor pressure, h > 0.5) can be attributed to the existence of the geometrically rough surface with a fractal dimension (D) value from about 2.3 to 2.7. The surface geometry with D values of this range is far from being implied as a flat surface (D = 2). Modification of the classic BET theory based on the notation of a fractal surface was successful for the moisture sorption of wood. A modified BET equation was suggested for vapor sorption in wood to account for the state/geometry dynamics of the sorbed water molecules/internal surfaces of the cell walls. In terms of the D values of 24 cases (four types of wood, three temperature levels, and two sorption conditions), the internal surfaces of the cell walls had variable D values between 0.4 to 0.96 of h values. The D values were less than 2, about 2.0, and tending towards 2.7. The corresponding moisture content for these three D values ranged from 0 to about 12%, 12% to 18%, and 18% to the fiber saturation point, respectively. Such D value dynamics indicated that the internal surfaces underwent a cumulative change with an increase in moisture content. A brand new sorption theory with an appropriate equation was brought into the family of sorption theories. Its derivation considered both molecular layering and non-layering (clustering) of sorption states. Its success showed that the state dynamics of the sorbed water molecules were stepwise instead of smooth and 3 or 4 steps (states) were identified. The moisture content of various sizes of specimens at about 0.92 relative vapor pressure did not indicate a consistently increasing or decreasing trend. For the resultant moisture content of about 16%, the weight of the adsorbed water and specimens' dimensions were measured to investigate the fractal dimension of the adsorbed water in both studied species of dimensions between 10 mm and 40 mm. The results indicated that D,„ value for the water was slightly below 3. These measurements did not conclusively exhibit that the water in wood was fractal at this moisture content and this specimen sizes range. In addition, unextracted western red cedar showed the lower hygroscopicity due to its high extractives content. Hysteresis was pronounced in the four types of wood in this study. Hygroscopicity decreased with an increase in temperature. No great difference in moisture content was found between the sapwood and heartwood in Douglas-fir. Extracted western red cedar and Douglas-fir showed no major difference in hygroscopicity.

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