Modeling and optimization of non-pressure borate treatment for Douglas fir and grand fir laminates

Abstract This study presents a sorption-based model approach to optimizing non-pressure borate treatment of Douglas fir ( Pseudotsuga menziesii ) and grand fir ( Abies grandis ) laminates for engineered wood products. Disodium octaborate tetrahydrate (DOT), a water-soluble borate compound, was used to treat wood specimens at various temperatures (23 °C, 40 °C, and 60 °C) and moisture contents (6%, 12%, and 18%) through dip immersion. A diffusion-inspired semi-empirical kinetic model was developed to predict borate retention under varying temperature and moisture conditions. The model demonstrated strong goodness of fit ( R 2 > 0.89), accurately capturing the influence of moisture content and temperature on borate uptake. Optimal dip durations derived from the model met the target retention threshold of ≥1.0 kg/m 3 B₂O₃. Laminated timber panels manufactured from the optimally treated samples were evaluated for bonding performance through block shear and cyclic delamination tests by AITC 107, AITC 110, and ASTM D905 standards. Results showed that borate treatment did not yield an apparent reduction in shear strength or wood failure percentage, with all treated samples exhibiting bond quality and durability well within accepted limits. Grand fir demonstrated higher B 2 O 3 retention and permeability than Douglas fir. The proposed model provides a valuable tool for balancing treatment efficacy, adhesive performance, and production efficiency in cross-laminated timber and glulam fabrication.