## 3 Results and Discussion  
### ABC Methodology  
The titration curves for different mixing times have very similar shapes, excluding the first few measurement points corresponding to 1-10 milliliters of titrant added. After reaching the boundary of pH 4, the curves are almost linear (Figure 2). A small displacement was caused by the different pH at the titration starting point. The data in Figure 2 also show the effect of the different latency time (suspension mixing prior to titration) that renders slight shifts in the curve position and, subsequently, may provide slightly different results--the final volume of the titrant added ranged between 70 mL and 82 mL. The ABC values can be predicted by two models, \(\beta\)-(\(\beta_{>4}\)) and \(\beta\)-(\(\beta_{>4}\), \(\beta_{4\text{-}3}\)), with a coefficient of determination as high as R\({}^{2}\) = 0.99. The RMSE values of 1.27 and 1.32 show differences between the predicted and observed values. The higher the RMSE value, the less accurate the model is. Thus, the \(\beta\)-(\(\beta_{>4}\), \(\beta_{4\text{-}3}\)) model seems to be slightly inferior, though both can be considered correct [18]. These models confirm that the buffering capacity of chip suspension under the boundary of pH 4 becomes irrelevant for the study. Moreover, the \"simplified\" \(\beta\)-(\(\beta_{>4}\)) model exhibited a slightly smaller  
Figure 2: Pine chip suspension titration curves. Different initial latency times render a different system response. The curves can be assumed as linear under the boundary of pH 4.  
coefficient of variation equal to 1.60 (Table 1). Hence, titration to pH 4 instead of pH 3 seems sufficient for a proper determination of the ABC of a woody material. As shown in Figure 3 and Table 2, particle size had a strong effect on the titration curves. Fractions of 0.15-1.0 mm provided an almost linear response, while the curves for 1.0-3.0 mm and 3.0-6.0 mm fractions became linear after some amount of time as the system required more time for equilibration. This indicates that the effective surface area of particles has a strong influence on the ABC measurement, as the equilibration rate is the highest for the smallest chips, as well as on the resultant ABC value. A high surface area in fine chips can be associated with an increased ABC. Thus, the data in Figure 3 indicate that it is not plausible to compare the ABCs found for different particle sizes. Surprisingly, the observation is contrary to reports by [PERSON] et al. who found that particle size did not impact the buffering capacity [11]; however, it is coherent with the findings of [PERSON] and [PERSON] who recognized that particle size had an effect on wood acidity [1]. However, it is noteworthy that the authors used a classic method based on the analysis of aqueous extracts as described by [PERSON] and [PERSON] [9]. The data in Table 2 clearly indicate that the observed acid buffering capacity decreases as the particle size increases. The initial pH of the suspension--after 60 min--reveals that a slower penetration of water into the particles' structure causes a slower diffusion of the extractives into water, hindering acidification. The pH curves for the chip suspensions shown in Figure 4 are quite similar in shape. After some amount of time all three become almost stable and linear. The changes in pH are dynamic for the first 10 min and come from the equilibration in the system. This suggests that starting the titration of the suspension--when mixing for at least 30 min is avoided--leads to serious errors caused by a significant change in the initial pH which, subsequently, provides an incorrect \(\Delta\)pH. \begin{table}
\begin{tabular}{c c c} \hline \hline Model & \(\beta\)-(\(\beta_{>4}\)) & \(\beta\)-(\(\beta_{>4}\), \(\beta_{4\text{-}3}\)) \\ RMSE & 1.27 & 1.32 \\ Coefficient of variation (\%) & 1.60 & 1.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Root-mean-square error (RMSE) and coefficient of variation (less = better) of linear regression models based on the same data.