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Cellulose (2021) 28:10183–10201
Results and discussion
the rate constant. The good fit of the pseudo-second- order model indicates that LBG adsorption is strongly influenced by the concentration of LBG in solution. The second-order reaction may reflect the potential of a single, high molar mass LBG polymer to form multiple bonds. Pseudo-second-order kinetics have also been observed for adsorption of several dyes and chemicals to pulp fibres (Li et al. 2018; Urruzola et al. 2013; Roy et al. 2013; Vucˇurovic´ et al. 2012). The adsorption rate constant and equilibrium adsorption amount at 25–45 C are summarized in Table 3. The rate constant ( k ) at 45 C is 12 times larger than at 25 C, and 3.7 times larger than at 35 C, indicating that LBG adsorption to NBSK pulp is strongly temperature dependent. The adsorption rate in an agitated pulp suspension depends on turbulent transport and Brownian motion (Zakrajsˇek et al. 2009; van De Ven 1994). When temperature increases, the collision frequency of particle and fibre increases thus increasing adsorption rate with temperature (Table 3). The large confidence intervals associated with the rate constant are due to propagation of the uncertainty of the intercepts predicted in Fig. 2. The equilibrium adsorption capacity ( q e ), however, decreased with increasing temperature from 25 to 45 C (Table 3). The equilibrium adsorption capacity at 45 C is 25% of that at 25 C. Since the amount adsorbed is a result of competition between adsorption and desorption, the decrease of q e indicates an increase in the escaping capacity of LBG at elevated temper- ature. To further investigate this temperature effect, adsorption isotherms are discussed below. The acti- vation energy was determined by linear regression of the Arrhenius equation. For LBG adsorption at 25 C to 45 C, the activation energy was 99.34 kJ mol - 1 ( ± 9.85 kJ mol - 1 , 95% confidence interval) with a pre-exponential factor of 4.76 9 10 17 L mol - 1 min - 1 (Supplementary information Fig. 9). The high activa- tion energy suggests that LBG adsorption to NBSK pulp is a chemisorption process (Laidler 1987). Russo (1959) studied partially methylated LBG adsorption to bleached sulfite pulp and determined the activation energy of adsorption to be 18.4 kJ mol - 1 leading Russo (1959) to propose that adsorption is a physical process dominated by diffusion or adsorption via van der Waals forces. The difference between this work and Russo (1959)’s might lie in the agitation. Russo (1959) applied a low agitation rate of 12 r.p.m., while this study applied an agitation rate of 150 r.p.m. When
Adsorption kinetics
The fraction of LBG adsorbed to NBSK pulp (Eq. 1) at 25 C is plotted as a function of time with LBG dosage of 0.2 wt% relative to o.d. pulp (Fig. 1). The initial adsorption rate was high with more than 52% adsorp- tion in 0.5 min and 82% adsorption within 5 min. After 10 min, the adsorption fraction plateaued at approxi- mately 93%. Adsorption equilibrium was achieved in 10 min as the LBG adsorption fraction was constant from 10 to 120 min. This result is consistent with previous research that found initial adsorption of hemicellulose is rapid and achieves equilibrium in a few minutes (Zakrajsˇek et al. 2009; Swanson et al. 1949) when low dosages are applied. Adsorption residence time was maintained at 10 min in all subsequent studies. Kinetic plots for LBG adsorption are presented in Fig. 2. The poor fit of the pseudo-first-order model ( R 2 = 0.635) at 25 o C suggests this model cannot describe LBG adsorption kinetics. The pseudo-second- order kinetics model fit well at all tested temperatures ( R 2 [ 0.997). The standard error on slopes are rela- tively small at all temperatures. Slope is used to calculate q e (Eq. 10). The standard error on intercepts increase with increasing temperature. The intercept and q e determined from the slope are used to determine
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Fig. 1 The fraction of LBG adsorbed to NBSK pulp at 25 Cas function of time. LBG dosage was 0.2 wt% relative to o.d. pulp and fibre consistency was 0.5 wt%; all runs were conducted with an agitation rate of 150 r.p.m
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