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Table 3 LBG adsorption capacity at equilibrium ( q e ) and adsorption rate constant ( k ) at temperature range of 25–45 C as determined by fitting pseudo-second-order kinetics. Temperature ( C) Equilibrium adsorption capacity, q e , (mg g - 1 o.d. fibre) Rate constant, k , (g mg - 1 min - 1 ) 25 1.91 ± 0.08 1.93 ± 1.46 35 1.16 ± 0.03 6.51 ± 7.20 45 0.48 ± 0.01 24.03 ± 45.05
95% confidence limits after ± ; all runs were conducted with an agitation rate of 150 r.p.m.
6
120
(b)
(a)
5
100
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80
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60
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40
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20
0
0
-0.5 0.0
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1.5
2.0
2.5
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0.5
1.0
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2.0
2.5
3.0
Dosage of LBG to o.d. pulp (%)
Dosage of LBG to o.d. pulp (%)
Fig. 3 LBG adsorbed to unrefined NBSK pulp fibre as a function of LBG dosage to o.d. fibre after 10 min at 25 C. a The fraction of LBG adsorbed and b the equilibrium concentration of LBG adsorbed. Error bars represent standard deviation of 2–4 trials
The nonlinear regression results of the Langmuir isotherm model and Freudlich isotherm model at 25 C and 35 C with unrefined and refined NBSK pulp are summarized in Table 4. To better illustrate the isotherm fitting, the experimentally determined and predicted adsorption amount, q e , was plotted as a function of aqueous phase LBG concentration at equilibrium ( C e ) in Fig. 4. Based on Bergmann and Machado (2015), the model with the best fit will have the lowest reduced chi-squared ( v 2 ) and highest R 2 adj . From Table 4, Langmuir isotherm fits better at 25 C for unrefined NBSK pulp. At 35 C, both isotherm models fit well with R 2 adj values close to unity. The temperature effect is discussed in Sect. 3.3.1. For LBG adsorption to refined NBSK pulp (3000 rev) at 25 C, the Freundlich isotherm model better fit the data as demonstrated by v 2 & 0 and R 2 adj =0.99. This result is discussed in Sect. 3.3.2. From Table 4 and Fig. 4, it was concluded that LBG adsorption to unrefined NBSK pulp at 25 C is
consistent with Langmuir adsorption principles, indi- cating that LBG adsorption is a chemisorption process limited to a finite number of sites. According to the Langmuir model, the maximum adsorption capacity ( Q max ) is 2.34 mg g - 1 ( ± 0.20 mg g - 1 , 95% confi- dence interval) at 25 C. Similar adsorption capacities to pulp fibre (Table 5) were observed for native LBG (1.8–5.0 mg g - 1 , Gruenhut 1953) and partially methylated LBG (0.61–12.34 mg g - 1 , Russo 1959). These values are much lower than adsorption capacity for cationic starch (20–66 mg g - 1 , Table 5). However, the capacity for native corn starch adsorption to pulp was 1.1–4.5 mg g - 1 (Cushing and Schuman 1959). Since the charge density of native starch is almost as low as that of LBG, it can be concluded that high positive charge density leads to high adsorption capacity. The equilibrium constant ( K e ) calculated from the Langmuir model is approximately 2.82 L mg - 1 ( ± 1.73 L mg - 1 , 95% confidence interval) at 25 C. The large confidence interval reflects the limited
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