Cellulose (2021) 28:10183–10201
10189
LBG adsorption for strength analysis
dq t
dt ¼ 15 Þ where k is rate constant (min - 1 in Eq. 14 and g mg - 1 min - 1 in Eq. 15), q e is the concentration of LBG (mg g - 1 o.d. fibre) adsorbed at equilibrium, same as in Eq. 10, and q t is concentration of LBG (mg g - 1 o.d. fibre) adsorbed at any time, t (min). Separating variables of the pseudo-first-order model yields: dq t q e q t ¼ kd t ð 16 Þ Using the boundary condition q t (0 s) = 0 mg g - 1 o.d. fibre and integrating, the pseudo-first-order model yields: ln q e q t ð Þ¼ kt þ lnq e ð 17 Þ Separating variables of the pseudo-second-order model yields: dq t q e q t ð Þ 2 ¼ kd t ð 18 Þ k q e q t ð Þ 2 ð Once again, using the boundary condition q t (0 s) = 0 mg g - 1 o.d. fibre and integrating, the pseudo-second-order model yields:
An aqueous LBG solution of 0.5 wt% consistency was hydrolyzed at 85 C for 10 min with constant stirring to produce a transparent viscous solution. The PFI mill was used to refine the pulp to 3000–9000 rev at 10wt% fibre consistency. A NBSK pulp suspension of 1.5 wt% fibre consistency was prepared after refining in the pulp disintegrator for 600 counts, which is equivalent to 1500 rev. The LBG solution was then added to NBSK pulp suspension to the desired dosage with manual stirring for 10 min at 25 C. Table 2 summarizes the combinations of LBG addition and refining tested. The treated pulp was next diluted to a fibre consistency of 0.3 wt%. A 2 L sample was collected for freeness testing, and the remaining suspension was used for handsheet making. Two to three replicates were conducted for each condition.
Freeness testing, handsheet preparation and strength analysis
Freeness (Canadian standard method) was tested according to Tappi Method T 227. Handsheets with an average grammage of 60 g m - 2 were prepared on a wire of 200 cm 2 according to Tappi Method T 205. The following handsheet properties were tested: weight and thickness (L&W micrometer), tensile strength (L&W Tensile Strength Tester, Tappi Method T 494), tear index (Elmendorf Tearing Tester, Tappi Method T 414) and burst index (Mullen Tester, Tappi Method T 403). Brightness and scattering coefficient were tested by Technidyne ColorTouch PC according to ISO 2470–1 and TAPPI T 525.
1 q e q t
1 q e ¼
ð 19 Þ
kt
Equation 19 can be rearranged as:
t q t ¼
1 k q e ð Þ
t q e
2 þ 20 Þ For pseudo-first-order adsorption kinetics, plotting ln(q e - q t ) as a function of t will yield a line with slope of - k and intercept of lnq e . For pseudo-second-order adsorption kinetics, plotting t q t as a function of t will yield a line with slope 1 q e and intercept of 1 k ð q e Þ 2 . ð
Table 2 Experimental design for investigation into the effects of LBG dosage and pulp refining on paper strength
Refining (rev)
Dosage relative to o.d. pulp (wt%)
0
0, 0.1, 0.5, 1
3000
0, 0.1, 0.5, 1
6000
0, 0.1, 0.5, 1
9000
0, 0.1, 0.5, 1
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