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the simulation lattice is frozen, and depolymerization events are executed. These events are repeated until ΣΔ t depoly , t ≥ Δ t deg . Finally, the macroscopic properties are updated in the last time step. This approach allows for the efficient simulation of the multiscale reactions that occur in the kraft pulping process, while also considering the impact of the system parameters on the dissolution and depolymerization reactions. The first reaction in the depolymerization kinetics is the peeling-off reaction, in which the end-wise degradation of a cellulose chain occurs, and one unit is removed from the reducing end of the cellulose chain. This reaction is a pseudo-first-order reaction that depends on the cellulose concentration and is represented by the following Equation [43,44]: d ( C glu ) dt = k 1 · C cel (1) where C glu is the glucose concentration, C cel is the cellulose concentration, and k 1 is the peeling-off reaction rate constant. The second reaction in the depolymerization kinetics is the stopping reaction, in which the reducing end group of the cellulose chain is converted into a stable end group leading to the formation of metasaccharinic acid. As with the peeling-off reaction, the stopping reaction is also a pseudo-first-order reaction that depends on the cellulose concentration and can be represented as follows: d ( C MSA ) dt = k 2 · C cel (2) where C MSA is the metasaccharinic acid concentration, and k 2 is the stopping reaction rate constant. The final depolymerization kinetics involve alkaline hydrolysis, where glycosidic bonds undergo base-catalyzed cleavage, and the cellulose chain is divided into two pieces, thus, resulting in a half-fold decrease in cellulose DP . This is a pseudo-first-order reaction that depends on the cellulose concentration as follows: d ( C cel ) dt = k 3 · C cel (3) where k 3 is the alkaline hydrolysis reaction rate constant. The kinetic parameters are esti- mated by applying the Arrhenius equation, and the rate constants are given as follows [43]: 1. log ( k 1 )= 16.21 − 5249 T ( R P ) Peeling off 2. log ( k 2 )= 17.12 − 6548 T ( R S ) Stopping 3. log ( k 3 )= 15.41 − 7461 T ( R H ) Alkaline hydrolysis The alkaline hydrolysis greatly impacts the cellulose DP by reducing it by half. The peeling-off and stopping reactions are considered null events as no action takes place when the R P and R S events are selected. When R H is chosen, the DP is also reduced to half. The probabilities for the three depolymerization mechanisms are shown in Table 1.
Table1. Probability distribution for cellulose depolymerization.
Probabilities
Depolymerization Mechanism
R P R P + R S + R H
0 < ξ ≤ R P R P + R S + R H R P + R S R P + R S + R H
Peeling-off (Null event) Stopping (Null event)
R P + R S R P + R S + R H
< ξ ≤
< ξ ≤ 1
Cellulose chain scission event
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