Kinetics of Cellulose Chain Scissions. A common means of following polymer degradation is to monitor the average

A common means of following polymer degradation is to monitor the average

molar mass, which is then used to calculate the rate constants for the degrading

reactions. Ekenstein proposed a first-order kinetics of bond scission when studying

the homogeneous degradation of the cellulose in phosphoric acid [22]:

Ln

DPt _

DP 0 __ k _ t _37_

If DP t and DP 0 are large, which is valid in the case of pulp polysaccharides, this

simplifies to a zero-order kinetics:

DPt _

DP 0 __ k _ t _38_

The degradation of cellulose chains is related to the increase in the numberaverage

moles of cellulose per tonne of pulp, m n. The number-average degrees of

polymerization, DP n, can be calculated in several ways. Godsays and Pearce published

an equation to convert intrinsic viscosity to DP n [23]:

DPn _ 961_38 _ Log _g__245_3 _39_

Equation (39) implies that the polydispersity of the molecular weight distribution

remains constant throughout the degradation reaction. Thus, the viscosityaverage

molecular weight, DP v, calculated from intrinsic viscosity according to

SCAN-CM-15:88, can be used instead, and this is certainly the most convenient

way. For a polymer with a random molecular weight distribution, the viscosity

average degree of polymerization, DPv, and the number average degree of polymerization,

DPn, have the following relationship [24]:

DPv _ DPn __a _ 1_ _C a_ 1 _ _1_a _40_

where a = exponent of the Kuhn–Houwink equation. Since it has been found that

a is close to unity, Eq. (40) can be simplified to DPv _ 2 · DPn.

7.3 Oxygen Delignification 685

The most reliable approach would be to determine the number-average molecular

weight directly, for example with gel-permeation chromatography (GPC) using

MALLS detection [25]. Using Eq. (40) to calculate the number average degree of polymerization,

themoles of cellulose per tonne of pulp, m n, can be calculated as follows:

mn _

162 _ DPn _41_

The moles of cellulose per tonne of pulp, m n, can be reconverted to the intrinsic

viscosity (SCAN-CM-15:88) by the following expression:

_g_

2882_75

m 0_76

n _42_

Assuming a zero-order reaction in m n and a nonlinear dependency on time similar

to the phase transformation concept, the following rate equation for cellulose

degradation can be given:

dmn

dt _ p _ k _ t _ p _1_

mn _ t _ _ mn _0_ _ k _ tp _43_

k _ A _ Exp _

EA

RT ___ OH _ m _ O 2 n

The kinetic parameters A, m and p were estimated from the regression analysis

on experimental data published by Jarrehult and Samuelson for a softwood kraft

pulp [20], while the remaining parameters, E A, and n were used from a study published

by Iribarne and Schroeder [12]. The kinetic parameters employed are summarized

in Tab. 7.18.

Tab. 7.18 Kinetic parameters of the apparent kinetic expression

for cellulose degradation during oxygen delignification adopted

from Ref. [12] and recalculated using the experimental data

provided by Jarrehult and Samuelson [21].

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