Page 122 - Biodegradable Polyesters

100 4 Synthesis, Properties, and Mathematical Modeling of Biodegradable Aliphatic Polyesters

theoretical curves show a delay with respect to the experimental curves. But the
absolute values of the differences are small, so part of them can be due to the exper-
imental error (which may have important contribution for discrepancies up to 3%
observed here) and the rest to additional phenomena are not included here, being
obviously of secondary significance. The value found for the exponent is 1.33,
implying lateral interactions between the adsorbate molecules, which is true for
the water molecules with their highly polar nature (hydrogen bond). The variation
of the total storage water capacity of the SiO particles increases with the amount
2
of SiO particles exhibiting a linear relationship for small values of SiO amount
2
2
and showing a kind of saturation for the largest value. With the parameter values
found by the fitting procedure, it is possible to predict the dynamics of the esterifi-
cation reaction and the water evaporation for any amount of silica particles using
the model developed above.

4.4.3
Modeling the Polycondensation Reaction Kinetics for the Synthesis of Aliphatic
Polyesters

In this section, the kinetics of the second step, that is, the polycondensation reac-
tion of aliphatic polyesters, is investigated and a simple theoretical model is pro-
posed to simulate both esterification and transesterification reactions taking place
during polycondensation.

4.4.3.1 Reaction Scheme
During polycondensation, it is well known that two main reactions take place:

1) transesterification or polycondensation where a glycol (i.e., EG, PG, or BG) is
produced;

k 1
2 CH CH 2 C O (CH ) OH
2
2 x
k /K 1
1
O
CH CH 2 C O (CH ) O C CH CH 2 + HO (CH ) OH
2
2 x
2 x
2
O O
2) esterification, where water is eliminated as by-product.
k 2
CH CH 2 C OH + HO (CH ) O C CH CH 2
2
2
2 x
k /K 2
2
O O
CH CH 2 C O (CH ) O C CH CH 2 + H O
2 x
2
2
2
O O