Page 117 - Biodegradable Polyesters

4.4 Mathematical Modeling of the Synthesis of Aliphatic Polyesters 95

1.1 1.05
1.0
1.00
0.9
0.95
0.8
Species weight fraction 0.6 PG 0.85 Volume fraction of reaction mixture
0.7
0.90
Oligomers
SA
0.5
Volume
0.80
0.4
0.3
0.75
0.2
0.70
0.1
0.0 0.65
0 50 100 150 200 250 300 350
Esterification time (min)
Figure 4.8 Normalized weight fraction of SA, PG, and oligomers, as well as volume fraction
∘
of reaction mixture as a function of time for the esterification of PPSu at 190 C [43].
1.0
Water
Molecular species (mol) 0.6 PG SA bSA
0.8

0.4

0.2 tPG tSA bPG
bDPG

0.0
0 50 100 150 200 250 300 350
Esterification time (min)

Figure 4.9 Mole number of all molecular species present in the reactor as a function of
∘
time for the esterification of PPSu at 190 C [43].
reaction (first step in polyester synthesis) as the maximum NADP reached is
between 4 and 7. Different glycols used do not influence the NADP values of the
oligomers produced during the esterification step much. In contrast, these values
are affected much by the amount of catalyst used, with larger catalyst molar ratio
giving a polymer with bigger average molecular weight.
The predictive capabilities of the model developed were illustrated by examining
the effect of the monomer initial molar ratio on the conversion of SA and PG, the
NADP of the oligomers formed, and the molar fraction of dipropylene glycol pro-
duced. Figure 4.11 shows how the fractional conversion of total acid end groups