Page 113 - Biodegradable Polyesters

4.4 Mathematical Modeling of the Synthesis of Aliphatic Polyesters 91

where MW and represent the molecular weight and density of the corresponding
material. W OLIG is used to express the weight of all oligomers presented in the
reaction mixture, that is, (tSA), (tG), (bSA), (bG), and (bDG).
Furthermore the material mole balance equations for a semi-batch reactor can
be written as
1 d(SA)
=−R − R 3 (4.19)
1
V dt
1 d(G)
=−R − R + R 5 (4.20)
1
2
V dt
d(W)
= V(R + R + R + R + R )− F = 0 (4.21)
w
1
6
4
3
2
dt
1 d(tSA)
= R − R + R − R 4 (4.22)
1
2
3
V dt
1 d(tG)
= R + R − R − R − 2R − 2R 6 (4.23)
1
2
5
4
3
V dt
1 d(bSA)
= R + R (4.24)
V dt 2 4
1 d(bG)
= R + R + R 5 (4.25)
3
4
V dt
1 d(bDG)
= R 6 (4.26)
V dt
In Equation 4.21, F W is used to represent the flow rate of the water vaporized
and removed from the reactor. Then, the total moles of water removed up to time
t, N , can be calculated from
W
t
N = F dt (4.27)
W ∫ W
0
Finally, conversion according to the water produced and removed can be calcu-
lated according to the following equation:
N MW W
W
X = (4.28)
W
M
W,th
The symbol M in the denominator is used to express the theoretical total
W,th
mass of water that should be produced when all acid will be reacted. For example,
a value of 19.8 was used in reference [43] corresponding to the complete reaction
of all 0.55 mol of SA initially used.
Molecular Characteristics of the Oligomers Produced Using the polymer segment
approach, the NADP of oligomers produced can be expressed as [38]
(tSA)+(bSA)+(tG)+(bG)+(bDG)
DP = (tSA)+(tG) (4.29)
n