**10. Kinetics of polymerization**

For the synthetized copolymers of **Table 1** the experimental viscosity-time curves are pre‐ sented in **Figure 4**, an adjustment of experimental data was done by using Eq. (4).

**Figure 4.** Viscosity-time data at 60°C and predicted data (–) from Eq. (4).

The numerical results of this regression are presented in **Table 2**.


**Table 2.** Kinetic parameters obtained from experimental data.

It was found that *kp* / *kt* 1/2 is proportional to the shear rate used in the synthesis. *kd* values are kept constant through all experiments, concluding that the initiation kinetics is independent of the shear rate. The copolymers were characterized to obtain a better understanding of the chemistry involved in the synthesis.

All copolymers were characterized by the following techniques: Fourier transform infrared spectroscopy (FTIR) in a Cary 600 Series spectrometer from Agilent®; differential scanning calorimetry (DSC) in an HP DSC 1 STAR® from Mettler Toledo® and rheology with a Physica MCR-301 Rheometer from Anton Paar®. The results of all these characterizations are presented in **Table 3**.


**Table 3.** FTIR, DSC and rheological characterization of AAm-AMPSNa copolymers.

The number 117.39 was calculated for the reactor filled with liquid water (viscosity of 0.001

The methodology used for the simulations is presented in **Figure 3**. The diagram contains the

For the synthetized copolymers of **Table 1** the experimental viscosity-time curves are pre‐

sented in **Figure 4**, an adjustment of experimental data was done by using Eq. (4).

) and by using the geometrical dimension of the system.

**1/2[L1/2mol−1/2s−1/2]**

Pa·s and density of 998.2 kg/m3

278 Modeling and Simulation in Engineering Sciences

**10. Kinetics of polymerization**

experimental test used to validate the simulation model.

**Figure 4.** Viscosity-time data at 60°C and predicted data (–) from Eq. (4).

**Table 2.** Kinetic parameters obtained from experimental data.

The numerical results of this regression are presented in **Table 2**.

**Experiment Shear rate [s−1] Stirrer speed [rpm] kv [s−1] kp/kt**

C1 10 26 7.36 × 10−03 0.00034 C2 30 56 7.87 × 10−03 0.00075 C3 60 92 8.32 × 10−03 0.00074 C4 90 123 7.21 × 10−03 0.00374 C5 120 151 7.66 × 10−03 0.00715 C6 150 177 7.03 × 10−03 0.00535 C7 200 217 7.67 × 10−03 0.01099 Based on the experimental results, the values of the Mv (molecular weight), Tg (glass transition temperature), and Tf (fusion temperature) increase according to the shear rate. Mv of polymers obtained under C6 and C7 conditions increased 281 and 317%, respectively, compared with C2. In all experiments, the AMPSNa molar composition of the copolymer chains was relatively constant (between 42 and 50%) according to the calculated F2 parameter. This result was supported by the FTIR results.

Copolymers synthetized at 150 and 200 s−1 increased their Tg by 12% and 29%, respectively, considering a reference value of Tg=245°C. Increased values of Tg and Tf are consequences of both Mv [23] and stiffness of the chains. The latter is a consequence of the incorporation of sulfonate groups (e.g. AMPSNa) into the polymer [24].
