ethene conversion / %
6.1 Study of thermal peroxide decomposition
6.2.6 Simulation of TEMPO–mediated styrene polymerization under high pressure
Styrene polymerizations have been intensively investigated and rate coefficients for most of the involved reactions have become available in the literature. Temperature and pressure dependences of kinetic coefficients are presented in Section 4.1.2. A major problem concerns the determination of invividual rate coefficients kc and kd. The simulations show that the equilibrium constant K = kd/kc rather than the absolute value of the rate constants kc and kd will determine the polymerization kinetics over the time scale of interest (see Section 4.2.7).
The pressure influence on activation and deactivation rate coefficients kd and kc is estimated by fitting the experimental data. The prediction concerning the pressure dependence of kc made in Section 4.4 (DV¹(kc) = DV¹(kt) = 22 cm3⋅mol–1) was verified by the simulations.
kd at 125°C was found to be 1.0⋅10–3 L⋅mol–1⋅s–1 at 1 bar and 6.2⋅10–4 L⋅mol–1⋅s–1 at 2000 bar.
This induces an activation volume close to 8 cm3⋅mol–1 for the dissociation reaction. As shown in Figure 6.13, these rate coefficients data allow for a good simulation of the polymerization rate and the molecular weight evolution with monomer conversion. The constant K = kd/kc has been varied but no better fit is obtained. Upon varying kc and kd by the same factor (K remains constant) within a certain range allows to adequatly simulate the experimental results. As kc and kd have not been directly measured, only the pressure dependence of K will be condidered. In this case, pressure induces a very low increase of K from 1.1⋅10–9 to 2.6⋅10–9 in going from 1 to 2000 bar, due to the higher pressure dependence of kc than the one of kd.
Fig. 6.13. Plot of ln([M]0/[M]) vs time and of polydispersity (filled points) and molecular weight (open points) as a function of styrene conversion for polymerizations in the presence of 0.11 mol% of styryl–TEMPO at 125°C and at pressures up to 2000 bar. The lines are from PREDICI® simulations, the data points are from experiments.
The estimated rate coefficient kd at 125°C for the bond cleavage of the dormant species from TEMPO and the growing radical is one order of magnitude higher than the value given in the literature for the bond dissociation of styryl–TEMPO 7–11, 17. kd is reported to be chain–length dependent and the value estimated in this work is close to the one determined by German et al.17 for the polymeric analog (approximately 75 units) by monitoring nitroxide concentration via ESR. The literature values are summarized in Table 6.14. The small difference at low monomer conversion between experimental and simulated data may be explained by the chain length dependence of kd, which is not considered in the model.
conditions 125°C
kc
L⋅mol–1⋅s–1
kd
s–1
K=kd/kc source
styryl–TEMPO, 1 bar 2.5⋅108 2 to 5⋅10–4 1 to 2⋅10–12 literature7–11 polystyryl–TEMPO1 bar – 3.2⋅10–3 – literature7–11
1 bar 9.0⋅105 1.0⋅10–3 1.1⋅10–9 this work
2000 bar 2.4⋅105 6.2⋅10–4 2.6⋅10–9 this work
Table 6.14. Summary of fitted rate coefficients kc and kd for the alkoxyamine styryl-TEMPO at 125°C and comparison with literature values.
The simulations performed for TEMPO–mediated polymerization at 115°C and 2000 bar are also presented in Figure 6.16. The rate coefficient of spontaneous thermal initiation of styrene at 115°C and 2000 bar was set to ki = 1.3⋅10–9 s-1, so that simulations are in good agreement with the experimental data from spontaneous thermal polymerization. Temperature and pressure dependencies of kc and kd are taken as determined for styryl–TEMPO : DV¹(kc)
= 22 cm3⋅mol–1, DV¹(kd) = 10 cm3⋅mol–1. The coefficients for the reversible dissociation of styryl–TEMPO used in PREDICI® simulations are reported in Table 6.15. They allow for satisfactory description of styrene polymerization in the presence of styryl–TEMPO at low temperature.
conditions kc
L⋅mol–1⋅s–1
kd
s–1
K = kd/kc source
125°C, 2000 bar 2.2⋅105 2.3⋅10–4 1.0⋅10–9 this work
Table 6.15. Summary of fitted rate coefficients kc and kd for the reversible dissociation of styryl–TEMPO at 115°C and 2000 bar.
Calculated molar mass distributions, polydispersity indices, and polymerization rates are very close to the experimental data. PREDICI® simulations represent the influence of the adduct concentration on polymerization rate and molar mass evolution as it was experimentally observed in Section 6.2.4. A lower alkoxyamine concentration induces a slight decrease of polymerization rate. The alkoxyamine concentration determines the molecular weight as theoretically predicted. A comparison of experimental and simulated MWDs for styrene polymerization in the presence of 0.11 mol% styryl–TEMPO at 2000 bar and 115°C is reported in Fig. 6.16. The good agreement between experimental and simulated MWDs indicates that the rate coefficients kc and kd are reasonable.
Fig. 6.16. Experimental (solid lines) and simulated (dashed lines) molecular weight distributions for styrene polymerization in the presence of 0.11 mol% styryl–
TEMPO at 2000 bar and 115°C. Data at approximately 50 % conversion in 9 hours.
PREDICI® simulations were also performed at lower temperatures in order to determine the temperature limit for controlled styrene polymerizations under pressure. The plot of molecular weight and polydispersity index as a function of monomer conversion for styryl–TEMPO–mediated styrene polymerizations at 2000 bar and at temperatures from 115°C up to 95°C are presented in Fig. 6.17. Simulations between 95°C and 115°C show that controlled styrene polymerization is possible under high pressure at these temperatures.
Polydispersity indices lower than 1.5 are obtained above 30 % conversion and molar masses increase with monomer conversion irrespective of the applied temperature. Polydispersity slightly increases with decreasing temperature but polydispersity indices at 50 % conversion are close to 1.25 and 1.35 at 115 and 95°C, respectively. Basically, controlled styrene polymerization is possible at 95°C but low temperature induces very low polymerization rate.
Polymerization time to reach 50 % conversion at 2000 bar is 7 hours at 115°C, 21 hours at 105°C and approaches 40 hours at 95°C.
These simulations show that mediator controlled styrene polymerization under high pressure may be carried out at reasonably low temperatures. High pressure presents a relevant advantage in that polymerization rate is increased.
Fig. 6.17. PREDICI® simulations of molecular weight and polydispersity index as a function of monomer conversion for styrene polymerizations in the presence of 0.220 mol% styryl–TEMPO at 2000 bar between 115 and 95°C.