(693c) Modelling of Entire Molecular Weight Distribution for Free-Radical Semi-Batch Solution Polymerisation

Polymer molecular weight distribution (MWD) is one of the most important polymer properties that determine the physical, mechanical, and rheological properties of industrial polymers [1]. It is common practice to control the leading averages of the MWD, usually number and weight average molecular weights. These averages represent compact characterisations of the polymer chain length distribution. However, in particular cases such as broad, highly skewed, or bimodal distributions, the control of these properties is not sufficient [2]. It is not uncommon that two polymers of different chain length distribution can exhibit similar molecular weight averages. Sometimes a slight variation in high or low molecular weight fractions causes significant differences in the polymer end-use properties, this being a motivation to predict, or control, the entire molecular weight distribution [1].

In the present work, we develop a mathematical model to determine the entire MWD for a free-radical solution polymerisation of styrene, taking place in batch and semi-batch reactors. It comprises a detailed kinetic model for this particular type of polymerisation, taking into account chain transfer to monomer and to solvent, and termination both by disproportionation and combination (coupling). The volume contraction during polymerisation is also included into the model [3]. At high monomer conversion, the viscosity of the reaction medium increases and there are diffusion limitations. This is known as ?gel-effect? and is also considered on the derived model, using a modified termination constant [2].

It is necessary to identify a suitable computational method for the above MWD model. Crowley and Choi [2, 4] proposed the method of finite molecular weight moments to calculate the chain length distribution on a methyl methacrylate (MMA) free-radical polymerisation process (termination via disproportionation) [2]. This strategy is based on discretising the polymer chain length distribution into finite elements structure and the derivation of moments for each finite element. This strategy considerably simplifies the computational load while simultaneously modelling the entire MWD. However, this study does not account for termination via combination, which is a prevalent and equally important termination mechanism in most polymerisation chemistries.

In our work, the detailed MWD model described above is solved using an extension of the computational method of Crowley and Choi [2, 4]. The extension includes the termination kinetics, both by combination and disproportionation. Since this is a simpler method and numerically easier to solve, it allows the adoption of fine discretisation of the chain lengths, without affecting significantly the computational time.

The model predicts results that are very similar to experimental data in the literature, using kinetic constants and components' parameters from the literature [5]. This is a more realistic approach to the polymerisation process behaviour, since we account for both types of termination steps (disproportionation and combination), that can be used to optimise [6, 7] some operating conditions like initiator design, temperature and initiator concentration profiles, among others. It also enables the development of reliable control strategies to run this kind of processes and attain desired MWD's [7, 8, 9].

References

1. W. J. Yoon, J. H. Ryu, C. Cheong, K. Y. Choi (1998). Calculation of molecular weight distribution in a batch thermal polymerisation of styrene. Macromol. Theory Simul., 7, 327-332

2. T. J. Crowley and K. Y. Choi (1997). Discrete optimal control of molecular weight distribution in a batch free radical polymerization process. Ind. Eng. Chem. Res., 36, 3676-3684

3. M. Rafizadeh (2001). Non-isothermal modelling of solution polymerization of methyl methacrylate for control purposes. Iranian Polymer Journal, 10, 251-263

4. T. J. Crowley and K. Y. Choi (1997). Calculation of Molecular weight Distribution from molecular weight moments in free radical polymerization. Ind. Eng. Chem. Res., 36, 1419-1423

5. S. P. Gretton-Watson, E. Alpay, J. H. G. Steinke, J. S. Higgins (2006). Multi-functional monomer derived hyperbranched poly(methyl methacrylate): Kinetic modelling and experimental validation. Chemical Engineering Science, 61, 1421-1433

6. C. Kiparissides (2006). Challenges in particulate polymerization reactor modelling and optimization: A population balance perspective. Journal of Process Control, 16, 205-224

7. D. C. M. Silva and N. M. C. Oliveira (2002). Optimization and nonlinear model predictive control of batch polymerization systems. Computers and Chemical Engineering, 26, 649-658

8. T. J. Crowley and K. Y. Choi (1998). Experimental studies on optimal molecular weight distribution control in a batch-free radical polymerization process. Chemical Engineering Science, 15, 2769-2790

9. M. F. Ellis, T. W. Taylor, K. F. Jensen (1994). On-line molecular weight distribution estimation and control in batch polymerization. AIChe Journal, 3, 445-462