(167q) Polypropylene Grafted with Maleic Anhydride: A Stochastic Model.

Grafting of maleic anhydride (MAH) onto polypropylene (PP) has been the subject of many studies, in pursuit of improving properties such as polarity, chromaticity, adhesion to metal, glass, or ceramic, and compatibility with other polymers such as polyamides and polyesters. This process has been studied experimentally using several production methods, reactive extrusion being the most predominant [1]. The final properties of the resulting grafted material depend on several variables, e.g., peroxide type and concentration, MAH concentration, reaction time, temperature, pressure, and other variables associated with the chosen production method [2].

Even though there is a large number of experimental works published on the subject, the complete reaction mechanism is still uncertain at some points [3-13]. There is, however, agreement on the mechanism's main steps. A peroxide is generally used to generate free radicals. It is generally accepted that those free radicals lead to the formation of secondary and tertiary alkyl radicals. Given the case of tertiary radicals in reactions at relatively high temperatures, the reaction of β-scission exhibits an important influence. This reaction results in the depropagation of the PP chain, leading to two shorter chains: a disproportioned dead chain and a live chain with a secondary alkyl radical at one of its ends. Besides, all radicals can be grafted by MAH. This process may include many secondary reactions, on which there is no general agreement in the literature. The most common ones are termination by disproportionation and MAH homopolymerization of grafted segments. Other reactions like chain transfer to polymer and different types of termination have been proven not to be negligible by several authors [3,4,9,12]. Moreover, it has been verified that the reaction of β-scission can happen after the grafting reaction, generating a stable grafted polymer and secondary alkyl polymer [4]. The influence of some parameters such as initiator and MAH concentrations on the grafting degree or the number-average molecular weight (Mn), among other variables, has been the source of debate as well. Nevertheless, this subject has been widely studied and some conclusions can be extracted for given reaction systems [4,6,10-12], allowing future experiments to be validated with these.

In this context, mathematical modeling emerges as an attractive alternative for discerning the reaction mechanism. A mathematical model capable of predicting a distributed property such as the molecular weight distribution (MWD) requires a precise description of the reactions and their effects. This level of precision may be hard to achieve. There are some works on the modeling of the grafting of MAH on PP reported in the literature. For example, Giudici et al. [9] presented a complete mechanism, using a fairly wide set of secondary reactions. This model is solved using the method of moments, which reduces an infinitely large system of mass balance differential equations to a finite one, allowing a much cheaper solution, computationally speaking. Nevertheless, this method does not provide detailed information on the evolution of some process variables and has also problems when dealing with some secondary reactions such as β-scission. Shi et al. [10] and Zhu et al. [11] presented a Monte Carlo algorithm with a simplified reaction mechanism that only contains the main reaction scheme described before, not taking into account many of the possible secondary reactions. These two works proved to be consistent with each other and gave a fair adjustment of the experimental data, yet failed to give a complete understanding of the reaction mechanism and to offer a detailed prediction of the molecular properties.

For this polymer system, a stochastic approach like the Monte Carlo method is very suitable. This technique provides a very detailed description of the variables of the process through time and the possibility to easily update and increase the set of reactions, however sometimes at the cost of a higher computational time.

The goal of this work is to propose a complete mechanism for the grafting of MAH on PP and to determine the most significant reaction steps. To achieve this, we implement a Monte Carlo algorithm and estimate the kinetic constants that best fit the model predictions to experimental data previously obtained by our research group. By doing this, we could determine the reactions that are most likely to occur and their influence on the final results, for the set of experimental data employed in the work. We also report a detailed description of the evolution of many important variables over time, such as the Mn, weight-average molecular weight (Mw), MWD, degree of grafting, average number of grafts by chain, number-average length of MAH grafted chains, normalized location of the grafts per chain and the concentration of all the species involved. A good fit of the experimental data is obtained. The mathematical model is programmed in MATLAB on a desktop PC with an Intel Core I5-3330 processor and 8 GB of RAM. Comparison with other experimental data sets is underway.

References

[1] Berzin, F., et al. (2013). "Grafting of maleic anhydride on polypropylene by reactive extrusion: effect of maleic anhydride and peroxide concentrations on reaction yield and products characteristics." Journal of Polymer Engineering 33(8): 673-682.

[2] Moad, G. (1999). "The synthesis of polyolefin graft copolymers by reactive extrusion." Progress in Polymer Science 24(1): 81-142.

[3] Aguiar, L. G., et al. (2011). "Mathematical modeling of the grafting of maleic anhydride onto poly (propylene): Model considering a heterogeneous medium." Macromolecular Theory and Simulations 20(9): 837-849.

[4] Zhang, R., et al. (2005). "Effect of the initial maleic anhydride content on the grafting of maleic anhydride onto isotactic polypropylene." Journal of Polymer Science Part A: Polymer Chemistry 43(22): 5529-5534.

[5] Severini, F., et al. (1999). "Free radical grafting of maleic anhydride in vapour phase on polypropylene film." Polymer 40(25): 7059-7064.

[6] Roover, B. D., et al. (1996). "Maleic anhydride homopolymerization during melt functionalization of isotactic polypropylene." Journal of Polymer Science Part A: Polymer Chemistry 34(7): 1195-1202.

[7] Oromiehie, A., et al. (2014). "Chemical modification of polypropylene by maleic anhydride: melt grafting, characterization and mechanism." International Journal of Chemical Engineering and Applications 5(2): 117.

[8] Heinen, W., et al. (1996). "13C NMR Study of the Grafting of Maleic Anhydride onto Polyethene, Polypropene, and Ethene−Propene Copolymers." Macromolecules 29(4): 1151-1157.

[9] Giudici, R. (2007). Mathematical modeling of the grafting of maleic anhydride onto polypropylene. Macromolecular Symposia, Wiley Online Library.

[10] Shi, D., et al. (2001). "Functionalization of isotactic polypropylene with maleic anhydride by reactive extrusion: mechanism of melt grafting." Polymer 42(13): 5549-5557.

[11] Zhu, Y., et al. (2003). "Monte Carlo Simulation of the Grafting of Maleic Anhydride onto Polypropylene at Higher Temperature." Macromolecules 36(10): 3714-3720.

[12] Ho, R. M., et al. (1993). "Functionalization of polypropylene via melt mixing." Polymer 34(15): 3264-3269.

[13] Shi, D., et al. (2006). "Nano‐reactors for controlling the selectivity of the free radical grafting of maleic anhydride onto polypropylene in the melt." Polymer Engineering & Science 46(10): 1443-1454.

[14] Hernández-Ortiz, J. C., et al. (2019). "A two-phase stochastic model to describe mass transport and kinetics during reactive processing of polyolefins." Chemical Engineering Journal 377: 119980.