(167f) Modeling ?-Olefin Copolymerization for Applications in Energy – Study of Alternatives of Synthesis

Over the last few decades, industrial production of mass-consumption polymers has evolved into large-scale processes that reduce costs and simplify production operations. However, these commodities are not suitable for high-value-added applications. Polyolefins are one example. Although they have advantageous properties such as excellent chemical resistance, their inert and non-polar characters limit their use in applications that require compatibility with other materials. In this context, to broaden and improve the range of applications of polyolefins, it is desirable to introduce alterations in their molecular structure by incorporating chemical groups with different functionalities or by inducing cross-linking or chain cleavage reactions.

Although different functionalization approaches have been reported, both during polymerization and as post-reactor processes, most of them are not applicable at the industrial level [1]. However, synthesis using homogeneous metallocene catalysts is promising in this respect. Polymerization processes using these catalysts have provided the opportunity to polymerize α-olefins with different comonomers. In particular, it is possible to prepare ethylene or propylene copolymers using as comonomer styrene and other cyclic monomers, obtaining high molecular weights, narrow molecular weight distributions, and a wide range of copolymer compositions [2,3]. Special emphasis has been placed on the production of reactive polyolefins that can later be functionalized, or used as macroinitiators in reversible deactivation radical polymerization for the production of graft or block copolymers. The comonomer must present good stability with the metallocene catalyst, good solubility in the reaction medium, and allow easy conversion of its reactive group into polar groups after polymerization. Suitable comonomers are those with benzyl, styrene, or organoborane groups [2,3]. Using this process, dielectric materials have been produced with superior efficiency and degradation characteristics [4,5,6], as well as superabsorbents for oil and its derivatives [7,8].

It should be noted that the success of the functionalization process can be measured in terms of the final properties of the material, such as its molecular weight, degree of crosslinking, and hydrophobicity, among others. These, in turn, depend on the degree of modification achieved in the polymer. Therefore, reaction conditions must be perfectly established to maximize the performance of the reactions that produce the desired transformations in the polymer and minimize undesirable side reactions. For this reason, it is necessary to optimize a large number of variables that control the process.

So far, despite the efforts made to understand and control functionalization processes, there is not yet comprehensive knowledge on the influence of the operational and design conditions necessary to produce functionalized polyolefins suitable for a given final application. In this sense, it is essential to develop mathematical models that accurately describe the functionalization of polyolefins by the mentioned combined process. Such models are very important tools for understanding the influence of the synthesis conditions on the molecular structure, and their influence on the final properties of interest. Besides, these mathematical models can be incorporated into design, optimization, and control approaches, to evaluate alternatives for the commercial application of these products. Understanding the physics and chemistry involved at multiple length scales is required to develop a model able to predict the physical and chemical properties of the final product [9].

In the present work, a comprehensive mathematical model of olefin copolymerization is proposed for the synthesis of materials with well-defined morphology. Such a model comprises three scales. Firstly, the microscale model takes into account the chemical kinetics, chain composition, molecular weights, and their distributions. At this point, our model is based on the kinetic mechanism proposed by Palza et al. [10], who depart from a previous model for propylene polymerization catalyzed by Me₂Si(2-Me-Ind)₂ZrCl₂/MAO in a semibatch reactor to analyze the synthesis of propylene-co-1-hexene. In this work, Palza et al. observed the “comonomer effect”, that is, the increment in productivity due to the addition of the comonomer to the reaction. To solve the infinite system of differential equations for the population of chains our model employs a more detailed version of the method of moments.

Secondly, modeling at the mesoscale comprises intraparticle mass and energy transport phenomena. For this scale, the present work is based on the Polymeric Multigrain Model (PMGM) employed by Sarkar et al. [11,12] to explain the broad molecular weight distribution induced by mass diffusional resistance. Not only the monomer concentration distribution within the macroparticle (catalyst and polymer) but also the effect of the growing polymer shell on monomer diffusivity is taken into account. For this purpose, the macroparticle is divided into concentric shells and a finite difference method is employed to discretize the partial differential equations of monomer diffusion.

Finally, regarding the macroscale, phase equilibria and thermodynamic properties are similar to those presented by Belelli et al. [13], who employed the Soave-Redlich-Kwong equation of state (SRK EOS) to estimate the equilibrium concentration of monomers at the gas-liquid interface.

The resulting system of equations considers mass and moment balances, together with the transient monomer concentration in the bulk. The model implementation is carried out using gPROMS, which offers tools for simulation in a stationary or dynamic state. It is capable of handling systems of partial differential equations with an unlimited number of dimensions. In addition, this software has efficient numerical methods for solving differential equations that arise from the modeling of this type of polymerization system and allows dynamic optimization and parameter fitting to experimental data.

The model fits well the experimental data on productivity and molecular weights reported by Palza et al. [10]. Besides, it allows predicting the distribution of molecular weights together with the evolution of the comonomer composition. The model predicts a dispersity of 2, which is consistent with the presence of a single active site, characteristic of systems catalyzed by metallocenes. Besides, the average incorporation of the comonomer is linear with respect to its concentration in the feed, in agreement with the comonomer equation. In addition, it is worth noting that, unlike most published models, this work provides an integral insight into the synthesis of functional polyolefins by simultaneously considering three length scales. This feature is essential when analyzing the microstructure required for a specific final application, such as dielectric materials.

The next step in this modeling effort is to incorporate the model into an optimization scheme so that appropriate design and operational conditions may be calculated for achieving the desired product.

References

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