**1. Introduction**

Functionalized copolymers are relevant at the industrial level due to their participation in chain extension, crosslinking, and polymer grafting reactions. The applications of these copolymers are diverse. They can be used as dispersants, surfactants, surface modifiers, compatibilizers, and drug delivery matrices [1]. Poly(styrene-co-glycidyl methacrylate) (St-GMA copolymers) are very interesting functional polymers. The epoxide group is useful for the chemical modification of copolymers, leading to a wide variety of applications. The glycidyl functional group has potential applications in functionalization with amines [1], compatibilized polymer blends [2], acids [3], cation-exchange adsorbents [4], and the chain extension of polyesters [5,6], leading to the production of materials with increased melt viscosities and strengths.

Industrial production of St-GMA copolymers is usually carried out by conventional free-radical polymerization (FRP) processes [7,8]. FRP has the advantages of undemanding operation conditions and versatility of monomers that can be used. The negative aspects of FRP include poor control of the molar mass and polymer microstructure of the product. St-GMA copolymers synthesized by FRP typically possess broad molar mass distributions [9].

Another disadvantage of FRP processes is temperature control. For instance, the free radical copolymerization of St and GMA proceeds very rapidly and exothermically.

**Citation:** Tenorio-López, J.A.; Benvenuta-Tapia, J.J.; García-Navarro, N.; Vivaldo-Lima, E.; Champagne, P.; Saldívar-Guerra, E. Mathematical Description of the RAFT Copolymerization of Styrene and Glycidyl Methacrylate Using the Terminal Model. *Polymers* **2022**, *14*, 1448. https://doi.org/10.3390/ polym14071448

Academic Editor: Nicolas Sbirrazzuoli

Received: 31 January 2022 Accepted: 27 March 2022 Published: 1 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Therefore, efficient heat removal is required to avoid reaching reactor-runaway conditions, which may result in the production of out-of-specification materials.

Reversible-deactivation radical polymerization (RDRP), also known as controlled radical polymerization (CRP), is important because it allows the synthesis of copolymers with not only narrow molar mass distributions and well-defined microstructures, but also more homogeneous composition distributions, compared to FRP [10].

The main RDRP techniques, namely, nitroxide-mediated polymerization (NMP) [11,12], atom transfer radical polymerization (ATRP) [13], and reversible addition-fragmentation chain transfer polymerization [14], have allowed the synthesis of functional polymers with predefined molar masses, low dispersity values, and defined microstructures.

Recently, the incorporation to RAFT polymerization of photoinduced electron/energy transfer (PET) and polymerization-induced self-assembly (PISA) methodologies into RAFT polymerization has been applied to the polymerization of various functional monomers, resulting in good control of molecular weight and molecular weight distributions, similar to thermally initiated systems, with supplementary advantages, such as mild reaction conditions and low energy consumption [15,16]. PET-RAFT polymerization was successfully conducted, obtaining polymer products with controlled molecular weights and narrow dispersities (Ð = 1.02–1.13) [15], while RAFT-PISA was successfully applied to the synthesis of block copolymer nano-objects with different morphologies [16].

Few experimental reports on the RAFT copolymerization of St and GMA are available, and to the best of our knowledge there are no reported studies on the production of functional St-GMA copolymers synthesized by RAFT polymerization above 100 ◦C [17], which is the range of interest in the synthesis of acrylate-containing copolymers.

As far as we are aware, only the syntheses of St-GMA copolymers by atom transfer radical polymerization using copper-based catalyst systems in bulk and in toluene, at 60 ◦C [18], and by nitroxide mediated polymerization in 50 wt.% 1,4-dioxane solution, at 90 ◦C, have been reported [19].

The control of polymer microstructural parameters, such as copolymer composition, copolymer sequence distributions and molar mass dispersities, is important in copolymerization processes. Parameter estimation of kinetic rate constants associated with copolymerization processes is important for accurate calculation of polymerization rates and copolymer sequence distributions, which are fundamental to the production of copolymers with predefined properties.

The application of fundamental polymerization models, including kinetic and reactor models, is necessary to understand the mechanisms and phenomena behind these processes. Kinetic studies are particularly important because they provide better control strategies during the production of polymers at an industrial scale [20]. These models can be used to calculate monomer conversion, polymer microstructure, molar mass averages, and full molar mass distributions (MMD) under various operating conditions. Furthermore, mathematical modeling may be used to better understand and operate polymerization processes, allowing the prediction of the effect of operating conditions on polymerization rate and polymer properties; a good model may simplify experimental programs. The industrial production of polymer materials usually involves high-temperature processes. Therefore, it is important to carry out kinetic studies at similarly high temperatures. To the best of our knowledge, the kinetic modeling of the RAFT copolymerization of St and GMA has not been reported so far. It is known that RAFT agents alter the concentration profiles of active species, compared to FRP [20–22]. This situation may favor the preferential incorporation of one of the comonomers, affecting both, copolymer composition and polymerization kinetics [21].

In this contribution, the kinetic modeling of the RAFT bulk copolymerization of St and GMA using 2-cyano-2-propyl dodecyl trithiocarbonate (CPDT) as a RAFT agent, and 1,1 -azobis (cyclohexane carbonitrile) as an initiator, at different levels of GMA content, is reported. Our objectives were to estimate the rate coefficients for RAFT reactions involved in the polymerization scheme and evaluate the performance of the model by comparing

model predictions against experimental data generated in our laboratory. In developing the model, it was assumed that the terminal model is valid and that the RAFT activation and transfer cycles proceed with the same kinetic parameters. Diffusion-controlled termination was considered using a model based on free-volume theory.

### **2. Experimental**

#### *2.1. Reagents*

GMA (97%) and styrene (99%) were purchased from Aldrich (Saint Louis, MO, USA) and purified as explained in one of our earlier studies. [9] 1,1 -azobis(cyclohexane carbonitrile) (ACHN, 98%) and 2-cyano-2-propyl dodecyl trithiocarbonate (97%) were both purchased from Aldrich (Saint Louis, MO, USA) and used as received.

#### *2.2. Size Exclusion Chromatography (SEC) Characterization Method*

Number- and weight-average molar masses (Mn and Mw, respectively), and molar mass dispersity (Ð = Mw/Mn) of the synthesized polymers were measured using a Waters 1515 gel permeation chromatograph (GPC, Waters, Milford, MA, USA) equipped with a refractive-index detector as well as HR 1, HR 3, and HR 4 columns. Calibration procedure and operating conditions were the same as described in an earlier report from our group [19].
