Benchmarking Stochastic and Deterministic Kinetic Modeling of Bulk and Solution Radical Polymerization Processes by Including Six Types of Factors Two

Keer, Lies De; Figueira, Freddy L.; Marien, Yoshi W.; Smit, Kyann De; Edeleva, Mariya; Steenberge, Paul H. M. Van; D’hooge, Dagmar

doi:10.1002/mats.202000065

Cited by 34 publications

(27 citation statements)

References 76 publications

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“…Examples of species whose three-dimensional (3D) positions are thus not explicitly tracked are provided in Figure c, differentiating between monomer molecules ( M ), RDRP initiator molecules ( R 0 X ), dormant chains ( R i X ), and dead chains ( Pi ) with i and j chain lengths. MFA is consistent with bulk/solution modeling studies on FRP, RDRP, and living polymerization, − in which one follows the variation of the concentrations as a function of synthesis time assuming perfect macroscale mixing and temperature control.…”

Section: Modeling Principles and Developmentsupporting

confidence: 79%

“…We use the population-weighted method to update the apparent average termination rate coefficient that codefines the global sampling of the termination reaction channel in the solution and corrects for diffusional limitations. Consistent with the work of De Keer et al no additional factor 2 is included to reflect the likelihood that the two radicals involved have a different chain length. For termination with only surface-tethered species, the reaction is only executed if (i) the two chain-ends are next to each other based on the allowed bond length in the region r ∈ [1,√3] and (ii) the chains are not hindered from propagation so that space is available to rearrange the chains.…”

Section: Modeling Principles and Developmentmentioning

confidence: 99%

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Conformational Variations for Surface-Initiated Reversible Deactivation Radical Polymerization: From Flat to Curved Nanoparticle Surfaces

Hernandez¹,

Steenberge²,

Sobieski

et al. 2021

Macromolecules

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Although progress in surface-initiated reversible deactivation radical polymerization (SI-RDRP) has already enabled the production of increasingly novel and advanced polymer structures on solid surfaces, fundamental kinetic questions remain regarding the impact of reaction conditions on the molecular properties of synthesized tethered chains. In the current work, we put forward a matrix-based kinetic Monte Carlo (kMC) model, which is based on an implicit SI-RDRP reaction scheme and continuous three-dimensional (3D) representations, capable of following the temporal evolution of the molecular properties of individual free and surface-tethered polymer chains. This is uniquely possible for variable surface curvature (nanoparticle radii from 4.5 to 32 nm; 353 K; monomer: methyl methacrylate), also including the comparison with the limiting case of a flat surface and addressing various (average) RDRP initiator surface coverages. For the tethered chains, we emphasize the prediction of the variation of the molecular height, monomer occupancy, and radius of gyration and also focus on the simulation of the chain length distribution (CLD) to enable a comparison with solution RDRP results. It is shown that confinement effects on the surface lead to the formation of heterogeneous polymer layers with a marked bimodality in the number CLD. This bimodality is, however, wiped out in experimental analysis based on log-molar mass distributions. It is also shown that an increase in the size of the spherical particles and, hence, a decrease in their curvature results in a deterioration of the control over molecular properties, leading to behavior more similar to that of flat surfaces. Average molecular heights and monomer occupancies can vary with a factor of 2. The impact of the targeted chain length is shown to be of lower importance.

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Section: Modeling Principles and Developmentsupporting

confidence: 79%

Section: Modeling Principles and Developmentmentioning

confidence: 99%

Conformational Variations for Surface-Initiated Reversible Deactivation Radical Polymerization: From Flat to Curved Nanoparticle Surfaces

Hernandez¹,

Steenberge²,

Sobieski

et al. 2021

Macromolecules

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“…The update interval corresponds to the feed interval. Further, information on the Gillespie algorithm is given by Drache 26 or De Keer et al 49 The addition of molecules is associated with an increase in the control volume, which is calculated at each feeding step from the known densities as a function of temperature of all components. Furthermore, volume contraction during polymerization caused by a higher density of polymer compared to that of monomer is calculated on the basis of the increase in solid content between the last two feeding steps.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

Modeling Semi-Batch Vinyl Acetate Polymerization Processes

Feuerpfeil

Drache

Jantke³

et al. 2021

Ind. Eng. Chem. Res.

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Poly(vinyl acetate) (PVAc) is a polymer of high industrial importance. The final properties of PVAc and products thereof are strongly dependent on its microstructure, which, in turn, is determined by the specific polymerization conditions and processes used for its production. In silico modeling approaches based on kinetic Monte Carlo simulations are of high interest since they can enable the prediction of the microstructural characteristics of the resulting polymer chains, as long as the model considers the specific (and complex) polymerization and process conditions. In this study, a robust and versatile kinetic Monte Carlo model was developed, allowing for the treatment of semi-batch radical polymerizations of vinyl acetate in methanol under reflux conditions. The kinetic model comprises a full kinetic scheme for the initiation, termination, propagation, and transfer reactions. The majority of the required rate coefficients for the elementary reactions is available from the literature. With respect to the diffusion-controlled termination reaction, the composite model, which represents the chain length dependence (CLD) of k t, has been extended to account for the polymer content in the system. The robustness of the kinetic model is demonstrated by the very good agreement between the experimental and calculated molar mass distributions of PVAc obtained at different reaction times and regardless of the feeding profiles used.

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“…An often overlooked consequence of the aforementioned lumping is that the interpretation of “distinguishable” and “nondistinguishable” species becomes more blurry, which has been highlighted in recent work of De Keer et al. [ 126 ] In particular, one needs to remove the extra factor 2 in the Gillespie formula for distinguishable species A and B in case one describes an average (or lumped) termination reactivity. In the overall termination rate, already from a low thus physically realistic i max onwards (e.g., 10), the cross‐contributions reflecting termination with separate chain lengths are dominant over the homo‐contributions reflecting termination with the same chain lengths, explaining the omittance of this factor 2.…”

Section: Kinetic Monte Carlo Principles and Model Parametersmentioning

confidence: 99%

Translating Simulated Chain Length and Molar Mass Distributions in Chain‐Growth Polymerization for Experimental Comparison and Mechanistic Insight

Marien

Edeleva

Figueira

et al. 2021

Macro Theory & Simulations

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From an industrial point of view, it has often been claimed that MMDs need to possess a sufficiently large mass average molar mass M m (e.g., 10 6 g mol −1 ) to ensure sufficient entanglements and must be broad, requiring dispersity (Ð) values well above 1.5. [5,8] For specific applications, such as coatings, MMD bimodality has even been put forward as the primary target, leading to dispersity values higher than 4. [15][16][17] For the determination of the radical propagation, [18][19][20][21][22][23] backbiting, [24][25][26][27] and β-scission [24,28] rate coefficients or the quantification of photo dissociation quantum yields, [29] a modulated MMD trace is beneficial. In contrast to modulated and broad MMDs, the more recent chemical development of living and reversible deactivation radical poly merization (L/RDRP) mechanisms has made clear that more niche applications (e.g., drug delivery or high-end cosmetics) can benefit from lower M m values (e.g., 10 4 g mol −1 ) and narrow monomodal MMDs with Ð values below 1.5. [30][31][32][33][34][35][36] This dedicated molecular tailoring is also related to control over end-group functionality to enable the synthesis of more special polymers such as block, gradient, and star (co)polymers. [37][38][39][40][41] Therefore, a dedicated knowledge of the relationship between reaction conditions and MMD is indispensable for any polymerization mechanism.The key analytical tool for MMD characterization is size exclusion chromatography (SEC) or equivalently gel permeation chromatography (GPC) in which longer chains-so species with higher molar masses-elute first, as they have fewer interactions with the smaller pores in the packed columns. The chains with the highest molar masses are thus located at the lowest retention times (RTs) in the chromatogram so that the recorded chromatogram corresponds to a "reverse" MMD. This is illustrated in Figure 1a employing a refractive index (RI) detector, which is also known as single GPC detection. Ideally, calibration takes place with standards of the same polymer type that are characterized by very narrow MMDs (Ð values close to 1), as demonstrated in Figure 1b. In many research groups, one finally aims at a log-MMD representation, requiring a normalization on logarithmic scale. This is illustrated by the arrow between Figure 1c,d and leadsThe molar mass distribution (MMD), which is also known as the molecular weight distribution (MWD), is a key molecular property for a polymerization process, as it determines polymer strength and polymeric material deformation. Several MMD and related chain length distribution (CLD) representations are however used interchangeably, often leading to biased conclusions. Herein it is highlighted how the most interesting simulated CLD/MMD representations, i.e., the number, mass, z-based, and logarithmic CLD/MMD, can be translated into each other and how they need to be corrected to facilitate comparison with experimental size exclusion chromatography traces. Their relevance is highlighted by including case st...

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Benchmarking Stochastic and Deterministic Kinetic Modeling of Bulk and Solution Radical Polymerization Processes by Including Six Types of Factors Two

Cited by 34 publications

References 76 publications

Conformational Variations for Surface-Initiated Reversible Deactivation Radical Polymerization: From Flat to Curved Nanoparticle Surfaces

Conformational Variations for Surface-Initiated Reversible Deactivation Radical Polymerization: From Flat to Curved Nanoparticle Surfaces

Modeling Semi-Batch Vinyl Acetate Polymerization Processes

Translating Simulated Chain Length and Molar Mass Distributions in Chain‐Growth Polymerization for Experimental Comparison and Mechanistic Insight

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