Chain‐by‐Chain Monte Carlo Simulation: A Novel Hybrid Method for Modeling Polymerization. Part I. Linear Controlled Radical Polymerization Systems

Özçam, Derya Demirel; Teymour, Fouad

doi:10.1002/mren.201600042

Cited by 19 publications

(8 citation statements)

References 80 publications

(164 reference statements)

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“…This matrix-based solution strategy is related to the one used in previous studies on the detailed simulation of individual (linear) chains as formed during polymerization. [45][46][47][48][49][50][51] With extra matrix elements it additionally tracks the complete reaction event history of every polyolefin based macrospecies, for example, the number of H abstractions it underwent. It can be understood that this matrix needs to be sufficiently large to be kinetically representative and therefore requires a high computer memory.…”

Section: Model Developmentmentioning

confidence: 99%

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

et al. 2017

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For postpolymerization modification, a novel kinetic Monte Carlo (kMC) modeling strategy for the description of the reaction event history and the evolution of the microstructure of individual macrospecies with a complex topology is presented. The kMC model allows the kinetic analysis of free radical induced grafting of vinyl monomers onto polyethylene (PE) chains, assuming isothermal conditions and perfect macromixing and accounting for diffusional limitations on the microscale. Not only average characteristics such as the monomer conversion, grafting selectivity and yield, but also the chain length distribution (CLD) of all macromolecular species types, the average “from/to” grafting and cross‐linking density, the number of grafts and cross‐links per individual macromolecule, the chain length of every graft, and the CLD of the grafted chains are calculated. Under typical grafting conditions, depropagation and diffusional limitations cannot be ignored. The functionalization occurs mainly on those macrospecies in the PE‐CLD with a high mass concentration. © 2017 American Institute of Chemical Engineers AIChE J, 2017

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Section: Model Developmentmentioning

confidence: 99%

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

et al. 2017

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“…A downside of analytical equations remains their limited applicability for more complex polymerization schemes with several reactive macrospecies types, strong viscosity variations, and many side reactions. [ 1,70–74 ] As a consequence, a wide variety of both deterministic [ 75–85 ] and stochastic [ 86–100 ] solvers has been developed in the last 30 years to calculate MMDs and CLDs. Earlier times of less computer power resources necessitated the calculation of only CLD/MMD averages with the deterministic method of moments being most widely applied.…”

Section: Introductionmentioning

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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“…Research on ATRP kinetics using the kinetic Monte Carlo method typically falls into one of the following categories: prediction of conversion trajectories and polydispersity indices under variable reaction conditions, , determination of composition in copolymerization, , and improving algorithm speed. − Particularly exciting is the visualization of polymer chains through the use of kinetic Monte Carlo methods . Van Steenberge et al developed an advanced kinetic Monte Carlo algorithm to visually depict the placement of different monomers in linear copolymers to determine the gradient quality .…”

Section: Introductionmentioning

confidence: 99%

Radical Lifetimes in Atom Transfer Radical Polymerization: A Monte Carlo and Deterministic Investigation

Keating

Plawsky

2020

Macromolecules

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Mean radical lifetimes and fluctuations in lifetime are shown to decrease with conversion and polydispersity index for atom transfer radical polymerization (ATRP) of both methyl methacrylate and styrene. In the first study of its kind, a comprehensive investigation of radical lifetimes in both ATRP and conventional free-radical polymerizations is reported using a kinetic Monte Carlo model. Quantile−quantile plots show the radical lifetimes to be exponentially distributed with equal mean and standard deviation. Radical lifetimes are shown to be thousands of times longer in conventional free-radical polymerization compared with ATRP. Reduced mean radical lifetimes and fluctuations offer a new perspective on the ATRP mechanism. Reduction in radical lifetime fluctuations ensures less variability in the number of monomer units added during the propagation steps and keeps the polydispersity index low. Deterministic models are used along with the kinetic Monte Carlo model to investigate several facets of these polymerization systems and are validated against experimental data.

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Chain‐by‐Chain Monte Carlo Simulation: A Novel Hybrid Method for Modeling Polymerization. Part I. Linear Controlled Radical Polymerization Systems

Cited by 19 publications

References 80 publications

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

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

Radical Lifetimes in Atom Transfer Radical Polymerization: A Monte Carlo and Deterministic Investigation

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