Stochastic modeling techniques have
emerged as a powerful tool
to study the time evolution of processes in many research fields including
(bio)chemical engineering and biology. One of the most applied techniques
is kinetic Monte Carlo (kMC) modeling according to the stochastic
simulation algorithm (SSA) as pioneered by Gillespie, in which MC
channels and time steps are discretely sampled from probability distributions.
In the last decades, the SSA algorithm, as originally developed for
systems with elemental species (e.g., A, B, C, etc.), has been further
adapted (i) to also tackle systems with distributed species, therefore,
populations and (ii) to enable faster algorithm execution. In the
present contribution, we highlight the most important developments,
taking bulk/solution polymerization as the reference distributed chemical
process. We address SSA principles based on conventional array data
structures, common acceleration methods (e.g., τ leaping and
the scaling method), and the strength of tree- and matrix-based data
structures for detailed storage of molecular information per distribution
type and even individual population member. In addition, we report
advancement regarding array programming and MC sampling methods complemented
by the introduction of the use of higher-order trees and root-finding
sampling tools. The contribution gives thus a detailed overview of
the available main kMC algorithm steps to study kinetics, irrespective
of the specific field of application due to their generic nature.
Chemical or feedstock recycling of poly(methyl methacrylate) (PMMA) by thermal degradation is an important societal challenge to enable polymer circularity. The annual PMMA world production capacity is over 2.4 × 106 tons, but currently only 3.0 × 104 tons are collected and recycled in Europe each year. Despite the rather simple chemical structure of MMA, a debate still exists on the possible PMMA degradation mechanisms and only basic batch and continuous reactor technologies have been developed, without significant knowledge of the decomposition chemistry or the multiphase nature of the reaction mixture. It is demonstrated in this review that it is essential to link PMMA thermochemical recycling with the PMMA synthesis as certain structural defects from the synthesis step are affecting the nature and relevance of the subsequent degradation reaction mechanisms. Here, random fission plays a key role, specifically for PMMA made by anionic polymerization. It is further highlighted that kinetic modeling tools are useful to further unravel the dominant PMMA degradation mechanisms. A novel distinction is made between global conversion or average chain length models, on the one hand, and elementary reaction step-based models on the other hand. It is put forward that only by the dedicated development of the latter models, the temporal evolution of degradation product spectra under specific chemical recycling conditions will become possible, making reactor design no longer an art but a science.
The time evolution of (bio)chemical processes, specifically
those
involving distributed species as in polymer synthesis and recycling,
can be obtained using Gillespie-based kinetic Monte Carlo simulations,
provided that a sufficiently high (Monte Carlo) control volume is
utilized with respect to the simulation targets (e.g., focus on only
conversion/yield or a combination of the former and average molar
masses, or even the combination with complete distributions with accurate
tail prediction). For more detailed kinetics and more demanding simulations
targets, currently, simulation results are mostly visually checked
to decide which control volume to practically use, taking into account
user time constraints. The present work puts forward a convergence
strategy that avoids relying on subjective visual analysis to set
the minimum control value that guarantees the minimization of the
stochastic noise for several simulation target combinations to acceptable
values. The strategy is illustrated for two (for simplicity, intrinsic)
non-dispersed phase bulk chain-growth polymerization processes, one
with high average chain lengths and a broad chain length distribution
(CLD), that is, free-radical polymerization (FRP), and one with low
average chain lengths and a narrow CLD, that is, nitroxide-mediated
polymerization (NMP). It is showcased that the monomer conversion
profile converges the fastest, with even the occurrence of noise-free
simulation results in the absence of numerical convergence. A sufficiently
accurate representation of the tail of the (number) CLD in FRP demands
a sufficiently high control volume so that relative errors below 0.5%
result for the z-based average chain length or molar
mass (M
z). This need to inspect M
z convergence further holds under NMP, in general,
reversible deactivation radical polymerization (RDRP) conditions,
in which it is uncommon to report such higher order averages. An automated
convergence check beyond threshold values is recommended to minimize
the impact of possible fluctuations in certain simulation targets,
specifically peak representations, for example, the initial spike
in the dispersity plot in RDRP. The convergence results are supported
by the number of radicals in the control volume with values much higher
than 2 to accurately represent termination kinetics for specifically
CLD prediction, already under intrinsic conditions.
The relevance of kinetic Monte Carlo (kMC) algorithms and modeling to obtain and tune detailed molecular information for (bio)chemical kinetic systems is growing. A bottleneck remains however the correct representation...
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