The Lifshitz–Slyozov–Wagner equation for reaction-controlled kinetics

Damialis, Apostolos

doi:10.1017/s0308210508000656

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…A stochastic analog of the Becker-Döring model has been investigated 13 and it has been shown that it converges to the deterministic counterpart when the initial magnitude of the monomer units grows large. A further coarsening step can be applied to the deterministic Becker-Döring equation to show their convergence to the Lifshitz-Slyozov model based on a transport partial differential equations 14,15 when the space of the particle sizes id scaled to the continuous. This approach is based on a socalled classical scaling where in the first place only nucleation occurs, and only after a large portion of the monomers has been spent in nucleations, the growths start to take place.…”

Section: Introductionmentioning

confidence: 99%

Final nanoparticle size distribution under unusual parameter regimes

Sabbioni,

Szabó,

Siri

et al. 2024

Preprint

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We explore the large-scale behaviour of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where n monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded. We delve into a previously unexplored parameter regime. Specifically, we consider a scenario where the growth rate of the first newly formed particle is of the same order of magnitude as the nucleation rate, in contrast to the classical scenario where in the initial stage nucleation dominates over growth. In this regime, we investigate the final size distribution as the initial number of monomers tends to infinity through extensive simulation studies utilizing state-of-the-art stochastic simulation methods with an efficient implementation and supported by high-performance computing infrastructure. We observe the emergence of a deterministic limit for the particle's final size density. To scale up the initial number of monomers to approximate the magnitudes encountered in real experiments, we introduce a novel approximation process aimed at faster simulation. Remarkably, this approximating process yields a final size distribution that becomes very close to that of the original process when the available monomers approach infinity. Simulations of the approximating process further support the evidence for the emergence of a deterministic limit.

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Section: Introductionmentioning

confidence: 99%

Final nanoparticle size distribution under unusual parameter regimes

Sabbioni,

Szabó,

Siri

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Its most common formulation is in terms of an infinite system of ordinary differential equations [17][18][19] . By employing a coarsening step, the discrete space of the particle sizes can be mapped to a continuous limit domain, and consequently the deterministic Becker-Döring model converges to a transport partial differential equation named after Lifshitz-Slyozov 20,21 .…”

Section: Introductionmentioning

confidence: 99%

Final nanoparticle size distribution under unusual parameter regimes

Sabbioni,

Szabó,

Siri

et al. 2024

Preprint

View full text Add to dashboard Cite

We explore the large-scale behavior of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where $n$ monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded. We delve into a previously unexplored parameter regime. Specifically, we consider a scenario where the growth rate of the first newly formed particle is of the same order of magnitude as the nucleation rate, in contrast to the classical scenario where in the initial stage nucleation dominates over growth. In this regime, we investigate the final size distribution as the initial number of monomers tends to infinity through extensive simulation studies utilizing state-of-the-art stochastic simulation methods with an efficient implementation and supported by high-performance computing infrastructure. We observe the emergence of a deterministic limit for the particle's final size density. To scale up the initial number of monomers to approximate the magnitudes encountered in real experiments, we introduce a novel approximation process aimed at faster simulation. Remarkably, this approximating process yields a final size distribution that becomes very close to that of the original process when the available monomers approach infinity. Simulations of the approximating process further support the conjecture of the emergence of a deterministic limit.

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