General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Szabó, Rebeka; Lente, Gábor

doi:10.1007/s10910-021-01265-z

Cited by 8 publications

(5 citation statements)

References 38 publications

(85 reference statements)

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“…The approaches to solve the set of the ordinary differential equations of the form () have been considered in several publications (see refs and and references therein). In particular, ref proposes the semianalytical recurrent method for obtaining the time dependence of B n .…”

Section: Formulation Of the Problem And Methods Of Its Solutionmentioning

confidence: 99%

Heterogeneous Model for Precursor-Mediated Nanoparticle Growth in Polymer Film

Bityurin,

Sapogova,

Pikulin

2023

J. Phys. Chem. C

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The inorganic nanoparticle growth within a polymer matrix is due to generation of the elementary species, the monomers, because of decomposition of the precursor compounds. The nucleation of the nanoparticles can be either homogeneous or heterogeneous. The model for heterogeneous nucleation and growth considered in this paper with some natural assumptions can explain experimentally observed exposure dependence of the UV-initiated CdS nanoparticle growth in poly(methyl methacrylate) (PMMA). The constraints on the values of the parameters imposed by the assumptions are discussed. Analytical solutions for the dynamics of the particle size distributions are obtained by reduction of the set of ordinary differential equations to the partial differential equation. The dependences of the particle size distributions on the parameters involved are found. This allows modeling the evolution of the optical absorption spectrum of the nanocomposite material due to nanoparticle growth.

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Section: Formulation Of the Problem And Methods Of Its Solutionmentioning

confidence: 99%

Heterogeneous Model for Precursor-Mediated Nanoparticle Growth in Polymer Film

Bityurin,

Sapogova,

Pikulin

2023

J. Phys. Chem. C

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“…After calcination at 740 °C for 10 s, the characteristic diffraction peak of Na2SO4 nearly disappeared, indicating that the reduction reaction of Na2SO4 was nearly complete at this point. Two commonly used gas-solid reduction reaction models were employed in the parameter fitting to reveal the reduction mechanism [16][17][18][19][20][21]. The change in the conversion rate with the time at different reduction temperatures was analyzed using the interface chemical reaction and nucleation-growth models; the fitting parameters are presented in Table 4.…”

Section: Characteristics Of the H 2 Reduction Of Na 2 So 4 In A Mixed...mentioning

confidence: 99%

“…The fitting results indicate that both models adequately described the Na2SO4 reduction. The interfacial chemical reaction model was used for the subsequen fitting, which was calculated as: Two commonly used gas-solid reduction reaction models were employed in the parameter fitting to reveal the reduction mechanism [16][17][18][19][20][21]. The change in the conversion rate with the time at different reduction temperatures was analyzed using the interface chemical reaction and nucleation-growth models; the fitting parameters are presented in Table 4.…”

Section: Characteristics Of the H 2 Reduction Of Na 2 So 4 In A Mixed...mentioning

confidence: 99%

H2 Reduction of Na2SO4 to Na2S Based on Dilute-Phase Fluidization

He,

Chen,

Zhao

et al. 2024

Processes

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Sodium sulfate (Na2SO4) is used in the ecofriendly production of sodium sulfide (Na2S) through H2 reduction, thereby facilitating the valorization of Na2SO4. However, studies on this technique remain at the laboratory stage. This paper proposes a novel process involving the external circulation of Na2S in a dilute-phase fluidized system to address the low-temperature eutectic formation between Na2S and Na2SO4 during the H2 reduction of Na2SO4 to Na2S. The process aims to increase the reaction temperature of the Na2SO4 while reducing the volume of the liquid phase formed to prevent sintering blockages and enhance the reduction rate. In a proprietary experimental setup, the H2 reduction process in a dilute-phase fluidized system was investigated. The Na2S/Na2SO4 ratio and reaction temperature were determined to be critical factors influencing the Na2SO4 reduction rate. The melting point of the system increased and the amount of liquid phase produced decreased as the Na2S content was increased to more than 60%. The Na2S–Na2SO4 mixture (mass ratio of 80:20) existed as a solid at the reaction temperature of 740 °C. After roasting for 10 s, the Na2SO4 reduction rate reached 93.7% and the Na2S content in the mixture increased to 98.74%.

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“…Beyond these classical models, there are several other approaches in the literature, most of them take into account the thermodynamic properties, as well, which are not spelled out here. Some of the latest results have derived some general explicit and approximated solutions for the final average sizes of a generalized model [23][24][25][26] , which is presented here, however from a different perspective.…”

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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General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Cited by 8 publications

References 38 publications

Heterogeneous Model for Precursor-Mediated Nanoparticle Growth in Polymer Film

Heterogeneous Model for Precursor-Mediated Nanoparticle Growth in Polymer Film

H2 Reduction of Na2SO4 to Na2S Based on Dilute-Phase Fluidization

Final nanoparticle size distribution under unusual parameter regimes

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