Deterministic approximation for the nucleation-growth type model of nanoparticle formation: A validation against stochastic simulations

Szabó, Rebeka; Lente, Gábor

doi:10.1016/j.cej.2022.137377

Cited by 6 publications

(5 citation statements)

References 37 publications

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“…The growth of nanomaterials is the nucleation‐growth mechanisms, mainly including the heterogeneous nucleation‐growth (LaMer growth) and the Ostwald ripening growth (ripening growth) 39,40 . However, inert CFs with a smooth surface may be inappropriate for the in‐situ growth of the LDHs crystals in this work.…”

Section: Resultsmentioning

confidence: 98%

Constructing a honeycomb‐inspired Ni‐Co LDHs@CFs enhanced polymer composites with high strength, aging resistance and excellent anti‐wear for tribological applications

Zhu

Zhang

Fei

et al. 2023

J of Applied Polymer Sci

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The development of carbon fibers/polymer composites (CFPCs) has made a profound impact on varied application prospects in the transmission and braking fields, where interface engineering between fibers/matrix holds the key to co‐enhanced mechanical and tribological properties. Herein, we designed a honeycomb‐inspired Ni‐Co layered double hydroxides (Ni‐Co LDHs) modified CFPCs, in which Ni‐Co LDHs interconnected nanosheets were grown in‐situ onto the carbon fibers (CFs) surface via the oxidation‐assisted hydrothermal method, and then polymer matrix fully impregnate and filled with both the CFs and LDHs porous containers by capillary forces. Benefiting from the special interface, the Ni‐Co LDHs grafted CFs reinforced polymer composites (Ni‐Co LDHs@CFs composites) possessed the excellent mechanical strength and outstanding tribological properties. The LDHs@CFs composites had 32% improvement in the tensile strength, and 84.9% strength retention ratio after the hydrothermal aging process. Furthermore, the friction coefficient was increased by 24% and wear rate was dramatically decreased by 42% from 6.148 × 10−14 to 3.557 × 10−14 m3 (N m)−1, indicating better torque transmitting capacity and anti‐wear properties. This work could provide a valuable reference for the construction of biomimetic interface to simultaneously improve the mechanical and tribological properties of the CFPCs.

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Section: Resultsmentioning

confidence: 98%

Constructing a honeycomb‐inspired Ni‐Co LDHs@CFs enhanced polymer composites with high strength, aging resistance and excellent anti‐wear for tribological applications

Zhu

Zhang

Fei

et al. 2023

J of Applied Polymer Sci

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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 . In what follows, we develop another approximate technique to obtain the nanoparticle size distribution.…”

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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“…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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Deterministic approximation for the nucleation-growth type model of nanoparticle formation: A validation against stochastic simulations

Cited by 6 publications

References 37 publications

Constructing a honeycomb‐inspired Ni‐Co LDHs@CFs enhanced polymer composites with high strength, aging resistance and excellent anti‐wear for tribological applications

Constructing a honeycomb‐inspired Ni‐Co LDHs@CFs enhanced polymer composites with high strength, aging resistance and excellent anti‐wear for tribological applications

Heterogeneous Model for Precursor-Mediated Nanoparticle Growth in Polymer Film

Final nanoparticle size distribution under unusual parameter regimes

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