On the incorrect use and interpretation of the model for colloidal, spherical crystal growth

Myers, T.G.; Fanelli, C.

doi:10.1016/j.jcis.2018.10.042

Cited by 10 publications

(37 citation statements)

References 20 publications

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“…Such a relationship is consistent with the diffusion-limited growth mechanism, while it is different from the result from the integration of eq . According to Myers and Fanelli, the early growth stage of CdSe nanocrystals and Pt nanocrystals exhibits an approximate-linear growth behavior. Figure b presents an enlarged view of Figure a around τ = 0.…”

Section: Resultsmentioning

confidence: 99%

“…Using the correlation between chemical potential and the monomer concentration, the growth rate of the nanocrystal size for diffusion-limited growth can be expressed as with δ as the distance between the nanocrystal surface and the bulk solution, and c b and c n as the concentrations of the monomers in the solution and those on the nanocrystal surface, respectively. As pointed out by Myers and Fanelli, the numerical value of δ can be infinite mathematically. In fact, the numerical value of δ can be a function of the growth time, depending on the rate processes controlling the growth of nanocrystals/precipitates.…”

Section: Discussionmentioning

confidence: 99%

“…Jung et al and Varghese and Rao in their analysis seemed to comment that the balance between the diffusion-limited growth and the reaction-limited growth ,,, determined the growth of the Au nanoparticles and Pt nanocrystals in respective conditions. However, one cannot obtain a constant growth rate for either δ ≫ a or δ ≪ a from eqs and .…”

Section: Discussionmentioning

confidence: 99%

“…The general formula of the mixed boundary condition on the surface of the spherical nanocrystal can be expressed as with k as a rate constant. Myers and Fanelli included a diffusion boundary layer in their work and used the thickness of the boundary layer in the calculation of the first term of eq for a spherical particle. Such a method allows for the use of the bulk concentration of monomers in eq , while the thickness of the boundary layer is undetermined.…”

Section: Mathematical Formulationmentioning

confidence: 99%

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Diffusion-Limited Growth of a Spherical Nanocrystal in a Finite Space

Yang

2021

Langmuir

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Reason for the work: The potential applications of nanoscale materials in nanophotonics, nanoelectronics, bioimaging, and biosensing have stimulated the research in the synthesis of nanocrystals, nanowires, and so forth. There is a great need to understand the spatiotemporal evolution of nanocrystals in the solution-route synthesis in order to better design advanced synthesis techniques for the manufacturing of monodisperse nanocrystals of high quality. Most significant results: We analyze the size effect on the diffusion-limited growth of a spherical nanoparticle in a finite space (spherical cavity) on the basis of the Gibbs−Thomson relation and obtain an analytical formulation of the monomer concentration in the finite space in an implicit form and an integro-differential equation for the growth rate of the spherical nanoparticle. The monomer concentration in the finite space decreases slower than that with a stationary nanoparticle. The growth of the spherical nanoparticle consists of two stages−an initially linear growth stage and a later power-law stage. The result from the infinite space with a stationary nanoparticle is inapplicable to the analysis of the growth of spherical nanoparticles in a finite space. Conclusions: There exists a size effect on the growth of nanocrystals in a finite space. The dependence of the growth behavior of nanocrystals on the growth time and temperature needs to be investigated in order to experimentally determine the fundamental mechanisms controlling the growth of nanocrystals in the solution-route synthesis.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

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Diffusion-Limited Growth of a Spherical Nanocrystal in a Finite Space

Yang

2021

Langmuir

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“…One approximation to the OFC is to assume that the exponential term in (1) can be linearised to give the two term expression s * ≈ s * ∞ (1 + α/r * p ) [13,14,28,35]. Obviously this expansion, which is based on α/r * p , is invalid for nanoparticles where capillary length is of the same order of magnitude as the particle radius [19]. Mantzaris [16] used an expansion for the exponential term in the OFC with n terms and showed that increasing n led to higher average growth rates and a narrowing of the PSD.…”

Section: Introductionmentioning

confidence: 99%

Nanocrystal growth via the precipitation method

Fanelli,

Cregan,

Font

et al. 2019

Preprint

Self Cite

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A mathematical model to describe the growth of an arbitrarily large number of nanocrystals from solution is presented. First, the model for a single particle is developed. By non-dimensionalising the system we are able to determine the dominant terms and reduce it to the standard pseudo-steady approximation. The range of applicability and further reductions are discussed. An approximate analytical solution is also presented. The one particle model is then generalised to N well dispersed particles. By setting N = 2 we are able to investigate in detail the process of Ostwald ripening. The various models, the N particle, single particle and the analytical solution are compared against experimental data, all showing excellent agreement. By allowing N to increase we show that the single particle model may be considered as representing the average radius of a system with a large number of particles. Following a similar argument the N = 2 model could describe an initially bimodal distribution. The mathematical solution clearly shows the effect of problem parameters on the growth process and, significantly, that there is a single controlling group. The model provides a simple way to understand nanocrystal growth and hence to guide and optimise the process.

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