A mathematical model for nanoparticle melting with density change

Font, Francesc; Myers, T.G.; Mitchell, Sarah

doi:10.1007/s10404-014-1423-x

Cited by 43 publications

(89 citation statements)

References 22 publications

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“…Curves on the right represent the liquid temperature, which decrease from T ¼ 1 at R ¼ 1 to T m at r ¼ R. To the left of the intersection with T m ; they are the curves for the solid temperature. The curves clearly have a similar form to those presented in Font and Myers (2013) and Font et al (2014) for nanosphere melting. As the melting front proceeds inwards, the phase change temperature is depressed further and the temperature difference, T H À T m , increases.…”

Section: Resultssupporting

confidence: 65%

“…The accuracy of this approach has been demonstrated in studies on nanosphere phase change by comparison with the numerical solution of the full problem (Font and Myers 2013;Font et al 2014). The temperatures are expressed in terms of series…”

Section: Solution Methodsmentioning

confidence: 99%

“…For this reason, only a small DT is required to completely melt the particle. Consequently, nanoparticle melting typically involves a large Stefan number (Font and Myers 2013;Font et al 2014). For gold, with DT ¼ 10, we find b % 40.…”

Section: Non-dimensional Modelmentioning

confidence: 99%

“…For this, we require a theoretical model. There have been a number of studies on the melting behaviour of nanospheres, such as (Font and Myers 2013;Font et al 2014;McCue et al 2009;Wu et al 2009a, b). All of these works use some form of Gibbs-Thomson relation to describe the melting point depression.…”

Section: Introductionmentioning

confidence: 99%

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The melting and solidification of nanowires

Florio

Myers

2016

J Nanopart Res

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A mathematical model is developed to describe the melting of nanowires. The first section of the paper deals with a standard theoretical situation, where the wire melts due to a fixed boundary temperature. This analysis allows us to compare with existing results for the phase change of nanospheres. The equivalent solidification problem is also examined. This shows that solidification is a faster process than melting; this is because the energy transfer occurs primarily through the solid rather than the liquid which is a poorer conductor of heat. This effect competes with the energy required to create new solid surface which acts to slow down the process, but overall conduction dominates. In the second section, we consider a more physically realistic boundary condition, where the phase change occurs due to a heat flux from surrounding material. This removes the singularity in initial melt velocity predicted in previous models of nanoparticle melting. It is shown that even with the highest possible flux the melting time is significantly slower than with a fixed boundary temperature condition.

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Section: Resultssupporting

confidence: 65%

Section: Solution Methodsmentioning

confidence: 99%

Section: Non-dimensional Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The melting and solidification of nanowires

Florio

Myers

2016

J Nanopart Res

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“…Theoretical, computational, and experimental studies have been performed to elucidate the melting mechanism as well as the exact dependency of the melting temperature on the particle diameter. The reported melting temperature of free‐standing metal nanoparticles is almost always linearly dependent on the inverse particle diameter ( T m ∼ d −1 ), see, e.g., the review by Nanda or the perspective by Li and Truhlar .…”

Section: Introductionmentioning

confidence: 99%

Size‐Dependence of the Melting Temperature of Individual Au Nanoparticles

Schlexer

Andersen

Sebők

et al. 2019

Part & Part Syst Charact

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Nanoparticles have an immense importance in various fields, such as medicine, catalysis, and various technological applications. Nanoparticles exhibit a significant depression in melting point as their size goes below ≈10 nm. However, nanoparticles are frequently used in high temperature applications such as catalysis where temperatures often exceed several 100 degrees which makes it interesting to study not only the melting temperature depression, but also how the melting progresses through the particle. Using high‐resolution transmission electron microscopy, the melting process of gold nanoparticles in the size range of 2–20 nm Au nanoparticles combined with molecular dynamics studies is investigated. A linear dependence of the melting temperature on the inverse particle size is confirmed; electron microscopy imaging reveals that the particles start melting at the surface and the liquid shell formed then rapidly expands to the particle core.

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On the approximation of the modified error function

Bougouffa

Khanfer

Bougoffa

2022

Math Methods in App Sciences

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In a recent research, the authors established an approximation to the modified error function (MEF) 𝜑 𝛿 for a small positive thermal conductivity coefficient 𝛿 > 0, leaving the problem open for the general case −1 < 𝛿 < ∞. The approximation represents an approximate solution to the Stephan problem with linear thermal conductivity in a semi-infinite body, which converges to the classical MEF as 𝛿 → 0 + . In this paper, a new approximation to the MEF is found for −1 < 𝛿 < ∞ and converges to the classical MEF as 𝛿 → 0 ± . A comparative analysis shows that our proposed approximation gives a better estimate than the one in this recent reasearch by Ceratani et al.

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A mathematical model for nanoparticle melting with density change

Cited by 43 publications

References 22 publications

The melting and solidification of nanowires

The melting and solidification of nanowires

Size‐Dependence of the Melting Temperature of Individual Au Nanoparticles

On the approximation of the modified error function

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