Limits...
Including nonequilibrium interface kinetics in a continuum model for melting nanoscaled particles.

Back JM, McCue SW, Moroney TJ - Sci Rep (2014)

Bottom Line: As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time.The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles.This small-particle regime appears to be closely related to the problem of melting a superheated particle.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia.

ABSTRACT
The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases. This relationship is most often modelled by a Gibbs-Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension. Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes. Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius. By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs-Thomson law regularises the continuum model, so that the mathematical blow up is suppressed. As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time. The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles. This small-particle regime appears to be closely related to the problem of melting a superheated particle.

No MeSH data available.


Related in: MedlinePlus

The size dependent nature of the melting temperature of gold nanoparticles demonstrated by experiment data (○) from Dick et al.2.The measurements are in good agreement with the Gibbs–Thomson relation equations (1)–(3), plotted here (dashed) with the thermodynamic constants for gold24.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4233348&req=5

f1: The size dependent nature of the melting temperature of gold nanoparticles demonstrated by experiment data (○) from Dick et al.2.The measurements are in good agreement with the Gibbs–Thomson relation equations (1)–(3), plotted here (dashed) with the thermodynamic constants for gold24.

Mentions: The constant σ* in equation (2) is a measure of the surface energy effects, also referred to as surface tension. One long-standing model for σ* is where and are the surface energies of the particle in the solid and liquid states, respectively1415. The Gibbs–Thomson relation (1)–(3) has been shown to be consistent with the experimental data for a variety of metals12416. To take one example, in Fig. 1 we show a comparison of this model against melting temperatures of gold particles, measured by Dick et al.2. Note that gold particles with a radius of 10 nm have a melting temperature of approximately 1250 K, which is noticeably lower than the bulk melting temperature ( for gold). For smaller particles we see the agreement in Fig. 1 is still quite good, even down to a radius of less than 1 nm.


Including nonequilibrium interface kinetics in a continuum model for melting nanoscaled particles.

Back JM, McCue SW, Moroney TJ - Sci Rep (2014)

The size dependent nature of the melting temperature of gold nanoparticles demonstrated by experiment data (○) from Dick et al.2.The measurements are in good agreement with the Gibbs–Thomson relation equations (1)–(3), plotted here (dashed) with the thermodynamic constants for gold24.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4233348&req=5

f1: The size dependent nature of the melting temperature of gold nanoparticles demonstrated by experiment data (○) from Dick et al.2.The measurements are in good agreement with the Gibbs–Thomson relation equations (1)–(3), plotted here (dashed) with the thermodynamic constants for gold24.
Mentions: The constant σ* in equation (2) is a measure of the surface energy effects, also referred to as surface tension. One long-standing model for σ* is where and are the surface energies of the particle in the solid and liquid states, respectively1415. The Gibbs–Thomson relation (1)–(3) has been shown to be consistent with the experimental data for a variety of metals12416. To take one example, in Fig. 1 we show a comparison of this model against melting temperatures of gold particles, measured by Dick et al.2. Note that gold particles with a radius of 10 nm have a melting temperature of approximately 1250 K, which is noticeably lower than the bulk melting temperature ( for gold). For smaller particles we see the agreement in Fig. 1 is still quite good, even down to a radius of less than 1 nm.

Bottom Line: As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time.The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles.This small-particle regime appears to be closely related to the problem of melting a superheated particle.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia.

ABSTRACT
The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases. This relationship is most often modelled by a Gibbs-Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension. Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes. Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius. By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs-Thomson law regularises the continuum model, so that the mathematical blow up is suppressed. As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time. The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles. This small-particle regime appears to be closely related to the problem of melting a superheated particle.

No MeSH data available.


Related in: MedlinePlus