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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 radius of the particle R(t) versus time t for the same parameter values as in Fig. 2.The (green) solid line is for the case , while the (black) dashed line is . For the  case, we have that the speed of the boundary blows up at Rc = 1.32, corresponding to tc = 400.98. The solution with a nonzero kinetic term  follows that for  very closely, except for times near the blow-up (inset). Here, the solution deviates away from the  case, so that the moving boundary propagates inwards past the critical radius and through the blow-up regime. The speed of the boundary increases dramatically until the boundary reaches the centre, and complete melting is achieved.
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f3: The radius of the particle R(t) versus time t for the same parameter values as in Fig. 2.The (green) solid line is for the case , while the (black) dashed line is . For the case, we have that the speed of the boundary blows up at Rc = 1.32, corresponding to tc = 400.98. The solution with a nonzero kinetic term follows that for very closely, except for times near the blow-up (inset). Here, the solution deviates away from the case, so that the moving boundary propagates inwards past the critical radius and through the blow-up regime. The speed of the boundary increases dramatically until the boundary reaches the centre, and complete melting is achieved.

Mentions: The dimensionless problem (9)–(15) is solved computationally using the numerical scheme detailed in the methods section. To illustrate our numerical results, we have chosen to use the (dimensionless) parameter values β = 0.30, k = 0.46 and c = 1.16, which corresponds to melting a pure lead nanoparticle. Temperature profiles are shown in Fig. 2, while the dependence of the solid-melt interface on time is illustrated in Fig. 3.


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

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

The radius of the particle R(t) versus time t for the same parameter values as in Fig. 2.The (green) solid line is for the case , while the (black) dashed line is . For the  case, we have that the speed of the boundary blows up at Rc = 1.32, corresponding to tc = 400.98. The solution with a nonzero kinetic term  follows that for  very closely, except for times near the blow-up (inset). Here, the solution deviates away from the  case, so that the moving boundary propagates inwards past the critical radius and through the blow-up regime. The speed of the boundary increases dramatically until the boundary reaches the centre, and complete melting is achieved.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: The radius of the particle R(t) versus time t for the same parameter values as in Fig. 2.The (green) solid line is for the case , while the (black) dashed line is . For the case, we have that the speed of the boundary blows up at Rc = 1.32, corresponding to tc = 400.98. The solution with a nonzero kinetic term follows that for very closely, except for times near the blow-up (inset). Here, the solution deviates away from the case, so that the moving boundary propagates inwards past the critical radius and through the blow-up regime. The speed of the boundary increases dramatically until the boundary reaches the centre, and complete melting is achieved.
Mentions: The dimensionless problem (9)–(15) is solved computationally using the numerical scheme detailed in the methods section. To illustrate our numerical results, we have chosen to use the (dimensionless) parameter values β = 0.30, k = 0.46 and c = 1.16, which corresponds to melting a pure lead nanoparticle. Temperature profiles are shown in Fig. 2, while the dependence of the solid-melt interface on time is illustrated in Fig. 3.

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