Thermodynamics of melting and freezing in small particles

Vanfleet, Richard; Mochel, J. M.

doi:10.1016/0039-6028(95)00728-8

Cited by 161 publications

(100 citation statements)

References 15 publications

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“…2,3 The drop-off rate will be mediated, though, by any change in the contact angle and deviation of the ratio ␥ / ⌬ fus H from its bulk value. In contrast, for a constant c Ͻ 90°, we expect the far rarer case of an increase in onset crystallization temperatures for sufficiently small confinement volumes, as has been observed for CCl 4 freezing in microporous activated carbon fibers. 54 Please note that Eq.…”

Section: ͪͮ ͑18͒mentioning

confidence: 74%

“…Our model is undoubtedly simplistic and could be improved by, among others, considering the effects of equilibrium fluctuations, 8 which become increasingly important as the confinement size decreases, incorporating dynamical nucleation theory 29,30 and the effects of surface stress, 22,60 adding an exponential term to account for short-range interactions between the nucleus and interface, [4][5][6]61 including a finite length interfacial region, and removing the assumptions that the phases are incompressible and the molecular volumes of the parent and daughter phases are the same. 27 However, the inclusion of these effects will inevitably prevent a simple analytical formulation for the onset crystallization temperature.…”

Section: Discussionmentioning

confidence: 99%

“…Here we are just extending this idea by also identifying the same criterion with the maximum possible freezing temperature of a confined object. 4,53 The value of R min is easily found from the condition that ⌬F = 0 on complete crystallization. It is given by…”

Section: A Crystallization From the Melt And Meltingmentioning

confidence: 99%

“…Despite these advances, the effect of confinement on the nucleation barrier has been much less studied. [4][5][6] We will show in this paper that consideration of this allows reliable critical nucleus sizes to be determined from nonisothermal crystallization experiments.…”

Section: Introductionmentioning

confidence: 99%

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A simple classical model for predicting onset crystallization temperatures on curved substrates and its implications for phase transitions in confined volumes

Cooper

Nicholson

Liu

2008

The Journal of Chemical Physics

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. For small confinement volumes, phase transition temperatures are determined by the scarcity of the crystallizing material, rather than the magnitude of the energy barrier, as the supply of molecules undergoing the phase transition can be depleted before a stable nucleus is attained. We show this for the case of crystallization from the melt and from the solution by using a simple model based on an extended classical nucleation theory. This has important implications because it enables a simple and direct measurement of the critical nucleus size in crystallization. It also highlights that predicting the observable melting points of nanoparticles by using the Gibbs-Thomson equation can lead to substantial errors.

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Section: ͪͮ ͑18͒mentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Section: A Crystallization From the Melt And Meltingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A simple classical model for predicting onset crystallization temperatures on curved substrates and its implications for phase transitions in confined volumes

Cooper

Nicholson

Liu

2008

The Journal of Chemical Physics

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“…The liquid nucleation and growth model suggests that melting starts by the nucleation of a liquid layer at the surface and moves into the solid as a slow process with a definite activation energy [37,38],…”

Section: Theoretical Models For T M (D) Functionsmentioning

confidence: 99%

Size Dependence of Structures and Properties of Magnetic Materials

Jiang¹,

Lang²

2007

TONANOJ

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Due to the involvement of high portion of atomic coordination imperfection in surfaces and interfaces, the properties of magnetic nanocrystals dramatically differ from that of the corresponding bulk counterparts, which have led to a surge in both experimental and theoretical investigations in the past decades. This review summarizes the studies for these size-dependent magnetic properties, and additional thermal or phase stabilities, and mechanical properties. To interpret the above phenomena, a thermodynamic model for the size dependence and interface dependences of these properties is described, which is based on Lindemann s criterion for melting, Mott s expression for the vibrational melting entropy, and Shi s model for the size-dependent melting temperature. The model without any adjustable parameter is confirmed by a large number of experimental results, and helps us to understand the structures and properties of the magnetic nanocrystals. Moreover, other theoretical works on the above properties are also mentioned and commented.

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Theory of Size, Confinement, and Oxidation Effects

Sun

2006

Synthesis, Properties, and Applications of Oxide Nanomaterials

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Thermodynamics of melting and freezing in small particles

Cited by 161 publications

References 15 publications

A simple classical model for predicting onset crystallization temperatures on curved substrates and its implications for phase transitions in confined volumes

A simple classical model for predicting onset crystallization temperatures on curved substrates and its implications for phase transitions in confined volumes

Size Dependence of Structures and Properties of Magnetic Materials

Theory of Size, Confinement, and Oxidation Effects

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