Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics

Bottomley, D. J.; Makkonen, Lasse; Kolari, Kari

doi:10.1016/j.susc.2008.10.023

Cited by 42 publications

(8 citation statements)

References 22 publications

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“…Surface energy and tension were related by Shuttleworth, who provided the relation σ = γ + A ( ∂ γ ∂ A ) The understanding of Shuttleworth’s equation () is a subject of considerable controversy. Many authors, see for example refs − , have argued against its validity. A discussion and summary of this point of view can be found in reviews by Marichev. , Others have reaffirmed its status as a fundamental relation. , We will return to a discussion of Shuttleworth’s equation later in this paper.…”

Section: Introductionmentioning

confidence: 99%

Surface Tension, Surface Energy, and Chemical Potential Due to Their Difference

Hui

Jagota

2013

Langmuir

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It is well-known that surface tension and surface energy are distinct quantities for solids. Each can be regarded as a thermodynamic property related first by Shuttleworth. Mullins and others have suggested that the difference between surface tension and surface energy cannot be sustained and that the two will approach each other over time. In this work we show that in a single-component system where changes in elastic energy can be neglected, the chemical potential difference between the surface and bulk is proportional to the difference between surface tension and surface energy. By further assuming that mass transfer is driven by this chemical potential difference, we establish a model for the kinetics by which mass transfer removes the difference between surface tension and surface energy.

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Section: Introductionmentioning

confidence: 99%

Surface Tension, Surface Energy, and Chemical Potential Due to Their Difference

Hui

Jagota

2013

Langmuir

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“…( 42)). Arguments based on Hermann's theory were used to criticise [3,63] the Shuttleworth equation and its consequences in different works [51,68,81], with much subsequent debate about the meaning and validity of this equation [4-8, 27-30, 40, 41, 45, 52]. However, in our view, there is no discrepancy between the equations derived here and Hermann's theory.…”

Section: Relationship Between Ss and Sfementioning

confidence: 75%

“…Being symmetrical, this tensor can be diagonalized, with the principal strain components denoted u (1) , u (2) , u (3) . Each component represents the relative extension (dx i − dx i )/dx i along the principal axis i.…”

Section: A Zero Temperaturementioning

confidence: 99%

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A unified description of Surface Free Energy and Surface Stress

Di Pasquale,

Davidchack

2019

Preprint

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Even though the study of interfacial phenomena dates back to Laplace and was formalised by Gibbs for liquid-liquid interfaces, it appears that some concepts and relations among them are still causing some confusion and debates in the literature. Moreover, ever since the Molecular Dynamics (MD) simulations have started to be widely used in the study of surface properties, these debates only intensified. In this work, we present a systematic description of the interfacial properties from the thermodynamic and statistical mechanics points of view. In particular, we link our derivations to MD simulations, describing precisely what different quantities represent and how they can be calculated.We do not follow the usual way that consists of describing the thermodynamics of the surfaces in general and then considering specific cases (e.g. liquid-liquid interface, liquid-solid interface).Instead, we present our analysis of various properties of surfaces in a hierarchical way, starting with the simplest case that we have identified: a single component liquid-vacuum interface, and then adding more and more complications when we progress to more complex interfaces involving solids. We propose that the term "surface tension" should not be used in the description of surfaces and interfaces involving solids, since its meaning is ambiguous. Only "Surface Free Energy" and "Surface Stress" are well defined and represent distinct, but related, properties of the interfaces. We demonstrate that these quantities, as defined in thermodynamics and measured in MD simulations, satisfy the Shuttleworth equation.

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“…Next, Hui and Jagota present their eq 7, which in terms of the surface energy γ reads γ = F s A They state that eq is the definition of surface energy. The erroneous nature of eq as a thermodynamic definition has been thoroughly discussed, − emphasizing that in thermodynamics an intensive property must be defined as a derivative of a state function with respect to an extensive property. Accordingly, the use of the definition in eq violates the mathematical structure of thermodynamics. − The correct definition of γ at a constant temperature reads γ = ∂ F normals ∂ A The surface energy γ in eq relates to the work spent in creating a new surface whereas the surface tension σ in eq relates to the work spent in stretching a solid surface.…”

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confidence: 99%

Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics

Cited by 42 publications

References 22 publications

Surface Tension, Surface Energy, and Chemical Potential Due to Their Difference

Surface Tension, Surface Energy, and Chemical Potential Due to Their Difference

A unified description of Surface Free Energy and Surface Stress

Misconceptions of the Relation between Surface Energy and Surface Tension on a Solid

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