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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Surface stress ： ウィキペディア英語版 Surface stress Surface stress was first defined by Josiah Willard Gibbs 〔J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Vol. 1 (Longmans-Green, London, 1906) p. 55.〕 (1839-1903) as the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface. A suggestion is surface stress define as association with the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface instead of up definition. A similar term called “surface free energy”, which represents the excess free energy per unit area needed to create a new surface, is easily confused with “surface stress”. Although surface stress and surface free energy of liquid–gas or liquid–liquid interface are the same, they are very different in solid–gas or solid–solid interface, which will be discussed in details later. Since both terms represent a force per unit length, they have been referred to as “surface tension”, which contributes further to the confusion in the literature. ==Thermodynamics of surface stress== Definition of surface free energy is seemly the amount of reversible work $dw$ performed to create new area $dA$ of surface, expressed as: :$dw\; =\; \backslash gamma\; dA$ Gibbs was the first to define another surface quantity, different from $\backslash gamma$, that is associated with the reversible work per unit area needed to elastically stretch a pre-existing surface. Surface stress can be derived from surface free energy as followed:〔R.C. Cammarata, Prog. in Surf. Sci. 46 (1994) 1–38.〕 One can define a surface stress tensor $f\_$ that relates the work associated with the variation in $\backslash gamma\; A$, the total excess free energy of the surface, owing to the strain $de\_$: :$d(\backslash gamma\; A)\; =\; Af\_d\backslash epsilon\_$ Now let's consider the two reversible paths showed in figure 0. The first path (clockwise), the solid object is cut into two same pieces. Then both pieces are elastically strained. The work associated with the first step (unstrained) is $W\_1\; =\; 2\; \backslash gamma\_0\; A\_0$, where $\backslash gamma\_0$ and $A\_0$ are the excess free energy and area of each of new surfaces. For the second step, work ($w\_2$), equals the work needed to elastically deform the total bulk volume and the four (two original and two newly formed) surfaces. In the second path (counter-clockwise), the subject is first elastically strained and then is cut in two pieces. The work for the first step here, $w\_1$ is equal to that needed to deform the bulk volume and the two surfaces. The difference $w\_2\; -\; w\_1$ is equal to the excess work needed to elastically deform two surfaces of area $A\_0$ to area $A(e\_)$ or: :$w\_2\; -\; w\_1\; =\; 2\; \backslash int\; (f\_\; d(A(\backslash epsilon\_))\; =\; 2\; \backslash int(Af\_\; d\backslash epsilon\_\; )$ the work associated with the second step of the second path can be expressed as $W\_2\; =2\backslash gamma(e\_)A(e\_)$, so that: :$W\_2\; -\; W\_1\; =\; 2(-\; \backslash gamma\_0\; \backslash \; A\_0)$ These two paths are completely reversible, or W2 – W1 = W2 – W1. It means: :$2(A\_0)=2\backslash int(Af\_\; d\backslash epsilon\_)$ Since d(γA) = γdA + Adγ, and dA = Aδijdeij. Then surface stress can be expressed as: :$f\_\; =\; \backslash gamma\; \backslash delta\_+\backslash partial\; \backslash gamma\; /\backslash partial\; e\_$ Where δij is the Kronecker delta and eij is elastic strain tensor. Differently from the surface free energy γ, which is a scalar, surface stress fij is a second rank tensor. However, for a general surface, set of principle axes that are off-diagonal components are identically zero. Surface that possesses a threefold or higher rotation axis symmetry, diagonal components are equal. Therefore, surface stress can be rewritten as a scalar: :$f\; =\; \backslash gamma+\backslash partial\; \backslash gamma/\; \backslash partial\; e$ Now it can be easily explained why f and γ are equal in liquid-gas or liquid-liquid interfaces. Due to the chemical structure of liquid surface phase, the term ∂γ/∂e always equals to zero meaning that surface free energy won’t change even if the surface is being stretched. However, ∂γ/∂e is not zero in solid surface due do the fact that surface atomic structure of solid are modified in elastic deformation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Surface stress」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.