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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 Ostwald–Freundlich equation ： ウィキペディア英語版 Ostwald–Freundlich equation The Ostwald–Freundlich equation governs boundaries between two phases; specifically, it relates the surface tension of the boundary to its curvature, the ambient temperature, and the vapor pressure or chemical potential in the two phases. The Ostwald–Freundlich equation for a droplet or particle with radius $R$ is: $\backslash frac\}\backslash right)\}$ $R\_\; =\; \backslash frac$ : $V\_$ : Atomic volume : $k\_B$ : Boltzmann constant : $\backslash gamma$ : Surface tension (J $\backslash cdot$ m−2) : $p\_$ : Equilibrium partial pressure (or chemical potential or concentration) : $p$ : Partial pressure (or chemical potential or concentration) : $T$ : Absolute temperature One consequence of this relation is that small liquid droplets (i.e., particles with a high surface curvature) exhibit a higher effective vapor pressure, since the surface is larger in comparison to the volume. Another notable example of this relation is Ostwald ripening, in which surface tension causes small precipitates to dissolve and larger ones to grow. Ostwald ripening is thought to occur in the formation of orthoclase megacrysts in granites as a consequence of subsolidus growth. See rock microstructure for more. ==History== In 1871, Lord Kelvin (William Thomson) obtained the following relation governing a liquid-vapor interface:〔Sir William Thomson (1871) ("On the equilibrium of vapour at a curved surface of liquid," ) ''Philosophical Magazine'', series 4, 42 (282) : 448-452. See equation (2) on page 450.〕 $p(r\_1\; ,\; r\_2)\; =\; P\; -\; \backslash frac\; )\}\backslash left\; (\; \backslash frac\; +\; \backslash frac\; \backslash right\; )$ where : $p(r)$ = vapor pressure at a curved interface of radius $r$ : $P$ = vapor pressure at flat interface ($r\; =\; \backslash infty$) = $p\_$ : $\backslash gamma$ = surface tension : $\backslash rho\backslash ,\; \_$ = density of vapor : $\backslash rho\backslash ,\; \_$ = density of liquid :$r\_1$ , $r\_2$ = radii of curvature along the principal sections of the curved interface. In his dissertation of 1885, Robert von Helmholtz (son of the German physicist Hermann von Helmholtz) derived the Ostwald–Freundlich equation and showed that Kelvin's equation could be transformed into the Ostwald–Freundlich equation.〔Robert von Helmholtz (1886) ("Untersuchungen über Dämpfe und Nebel, besonders über solche von Lösungen" ) (Investigations of vapors and mists, and especially of such things from solutions), ''Annalen der Physik'', 263 (4) : 508-543. On pages 522-525 Helmholtz derives the Ostwald-Freundlich equation and subsequently converts Kelvin's equation into the Ostwald-Freundlich equation.〕〔Robert von Helmholtz's derivation of the Ostwald-Freundlich equation from Kelvin's equation appears on the "Talk" page of this article.〕 The German physical chemist Wilhelm Ostwald derived the equation apparently independently in 1900;〔Ostwald, W. (1900) ( "Über die vermeintliche Isomerie des roten und gelben Quecksilbersoxyds und die Oberflächenspannung fester Körper" ) (On the supposed isomerism of red and yellow mercury oxide and the surface tension of solid bodies) ''Zeitschrift für physikalische Chemie'', 34 : 495-503. Ostwald’s equation relating temperature, solubility, surface tension, and the radius of curvature of a phase boundary appears on (page 503 ).〕 however, his derivation contained a minor error which the German chemist Herbert Freundlich corrected in 1909.〔Freundlich, Herbert, ''Kapillarchemie: Eine Darstellung der Chemie der Kolloide und verwandter Gebiete'' (Chemistry: A presentation of colloid chemistry and related fields ) (Leipzig, Germany: Akademische Verlagsgesellschaft, 1909), (page 144 ).〕 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「Ostwald–Freundlich equation」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.