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Journal ArticleDOI

Free Energy of a Nonuniform System. I. Interfacial Free Energy

John W. Cahn, +1 more
- 01 Feb 1958 - 
- Vol. 28, Iss: 2, pp 258-267
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TLDR
In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Abstract
It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.

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Citations
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Journal ArticleDOI

Liquid-vapor interface, cavitation, and the phase diagram of water

TL;DR: It is shown how two different equations of state proposed for water, combined with the van der Waals-Cahn-Hilliard theory of a nonuniform system, lead to qualitatively different predictions.
Journal ArticleDOI

Enantioselective discrimination of alcohols by hydrogen bonding: a SERS study.

TL;DR: A particular advantage of this approach is that it is label-free and does not employ any chiral reagents, including chiral light, which opens a new avenue leading to the development of novel enantiosensing strategies.
Journal ArticleDOI

Dynamics of Hollow Nanofiber Formation During Solidification Subjected to Solvent Evaporation

TL;DR: In this article, a new theoretical approach has been developed in the context of Cahn-Hilliard time evolution equation, alternatively known as time-dependent Ginzburg-Landau equation (Model B) involving concentration order parameter.
Journal ArticleDOI

A density functional theory for inhomogeneous charged fluids

TL;DR: In this article, a density functional theory for the one particle densities and the thermodynamic properties of multicomponent, classical, inhomogeneous, charged fluids was formulated and applied to the liquid-vapour interface of a molten alkali halide and some formally exact results for ionic density profiles and surface tension were derived.
Journal ArticleDOI

Phase-field simulation of counter-current spontaneous imbibition in a fractured heterogeneous porous medium

TL;DR: In this article, a pore-level numerical study of counter-current spontaneous imbibition was performed using coupled Cahn-Hilliard phase field and Navier-Stokes equations, solved by a finite element method.
References
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Journal ArticleDOI

The Principle of Corresponding States

TL;DR: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of liquid and the triple point temperature and pressure, the heat capacity of liquid, and the surface tension of liquid as mentioned in this paper.
Book ChapterDOI

Zur Theorie des Austauschproblems und der Remanenzerscheinung der Ferromagnetika

TL;DR: The Slatersche Methode as mentioned in this paper is an analog zur Jordan-Kleinschen Theorie in eine nichtlineare Wellengleichung im dreidimensionalen Raum, wobei das Absolutquadrat der Wellenfunktion anschaulich als Spindichte gedeutet werden kann.
Journal ArticleDOI

Die Keimbildung bei der Ausscheidung in metallischen Mischkristallen

R. Becker
- 01 Jan 1938 - 
TL;DR: In this article, ausscheidung in einem ubersattigten binaren Mischkristall is considered, das die Energie eines Misch-kristalls durch einfache Addition of Nachbarbindungen berechnet werden darf.
Journal ArticleDOI

Domain Structure of Rochelle Salt and K H 2 P O 4

TL;DR: In this paper, it has been shown that rochelle salt in the ferroelectric state consists of many domains and that the domain structure in an annealed crystal is caused by the electrostatic self energy.
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