Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
Reads0
Chats0
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.read more
Citations
More filters
Journal ArticleDOI
Neutral and charged polymers at interfaces
Roland R. Netz,David Andelman +1 more
TL;DR: In this article, the authors discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure.
Journal ArticleDOI
On the Equilibrium Thickness of Intergranular Glass Phases in Ceramic Materials
TL;DR: In this paper, it was shown that there will exist a stable thickness for the intergranular film and that it will be of the order of 1 nm, a value commensurate with that observed experimentally in a wide range of materials.
Journal ArticleDOI
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer
TL;DR: A comprehensive review of the lattice Boltzmann (LB) method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multi-phase flows with phase change, is provided in this paper.
Journal ArticleDOI
Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
Oliver Penrose,Paul C. Fife +1 more
TL;DR: In this article, a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space.
Journal ArticleDOI
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
TL;DR: A phase field model for the mixture of two incompressible fluids is presented in this article, which is based on an energetic variational formulation, consisting of a Navier-Stokes system coupled with a Cahn-Hilliard equation through an extra stress term and the transport term.
References
More filters
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
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
Toshito Mitsui,Jiro Furuichi +1 more
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.