Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
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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
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Journal ArticleDOI
Atomistic simulations of spinodal phase separation preceding polymer crystallization
TL;DR: Large-scale computer simulations reveal a ‘coexistence period’ in the ordering before crystallization, where nucleation and growth mechanisms coexist with a phase-separation mechanism.
Journal ArticleDOI
Late stage spinodal decomposition of a binary polymer mixture. II. Scaling analyses on Qm(τ) and Im(τ)
TL;DR: In this paper, the early to late stage of spinodal decomposition of critical mixtures of polystyrene and polyvinyl methyl ether was investigated by the time-resolved light scattering technique.
Journal ArticleDOI
Some global dynamical properties of a class of pattern formation equations
TL;DR: On etudie deux equations d'evolution non lineaires as discussed by the authors : l'equation de Kuramoto-Sevashinsky and theequation of Cahn-Hilliard.
Journal ArticleDOI
Phase field modeling and simulation of three-phase flows
Junseok Kim,John Lowengrub +1 more
TL;DR: A stable conservative, second order accurate fully implicit fully implicit discre tization of the NS and three-phase (ternary) CH system and uses a nonlinear multigrid method to efficiently solve the dis crete ternary CH system at the implicit time-level.
Journal ArticleDOI
The sharp-interface limit of the Cahn-Hilliard/Navier-Stokes model for binary fluids
TL;DR: In this article, it is shown that the mobility is an effective parameter to be chosen proportional to the square of the interface thickness, and the theoretical results are confirmed by numerical simulations for two prototypal flows, namely capillary waves riding the interface and droplets coalescence.
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
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.