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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Global existence of weak solutions to a nonlocal Cahn–Hilliard–Navier–Stokes system
TL;DR: In this article, the authors considered a variant of the Navier-Stokes equations where the standard Cahn-Hilliard equation is replaced by its nonlocal version, where the gradient term in the free energy functional was replaced by a spatial convolution operator acting on the order parameter φ, while the potential F may have any polynomial growth.
Journal ArticleDOI
A phase field model of unsaturated flow
TL;DR: In this paper, a phase field model is proposed to explain the formation of gravity fingers during water infiltration in soil, and the model predicts a saturation overshoot at the wetting front, in good agreement with experimental measurements.
Book
Phase-Separated Interpenetrating Polymer Networks
Yuri S. Lipatov,T. T. Alekseeva +1 more
TL;DR: In this article, the formation and properties of interpenetrating polymer networks (IPNs) are considered, and the physicochemical properties of phase-separated IPNs are analyzed.
Thin liquid films on a slightly inclined heated plate - eScholarship
Uwe Thiele,Edgar Knobloch +1 more
TL;DR: In this paper, the behavior of a thin liquid film on a uniformly heated substrate is considered and the relation between these states is discussed and their stability properties with respect to longitudinal perturbations are determined.
Journal ArticleDOI
Dynamics of surface directed mesophase formation in block copolymer melts
TL;DR: In this article, the dynamic mean-field density functional method is adapted to describe phase separation in the presence of geometrical constraints, and effects of polymer-surface interactions on morphology formation are investigated in detail.
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.