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
Interrupted Motility Induced Phase Separation in Aligning Active Colloids.
Marjolein N. van der Linden,Marjolein N. van der Linden,Lachlan C. Alexander,Dirk G. A. L. Aarts,Olivier Dauchot +4 more
TL;DR: In this paper, the phase separation process is interrupted when large enough clusters start breaking apart, and the structural ordering and alignment in the growing clusters are characterized and the mechanisms at play in these regimes.
Journal ArticleDOI
Classical dynamical density functional theory: from fundamentals to applications
TL;DR: The classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics and has been applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics.
Journal ArticleDOI
Phase field simulations of early stage structure formation during immersion precipitation of polymeric membranes in 2D and 3D
Bo Zhou,Adam C. Powell +1 more
TL;DR: In this paper, a ternary Cahn-Hilliard formulation incorporating a Flory-Huggins homogeneous free energy function is used to simulate the liquid-liquid demixing stage of the immersion precipitation process, which determines much of the final morphology of membranes.
Book ChapterDOI
Finite size effects at phase transitions
TL;DR: In this article, the phenomenological theory of finite size scaling is reviewed with emphasis on the concept of probability distributions of order parameter and/or energy, and attention is also drawn to recent developments concerning anisotropic geometries and critical behavior, as well as crossover phenomena from one universality class to another.
Journal ArticleDOI
Two-scale FE–FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior
Julian Kochmann,Stephan Wulfinghoff,Stefanie Reese,Jaber Rezaei Mianroodi,Bob Svendsen,Bob Svendsen +5 more
TL;DR: In this paper, a two-scale phase-field-based computational model for coupled microstructure evolution and macroscopic mechanical material behavior is developed, which is based on a model for each of its material elements or points as a unit cell whose average properties determine those of the corresponding material point.
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.