Free Energy of a Nonuniform System. I. Interfacial Free Energy.¶
Cahn, J. W., & Hilliard, J. E. (1958). Free Energy of a Nonuniform System. I. Interfacial Free Energy.: I. Interfacial Free Energy. Journal of Chemical Physics, 28(2), 258-267.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Phase Diagram
- 4. Mark critical and multicritical endpoints where coexistence curves terminate: the triple point (three phases meet), the critical point (liquid-gas distinction vanishes), the spinodal line
This sourceTheory of spinodal decomposition and the spinodal curve (limit of metastability); explains the region between coexistence and stability limits in phase diagrams.
- 4. Mark critical and multicritical endpoints where coexistence curves terminate: the triple point (three phases meet), the critical point (liquid-gas distinction vanishes), the spinodal line
- Phase Separation
- The spontaneous endogenous sorting proceeds by two distinct routes the prime names: inside the spinodal (where \(\partial^2 G/\partial x^2 < 0\)) the mixture is unstable to infinitesimal fluctuations and demixes everywhere at once by spinodal decomposition; between the spinodal and the binodal it is metastable and demixes only by nucleation-and-growth from seeds.
This sourceFoundational theory of spinodal decomposition and interfacial energy in non-uniform mixtures.
- The spontaneous endogenous sorting proceeds by two distinct routes the prime names: inside the spinodal (where \(\partial^2 G/\partial x^2 < 0\)) the mixture is unstable to infinitesimal fluctuations and demixes everywhere at once by spinodal decomposition; between the spinodal and the binodal it is metastable and demixes only by nucleation-and-growth from seeds.
- Spinodal Decomposition
- In materials science and metallurgy — the canonical case — glass-ceramics, polymer blends, and alloys below the spinodal curve separate without nucleation into interpenetrating networks at a preferred wavelength, engineered for toughness.
This sourceIntroduces the gradient-energy free-energy functional underlying spinodal decomposition, where a region of negative curvature (f''<0) makes the homogeneous state unstable.
Supported in partVerified against the publisher's abstract
The abstract gives the free-energy functional of a nonuniform system (f0(c) plus a gradient term), but never states the f''(c)<0 curvature condition or that the uniform state is a free-energy maximum.
“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 [f0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f0 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 …”
- In materials science and metallurgy — the canonical case — glass-ceramics, polymer blends, and alloys below the spinodal curve separate without nucleation into interpenetrating networks at a preferred wavelength, engineered for toughness.
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