Diffuse interfaces and the general minimization of the mean field free energy

R. W. Hopper; D. R. Uhlmann

doi:10.1016/0021-9797(74)90081-2

Diffuse interfaces and the general minimization of the mean field free energy

R. W. Hopper, D. R. Uhlmann

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A mean field pair interaction theory of interfaces is presented. The theory is related to diffuse interface theories based on gradient energy expansions, but avoids certain mathematical approximations. The theory consists of obtaining a general expression for the mean field pair interaction free energy of the system and obtaining that composition profile which minimizes this free energy. A condition for the minimization is obtained from variational principles and solved numerically. The interface profiles are compared with those of standard diffuse interface theory and are found to be similar. The theory is a mean field theory because the local configurational entropy is taken as ideal.

Original language	English (US)
Pages (from-to)	77-85
Number of pages	9
Journal	Journal of Colloid And Interface Science
Volume	47
Issue number	1
DOIs	https://doi.org/10.1016/0021-9797(74)90081-2
State	Published - Apr 1974
Externally published	Yes

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Biomaterials
Surfaces, Coatings and Films
Colloid and Surface Chemistry

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10.1016/0021-9797(74)90081-2

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title = "Diffuse interfaces and the general minimization of the mean field free energy",

abstract = "A mean field pair interaction theory of interfaces is presented. The theory is related to diffuse interface theories based on gradient energy expansions, but avoids certain mathematical approximations. The theory consists of obtaining a general expression for the mean field pair interaction free energy of the system and obtaining that composition profile which minimizes this free energy. A condition for the minimization is obtained from variational principles and solved numerically. The interface profiles are compared with those of standard diffuse interface theory and are found to be similar. The theory is a mean field theory because the local configurational entropy is taken as ideal.",

author = "Hopper, {R. W.} and Uhlmann, {D. R.}",

note = "Funding Information: The present work was supported by the American Optical Company, who provided one of the authors (RWH) with the American Optical Fellowship in Materials Science, and by the National Science Foundation. This support is gratefully acknowledged.",

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T1 - Diffuse interfaces and the general minimization of the mean field free energy

AU - Hopper, R. W.

AU - Uhlmann, D. R.

N1 - Funding Information: The present work was supported by the American Optical Company, who provided one of the authors (RWH) with the American Optical Fellowship in Materials Science, and by the National Science Foundation. This support is gratefully acknowledged.

PY - 1974/4

Y1 - 1974/4

N2 - A mean field pair interaction theory of interfaces is presented. The theory is related to diffuse interface theories based on gradient energy expansions, but avoids certain mathematical approximations. The theory consists of obtaining a general expression for the mean field pair interaction free energy of the system and obtaining that composition profile which minimizes this free energy. A condition for the minimization is obtained from variational principles and solved numerically. The interface profiles are compared with those of standard diffuse interface theory and are found to be similar. The theory is a mean field theory because the local configurational entropy is taken as ideal.

AB - A mean field pair interaction theory of interfaces is presented. The theory is related to diffuse interface theories based on gradient energy expansions, but avoids certain mathematical approximations. The theory consists of obtaining a general expression for the mean field pair interaction free energy of the system and obtaining that composition profile which minimizes this free energy. A condition for the minimization is obtained from variational principles and solved numerically. The interface profiles are compared with those of standard diffuse interface theory and are found to be similar. The theory is a mean field theory because the local configurational entropy is taken as ideal.

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JO - Journal of Colloid And Interface Science

JF - Journal of Colloid And Interface Science

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Diffuse interfaces and the general minimization of the mean field free energy

Abstract

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