Maier-Saupe mean field model: Difference between revisions
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The '''Maier-Saupe model''' is widely used as a | The '''Maier-Saupe model''' <ref>W. Maier and A. Saupe "EINE EINFACHE MOLEKULARE THEORIE DES NEMATISCHEN KRISTALLINFLUSSIGEN ZUSTANDES", Zeitschrift für Naturforschung A '''13''' pp. 564-566 (1958)</ref> | ||
<ref>W. Maier and A. Saupe "EINE EINFACHE MOLEKULAR-STATISTISCHE THEORIE DER NEMATISCHEN KRISTALLINFLUSSIGEN PHASE .1", Zeitschrift für Naturforschung A '''14''' pp. 882-889 (1959)</ref> | |||
<ref>W. Maier and A. Saupe "EINE EINFACHE MOLEKULAR-STATISTISCHE THEORIE DER NEMATISCHEN KRISTALLINFLUSSIGEN PHASE .2", Zeitschrift für Naturforschung A '''15''' pp. 287-292 (1960)</ref> is widely used as a [[Mean field models | mean field ]] description of the [[nematic phase]]. | |||
The Maier-Saupe model is based on long-range dispersion forces, and has the form | The Maier-Saupe model is based on long-range dispersion forces, and has the form | ||
:<math>U (\cos \theta) = \overline u_2 \overline P_2 P_2 (\cos \theta)</math> | :<math>U (\cos \theta) = \overline u_2 \overline P_2 P_2 (\cos \theta)</math> | ||
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is the [[Order parameters | uniaxial order parameter]]. | is the [[Order parameters | uniaxial order parameter]]. | ||
==References== | ==References== | ||
<references/> | |||
'''Related reading''' | |||
*[http://dx.doi.org/10.1088/0022-3719/6/20/005 P A Vuillermot and M V Romerio "Exact solution of the Maier-Saupe model for a nematic liquid crystal on a one-dimensional lattice", Journal of Physics C: Solid State Physics '''6''' pp. 2922-2930 (1973)] | |||
*[http://dx.doi.org/10.1038/267412b0 G. R. LUCKHURST and C. ZANNONI "Why is the Maier−Saupe theory of nematic liquid crystals so successful?", Nature '''267''' pp. 412 - 414 (1977)] | |||
[[category: models]] | [[category: models]] | ||
[[category:liquid crystals]] | [[category:liquid crystals]] | ||
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The Maier-Saupe model [1] [2] [3] is widely used as a mean field description of the nematic phase. The Maier-Saupe model is based on long-range dispersion forces, and has the form
where is the angle between the molecular symmetry axis and the director. is the uniaxial order parameter.
References[edit]
- ↑ W. Maier and A. Saupe "EINE EINFACHE MOLEKULARE THEORIE DES NEMATISCHEN KRISTALLINFLUSSIGEN ZUSTANDES", Zeitschrift für Naturforschung A 13 pp. 564-566 (1958)
- ↑ W. Maier and A. Saupe "EINE EINFACHE MOLEKULAR-STATISTISCHE THEORIE DER NEMATISCHEN KRISTALLINFLUSSIGEN PHASE .1", Zeitschrift für Naturforschung A 14 pp. 882-889 (1959)
- ↑ W. Maier and A. Saupe "EINE EINFACHE MOLEKULAR-STATISTISCHE THEORIE DER NEMATISCHEN KRISTALLINFLUSSIGEN PHASE .2", Zeitschrift für Naturforschung A 15 pp. 287-292 (1960)
Related reading
- P A Vuillermot and M V Romerio "Exact solution of the Maier-Saupe model for a nematic liquid crystal on a one-dimensional lattice", Journal of Physics C: Solid State Physics 6 pp. 2922-2930 (1973)
- G. R. LUCKHURST and C. ZANNONI "Why is the Maier−Saupe theory of nematic liquid crystals so successful?", Nature 267 pp. 412 - 414 (1977)