# A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state

@article{FrancoMelgar2008AGO, title={A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state}, author={Mario Franco-Melgar and Andrew J. Haslam and George Jackson}, journal={Molecular Physics}, year={2008}, volume={106}, pages={649 - 678} }

The molecular theory of Onsager [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for liquid crystals is developed and extended to describe ordering transitions in systems of generic cylindrically symmetrical molecules. A number of new analytical results are discussed for particles characterised by a general form of the excluded-volume interaction. Our description makes use of the Onsager trial function (OTF) to represent the orientational distribution and degree of anisotropy. Algebraic…

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## References

SHOWING 1-10 OF 129 REFERENCES

Liquid Crystals

- GeologyNature
- 1912

The subject is not easily understood, and most of the experiments upon which it is founded cannot be performed without special apparatus, so it has so far received scanty attention in this country, and its extreme importance is perhaps not fully realised.

MATH

- Biology
- 1992

It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.

Equations of State for Fluids and Fluid Mixtures

- Geology
- 1991

Fluids1) abound during the formation of most rocks and mineral deposits. In the majority of geological environments, they tend to be mixtures of a number of species like H2O, CO2, CH4, CO, H2, N2,…

[C]

- PhysicsThe Works of Thomas De Quincey, Vol. 1: Writings, 1799–1820
- 2000

In supernova (SN) spectroscopy relatively little attention has been given to the properties of optically thick spectral lines in epochs following the photosphere’s recession. Most treatments and…

Mathematical Methods for Physicists

- Mathematics
- 1966

Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations.…

Theory of molecular fluids

- Chemistry, Physics
- 1984

1. Thermodynamic Properties of Pure Fluids 2. Thermodynamic Properties of Mixtures 3. Surface Properties 4. Structure Factor 5. Dielectric Properties 6. Spectroscopic Properties

Statistical Physics

- PhysicsNature
- 1971

Statistical Physics. By F. Mandl. Pp. xiii + 379. (Wiley: London and New York, July 1971.) £2.75. Statistical Physics. By A. Isihara. Pp. xv + 439. (Academic: New York and London, June 1971.) $18.50;…

APPL

- Computer Science
- 2001

A prototype probability package named APPL (A Probability Programming Language) is presented that can be used to manipulate random variables and examples illustrate its use.

Ann

- Psychology
- 2005

Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed…

Macromolecules 19

- 2313
- 1986