Hard spherocylinders: Difference between revisions

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[[Image:spherocylinder_purple.png|thumb|right]]
[[Image:spherocylinder_purple.png|thumb|right]]
The '''hard spherocylinder''' model consists on an  impenetrable cylinder, capped at both ends  
The '''hard spherocylinder''' model consists on an  impenetrable cylinder, capped at both ends  
by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model
by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model
has been studied extensively because of its propensity to form both [[Nematic phase | nematic]] and [[Smectic phases | smectic]] [[Liquid crystals | liquid crystalline]] phases. One of the first simulations of hard spherocylinders was in the classic work of Jacques Vieillard-Baron  (Ref. 1).
has been studied extensively because of its propensity to form both [[Nematic phase | nematic]] and [[Smectic phases | smectic]] [[Liquid crystals | liquid crystalline]] phases. One of the first studies of hard spherocylinders was undertaken by Cotter and Martire (Ref. 1) using [[scaled-particle theory]], and one if the first simulations was in the classic work of Jacques Vieillard-Baron  (Ref. 2).
==Volume==
==Volume==
The molecular volume of the spherocylinder  is given by  
The molecular volume of the spherocylinder  is given by  
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*[[Charged hard spherocylinders]]
*[[Charged hard spherocylinders]]
==References==
==References==
#[http://dx.doi.org/10.1063/1.1673232  Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics  '''52''' pp. 1909-1919 (1970)]
#[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron  "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]
#[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron  "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]
#[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
#[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
#[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]
#[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]
[[Category: Models]]
[[Category: Models]]

Revision as of 14:08, 23 July 2008

The hard spherocylinder model consists on an impenetrable cylinder, capped at both ends by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model has been studied extensively because of its propensity to form both nematic and smectic liquid crystalline phases. One of the first studies of hard spherocylinders was undertaken by Cotter and Martire (Ref. 1) using scaled-particle theory, and one if the first simulations was in the classic work of Jacques Vieillard-Baron (Ref. 2).

Volume

The molecular volume of the spherocylinder is given by

where is the length of the cylindrical part of the spherocylinder and is the diameter.

Minimum distance

The minimum distance between two spherocylinders can be calculated using an algorithm published by Vega and Lago (Ref. 1). The source code can be found here. Such an algorithm is essential in, for example, a Monte Carlo simulation, in order to check for overlaps between two sites.

  1. Carlos Vega and Santiago Lago "A fast algorithm to evaluate the shortest distance between rods", Computers & Chemistry 18 pp. 55-59 (1994)

Virial coefficients

Main article: Hard spherocylinders: virial coefficients

Phase diagram

Main aritcle: Phase diagram of the hard spherocylinder model

See also

References

  1. Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics 52 pp. 1909-1919 (1970)
  2. Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics 28 pp. 809-818 (1974)
  3. Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry 91 pp. 4912-4916 (1987)
  4. D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature 332 p. 822 (1988)