Editing Hard spherocylinders
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The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends | The '''hard spherocylinder''' model consists of 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 <ref>[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)]</ref> as well as forming a [[Plastic crystals | plastic crystal]] phase for short <math>L</math> <ref>[http://dx.doi.org/10.1063/1.474626 C. Vega and P. A. Monson "Plastic crystal phases of hard dumbbells and hard spherocylinders", Journal of Chemical Physics '''107''' pp. 2696-2697 (1997)]</ref> . One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[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)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[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)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods |hard rod model]], and in the limit <math>L=0</math> one has the [[hard sphere model | has been studied extensively because of its propensity to form both [[Nematic phase | nematic]] and [[Smectic phases | smectic]] [[Liquid crystals | liquid crystalline]] phases <ref>[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)]</ref> as well as forming a [[Plastic crystals | plastic crystal]] phase for short <math>L</math> <ref>[http://dx.doi.org/10.1063/1.474626 C. Vega and P. A. Monson "Plastic crystal phases of hard dumbbells and hard spherocylinders", Journal of Chemical Physics '''107''' pp. 2696-2697 (1997)]</ref> . One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[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)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[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)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods |hard rod model]], and in the limit <math>L=0</math> one has the [[hard sphere model]]. | ||
==Volume== | ==Volume== | ||
The molecular volume of the spherocylinder is given by | The molecular volume of the spherocylinder is given by | ||
| Line 11: | Line 11: | ||
==Minimum distance== | ==Minimum distance== | ||
The minimum distance between two spherocylinders can be calculated using an algorithm published by Vega and Lago <ref>[http://dx.doi.org/10.1016/0097-8485(94)80023-5 Carlos Vega and Santiago Lago "A fast algorithm to evaluate the shortest distance between rods", Computers & Chemistry '''18''' pp. 55-59 (1994)]</ref>. The [[Source code for the minimum distance between two rods | 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. | The minimum distance between two spherocylinders can be calculated using an algorithm published by Vega and Lago <ref>[http://dx.doi.org/10.1016/0097-8485(94)80023-5 Carlos Vega and Santiago Lago "A fast algorithm to evaluate the shortest distance between rods", Computers & Chemistry '''18''' pp. 55-59 (1994)]</ref>. The [[Source code for the minimum distance between two rods | 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. | ||
==Virial coefficients== | ==Virial coefficients== | ||
:''Main article: [[Hard spherocylinders: virial coefficients]]'' | |||
==Phase diagram== | ==Phase diagram== | ||
[[ | :''Main aritcle: [[Phase diagram of the hard spherocylinder model]]'' | ||
==See also== | ==See also== | ||
*[[Charged hard spherocylinders]] | *[[Charged hard spherocylinders]] | ||
==References== | ==References== | ||
<references/> | <references/> | ||
'''Related reading''' | '''Related reading''' | ||
*[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)] | ||
[[Category: Models]] | [[Category: Models]] | ||