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<div>[[Image:spherocylinder_purple.png|thumb|right]]<br />
The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends <br />
by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model<br />
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 of the first simulations was in the classic work of Jacques Vieillard-Baron (Ref. 2). In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods |hard rod model]].<br />
==Volume==<br />
The molecular volume of the spherocylinder is given by <br />
<br />
:<math>v_0 = \pi \left( \frac{LD^2}{4} + \frac{D^3}{6} \right)</math><br />
<br />
where <math>L</math> is the length of the cylindrical part of the spherocylinder and <math>D</math> is the diameter.<br />
==Minimum distance==<br />
The minimum distance between two spherocylinders can be calculated using an algorithm published by Vega and Lago (Ref. 1). 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.<br />
#[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)]<br />
==Virial coefficients==<br />
:''Main article: [[Hard spherocylinders: virial coefficients]]''<br />
==Phase diagram==<br />
:''Main aritcle: [[Phase diagram of the hard spherocylinder model]]''<br />
==See also==<br />
*[[Charged hard spherocylinders]]<br />
==References==<br />
#[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)]<br />
#[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)]<br />
#[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]<br />
#[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)]<br />
[[Category: Models]]</div>143.210.122.169