Hard spherocylinders
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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 simulations of hard spherocylinders was in the classic work of Jacques Vieillard-Baron (Ref. 1).
Volume
The molecular volume of the spherocylinder is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_0 = \pi \left( \frac{LD^2}{4} + \frac{D^3}{6} \right)}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L} is the length of the cylindrical part of the spherocylinder and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D} 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.
Virial coefficients
- Main article: Hard spherocylinders: virial coefficients
Phase diagram
- Main aritcle: Phase diagram of the hard spherocylinder model