Hard spherocylinders

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.

References

1. Giorgio Cinacchi and Yuri Martínez-Ratón and Luis Mederos and Enrique Velasco "Smectic, nematic, and isotropic phases in binary mixtures of thin and thick hard spherocylinders", Journal of Chemical Physics 124 pp. 234904 (2006)
2. P. Bolhuis and D. Frenkel "Tracing the phase boundaries of hard spherocylinders", Journal of Chemical Physics 106 pp. 666-687 (1997)
3. S. C. McGrother and D. C. Williamson and G. Jackson "A re-examination of the phase diagram of hard spherocylinders", Journal of Chemical Physics 104 pp. 6755-6771 (1996)