Tangent linear hard sphere chains

Example of the tangent linear hard sphere chain model, with m=6.

This model consists of, as the name suggests, chains of varying monomer length ($m$), placed tangentially in a linear configuration. Each monomer is a hard sphere model and each molecule is rigid.

Liquid crystals

For $m=5$ smectic-A phase becomes stable. For $m=6$ the nematic phase becomes stable (See Ref. 1).

Excluded volume

The excluded volume for this model is given by (Ref. 2 Eq. 30):

$v_{\mathrm {excluded} }(\gamma )=(11m-3)v_{s}+(m-1)^{2}v_{c}(\gamma )$

where $\gamma$ is the relative orientation of the principal axes of the molecules. See Ref. 2 for details of $v_{s}$ and $v_{c}(\gamma )$.

References

1. Carlos Vega, Carl McBride, and Luis G. MacDowell "Liquid crystal phase formation for the linear tangent hard sphere model from Monte Carlo simulations", Journal of Chemical Physics 115 pp. 4203-4211 (2001)
2. Dave C. Williamson and George Jackson "Excluded volume for a pair of linear chains of tangent hard spheres with an arbitrary relative orientation", Molecular Physics 86 pp. 819-836 (1995)