Tangent linear hard sphere chains

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

The tangent linear hard sphere chain 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 .

Excluded volume

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

$v_{\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d}}(\gamma )=(11m-3)v_s+(m-1{)}^2{v}_c(\gamma )$

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

Related reading

• Thijs van Westen, Bernardo Oyarzún, Thijs J.H. Vlugt and Joachim Gross "An equation of state for the isotropic phase of linear, partially flexible and fully flexible tangent hard-sphere chain fluids", Molecular Physics 112 pp. 919-928 (2014)