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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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):

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

where $\gamma$ is the relative orientation of the principal axes of the molecules. See Ref. 2 for details of Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle v_{s}} 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 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)