Tangent linear hard sphere chains
This model consists of, as the name suggests, chains of varying monomer length (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 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 (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 m=5} smectic-A phase becomes stable. For 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 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):
- 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_{\mathrm {excluded}}(\gamma)= (11m -3)v_s + (m-1)^2 v_c(\gamma)}
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 \gamma} is the relative orientation of the principal axes of the molecules. See Ref. 2 for details of 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_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
- 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)
- 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)