Tangent linear hard sphere chains: Difference between revisions
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This model consists of, as the name suggests, chains of varying monomer length (<math>m</math>), placed tangentially | This model consists of, as the name suggests, chains of varying monomer length (<math>m</math>), placed tangentially | ||
in a linear configuration. Each monomer is a [[hard sphere model]] and each | in a linear configuration. Each monomer is a [[hard sphere model]] and each molecule is rigid. | ||
For <math>m=5</math> [[smectic-A phase]] | ==Liquid crystals== | ||
For <math>m=5</math> [[Smectic phases |smectic-A phase]] becomes stable. For <math>m=6</math> the [[nematic phase]] becomes stable (See Ref. 1). | |||
==Excluded volume== | |||
The [[excluded volume]] for this model is given by (Ref. 2 Eq. 30): | |||
:<math>v_{\mathrm {excluded}}(\gamma)= (11m -3)v_s + (m-1)^2 v_c(\gamma)</math> | |||
where <math>\gamma</math> is the relative orientation of the principal axes of the molecules. See Ref. 2 for details | |||
of <math>v_s</math> and <math>v_c(\gamma)</math>. | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.1389095 | #[http://dx.doi.org/10.1063/1.1389095 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)] | ||
#[http://dx.doi.org/10.1080/00268979500102391 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)] | #[http://dx.doi.org/10.1080/00268979500102391 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)] | ||
[[category:models]] | [[category:models]] | ||
Revision as of 14:01, 31 January 2008
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)