Editing Tangent linear hard sphere chains

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[[Image:LTHS.png|Example of the tangent linear hard sphere chain model, with m=6.|thumb|right]]
[[Image:LTHS.png|Example of the tangent linear hard sphere chain model, with m=6.|thumb|right]]


The '''tangent linear hard sphere chain''' 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 molecule is rigid.
in a linear configuration. Each monomer is a [[hard sphere model]] and each molecule is rigid.
==Liquid crystals==
==Liquid crystals==
For <math>m=5</math> [[Smectic phases |smectic-A phase]] becomes stable. For  <math>m=6</math> the [[nematic phase]] becomes stable <ref>[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)]</ref>.
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==
==Excluded volume==
The [[excluded volume]] for this model is given by (<ref>[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)]</ref> Eq. 30):
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>
:<math>v_{\mathrm {excluded}}(\gamma)= (11m -3)v_s + (m-1)^2 v_c(\gamma)</math>
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of <math>v_s</math> and <math>v_c(\gamma)</math>.
of <math>v_s</math> and <math>v_c(\gamma)</math>.
==References==
==References==
<references/>
#[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)]
;Related reading
#[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/10.1080/00268976.2013.812257 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)]
[[category:models]]
[[category:models]]
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