Tangent linear hard sphere chains - Revision history

Carl McBride: Added a recent publication

2014-05-05T13:56:03Z

Added a recent publication

← Older revision		Revision as of 15:56, 5 May 2014
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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]]

	~~This~~ model consists of, as the name suggests, chains of varying monomer length (<math>m</math>), placed tangentially		The '''tangent linear hard sphere chain''' 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 ~~(See Ref~~. 1).		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>.
	==Excluded volume==		==Excluded volume==
	The [[excluded volume]] for this model is given by (~~Ref~~. 2 Eq. 30):		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):

	:<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==
	#[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)]~~		<references/>
	~~#[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~~)]		;Related reading
			*[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]]

Carl McBride at 13:01, 31 January 2008

2008-01-31T13:01:19Z

← Older revision		Revision as of 15:01, 31 January 2008
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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 ''molecule'' is rigid.		in a linear configuration. Each monomer is a [[hard sphere model]] and each molecule is rigid.
	For <math>m=5</math> [[smectic-A phase]] ~~beomes~~ stable. For <math>m=6</math> the [[nematic phase]] becomes stable.		==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 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/10.1063/1.1389095 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]]

Carl McBride: /* References */

2008-01-31T12:30:51Z

References

← Older revision		Revision as of 14:30, 31 January 2008
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	==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)]		#[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)]
	[[category:models]]		[[category:models]]

Carl McBride at 08:36, 29 May 2007

2007-05-29T08:36:37Z

← Older revision		Revision as of 10:36, 29 May 2007
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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]]

			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.
			For <math>m=5</math> [[smectic-A phase]] beomes stable. For <math>m=6</math> the [[nematic phase]] becomes stable.
	==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)]		#[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)]
	[[category:models]]		[[category:models]]

Carl McBride at 14:01, 22 March 2007

2007-03-22T14:01:11Z

← Older revision		Revision as of 16:01, 22 March 2007
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	[[Image:LTHS.png\|thumb\|right]]		[[Image:LTHS.png\|Example of the tangent linear hard sphere chain model, with m=6.\|thumb\|right]]
	==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)]		#[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)]
	[[category:models]]		[[category:models]]

Carl McBride at 13:58, 22 March 2007

2007-03-22T13:58:45Z

← Older revision		Revision as of 15:58, 22 March 2007
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			[[Image:LTHS.png\|thumb\|right]]
	==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)]		#[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)]
	[[category:models]]		[[category:models]]

Carl McBride: New page: ==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 Mo...

2007-03-20T14:54:28Z

New page: ==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 Mo...

New page

==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)]
[[category:models]]