Hard spherocylinders - Revision history

145.107.78.86: The DOI link for Alejandro Cuetos and Marjolein Dijkstra was messed up

2022-05-20T11:47:18Z

The DOI link for Alejandro Cuetos and Marjolein Dijkstra was messed up

← Older revision		Revision as of 13:47, 20 May 2022
Line 31:		Line 31:
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]		*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
	*[http://dx.doi.org/10.1103/PhysRevLett.98.~~09570~~ Alejandro Cuetos and Marjolein Dijkstra "Kinetic Pathways for the Isotropic-Nematic Phase Transition in a System of Colloidal Hard Rods: A Simulation Study", Physical Review Letters '''98''' 095701 (2007)]		*[http://dx.doi.org/10.1103/PhysRevLett.98.095701 Alejandro Cuetos and Marjolein Dijkstra "Kinetic Pathways for the Isotropic-Nematic Phase Transition in a System of Colloidal Hard Rods: A Simulation Study", Physical Review Letters '''98''' 095701 (2007)]
	*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]		*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]
	[[Category: Models]]		[[Category: Models]]

Carl McBride: Included related stub pages.

2011-04-28T10:48:42Z

Included related stub pages.

← Older revision		Revision as of 12:48, 28 April 2011
Line 15:		Line 15:

	==Virial coefficients==		==Virial coefficients==
	:''~~Main article: [~~[~~Hard spherocylinders~~: ~~virial~~ coefficients]]''		[[Virial equation of state \| Virial coefficients]] of the hard spherocylinder model
			<ref>[http://dx.doi.org/10.1080/00268977800100991 Peter A. Monson and Maurice Rigby "Virial equation of state for rigid spherocylinders", Molecular Physics '''35''' pp. 1337-1342 (1978)]</ref>
			<ref>[http://dx.doi.org/10.1080/00268978900100861 W. R. Cooney, S. M. Thompson and K. E. Gubbins " Virial coefficients for the hard oblate spherocylinder fluid", Molecular Physics '''66''' pp. 1269-1272 (1989)]</ref>
			<ref>[http://dx.doi.org/10.1021/jp049502f Tomás Boublík "Third and Fourth Virial Coefficients and the Equation of State of Hard Prolate Spherocylinders", Journal of Physical Chemistry B '''108''' pp. 7424-7429 (2004)]</ref>.
	==Phase diagram==		==Phase diagram==
	~~:''Main aritcle:~~ [[Phase diagram of the hard spherocylinder model]]''		[[Phase diagrams \|Phase diagram]] of the hard spherocylinder model
			<ref>[http://dx.doi.org/10.1063/1.471343 S. C. McGrother and D. C. Williamson and G. Jackson "A re-examination of the phase diagram of hard spherocylinders", Journal of Chemical Physics '''104''' pp. 6755-6771 (1996)]</ref>
			<ref>[http://dx.doi.org/10.1063/1.473404 P. Bolhuis and D. Frenkel "Tracing the phase boundaries of hard spherocylinders", Journal of Chemical Physics '''106''' pp. 666-687 (1997)]</ref>
	==See also==		==See also==
	*[[Charged hard spherocylinders]]		*[[Charged hard spherocylinders]]
Line 26:		Line 31:
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]		*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
	~~[[Category: Models]]~~
	*[http://dx.doi.org/10.1103/PhysRevLett.98.09570 Alejandro Cuetos and Marjolein Dijkstra "Kinetic Pathways for the Isotropic-Nematic Phase Transition in a System of Colloidal Hard Rods: A Simulation Study", Physical Review Letters '''98''' 095701 (2007)]		*[http://dx.doi.org/10.1103/PhysRevLett.98.09570 Alejandro Cuetos and Marjolein Dijkstra "Kinetic Pathways for the Isotropic-Nematic Phase Transition in a System of Colloidal Hard Rods: A Simulation Study", Physical Review Letters '''98''' 095701 (2007)]
	~~[[Category: Models]]~~
	*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]		*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]
	[[Category: Models]]		[[Category: Models]]

83.83.24.238: /* References */

2011-04-27T20:08:11Z

References

← Older revision		Revision as of 22:08, 27 April 2011
Line 27:		Line 27:
	*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]		*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
	[[Category: Models]]		[[Category: Models]]
	*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]		*[http://dx.doi.org/10.1103/PhysRevLett.98.09570 Alejandro Cuetos and Marjolein Dijkstra "Kinetic Pathways for the Isotropic-Nematic Phase Transition in a System of Colloidal Hard Rods: A Simulation Study", Physical Review Letters '''98''' 095701 (2007)]
			[[Category: Models]]
			*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]
	[[Category: Models]]		[[Category: Models]]

83.83.24.238: /* References */

2011-04-27T20:01:52Z

References

← Older revision		Revision as of 22:01, 27 April 2011
Line 27:		Line 27:
	*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]		*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
	[[Category: Models]]		[[Category: Models]]
	*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods		*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)]
	", Physical Review Letters '''105''' ~~pp.~~ 088302 (2010)]
	[[Category: Models]]		[[Category: Models]]

83.83.24.238: /* References */

2011-04-27T20:01:11Z

References

← Older revision		Revision as of 22:01, 27 April 2011
Line 26:		Line 26:
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]		*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
			[[Category: Models]]
			*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods
			", Physical Review Letters '''105''' pp. 088302 (2010)]
	[[Category: Models]]		[[Category: Models]]

193.6.32.101: /* Minimum distance */

2011-03-09T11:12:16Z

Minimum distance

← Older revision		Revision as of 13:12, 9 March 2011
Line 11:		Line 11:
	==Minimum distance==		==Minimum distance==
	The minimum distance between two spherocylinders can be calculated using an algorithm published by Vega and Lago <ref>[http://dx.doi.org/10.1016/0097-8485(94)80023-5 Carlos Vega and Santiago Lago "A fast algorithm to evaluate the shortest distance between rods", Computers & Chemistry '''18''' pp. 55-59 (1994)]</ref>. The [[Source code for the minimum distance between two rods \| source code can be found here]]. Such an algorithm is essential in, for example, a [[Monte Carlo]] simulation, in order to check for overlaps between two sites.		The minimum distance between two spherocylinders can be calculated using an algorithm published by Vega and Lago <ref>[http://dx.doi.org/10.1016/0097-8485(94)80023-5 Carlos Vega and Santiago Lago "A fast algorithm to evaluate the shortest distance between rods", Computers & Chemistry '''18''' pp. 55-59 (1994)]</ref>. The [[Source code for the minimum distance between two rods \| source code can be found here]]. Such an algorithm is essential in, for example, a [[Monte Carlo]] simulation, in order to check for overlaps between two sites.

			The original code did not give the symmetry property of the distance for almost parallel rods. The revised algorithm in C for systems with periodic boundary conditions can be found [[Rev. source code for the minimum distance between two rods in C \| here]].

	==Virial coefficients==		==Virial coefficients==
	:''Main article: [[Hard spherocylinders: virial coefficients]]''		:''Main article: [[Hard spherocylinders: virial coefficients]]''

Carl McBride: Added an internal link

2011-03-02T11:22:41Z

Added an internal link

← Older revision		Revision as of 13:22, 2 March 2011
Line 2:		Line 2:
	The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends		The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends
	by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model		by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model
	has been studied extensively because of its propensity to form both [[Nematic phase \| nematic]] and [[Smectic phases \| smectic]] [[Liquid crystals \| liquid crystalline]] phases <ref>[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]</ref> as well as forming a [[Plastic crystals \| plastic crystal]] phase for short <math>L</math> <ref>[http://dx.doi.org/10.1063/1.474626 C. Vega and P. A. Monson "Plastic crystal phases of hard dumbbells and hard spherocylinders", Journal of Chemical Physics '''107''' pp. 2696-2697 (1997)]</ref> . One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[http://dx.doi.org/10.1063/1.1673232 Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics '''52''' pp. 1909-1919 (1970)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods \|hard rod model]], and in the limit <math>L=0</math> one has the [[hard sphere model]].		has been studied extensively because of its propensity to form both [[Nematic phase \| nematic]] and [[Smectic phases \| smectic]] [[Liquid crystals \| liquid crystalline]] phases <ref>[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]</ref> as well as forming a [[Plastic crystals \| plastic crystal]] phase for short <math>L</math> <ref>[http://dx.doi.org/10.1063/1.474626 C. Vega and P. A. Monson "Plastic crystal phases of hard dumbbells and hard spherocylinders", Journal of Chemical Physics '''107''' pp. 2696-2697 (1997)]</ref> . One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[http://dx.doi.org/10.1063/1.1673232 Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics '''52''' pp. 1909-1919 (1970)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods \|hard rod model]], and in the limit <math>L=0</math> one has the [[hard sphere model]]. A closely related model is that of the [[Oblate hard spherocylinders \| oblate hard spherocylinder]].
	==Volume==		==Volume==
	The molecular volume of the spherocylinder is given by		The molecular volume of the spherocylinder is given by

Carl McBride: /* See also */ Added an internal link to Oblate hard spherocylinders

2011-03-02T11:20:37Z

See also: Added an internal link to Oblate hard spherocylinders

← Older revision		Revision as of 13:20, 2 March 2011
Line 17:		Line 17:
	==See also==		==See also==
	*[[Charged hard spherocylinders]]		*[[Charged hard spherocylinders]]
			*[[Oblate hard spherocylinders]]

	==References==		==References==
	<references/>		<references/>

Carl McBride: Added mention of a plastic crystal phase.

2010-11-30T17:02:38Z

Added mention of a plastic crystal phase.

← Older revision		Revision as of 19:02, 30 November 2010
Line 2:		Line 2:
	The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends		The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends
	by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model		by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model
	has been studied extensively because of its propensity to form both [[Nematic phase \| nematic]] and [[Smectic phases \| smectic]] [[Liquid crystals \| liquid crystalline]] phases <ref>[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]</ref>. One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[http://dx.doi.org/10.1063/1.1673232 Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics '''52''' pp. 1909-1919 (1970)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods \|hard rod model]].		has been studied extensively because of its propensity to form both [[Nematic phase \| nematic]] and [[Smectic phases \| smectic]] [[Liquid crystals \| liquid crystalline]] phases <ref>[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]</ref> as well as forming a [[Plastic crystals \| plastic crystal]] phase for short <math>L</math> <ref>[http://dx.doi.org/10.1063/1.474626 C. Vega and P. A. Monson "Plastic crystal phases of hard dumbbells and hard spherocylinders", Journal of Chemical Physics '''107''' pp. 2696-2697 (1997)]</ref> . One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[http://dx.doi.org/10.1063/1.1673232 Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics '''52''' pp. 1909-1919 (1970)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods \|hard rod model]], and in the limit <math>L=0</math> one has the [[hard sphere model]].
	==Volume==		==Volume==
	The molecular volume of the spherocylinder is given by		The molecular volume of the spherocylinder is given by

Nice and Tidy at 16:43, 30 November 2010

2010-11-30T16:43:12Z

← Older revision		Revision as of 18:43, 30 November 2010
Line 2:		Line 2:
	The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends		The '''hard spherocylinder''' model consists of an impenetrable cylinder, capped at both ends
	by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model		by hemispheres whose diameters are the same as the diameter of the cylinder. The hard spherocylinder model
	has been studied extensively because of its propensity to form both [[Nematic phase \| nematic]] and [[Smectic phases \| smectic]] [[Liquid crystals \| liquid crystalline]] phases. One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[http://dx.doi.org/10.1063/1.1673232 Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics '''52''' pp. 1909-1919 (1970)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods \|hard rod model]].		has been studied extensively because of its propensity to form both [[Nematic phase \| nematic]] and [[Smectic phases \| smectic]] [[Liquid crystals \| liquid crystalline]] phases <ref>[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]</ref>. One of the first studies of hard spherocylinders was undertaken by Cotter and Martire <ref>[http://dx.doi.org/10.1063/1.1673232 Martha A. Cotter and Daniel E. Martire "Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned to Isotropic Transition in a Fluid of Rigid Spherocylinders", Journal of Chemical Physics '''52''' pp. 1909-1919 (1970)]</ref> using [[scaled-particle theory]], and one of the first simulations was in the classic work of Jacques Vieillard-Baron <ref>[http://dx.doi.org/10.1080/00268977400102161 Jacques Vieillard-Baron "The equation of state of a system of hard spherocylinders", Molecular Physics '''28''' pp. 809-818 (1974)]</ref>. In the limit of zero diameter the hard spherocylinder becomes a line segment, often known as the [[3-dimensional hard rods \|hard rod model]].
	==Volume==		==Volume==
	The molecular volume of the spherocylinder is given by		The molecular volume of the spherocylinder is given by
Line 21:		Line 21:
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]		*[http://dx.doi.org/10.1021/j100303a008 Daan Frenkel "Onsager's spherocylinders revisited", Journal of Physical Chemistry '''91''' pp. 4912-4916 (1987)]
	*[http://dx.doi.org/10.1038/332822a0 D. Frenkel, H. N. W. Lekkerkerker and A. Stroobants "Thermodynamic stability of a smectic phase in a system of hard rods", Nature '''332''' p. 822 (1988)]
	[[Category: Models]]		[[Category: Models]]