Kern and Frenkel patchy model - Revision history

128.42.195.43 at 00:41, 21 September 2023

2023-09-21T00:41:05Z

← Older revision		Revision as of 02:41, 21 September 2023
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	The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with		The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with
	attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.		attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman (1988) <ref name="Chapman">[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.
	The potential has an angular aspect, given by (Eq. 1)		The potential has an angular aspect, given by (Eq. 1)

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	</math>		</math>

	then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with [[Wertheim's first order thermodynamic perturbation theory (TPT1)\| Wertheim theory]] <ref name="bianchi"/><ref name="rovigatti"/>		then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with [[Wertheim's first order thermodynamic perturbation theory (TPT1)\| Wertheim theory]] <ref name="Chapman"/><ref name="bianchi"/><ref name="rovigatti"/>

	==Hard ellipsoid model==		==Hard ellipsoid model==

128.42.195.43 at 00:38, 21 September 2023

2023-09-21T00:38:29Z

← Older revision		Revision as of 02:38, 21 September 2023
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	The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with		The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with
	attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later by Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.		attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.
	The potential has an angular aspect, given by (Eq. 1)		The potential has an angular aspect, given by (Eq. 1)

128.42.195.43 at 00:38, 21 September 2023

2023-09-21T00:38:08Z

← Older revision		Revision as of 02:38, 21 September 2023
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	The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with		The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with
	attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.		attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later by Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.
	The potential has an angular aspect, given by (Eq. 1)		The potential has an angular aspect, given by (Eq. 1)

128.42.195.43 at 00:37, 21 September 2023

2023-09-21T00:37:42Z

← Older revision		Revision as of 02:37, 21 September 2023
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	The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with		The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with
	attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman(1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.		attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.
	The potential has an angular aspect, given by (Eq. 1)		The potential has an angular aspect, given by (Eq. 1)

128.42.195.43 at 00:36, 21 September 2023

2023-09-21T00:36:49Z

← Older revision		Revision as of 02:36, 21 September 2023
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	where <math>\delta</math> is the solid angle of a patch (<math>\alpha, \beta, ...</math>) whose axis is <math>\hat{e}</math> (see Fig. 1 of Ref. 1), forming a conical segment.		where <math>\delta</math> is the solid angle of a patch (<math>\alpha, \beta, ...</math>) whose axis is <math>\hat{e}</math> (see Fig. 1 of Ref. 1), forming a conical segment.
	==Multiple patches==		==Multiple patches==
	The "two-patch" and "four-patch" Bol (Chapman or Kern and Frenkel) model was extensively studied by Chapman and co-workers for bulk and interfacial systems using hard sphere and Lennard-Jones ~~references~~. Later other groups, including Sciortino and co-workers, considered stronger association energies for the "two-patch" hard sphere reference <ref name="bianchi">[http://dx.doi.org/10.1063/1.2730797 F. Sciortino, E. Bianchi, J. Douglas and P. Tartaglia "Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation", Journal of Chemical Physics '''126''' 194903 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3415490 Achille Giacometti, Fred Lado, Julio Largo, Giorgio Pastore, and Francesco Sciortino "Effects of patch size and number within a simple model of patchy colloids", Journal of Chemical Physics 132, 174110 (2010)]</ref><ref name="rovigatti">[http://dx.doi.org/10.1063/1.4737930 José Maria Tavares, Lorenzo Rovigatti, and Francesco Sciortino "Quantitative description of the self-assembly of patchy particles into chains and rings", Journal of Chemical Physics '''137''' 044901 (2012)]</ref>.		The "two-patch" and "four-patch" Bol (Chapman or Kern and Frenkel) model was extensively studied by Chapman and co-workers for bulk and interfacial systems using hard sphere and Lennard-Jones reference systems. Later other groups, including Sciortino and co-workers, considered stronger association energies for the "two-patch" hard sphere reference <ref name="bianchi">[http://dx.doi.org/10.1063/1.2730797 F. Sciortino, E. Bianchi, J. Douglas and P. Tartaglia "Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation", Journal of Chemical Physics '''126''' 194903 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3415490 Achille Giacometti, Fred Lado, Julio Largo, Giorgio Pastore, and Francesco Sciortino "Effects of patch size and number within a simple model of patchy colloids", Journal of Chemical Physics 132, 174110 (2010)]</ref><ref name="rovigatti">[http://dx.doi.org/10.1063/1.4737930 José Maria Tavares, Lorenzo Rovigatti, and Francesco Sciortino "Quantitative description of the self-assembly of patchy particles into chains and rings", Journal of Chemical Physics '''137''' 044901 (2012)]</ref>.

	==Four patches==		==Four patches==

128.42.195.43 at 00:35, 21 September 2023

2023-09-21T00:35:36Z

← Older revision		Revision as of 02:35, 21 September 2023
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	The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] is an amalgamation of the [[hard sphere model]] with		The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] published in 2003 is an amalgamation of the [[hard sphere model]] with
	attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982) <ref>[W. Bol, Molecular Physics 45, 605 (1982)]</ref> and later ~~reinvented by~~ Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.		attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982),<ref>[http://dx.doi.org/10.1080/00268978200100461 W. Bol "Monte Carlo simulations of fluid systems of waterlike molecules", Molecular Physics '''45''' pp. 605-616 (1982)]</ref> and later Chapman(1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.
	The potential has an angular aspect, given by (Eq. 1)		The potential has an angular aspect, given by (Eq. 1)

128.42.195.43 at 00:25, 21 September 2023

2023-09-21T00:25:41Z

← Older revision		Revision as of 02:25, 21 September 2023
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	The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] is an amalgamation of the [[hard sphere model]] with		The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles \|patchy model]] is an amalgamation of the [[hard sphere model]] with
	attractive [[Square well model \| square well]] patches (HSSW). The potential has an angular aspect, given by (Eq. 1)		attractive [[Square well model \| square well]] patches (HSSW). The model was originally developed by Bol (1982) <ref>[W. Bol, Molecular Physics 45, 605 (1982)]</ref> and later reinvented by Chapman (1988) <ref>[W.G. Chapman, Doctoral Thesis, Cornell University (1988)]</ref> <ref>[G. Jackson, W.G. Chapman, K.E. Gubbins, Molecular Physics 65, 1-31 (1988)]</ref> as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.
			The potential has an angular aspect, given by (Eq. 1)


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	where <math>\delta</math> is the solid angle of a patch (<math>\alpha, \beta, ...</math>) whose axis is <math>\hat{e}</math> (see Fig. 1 of Ref. 1), forming a conical segment.		where <math>\delta</math> is the solid angle of a patch (<math>\alpha, \beta, ...</math>) whose axis is <math>\hat{e}</math> (see Fig. 1 of Ref. 1), forming a conical segment.
	==~~Two~~ patches==		==Multiple patches==
	The "two-patch" Kern and Frenkel model ~~has been~~ extensively studied by Sciortino and co-workers <ref name="bianchi">[http://dx.doi.org/10.1063/1.2730797 F. Sciortino, E. Bianchi, J. Douglas and P. Tartaglia "Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation", Journal of Chemical Physics '''126''' 194903 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3415490 Achille Giacometti, Fred Lado, Julio Largo, Giorgio Pastore, and Francesco Sciortino "Effects of patch size and number within a simple model of patchy colloids", Journal of Chemical Physics 132, 174110 (2010)]</ref><ref name="rovigatti">[http://dx.doi.org/10.1063/1.4737930 José Maria Tavares, Lorenzo Rovigatti, and Francesco Sciortino "Quantitative description of the self-assembly of patchy particles into chains and rings", Journal of Chemical Physics '''137''' 044901 (2012)]</ref>.		The "two-patch" and "four-patch" Bol (Chapman or Kern and Frenkel) model was extensively studied by Chapman and co-workers for bulk and interfacial systems using hard sphere and Lennard-Jones references. Later other groups, including Sciortino and co-workers, considered stronger association energies for the "two-patch" hard sphere reference <ref name="bianchi">[http://dx.doi.org/10.1063/1.2730797 F. Sciortino, E. Bianchi, J. Douglas and P. Tartaglia "Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation", Journal of Chemical Physics '''126''' 194903 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3415490 Achille Giacometti, Fred Lado, Julio Largo, Giorgio Pastore, and Francesco Sciortino "Effects of patch size and number within a simple model of patchy colloids", Journal of Chemical Physics 132, 174110 (2010)]</ref><ref name="rovigatti">[http://dx.doi.org/10.1063/1.4737930 José Maria Tavares, Lorenzo Rovigatti, and Francesco Sciortino "Quantitative description of the self-assembly of patchy particles into chains and rings", Journal of Chemical Physics '''137''' 044901 (2012)]</ref>.

	==Four patches==		==Four patches==

83.87.137.83 at 21:03, 25 May 2021

2021-05-25T21:03:50Z

← Older revision		Revision as of 23:03, 25 May 2021
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	f_{ij} \left(\hat{ {\mathbf r}}_{ij}; \tilde{ {\mathbf \Omega}}_i, \tilde{ {\mathbf \Omega}}_j \right) =		f_{ij} \left(\hat{ {\mathbf r}}_{ij}; \tilde{ {\mathbf \Omega}}_i, \tilde{ {\mathbf \Omega}}_j \right) =
	\left\{ \begin{array}{clc}		\left\{ \begin{array}{clc}
	1 & \mathrm{if} & \left\{ \begin{array}{ccc} & (\hat{e}_\alpha\cdot\hat{r}_{ij} \~~leq~~ \cos \delta) & \mathrm{for~some~patch~\alpha~on~}i \\		1 & \mathrm{if} & \left\{ \begin{array}{ccc} & (\hat{e}_\alpha\cdot\hat{r}_{ij} \geq \cos \delta) & \mathrm{for~some~patch~\alpha~on~}i \\
	\mathrm{and} & (\hat{e}_\beta\cdot\hat{r}_{ji} \~~leq~~ \cos \delta) & \mathrm{for~some~patch~\beta~on~}j \end{array} \right. \\		\mathrm{and} & (\hat{e}_\beta\cdot\hat{r}_{ji} \geq \cos \delta) & \mathrm{for~some~patch~\beta~on~}j \end{array} \right. \\
	0 & \mathrm{otherwise} & \end{array} \right.		0 & \mathrm{otherwise} & \end{array} \right.
	</math>		</math>

Carl McBride: Added Hard ellipsoid model variant

2016-12-12T16:03:38Z

Added Hard ellipsoid model variant

← Older revision		Revision as of 18:03, 12 December 2016
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	then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with [[Wertheim's first order thermodynamic perturbation theory (TPT1)\| Wertheim theory]] <ref name="bianchi"/><ref name="rovigatti"/>		then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with [[Wertheim's first order thermodynamic perturbation theory (TPT1)\| Wertheim theory]] <ref name="bianchi"/><ref name="rovigatti"/>

			==Hard ellipsoid model==
			The [[hard ellipsoid model]] has also been used as the 'nucleus' of the Kern and Frenkel patchy model <ref>[http://dx.doi.org/10.1063/1.4969074 T. N. Carpency, J. D. Gunton and J. M. Rickman "Phase behavior of patchy spheroidal fluids", Journal of Chemical Physics '''145''' 214904 (2016)]</ref>.
	==References==		==References==
	<references/>		<references/>

Carl McBride: /* References */ Added a recent publicatoin

2016-09-02T11:42:04Z

References: Added a recent publicatoin

← Older revision		Revision as of 13:42, 2 September 2016
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	*[http://dx.doi.org/10.1063/1.3689308 Christoph Gögelein, Flavio Romano, Francesco Sciortino, and Achille Giacometti "Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory", Journal of Chemical Physics '''136''' 094512 (2012)]		*[http://dx.doi.org/10.1063/1.3689308 Christoph Gögelein, Flavio Romano, Francesco Sciortino, and Achille Giacometti "Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory", Journal of Chemical Physics '''136''' 094512 (2012)]
	*[http://dx.doi.org/10.1063/1.4722477 Emanuela Bianchi, Günther Doppelbauer, Laura Filion, Marjolein Dijkstra, and Gerhard Kahl "Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms", Journal of Chemical Physics '''136''' 214102 (2012)]		*[http://dx.doi.org/10.1063/1.4722477 Emanuela Bianchi, Günther Doppelbauer, Laura Filion, Marjolein Dijkstra, and Gerhard Kahl "Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms", Journal of Chemical Physics '''136''' 214102 (2012)]
			*[http://dx.doi.org/10.1063/1.4960423 Z. Preisler, T. Vissers, F. Smallenburg and F. Sciortino "Crystals of Janus colloids at various interaction ranges", Journal of Chemical Physics '''145''' 064513 (2016)]


	[[category: models]]		[[category: models]]