Kern and Frenkel patchy model: Difference between revisions
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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== | ==Two patches== | ||
The "two-patch" Kern and Frenkel model has been extensively studied by Sciortino and co-workers <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>[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" Kern and Frenkel model has been extensively studied by Sciortino and co-workers <ref>[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>[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== | ||
:''Main article: [[Anisotropic particles with tetrahedral symmetry]]'' | :''Main article: [[Anisotropic particles with tetrahedral symmetry]]'' | ||
==Single-bond-per-patch-condition== | |||
If the two parameters <math>\delta</math> and <math>\lambda</math> fullfil the condition | |||
<math> | |||
\sin{\delta} \leq \dfrac{1}{2(1+\lambda\sigma)} | |||
</math> | |||
then the patch can not be involved in more than one bond. | |||
==References== | ==References== |
Revision as of 10:29, 11 December 2012
The Kern and Frenkel [1] patchy model is an amalgamation of the hard sphere model with attractive square well patches (HSSW). The potential has an angular aspect, given by (Eq. 1)
where the radial component is given by the square well model (Eq. 2)
and the orientational component is given by (Eq. 3)
where is the solid angle of a patch () whose axis is (see Fig. 1 of Ref. 1), forming a conical segment.
Two patches
The "two-patch" Kern and Frenkel model has been extensively studied by Sciortino and co-workers [2][3][4].
Four patches
- Main article: Anisotropic particles with tetrahedral symmetry
Single-bond-per-patch-condition
If the two parameters and fullfil the condition
then the patch can not be involved in more than one bond.
References
- ↑ Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)
- ↑ 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)
- ↑ 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)
- ↑ 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)
- Related reading
- 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)
- 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)