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/10.1063/1.2730797  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>.
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>.


==Four patches==
==Four patches==
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</math>
</math>


then the patch cannot be involved in more than one bond.
then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with Wertheim theory <ref name="bianchi"/><ref name="rovigatti"/>


==References==
==References==

Revision as of 15:59, 26 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 cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with Wertheim theory [2][4]

References

Related reading