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| [[Image:patchy_4.png|thumb|right| Artists impression of a tetrahedral patchy particle]] | | [[Image:patchy_4.png|thumb|right| Artists impression of a tetrahedral patchy particle]] |
| '''Anisotropic particles with tetrahedral symmetry''' | | The '''phase diagram of tetrahedral''' [[patchy particles]] <ref>[http://dx.doi.org/10.1021/jp9081905 F. Romano, E. Sanz and F. Sciortino "Role of the Range in the Fluid−Crystal Coexistence for a Patchy Particle Model", Journal of Physical Chemistry B '''113''' pp. 15133–15136 (2009)]</ref> |
| ==Kern and Frenkel model==
| | exhibits the following solid phases: [[Building up a diamond lattice |diamond crystal]] (DC), |
| ===Phase diagram===
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| The [[Phase diagrams |phase diagram]] of the tetrahedral [[Kern and Frenkel patchy model | Kern and Frenkel ]] [[patchy particles | patchy model]] exhibits the following solid phases<ref>[http://dx.doi.org/10.1021/jp9081905 Flavio Romano, Eduardo Sanz and Francesco Sciortino "Role of the Range in the Fluid−Crystal Coexistence for a Patchy Particle Model", Journal of Physical Chemistry B '''113''' pp. 15133–15136 (2009)]</ref><ref>[http://dx.doi.org/10.1063/1.3393777 Flavio Romano, Eduardo Sanz and Francesco Sciortino "Phase diagram of a tetrahedral patchy particle model for different interaction ranges", Journal of Chemical Physics '''132''' 184501 (2010)]</ref>:
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| [[Building up a diamond lattice |diamond crystal]] (DC), | |
| [[Building up a body centered cubic lattice | body centred cubic]] (BCC) and [[Building up a face centered cubic lattice |face centred cubic]] (FCC). The gas-liquid [[critical points | critical point]] becomes metastable with respect | | [[Building up a body centered cubic lattice | body centred cubic]] (BCC) and [[Building up a face centered cubic lattice |face centred cubic]] (FCC). The gas-liquid [[critical points | critical point]] becomes metastable with respect |
| to the diamond crystal when the range of the interaction becomes short (roughly less than 15% of the | | to the diamond crystal when the range of the interaction becomes short (roughly less than 15% of the |
| diameter). | | diameter). |
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| :[[Image:romanojpcb09.gif]] | | :[[Image:romanojpcb09.gif]] |
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| In contrast to isotropic models, the critical point becomes only weakly metastable with respect to the solid as the interaction range | | In contrast to isotropic models, the critical point becomes only weakly metastable with respect to the solid as the interaction range |
| narrows (from left to right in the figure). | | narrows (from left to right in the figure). |
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| ===Crystallization===
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| Tetrahedral Kern-Frenkel patchy particles crystallise spontaneously into open tetrahedral networks for narrow patches (solid angle < 30). The interaction range does not play an important role in crystallisation <ref>[http://dx.doi.org/10.1063/1.3578182 Flavio Romano, Eduardo Sanz, and Francesco Sciortino "Crystallization of tetrahedral patchy particles in silico", Journal of Chemical Physics '''134''' 174502 (2011)]</ref>
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| [[Image:fig5.jpg]]
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| Interaction range, <math>\delta</math>, versus patch angular width.
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| Diamonds correspond to crystallising and circles to glass–forming models.
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| The point studied in Ref. <ref>[http://dx.doi.org/10.1063/1.3578182 Zhenli Zhang, Aaron S. Keys, Ting Chen, and Sharon C. Glotzer "Self-Assembly of Patchy Particles into Diamond Structures through Molecular Mimicry", Langmuir '''21''' 11547 (2005)]</ref> is included.
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| When the patches in this model are made even wider (while still enforcing the limit of a single bond per patch), the diamond phase becomes metastable with respect to a liquid phase, which is stable even in the zero-temperature limit <ref>[http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2693.html Frank Smallenburg and Francesco Sciortino "Liquids more stable than crystals in particles with limited valence and flexible bonds", Nature Physics '''9''' 554 (2013)]</ref>.
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| ==Modulated patchy Lennard-Jones model==
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| The solid phases of the [[modulated patchy Lennard-Jones model]] has also been studied <ref>[http://dx.doi.org/10.1063/1.3454907 Eva G. Noya, Carlos Vega, Jonathan P. K. Doye, and Ard A. Louis "The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry", Journal of Chemical Physics '''132''' 234511 (2010)]</ref>
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| ==Lattice model==
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| <ref>[http://dx.doi.org/10.1080/00268976.2010.523521 N. G. Almarza and E. G. Noya "Phase transitions of a lattice model for patchy particles with tetrahedral symmetry", Molecular Physics '''109''' pp. 65-74 (2011)]</ref>
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| ==See also== | | ==See also== |
| *[[PMW]] (primitive model for [[water]]) | | *[[PMW]] (primitive model for water) |
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| == References == | | == References == |
| <references/> | | <references/> |
| ;Related reading
| | '''Related reading''' |
| *[http://dx.doi.org/10.1063/1.3582904 G. Munaó, D. Costa, F. Sciortino, and C. Caccamo "Simulation and theory of a model for tetrahedral colloidal particles", Journal of Chemical Physics '''134''' 194502 (2011)] | | *[http://dx.doi.org/10.1080/00268978700101051 Jiří Kolafa and Ivo Nezbeda "Monte Carlo simulations on primitive models of water and methanol", Molecular Physics '''61''' pp. 161-175 (1987)] |
| *[http://dx.doi.org/10.1063/1.4840695 Ivan Saika-Voivod, Frank Smallenburg and Francesco Sciortino "Understanding tetrahedral liquids through patchy colloids", Journal of Chemical Physics '''139''' 234901 (2013)] | | *[http://dx.doi.org/10.1088/0953-8984/19/32/322101 Flavio Romano, Piero Tartaglia and Francesco Sciortino "Gas–liquid phase coexistence in a tetrahedral patchy particle model", Journal of Physics: Condensed Matter '''19''' 322101 (2007)] |
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| [[category: models]] | | [[category: models]] |