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[[Image:polyhedron.png|thumb|right]]
 
The '''hard polyhedra model''' is an approximation to describe the behavior of anisotropic colloidal particles<ref>[http://dx.doi.org/10.1038/nmat1949 Sharon C. Glotzer and Michael Solomon "Anisotropy of building blocks and their assembly into complex structures", Nature Materials '''6''' pp. 557 - 562 (2007)]</ref> with screened interaction.
 
The '''hard polyhedra model''' is an approximation to describe the behavior of anisotropic colloidal particles<ref>[http://dx.doi.org/10.1038/nmat1949 Sharon C. Glotzer and Michael Solomon "Anisotropy of building blocks and their assembly into complex structures", Nature Materials '''6''' pp. 557 - 562 (2007)]</ref> with screened interaction.
  
 
It was first pointed out by Agarwal and Escobedo <ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230–235 (2011)]</ref> the possibility that measures of shape could lead to a roadmap of the structures to be self-assembled: very anisotropic particles would lead to the formation of liquid crystals while very spherical ones would form plastic crystals at intermediate packing fractions.
 
It was first pointed out by Agarwal and Escobedo <ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230–235 (2011)]</ref> the possibility that measures of shape could lead to a roadmap of the structures to be self-assembled: very anisotropic particles would lead to the formation of liquid crystals while very spherical ones would form plastic crystals at intermediate packing fractions.
  
Later, Damasceno, Engel and Glotzer <ref>[http://dx.doi.org/10.1126/science.1220869 Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Predictive Self-Assembly of Polyhedra into Complex Structures", Science '''337''' pp. 453-457 (2012)]</ref>. showed that, in addition to the sphericity of the particle (measured by calculating its isoperimetric quotient), by knowing the types of "bonds" that a given polyhedron is able to make already in the dense liquid the class of crystalline structure could be predicted. That was made possible due to the observation that facetted particles tend to maximize their face-to-face contacts at intermediate packing fractions. <ref>[http://dx.doi.org/10.1021/nn204012y Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces", ACS Nano '''6''' pp. 609-614 (2012)]</ref>.
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Later, Damasceno, Engel and Glotzer[http://dx.doi.org/10.1126/science.1220869 Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Predictive Self-Assembly of Polyhedra into Complex Structures", Science '''337''' pp. 453-457 (2012)]</ref>. showed that, in addition to the sphericity of the particle - measured by calculating its isoperimetric quotient, by knowing the types of "bonds" that a given polyhedron is able to make already in the dense liquid the class of crystalline structure could be predicted. That was made possible due to the observation that facetted particles tend to maximize their face-to-face contacts at intermediate packing fractions.[http://dx.doi.org/10.1021/nn204012y Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces", ACS Nano '''6''' pp. 609-614 (2012)]</ref>.
  
 
==References==
 
==References==
 
<references/>
 
<references/>
 
'''Related reading'''
 
'''Related reading'''
*[http://dx.doi.org/10.1126/science.1226162 de Graaf and Manna "A Roadmap for the Assembly of Polyhedral Particles", Science '''337''' pp. 417-418 (2012)]
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*[http://dx.doi.org/10.1126/science.1226162 de Graaf and Mana "A Roadmap for the Assembly of Polyhedral Particles", Science '''337''' pp. 417-418 (2012)]
*[http://dx.doi.org/10.1103/PhysRevX.4.011024 Elizabeth R. Chen, Daphne Klotsa, Michael Engel, Pablo F. Damasceno, and Sharon C. Glotzer "Complexity in Surfaces of Densest Packings for Families of Polyhedra", Physical Review X '''4''' 011024 (2014)]  
 
  
 
[[category: models]]
 
[[category: models]]

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