Editing Patchy particles
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''' | The general model for a '''patchy particle''' <ref>[http://dx.doi.org/10.1021/nl0493500 Zhenli Zhang and Sharon C. Glotzer "Self-Assembly of Patchy Particles", Nano Letters '''4''' pp. 1407-1413 (2004)]</ref> is given by | ||
<ref>[http://dx.doi.org/10.1039/b614955c Jonathan P. K. Doye, Ard A. Louis, I-Chun Lin, Lucy R. Allen, Eva G. Noya, Alex W. Wilber, Hoong Chwan Kok and Rosie Lyus "Controlling crystallization and its absence: proteins, colloids and patchy models", Physical Chemistry Chemical Physics '''9''' pp. 2197-2205 (2007)]</ref> | |||
== | |||
Anisotropy dimensions is a classification scheme for patchy particles <ref>[http://dx.doi.org/10.1038/nmat1949 Sharon C. Glotzer and Michael J. Solomon "Anisotropy of building blocks and their assembly into complex structures", Nature Materials '''6''' pp. 557-562 (2007)]</ref>. | :<math>u_{\mathrm {patchy}}({\mathbf r}_{ij},{\mathbf \Omega}_i,{\mathbf \Omega}_j) = | ||
\left\{ \begin{array}{lll} | |||
u_{\mathrm {LJ}}(r_{ij}) & ; & r_{ij} < \sigma_{\mathrm {LJ}} \\ | |||
u_{\mathrm{LJ}}(r_{ij}) \exp \left(-\frac{\theta_{k_{min},ij}^2}{2\sigma^2 } \right) \exp \left(-\frac{\theta_{l_{min},ji}^2}{2\sigma^2 } \right) | |||
& ; & r_{ij} \ge \sigma_{\mathrm{LJ}} | |||
\end{array} \right. | |||
</math> | |||
where <math>u_{\mathrm {LJ}}(r_{ij})</math> is the [[Lennard-Jones model | Lennard-Jones potential]] and | |||
[[Image:patchy_model.png|center]] | |||
==Anisotropy dimensions== | |||
Anisotropy dimensions is a classification scheme for patchy particles (See Figure 2 of <ref>[http://dx.doi.org/10.1038/nmat1949 Sharon C. Glotzer and Michael J. Solomon "Anisotropy of building blocks and their assembly into complex structures", Nature Materials '''6''' pp. 557-562 (2007)]</ref>). | |||
The eight attributes are as follows: | The eight attributes are as follows: | ||
====Surface coverage (A)==== | ====Surface coverage (A)==== | ||
====Aspect ratio (B)==== | ====Aspect ratio (B)==== | ||
====Faceting (C)==== | ====Faceting (C)==== | ||
====Pattern quantisation (D)==== | ====Pattern quantisation (D)==== | ||
====Branching (E)==== | ====Branching (E)==== | ||
====Chemical ordering (F)==== | ====Chemical ordering (F)==== | ||
====Shape gradient (G)==== | ====Shape gradient (G)==== | ||
====Roughness (H)==== | ====Roughness (H)==== | ||
==See also== | ==See also== | ||
*[[Colloids]] | *[[Colloids]] | ||
*[[Emulsions]] | *[[Emulsions]] | ||
*[[Janus particles]] | *[[Janus particles]] | ||
*[[Kern and Frenkel patchy model]] | |||
*[[Phase diagram of anisotropic particles with octahedral symmetry]] | *[[Phase diagram of anisotropic particles with octahedral symmetry]] | ||
*[[ | *[[Phase diagram of anisotropic particles with tetrahedral symmetry]] | ||
*[[Smith and Nezbeda associated fluid model]] | |||
*[[Wertheim's first order thermodynamic perturbation theory (TPT1)]] | *[[Wertheim's first order thermodynamic perturbation theory (TPT1)]] | ||
==References== | ==References== | ||
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'''Related reading''' | '''Related reading''' | ||
*[http://dx.doi.org/10.1002/marc.200900614 Amar B. Pawar and Ilona Kretzschmar "Fabrication, Assembly, and Application of Patchy Particles", Macromolecular Rapid Communications '''31''' pp. 150-168 (2010)] | *[http://dx.doi.org/10.1002/marc.200900614 Amar B. Pawar and Ilona Kretzschmar "Fabrication, Assembly, and Application of Patchy Particles", Macromolecular Rapid Communications '''31''' pp. 150-168 (2010)] | ||
[[category: models]] | [[category: models]] |