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| '''Patchy particles''' <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> are models designed to keep pace with the rapid advances in the field of [[colloids]]. It is now possible to synthesise or fabricate tiny particles that have a variety of shapes, composition etc. In order to simulate these structures, there is a corresponding growth in the number of [[idealised models]] being developed and studied. With a view to classifying | | The general model for a '''patchy particle''' is given by |
| these "patchy" models the idea of "anisotropy dimensions" has been put forward.
| | <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> |
| ==Taxonomy: anisotropy dimensions==
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| 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>.
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| The eight attributes are as follows:
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| ====Surface coverage (A)====
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| :[[Image:patchy_dimension_A.png|500px]]
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| ====Aspect ratio (B)====
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| :::[[Image:patchy_dimension_B.png|500px]]
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| ====Faceting (C)====
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| :[[Image:patchy_dimension_C.png|500px]]
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| ====Pattern quantisation (D)====
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| :[[Image:patchy_dimension_D.png|500px]]
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| ====Branching (E)====
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| :[[Image:patchy_dimension_E.png|500px]]
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| ====Chemical ordering (F)====
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| :::[[Image:patchy_dimension_F.png|500px]]
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| ====Shape gradient (G)====
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| :::[[Image:patchy_dimension_G.png|500px]]
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| ====Roughness (H)====
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| ::[[Image:patchy_dimension_H.png|500px]]
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| ==Models== | | :<math>u_{\mathrm {patchy}}({\mathbf r}_{ij},{\mathbf \Omega}_i,{\mathbf \Omega}_j) = |
| *[[Bol model of water]]
| | \left\{ \begin{array}{lll} |
| *[[Dahl and Andersen model of water]]
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| *[[Inverse patchy colloids]]
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| *[[Kern and Frenkel patchy model]]
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| *[[Modulated patchy Lennard-Jones model]]
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| *[[Smith and Nezbeda associated fluid model]]
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| *[[Laponite]]
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| | u_{\mathrm {LJ}}(r_{ij}) & ; & r_{ij} < \sigma_{\mathrm {LJ}} \\ |
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| | 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]] |
| ==See also== | | ==See also== |
| *[[Colloids]]
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| *[[Emulsions]]
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| *[[Janus particles]]
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| *[[Phase diagram of anisotropic particles with octahedral symmetry]] | | *[[Phase diagram of anisotropic particles with octahedral symmetry]] |
| *[[Anisotropic particles with tetrahedral symmetry]] | | *[[Phase diagram of anisotropic particles with tetrahedral symmetry]] |
| *[[Wertheim's first order thermodynamic perturbation theory (TPT1)]]
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| *[[TPT-CF| Multi-patch RTPT-CF]]
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| ==References== | | ==References== |
| <references/> | | <references/> |
| '''Related reading'''
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| *[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)]
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| *[http://dx.doi.org/10.1038/nmat2927 Willem K. Kegel and Henk N. W. Lekkerkerker "Colloidal gels: Clay goes patchy", Nature Materials '''10''' pp. 5-6 (2011)]
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| *[http://dx.doi.org/10.1021/la3017563 Zhenping He and Ilona Kretzschmar "Template-Assisted Fabrication of Patchy Particles with Uniform Patches", Langmuir '''28''' pp. 9915-9919 (2011)]
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| [[category: models]] | | [[category: models]] |