Patchy particles: Difference between revisions
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The general model for a '''patchy particle''' is given by | 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> | <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> | ||
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where <math>u_{\mathrm {LJ}}(r_{ij})</math> is the [[Lennard-Jones model | Lennard-Jones potential]] and | where <math>u_{\mathrm {LJ}}(r_{ij})</math> is the [[Lennard-Jones model | Lennard-Jones potential]] and | ||
[[Image:patchy_model.png|center]] | [[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: | |||
====Surface coverage (A)==== | |||
====Aspect ratio (B)==== | |||
====Faceting (C)==== | |||
====Pattern quantisation (D)==== | |||
====Branching (E)==== | |||
====Chemical ordering (F)==== | |||
====Shape gradient (G)==== | |||
====Roughness (H)==== | |||
==See also== | ==See also== | ||
*[[Colloids]] | |||
*[[Emulsions]] | |||
*[[Janus particles]] | |||
*[[Phase diagram of anisotropic particles with octahedral symmetry]] | *[[Phase diagram of anisotropic particles with octahedral symmetry]] | ||
*[[Phase diagram of anisotropic particles with tetrahedral symmetry]] | *[[Phase diagram of anisotropic particles with tetrahedral symmetry]] | ||
*[[Wertheim's first order thermodynamic perturbation theory (TPT1)]] | |||
==References== | ==References== | ||
<references/> | <references/> | ||
'''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)] | |||
[[category: models]] | [[category: models]] | ||
Revision as of 13:16, 22 February 2010
The general model for a patchy particle [1] is given by [2]
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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. }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u_{\mathrm {LJ}}(r_{ij})} is the Lennard-Jones potential and
Anisotropy dimensions
Anisotropy dimensions is a classification scheme for patchy particles (See Figure 2 of [3]). The eight attributes are as follows:
Surface coverage (A)
Aspect ratio (B)
Faceting (C)
Pattern quantisation (D)
Branching (E)
Chemical ordering (F)
Shape gradient (G)
Roughness (H)
See also
- Colloids
- Emulsions
- Janus particles
- Phase diagram of anisotropic particles with octahedral symmetry
- Phase diagram of anisotropic particles with tetrahedral symmetry
- Wertheim's first order thermodynamic perturbation theory (TPT1)
References
- ↑ Zhenli Zhang and Sharon C. Glotzer "Self-Assembly of Patchy Particles", Nano Letters 4 pp. 1407-1413 (2004)
- ↑ 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)
- ↑ Sharon C. Glotzer and Michael J. Solomon "Anisotropy of building blocks and their assembly into complex structures", Nature Materials 6 pp. 557-562 (2007)
Related reading