SklogWiki - User contributions [en]

User talk:Lrovigatti

2015-03-04T14:11:57Z

Lrovigatti: /* UNIQ-QINU problem */

Dear Lrovigatti,
:I am sorry to have had to undo part of your recent change to the [[Materials modelling and computer simulation codes]] page. The reason for this is that part of your change seems to have caused a problem (type: UNIQ QINU) with some part of one of the MediaWiki parsers that I am using. In particular it *seems* to be related to the [http://www.mediawiki.org/wiki/Extension:Cite Cite extension]. I have just downloaded the latest release of Cite ((201992c) of 21:25, 2 February 2015) which does not look to have retrospectively solved the situation. If you would like to retry your page edit you are most welcome. Sorry for the inconvenience.
::All the best, --[[User:Carl McBride | Carl McBride]] ([[User_talk:Carl_McBride |talk]]) 13:44, 4 February 2015 (CET)

== UNIQ-QINU problem ==

Dear Lrovigatti
:I have upgraded to MediaWiki 1.23.8 and uninstalled [http://www.mediawiki.org/wiki/Extension:MathJax MathJax] which, on the one hand seems to be no longer supported, and on the other I think was the source of the parser errors on this site. Hopefully now all is in working order.
::All the best, --[[User:Carl McBride | Carl McBride]] ([[User_talk:Carl_McBride |talk]]) 13:08, 9 February 2015 (CET)

Dear Carl,
:thank you for your help and I'm sorry to have generated this issue in the first place!
:: best, Lorenzo

Materials modelling and computer simulation codes

2015-02-04T11:43:15Z

Lrovigatti:

The following is a sortable list (to change sort criteria click on the square icon next to the column title) of software for use in materials modelling and computer simulation. The use of simulation software whose source code you have access to (for example, Open Source, or GNU General Public License) is a fundamental tenet of good practice, and is highly recommended UNIQa911968f3393a19a-ref-00000004-QINU.
{| class="wikitable sortable" border="1" cellpadding="5" cellspacing="0"
|-
! Computer program !! Focus !! class="unsortable" | Notes !! License
|-
|[[Abalone]]
|[[molecular dynamics]], visualisation
|biopolimers
|Free
|-
|[[ACEMD]]
|[[molecular dynamics]]
|biopolimers
|commercial
|-
|[[AMBER -- Assisted Model Building with Energy Refinement | AMBER]]
|[[molecular dynamics]]
|Assisted Model Building with Energy Refinement
|commercial
|-
|[[AVOGADRO]] [http://avogadro.openmolecules.net/wiki/Main_Page]
|visualisation
|molecule editor and visualizer
|free
|-
|[[BD_BOX]]
|[[Brownian dynamics]]
|scalable (CPU/GPU) Brownian dynamics package for UNIX/LINUX platforms
|GNU Public License
|-
|[[BOSS]]
|
| '''B'''iochemical and '''O'''rganic '''S'''imulation '''S'''ystem
|commercial
|-
|[[BRAHMS]]
|[[molecular dynamics]]
|'''B'''iomembrane '''R'''educed-'''A'''pproac'''H''' '''M'''olecular '''S'''imulator
|in development
|-
|[[CASTEP]]
|[[density-functional theory]]
|
|commercial (free in United Kingdom)
|-
|[[CCP5 Program Library]]
|various
|program library
|free to academics
|-
|[[CHARMM]]
|
|'''C'''hemistry at '''HAR'''vard '''M'''olecular '''M'''echanics
|commercial
|-
|[[CPMD]]
|[[ab initio molecular dynamics]]
|'''C'''arr-'''P'''arrinello '''M'''olecular '''D'''ynamics
|free with [http://www.cpmd.org/cpmd_licence.html license]
|-
|[[Dalton]]
|
|Computational chemistry
|free with [http://www.theochem.kth.se/dalton/ license]
|-
|[[DiMol2D]]
|[[molecular dynamics]]
|Molecular dynamics visualization
|free executable
|-
|[[DL_MESO]]
|[[dissipative particle dynamics]]
|Mesoscale simulation package
|free source with [http://www.cse.scitech.ac.uk/ccg/software/DL_MESO/Registration.shtml academic license]
|-
|[[DL_POLY]]
|[[molecular dynamics]]
|Molecular simulation package
|free source with [http://www.cse.scitech.ac.uk/ccg/software/DL_POLY/Registration.shtml academic license]
|-
|[[DYNAMO]]
|[[molecular dynamics]]
|[[Event-driven molecular dynamics]]
|free source
|-
|[[EGO VIII]]
|[[molecular dynamics]]
|
|free
|-
|[[ENCAD]]
|[[molecular dynamics]]
|'''En'''ergy '''Ca'''lculation and '''D'''ynamics
|
|-
|[[ESPResSo]]
|[[molecular dynamics]]
|'''E'''xtensible '''S'''imulation '''P'''ackage for '''Res'''earch on '''So'''ft matter
|free
|-
|[[Etomica]]
|
|development environment
|free
|-
|[[FOCUS]]
|molecular dynamics analysis
|
|
|-
|[[Gaussian]]
|electronic structure
|Computational chemistry
|commercial
|-
|[[gdpc]]
|visualisation
|molecular dynamics visualisation
|free (GNU license)
|-
|[[GPEC]] [http://gpec.phasety.com]
|[[Binary phase diagrams]]
|'''G'''lobal '''P'''hase '''E'''quilibrium '''C'''alculations
|free
|-
|[[GPIUTMD]]
|[[molecular dynamics]]
|'''G'''raphical '''P'''rocessors at '''I'''sfahan '''U'''niversity of '''T'''echnology for '''M'''any-particle '''D'''ynamics
|not free, commercial
|-
|[[GROMACS]]
|[[molecular dynamics]]
|
|free source
|-
|[[GROMOS]]
|[[molecular dynamics]]
|biomolecular systems
|free for academics, fee otherwise
|-
|[[GULP]]
|[[lattice dynamics]]
|'''G'''eneral '''U'''tility '''L'''attice '''P'''rogram
|free for academics, fee otherwise
|-
|[[HOOMD]]
|[[molecular dynamics]]
|'''H'''ighly '''O'''ptimized '''O'''bject Oriented '''M'''olecular '''D'''ynamics.
|free, Open Source
|-
|[[IMD]]
|[[molecular dynamics]]
|
|
|-
|[[Jmol]]
|visualisation
|
|free
|-
|[[LAMMPS]]
|[[molecular dynamics]]
|
|free source (GNU license)
|-
|[[MACSIMUS]]
|[[molecular dynamics]]
|'''MAC'''romolecule '''SIMU'''lation '''S'''oftware
|free
|-
|[[MAPS]] [http://www.scienomics.com/products/molecular-modeling-platform]
|simulation front-end
|'''Ma'''terials '''P'''rocesses and '''S'''imulations
|commercial
|-
|[[Materials Studio]]
|various
|
|commercial
|-
|[[MCCCS Towhee]]
|[[Monte Carlo]]
|
|free source
|-
|[[MCPRO]]
|[[Monte Carlo]]
|peptides, proteins, and nucleic acids in solution
|commercial
|-
|[[MDynaMix]]
|[[molecular dynamics]]
|molecular dynamics of mixtures
|free (GNU license)
|-
|[[MOIL]]
|[[molecular dynamics]]
|
|Open Source
|-
|[[Moldy]]
|[[molecular dynamics]]
|
|free
|-
|[[Molecular Workbench]]
|
|Interactive simulations
|free, Open Source
|-
|[[Moscito]]
|[[molecular dynamics]]
|
|free (General Public License)
|-
|[[Music]]
|
|'''Mu'''ltipurpose '''Si'''mulation '''C'''ode
|free (General Public License)
|-
|[[NAMD]]
|[[molecular dynamics]]
|
|free
|-
|[[NWChem]]
|
|Computational chemistry
|free
|-
|[[OCCAM]]
|[[molecular dynamics]]
|
|free
|-
|[[OpenMD]]
|[[molecular dynamics]]
|
|free - Open Source
|-
|[[ORAC]]
|[[molecular dynamics]]
|
|free
|-
|[https://dna.physics.ox.ac.uk/index.php/Main_Page oxDNA]
|[[Monte Carlo]] and [[brownian dynamics]]
|simulation code that implements coarse-grained model for DNA and RNA [http://dx.doi.org/10.1063/1.3552946]
|free (GNU General Public License)
|-
|[[Packmol]]
|[[molecular dynamics]]
|creates an initial configuration for use in simulations
|free (GNU license)
|-
|[[Peacemaker]]
|statistical thermodynamics
|Quantum cluster equilibrium calculations.
|free (GNU GPL v3)
|-
|[[PINY_MD]]
|[[molecular dynamics]]
|
|free
|-
|[[Protein Explorer]]
|visualisation
|molecular graphics
|free
|-
|[[PyMol]] [http://www.pymol.org/]
|visualisation
|molecular graphics
|commercial (academic: free)
|-
|[[Q]] [http://xray.bmc.uu.se/~aqwww/q/]
|[[molecular dynamics]]
|[[Helmholtz energy function |free energy]] calculations in [[Biological systems | biomolecular systems]]
|free with [http://xray.bmc.uu.se/~aqwww/q/q_license.pdf licence]
|-
|[[QMGA]]
|visualisation
|molecular graphics
|free source
|-
|[[RasMol]]
|visualisation
|molecular graphics
|free source
|-
|[[RedMD]]
|[[molecular dynamics]]
|'''Red'''uced '''M'''olecular '''D'''ynamics
|free, Open source
|-
|[[SageMD]]
|simulation front and back end
|
|
|-
|[[SIESTA]]
|[[ab initio molecular dynamics]]
|'''S'''panish '''I'''nitiative for '''E'''lectronic '''S'''imulations with '''T'''housands of '''A'''toms
|free for academics, fee otherwise
|-
|[[SMMP]]
|[[Monte Carlo]]
|'''S'''imple '''M'''olecular '''M'''echanics for '''P'''roteins
|free (General Public License) with restrictions
|-
|[[SYBYL]]
|various
|
|commercial
|-
|[[Tesla Bio Workbench]]
|
|GPU computing
|
|-
|[[TINKER]]
|
|Software tools for molecular design
|free source
|-
|[[toyMD]]
|[[molecular dynamics]]
|
|free (non-commercial)
|-
|[[UHBD]]
|[[brownian dynamics]]
|'''U'''niversity of '''H'''ouston '''B'''rownian '''D'''ynamics
|license required
|-
|[[VASP]]
|[[ab initio molecular dynamics]]
|
|
|-
|[[VMD]]
|visualisation
|Molecular dynamics visualisation in 3-dimensions
|free
|-
|[[WIEN2K]]
|
|Electronic structure calculation in solids
|commercial
|-
|[[XCrysDen]]
|visualisation
|Crystalline and molecular structure visualisation
|free (General Public License)
|-
|[[XMakemol]] [http://www.nongnu.org/xmakemol/]
|visualisation
|
|free
|-
|[[X-PLOR]]
|
|Computational structural biology
|
|-
|[[YASARA]]
|
|
|free & commercial
|-
|[[YASP]] [http://www.theo.chemie.tu-darmstadt.de/group/services/yaspdoc/yaspdoc.html]
|[[molecular dynamics]]
|
|
|}

UNIQa911968f3393a19a-references-00000005-QINU
[[category: Materials modelling and computer simulation codes]]

Hard core Yukawa potential

2014-02-14T15:11:43Z

Lrovigatti: /* Critical point */

The '''hard core Yukawa''' potential <ref>[http://dx.doi.org/10.1016/0378-4371(89)90108-8 J. S. Rowlinson "The Yukawa potential", Physica A: Statistical Mechanics and its Applications '''156''' pp. 15-34 (1989)]</ref>
has two forms, the attractive Yukawa potential:

:<math>
\Phi_{12}\left( r \right) =
\left\{ \begin{array}{lll}
\infty & ; & r < \sigma \\
- \left( \frac{ \epsilon \sigma }{r}\right) \exp \left[- \kappa \left( \frac{r}{\sigma} - 1 \right) \right] & ; & r \ge \sigma
\end{array} \right.
</math>

and the repulsive form

:<math>
\Phi_{12}\left( r \right) =
\left\{ \begin{array}{lll}
\infty & ; & r < \sigma \\
\left( \frac{ \epsilon \sigma }{r}\right) \exp \left[- \kappa \left( \frac{r}{\sigma} - 1 \right) \right] & ; & r \ge \sigma
\end{array} \right.
</math>

where <math> \Phi\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> is the distance between site 1 and site 2,
<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
<math> \kappa </math> is a parameter that controls the interaction range (<math> \kappa > 0 </math>).

The repulsive form has been used to study charge-stabilised [[Colloids |colloid-colloid]] interactions.
==Critical point==
For the attractive form of the potential, from a study of the [[law of corresponding states]], one has (Eq. 3 in <ref>[http://dx.doi.org/10.1063/1.2883694 Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics '''128''' 134508 (2008)]</ref>)

:<math>P_c = 0.0228 + 0.0742 T_c</math>

and (Eq. 4)

:<math>\rho_c = 0.2534 + 0.071 \frac{1}{T_c}</math>
The repulsive form of the potential has no [[Critical points | critical point]].

==Triple points==
The [[triple point |triple points]] for this model have been studied by Azhar and co-workers
<ref>[http://dx.doi.org/10.1063/1.481068 Fouad El Azhar, Marc Baus, Jean-Paul Ryckaert and Evert Jan Meijer "Line of triple points for the hard-core Yukawa model: A computer simulation study", Journal of Chemical Physics '''112''' pp. 5121- (2000)]</ref>.
==Virial coefficients==
For the attractive form of the potential the [[Virial equation of state |virial coefficients]] have been calculated by Naresh and Singh <ref>[http://dx.doi.org/10.1016/j.fluid.2009.06.019 D.J. Naresh and Jayant K. Singh "Virial coefficients of hard-core attractive Yukawa fluids", Fluid Phase Equilibria '''285''' pp. 36-43 (2009)]</ref>.
==Liquid-vapour coexistence==
<ref>[http://dx.doi.org/10.1063/1.3385894 E. B. El Mendoub, J.-F. Wax, and N. Jakse "Evolution of the liquid-vapor coexistence of the hard-core Yukawa fluid as a function of the interaction range", Journal of Chemical Physics '''132''' 164503 (2010)]</ref>
==Surface tension==
[[Surface tension]] <ref>[http://dx.doi.org/10.1063/1.3578637 G. Odriozola, M. Bárcenas, and P. Orea "Vapor–liquid surface tension of strong short-range Yukawa fluid", Journal of Chemical Physics '''134''' 154702 (2011)]</ref>.
==Radial distribution function==
[[Radial distribution function]]<ref>[http://dx.doi.org/10.1080/00268976.2010.505586 Douglas Henderson and Dezső Boda "Mean spherical approximation for the Yukawa fluid radial distribution function", Molecular Physics '''109''' pp. 1009-1013 (2011)]</ref>
==Phase diagram==
[[Phase diagrams | Phase diagram]]
<ref>[http://dx.doi.org/10.1063/1.466781 Enrique Lomba and Noé G. Almarza "Role of the interaction range in the shaping of phase diagrams in simple fluids. The hard sphere Yukawa fluid as a case study", Journal of Chemical Physics '''100''' pp. 8367-8372 (1994)]</ref>
<ref>[http://dx.doi.org/10.1063/1.467526 M. H. J. Hagen and D. Frenkel "Determination of phase diagrams for the hard-core attractive Yukawa system", Journal of Chemical Physics '''101''' pp. 4093-4097 (1994)]</ref>
<ref>[http://dx.doi.org/10.1063/1.2743623 Yurko Duda, Ascención Romero-Martínez, and Pedro Orea "Phase diagram and surface tension of the hard-core attractive Yukawa model of variable range: Monte Carlo simulations", Journal of Chemical Physics '''126''' 224510 (2007)]</ref>
<ref>[http://dx.doi.org/10.1063/1.2883694 Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics '''128''' 134508 (2008)]</ref>
==Density-functional theory==
[[Density-functional theory]] <ref>[http://dx.doi.org/10.1063/1.4742154 Marius M. Hatlo, Priyanka Banerjee, Jan Forsman, and Leo Lue "Density functional theory for Yukawa fluids", Journal of Chemical Physics '''137''' 064115 (2012)]</ref>.
==Two-term Yukawa potentials==
Both the attractive and the repulsive form have been combined to produce the ''hard-sphere plus two Yukawa potential'' (H2Y) <ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref>.
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.3281416 J. Torres-Arenas, L. A. Cervantes, A. L. Benavides, G. A. Chapela, and F. del Río "Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials", Journal of Chemical Physics '''132''' 034501 (2010)]
*[http://dx.doi.org/10.1063/1.3357352 Pedro Orea, Carlos Tapia-Medina, Davide Pini, and Albert Reiner "Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory", Journal of Chemical Physics '''132''' 114108 (2010)]
*[http://dx.doi.org/10.1063/1.3610400 Eun-Young Kim, Soon-Chul Kim, and Baek-Seok Seong "Structure and thermodynamics of hard-core Yukawa fluids: Thermodynamic perturbation approaches", Journal of Chemical Physics '''135''' 034505 (2011)]

[[Category: Models]]

Dipolar hard spheres

2013-09-04T08:06:40Z

Lrovigatti: /* Phase diagram */

{{Stub-general}}
'''Dipolar hard spheres''' consist of the [[hard sphere model]] in conjunction with a [[dipole moment]].
==Virial coefficients==
The [[Virial equation of state | virial coefficients]] <ref>[http://dx.doi.org/10.1063/1.2736370 Konstantin I. Morozov "The dielectric virial expansion and the models of dipolar hard-sphere fluid", Journal of Chemical Physics '''126''' 194506 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3615723 Douglas Henderson "Second virial coefficient for the dipolar hard sphere fluid", Journal of Chemical Physics '''135''' 044514 (2011)]</ref>.
==Phase diagram==
<ref>[http://dx.doi.org/10.1103/PhysRevLett.71.2729 J. J. Weis and D. Levesque "Chain formation in low density dipolar hard spheres: A Monte Carlo study", Physical Review Letters '''71''' pp. 2729-2732 (1993)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevLett.71.3991 M. E. van Leeuwen and B. Smit "What makes a polar liquid a liquid?", Physical Review Letters '''71''' pp. 3991-3994 (1993)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevE.48.3728 J. J. Weis and D. Levesque "Ferroelectric phases of dipolar hard spheres", Physical Review E '''48''' pp. 3728-3740 (1993)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevLett.76.2310 Richard P. Sear "Low-Density Fluid Phase of Dipolar Hard Spheres", Physical Review Letters '''76''' pp. 2310-2313 (1996)]</ref>
<ref>[http://dx.doi.org/10.1209/0295-5075/80/56002 Y. V. Kalyuzhnyi, I. A. Protsykevytch and P. T. Cummings "Thermodynamic properties and liquid-gas phase diagram of the dipolar hard-sphere fluid", Europhysics Letters '''80''' 56002 (2007)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevLett.107.237801 L. Rovigatti, J. Russo and F. Sciortino "No Evidence of Gas-Liquid Coexistence in Dipolar Hard Spheres", Physical Review Letters '''107''' p. 237801 (2011)]</ref>
<ref>[http://dx.doi.org/10.1080/00268976.2011.610368 D. Levesque and J.-J. Weis "Stability of solid phases in the dipolar hard sphere system", Molecular Physics '''109''' pp. 2747-2756 (2011)]</ref>

==References==
<references/>
[[category:models]]
[[category:hard sphere]]

Kern and Frenkel patchy model

2012-12-26T14:59:28Z

Lrovigatti:

The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles |patchy model]] is an amalgamation of the [[hard sphere model]] with
attractive [[Square well model | square well]] patches (HSSW). The potential has an angular aspect, given by (Eq. 1)

:<math>\Phi_{ij}({\mathbf r}_{ij}; \tilde{{\mathbf \Omega}}_i, \tilde{{\mathbf \Omega}}_j) =\Phi_{ij}^{ \mathrm{HSSW}}({\mathbf r}_{ij}) \cdot f(\tilde{{\mathbf \Omega}}_i, \tilde{{\mathbf \Omega}}_j) </math>

where the radial component is given by the square well model (Eq. 2)

:<math>
\Phi_{ij}^{ \mathrm{HSSW}} \left({\mathbf r}_{ij} \right) =
\left\{ \begin{array}{ccc}
\infty & ; & r < \sigma \\
- \epsilon & ; &\sigma \le r < \lambda \sigma \\
0 & ; & r \ge \lambda \sigma \end{array} \right.
</math>

and the orientational component is given by (Eq. 3)

:<math>
f_{ij} \left(\hat{ {\mathbf r}}_{ij}; \tilde{{\mathbf \Omega}}_i, \tilde{{\mathbf \Omega}}_j \right) =
\left\{ \begin{array}{clc}
1 & \mathrm{if} & \left\{ \begin{array}{ccc} & (\hat{e}_\alpha\cdot\hat{r}_{ij} \leq \cos \delta) & \mathrm{for~some~patch~\alpha~on~}i \\
\mathrm{and} & (\hat{e}_\beta\cdot\hat{r}_{ji} \leq \cos \delta) & \mathrm{for~some~patch~\beta~on~}j \end{array} \right. \\
0 & \mathrm{otherwise} & \end{array} \right.
</math>

where <math>\delta</math> is the solid angle of a patch (<math>\alpha, \beta, ...</math>) whose axis is <math>\hat{e}</math> (see Fig. 1 of Ref. 1), forming a conical segment.
==Two patches==
The "two-patch" Kern and Frenkel model has been extensively studied by Sciortino and co-workers <ref name="bianchi">[http://dx.doi.org/10.1063/1.2730797 F. Sciortino, E. Bianchi, J. Douglas and P. Tartaglia "Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation", Journal of Chemical Physics '''126''' 194903 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3415490 Achille Giacometti, Fred Lado, Julio Largo, Giorgio Pastore, and Francesco Sciortino "Effects of patch size and number within a simple model of patchy colloids", Journal of Chemical Physics 132, 174110 (2010)]</ref><ref name="rovigatti">[http://dx.doi.org/10.1063/1.4737930 José Maria Tavares, Lorenzo Rovigatti, and Francesco Sciortino "Quantitative description of the self-assembly of patchy particles into chains and rings", Journal of Chemical Physics '''137''' 044901 (2012)]</ref>.

==Four patches==
:''Main article: [[Anisotropic particles with tetrahedral symmetry]]''

==Single-bond-per-patch-condition==
If the two parameters <math>\delta</math> and <math>\lambda</math> fullfil the condition

:<math>
\sin{\delta} \leq \dfrac{1}{2(1+\lambda\sigma)}
</math>

then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with Wertheim theory <ref name="bianchi"/><ref name="rovigatti"/>

==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1063/1.3689308 Christoph Gögelein, Flavio Romano, Francesco Sciortino, and Achille Giacometti "Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory", Journal of Chemical Physics '''136''' 094512 (2012)]
*[http://dx.doi.org/10.1063/1.4722477 Emanuela Bianchi, Günther Doppelbauer, Laura Filion, Marjolein Dijkstra, and Gerhard Kahl "Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms", Journal of Chemical Physics '''136''' 214102 (2012)]

[[category: models]]

Kern and Frenkel patchy model

2012-12-11T09:29:32Z

Lrovigatti:

The '''Kern and Frenkel''' <ref>[http://dx.doi.org/10.1063/1.1569473 Norbert Kern and Daan Frenkel "Fluid–fluid coexistence in colloidal systems with short-ranged strongly directional attraction", Journal of Chemical Physics 118, 9882 (2003)]</ref> [[Patchy particles |patchy model]] is an amalgamation of the [[hard sphere model]] with
attractive [[Square well model | square well]] patches (HSSW). The potential has an angular aspect, given by (Eq. 1)

:<math>\Phi_{ij}({\mathbf r}_{ij}; \tilde{{\mathbf \Omega}}_i, \tilde{{\mathbf \Omega}}_j) =\Phi_{ij}^{ \mathrm{HSSW}}({\mathbf r}_{ij}) \cdot f(\tilde{{\mathbf \Omega}}_i, \tilde{{\mathbf \Omega}}_j) </math>

where the radial component is given by the square well model (Eq. 2)

:<math>
\Phi_{ij}^{ \mathrm{HSSW}} \left({\mathbf r}_{ij} \right) =
\left\{ \begin{array}{ccc}
\infty & ; & r < \sigma \\
- \epsilon & ; &\sigma \le r < \lambda \sigma \\
0 & ; & r \ge \lambda \sigma \end{array} \right.
</math>

and the orientational component is given by (Eq. 3)

:<math>
f_{ij} \left(\hat{ {\mathbf r}}_{ij}; \tilde{{\mathbf \Omega}}_i, \tilde{{\mathbf \Omega}}_j \right) =
\left\{ \begin{array}{clc}
1 & \mathrm{if} & \left\{ \begin{array}{ccc} & (\hat{e}_\alpha\cdot\hat{r}_{ij} \leq \cos \delta) & \mathrm{for~some~patch~\alpha~on~}i \\
\mathrm{and} & (\hat{e}_\beta\cdot\hat{r}_{ji} \leq \cos \delta) & \mathrm{for~some~patch~\beta~on~}j \end{array} \right. \\
0 & \mathrm{otherwise} & \end{array} \right.
</math>

where <math>\delta</math> is the solid angle of a patch (<math>\alpha, \beta, ...</math>) whose axis is <math>\hat{e}</math> (see Fig. 1 of Ref. 1), forming a conical segment.
==Two patches==
The "two-patch" Kern and Frenkel model has been extensively studied by Sciortino and co-workers <ref>[http://dx.doi.org/10.1063/1.2730797 F. Sciortino, E. Bianchi, J. Douglas and P. Tartaglia "Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation", Journal of Chemical Physics '''126''' 194903 (2007)]</ref><ref>[http://dx.doi.org/10.1063/1.3415490 Achille Giacometti, Fred Lado, Julio Largo, Giorgio Pastore, and Francesco Sciortino "Effects of patch size and number within a simple model of patchy colloids", Journal of Chemical Physics 132, 174110 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4737930 José Maria Tavares, Lorenzo Rovigatti, and Francesco Sciortino "Quantitative description of the self-assembly of patchy particles into chains and rings", Journal of Chemical Physics '''137''' 044901 (2012)]</ref>.

==Four patches==
:''Main article: [[Anisotropic particles with tetrahedral symmetry]]''

==Single-bond-per-patch-condition==
If the two parameters <math>\delta</math> and <math>\lambda</math> fullfil the condition

<math>
\sin{\delta} \leq \dfrac{1}{2(1+\lambda\sigma)}
</math>

then the patch can not be involved in more than one bond.

==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1063/1.3689308 Christoph Gögelein, Flavio Romano, Francesco Sciortino, and Achille Giacometti "Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory", Journal of Chemical Physics '''136''' 094512 (2012)]
*[http://dx.doi.org/10.1063/1.4722477 Emanuela Bianchi, Günther Doppelbauer, Laura Filion, Marjolein Dijkstra, and Gerhard Kahl "Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms", Journal of Chemical Physics '''136''' 214102 (2012)]

[[category: models]]