Colloids with Anisotropic Interactions

Colloids with Anisotropic Interactions
Zdenek Preisler
Teun Vissers, Francesco Sciortino
Università di Roma, La Sapienza
PhD Research Project, 2012
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
1 / 15
Introduction
New Generation of Colloids
Building blocks of new materials – new bottom up approaches
Anisotropy of shape, anisotropy of interaction
Sharon C. Glotzer, Michael J. Solomon, Nature Materials 6, 557 - 562 (2007)
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
2 / 15
Bottom up approach, designing new materials example
Experimental, quasi-2D, Kagome lattice
Qian Chen, Sung Chul Bae and Steve Granick, Nature Materials 10, 171 (2011)
Simulation
Flavio Romano and Francesco Sciortino, Soft Matter, (2011)
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
3 / 15
Simulation on 4 free energy candidate structures
Flavio Romano, Eduard Sanz and Francesco Sciortino, Journal of chemical
physics 132,184501, (2010)
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
4 / 15
Stability of tetrahedral patchy particles
Eva G. Noya, Carlos Vega, Jonathan P. K. Doye and Ard A. Louis, Journal of
chemical physics 132,234511, (2010)
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
5 / 15
New systematic approach using novel floppy box method
No general way of finding crystal structures
• Idea is to generate crystal unit cell using Monte Carlo simulations
•
(using small number of particle N ' 1, 2, . . . , 16)
Fast and efficient way of generating possible structures
Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra.
Efficient method for predicting crystal structures at finite temperature: Variable
box shape simulations. Physical Review Letters, 103(188302), 2009.
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
6 / 15
The plan
1
Generate possible crystal structures
– crystal candidates
2
Check stability using NPT simulation
3
Identify different crystal structures
4
For suitable candidates calculate free energies
5
Evaluate phase diagram
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
7 / 15
Simple system with anisotropic interactions – Janus
Extensively studied system by theory, simulations and experiments
Hard
Attractive
Half of the surface is attractive
and the other half is hard – no interaction
Example: Gold covered
silica particles
Ivo Buttinoni, Clemens Bechinger, University
Stuttgart
Zdenek Preisler (La Sapienza)
Interesting phase behavior
F. Sciortino, A. Giacometti and G. Pastore,
Phys. Rev. Lett. 103, 237801, (2009)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
8 / 15
Simple system with anisotropic interactions – Janus
Extensively studied system by theory, simulations and experiments
Hard
Attractive
Crystal phase diagram is still to be evaluated
Example: Gold covered
silica particles
Ivo Buttinoni, Clemens Bechinger, University
Stuttgart
Zdenek Preisler (La Sapienza)
Interesting phase behavior
F. Sciortino, A. Giacometti and G. Pastore,
Phys. Rev. Lett. 103, 237801, (2009)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
8 / 15
Simulation Model – Kernel-Frenkel potential
u(rij ) = u sw (rij )f (Ωij )


 r̂ij · n̂ > cos θ



and
1 if
f (Ωij ) =

r̂
·
n̂
>
cos
θ

ji


0
θ
r̂
n̂
Norbert Kern and Daan Frenkel, Journal of Chemical Physics, 118, 21 (2003)
u(rij )sw

 ∞, rij < σ core
ij , σ core < rij < σ well
=

0, rij > σ well
Example of Janus and triblock particle
interactions
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
9 / 15
Monte Carlo moves
Standard NVT Monte Carlo moves
rotation and translation of particles
Volume changes moves
Additional shape changing moves
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
10 / 15
Crystal Structures Search
Janus Particles
First, We generate crystal structure using floppy box method for small
number of particles
N ' 2, . . . , 8
The crystals are generated for
N
copied
• different phase points – different
pressures and temperatures
• for each phase point – series of
2
different random number seeds
From each simulation we collect
candidate configurations
4
Large number of structures can be very
easily generated
8
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
11 / 15
Selecting suitable candidates
Copy to big floppy box
Stability check
Identify structures
Free energy calculations
Equation of state
Thermodynamic integrations
Etc.
Structures are identified according to their properties
• energy
• density
• number of bonds
• bonds pointing directions
• radial distribution function
• etc.
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
12 / 15
New Simulation Software
For our purpose, plenty of new simulation programming code / algorithms
needed to be developed and implemented
We implemented
Simulation code for various ensembles
• isothermal-isobaric (NPT)
• canonical (NVT)
‘Floppy box’ method to facilitate variable box shapes
Free energy calculations – Frenkel-Ladd method
Thermodynamic integration
Structural analysis
Visualization
etc.
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
13 / 15
Possible candidates
Janus particles
I
III
1.0
1.0
0.5
0.5
0.0
0.0
−0.5
−0.5
−1.0
−1.0
1.0
1.0
0.5
0.5
−1.0
0.0
0.0
−0.5
0.0
−1.0
−0.5
0.5
1.0
−0.5
−0.5
0.0
0.5
1.0
−1.0
II
−1.0
IV
1.0
1.0
0.5
0.5
0.0
0.0
−0.5
−1.0
−0.5
−0.5
0.0
1.0
Zdenek Preisler (La Sapienza)
1.0
−1.0
0.5
0.5
−1.0
−0.5
0.0
0.5
1.0
−1.0
Colloids with Anisotropic Interactions
0.0
0.0
−0.5
−0.5
−1.0
0.5
−1.0
1.0
PhD Research Project, 2012
14 / 15
Future Outlook
Calculating Phase diagram for Janus particle crystals
Exploring parameter space for our model
• changing interaction coverage angle
• changing interaction range
Changing interactions
• triblock Janus particles
• etc.
Zdenek Preisler (La Sapienza)
Colloids with Anisotropic Interactions
PhD Research Project, 2012
15 / 15