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![Page 1: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/1.jpg)
Random packing of mixtures of
hard rods and spheres
Claudia Ferreiro School of Chemistry, University of Bristol
22/03/2013
![Page 2: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/2.jpg)
Introduction (Colloidal Liquid Crystals)
Random Close Packing
Monte Carlo-like compression
Mechanical Contraction Method
Hybrid method
Mixtures of Spheres and Spherocylinders
![Page 3: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/3.jpg)
• Hard spherocylinders provide a good model for liquid crystals and have been used to
study phase transitions.
• P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).
Introduction
![Page 4: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/4.jpg)
• Hard spherocylinders provide a good model for liquid crystals and have been used to
study phase transitions.
• P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).
• For high aspect ratios the nematic phase occurs at low densities. This can be used to make suspensions of rodlike particles, with small amount of these, that present liquid crystal behaviour.
Introduction
![Page 5: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/5.jpg)
• Colloidal suspensions of rodlike particles can exhibit LC phases depending on the concentration. One kind of colloidal particle that can be used is Sepiolite clay. Suspensions of these clays have been proved to show nematic phases.
Introduction Colloidal Liquid Crystals
![Page 6: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/6.jpg)
• N. Yasarawan and J. S. van Duijneveldt, Langmuir 24, 7184 (2008).
• Colloidal suspensions of rodlike particles can exhibit LC phases depending on the concentration. One kind of colloidal particle that can be used is Sepiolite clay. Suspensions of these clays have been proved to show nematic phases.
Introduction Colloidal Liquid Crystals
![Page 7: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/7.jpg)
• N. Yasarawan and J. S. van Duijneveldt, Langmuir 24, 7184 (2008).
• One thing to take into account is that these systems have a relative length polydispersity of around 40%, which make them behave slightly different than what is predicted.
Introduction Colloidal Liquid Crystals
![Page 8: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/8.jpg)
• N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).
• The addition of spheres to these rod suspensions will strongly affect the isotropic-nematic phase transition, giving rise to some interesting behaviors.
L/D=30 d≈L
Introduction Colloidal Liquid Crystals
![Page 9: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/9.jpg)
• N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).
• The addition of spheres to these rod suspensions will strongly affect the isotropic-nematic phase transition, giving rise to some interesting behaviors.
L/D=30 d≈L
Introduction Colloidal Liquid Crystals
![Page 10: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/10.jpg)
• N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).
• The addition of spheres to these rod suspensions will strongly affect the isotropic-nematic phase transition, giving rise to some interesting behaviors.
L/D=30 d≈L
Introduction Colloidal Liquid Crystals
![Page 11: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/11.jpg)
• N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).
• Because of different factors, like polydispersity or the formation of bundles, the study of these mixtures in a different way may have a better resemblance with what is seen in experiments.
• In this work we are interested on the study of random packing of mixtures of spheres and spherocylinders.
• First a study of random packing of pure systems was carried out to select a method.
Introduction Colloidal Liquid Crystals
![Page 12: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/12.jpg)
Random Close Packing
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• How we can model these kind of systems? • Sequential generation models • Collective rearrangement models
Random Close Packing
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Monte Carlo-like compression
Initial configuration
Random Close Packing MC-like compression
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Initial configuration Compression
Monte Carlo-like compression
Random Close Packing MC-like compression
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Random Close Packing MC-like compression
Initial configuration Compression
Movements
Monte Carlo-like compression
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Initial configuration Compression
Movements
Monte Carlo-like compression
Random Close Packing MC-like compression
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Initial configuration Compression
Movements Compression
Monte Carlo-like compression
Random Close Packing MC-like compression
![Page 19: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/19.jpg)
Packing fractions of spherocylindres for different aspect ratios.
• S. R. Williams and A. P. Philipse, Phys. Rev. E 67, 051301 (2003). • P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).
Random Close Packing MC-like compression
![Page 20: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/20.jpg)
L/D=0 L/D=0.5
L/D=3 L/D=10
Random Close Packing MC-like compression
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The orientational pair distribution function g2(r) is used to measure the degree of order.
Random Close Packing MC-like compression
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Mechanical Contraction Method[*]
This method was developed by Philipse and Williams. Each particle is moved away from
its overlapping particles with a speed:
• S. R. Williams and A. P. Philipse, Phys. Rev. E 67, 051301 (2003).
Random Close Packing MCM
![Page 23: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/23.jpg)
Mechanical Contraction Method[*]
This method was developed by Philipse and Williams. Each particle is moved away from
its overlapping particles with a speed:
Random Close Packing MCM
• S. R. Williams and A. P. Philipse, Phys. Rev. E 67, 051301 (2003).
![Page 24: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/24.jpg)
Mechanical Contraction Method[*]
This method was developed by Philipse and Williams. Each particle is moved away from
its overlapping particles with a speed:
Random Close Packing MCM
n
• S. R. Williams and A. P. Philipse, Phys. Rev. E 67, 051301 (2003).
![Page 25: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/25.jpg)
Mechanical Contraction Method[*]
This method was developed by Philipse and Williams. Each particle is moved away from
its overlapping particles with a speed:
Random Close Packing MCM
r
• S. R. Williams and A. P. Philipse, Phys. Rev. E 67, 051301 (2003).
![Page 26: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/26.jpg)
Random Close Packing MCM
Initial configuration
Mechanical Contraction Method
![Page 27: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/27.jpg)
Random Close Packing MCM
Initial configuration Compression
Mechanical Contraction Method
![Page 28: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/28.jpg)
Random Close Packing MCM
Initial configuration Compression
Calculations
Mechanical Contraction Method
![Page 29: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/29.jpg)
Random Close Packing MCM
Initial configuration Compression
Calculations Movements
Mechanical Contraction Method
![Page 30: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/30.jpg)
• Our approach:
• MCM until loose packing has been reached.
• Monte Carlo-like compression.
Random Close Packing MCM
![Page 31: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/31.jpg)
Packing fractions of spherocylindres for different aspect ratios.
Random Close Packing MCM
• S. R. Williams and A. P. Philipse, Phys. Rev. E 67, 051301 (2003). • P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).
![Page 32: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/32.jpg)
L/D=0.5 L/D=2.0
L/D=5.0 L/D=10.0
Random Close Packing MCM
![Page 33: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/33.jpg)
The orientational pair distribution function g2(r) is used to measure the degree of order.
Random Close Packing MCM
![Page 34: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/34.jpg)
• Mixtures of rods and spheres have a different packing efficiency than spheres or rods, which depends on the factor L/d.
Mixtures Spheres and Spherocylinders
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?
• Mixtures of rods and spheres have a different packing efficiency than spheres or rods, which depends on the factor L/d.
• How the packing fraction changes with different mixtures of spheres and spherocylinders?
Mixtures Spheres and Spherocylinders
![Page 36: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/36.jpg)
L/D=5 L/d≈1
?
• Mixtures of rods and spheres have a different packing efficiency than spheres or rods, which depends on the factor L/d.
• How the packing fraction changes with different mixtures of spheres and spherocylinders?
• The same hybrid model is used to study these mixtures.
Mixtures Spheres and Spherocylinders
![Page 37: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/37.jpg)
• L/D=5.0, d=L.
=0.561 hsc=0.503 hs=0.058
=0.569 hsc=0.459 hs=0.110
hsc=0.601 hsc=0.399 hs=0.202
Mixtures Spheres and Spherocylinders
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hs=0.057
hs=0.110
hs=0.202
• L/D=5.0, d=L.
Mixtures Spheres and Spherocylinders
![Page 39: Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013](https://reader031.vdocuments.site/reader031/viewer/2022022503/5ab1b7f47f8b9a00728cac2e/html5/thumbnails/39.jpg)
Diagram of packing fractions of spherocylinders and spheres mixtures, which includes the pure sphere and spherocylinder systems.
Mixtures Spheres and Spherocylinders
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Thanks to:
•Dr. Jeroen van Duijneveldt
•JSvD Group
•ACRC, University of Bristol
•CONACYT
And thank you for listening!