Random packing of mixtures of hard rods and spheres · PDF fileRandom packing of mixtures of...

Random packing of mixtures of

hard rods and spheres

Claudia Ferreiro School of Chemistry, University of Bristol

22/03/2013

Introduction (Colloidal Liquid Crystals)

Random Close Packing

Monte Carlo-like compression

Mechanical Contraction Method

Hybrid method

Mixtures of Spheres and Spherocylinders

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

Random Close Packing

• How we can model these kind of systems? • Sequential generation models • Collective rearrangement models

Random Close Packing

Monte Carlo-like compression

Initial configuration

Random Close Packing MC-like compression

Initial configuration Compression

Monte Carlo-like compression

Random Close Packing MC-like compression

Random Close Packing MC-like compression

Initial configuration Compression

Movements

Monte Carlo-like compression

Initial configuration Compression

Movements

Monte Carlo-like compression

Random Close Packing MC-like compression

Initial configuration Compression

Movements Compression

Monte Carlo-like compression

Random Close Packing MC-like compression

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

L/D=0 L/D=0.5

L/D=3 L/D=10

Random Close Packing MC-like compression

The orientational pair distribution function g2(r) is used to measure the degree of order.

Random Close Packing MC-like compression

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

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).

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).

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).

Random Close Packing MCM

Initial configuration

Mechanical Contraction Method

Random Close Packing MCM

Initial configuration Compression

Mechanical Contraction Method

Random Close Packing MCM

Initial configuration Compression

Calculations

Mechanical Contraction Method

Random Close Packing MCM

Initial configuration Compression

Calculations Movements

Mechanical Contraction Method

• Our approach:

• MCM until loose packing has been reached.

• Monte Carlo-like compression.

Random Close Packing MCM

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).

L/D=0.5 L/D=2.0

L/D=5.0 L/D=10.0

Random Close Packing MCM

The orientational pair distribution function g2(r) is used to measure the degree of order.

Random Close Packing MCM

• 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

?

• 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

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

• 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

hs=0.057

hs=0.110

hs=0.202

• L/D=5.0, d=L.

Mixtures Spheres and Spherocylinders

Diagram of packing fractions of spherocylinders and spheres mixtures, which includes the pure sphere and spherocylinder systems.

Mixtures Spheres and Spherocylinders

Thanks to:

•Dr. Jeroen van Duijneveldt

•JSvD Group

•ACRC, University of Bristol

•CONACYT

And thank you for listening!