Random packing of mixtures of hard rods and spheres

Transcription

1 Random packing of mixtures of hard rods and spheres Claudia Ferreiro School of Chemistry, University of Bristol 22/03/2013

2 Introduction (Colloidal Liquid Crystals) Random Close Packing Monte Carlo-like compression Mechanical Contraction Method Hybrid method Mixtures of Spheres and Spherocylinders

3 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).

4 Introduction Hard spherocylinders provide a good model for liquid crystals and have been used to study phase transitions. 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. P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).

5 Introduction Colloidal Liquid Crystals 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.

6 Introduction Colloidal Liquid Crystals 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. N. Yasarawan and J. S. van Duijneveldt, Langmuir 24, 7184 (2008).

7 Introduction Colloidal Liquid Crystals 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. N. Yasarawan and J. S. van Duijneveldt, Langmuir 24, 7184 (2008).

8 Introduction Colloidal Liquid Crystals 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 N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).

9 Introduction Colloidal Liquid Crystals 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 N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).

10 Introduction Colloidal Liquid Crystals 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 N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).

11 Introduction Colloidal Liquid Crystals 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. N. Yasarawa and J. S. van Duijneveldt, Soft Matter 6, 353 (2010).

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

14 MC-like compression Monte Carlo-like compression Initial configuration

15 MC-like compression Monte Carlo-like compression Initial configuration Compression

16 MC-like compression Monte Carlo-like compression Initial configuration Compression Movements

17 MC-like compression Monte Carlo-like compression Initial configuration Compression Movements

18 MC-like compression Monte Carlo-like compression Initial configuration Compression Movements Compression

19 MC-like compression Packing fractions of spherocylindres for different aspect ratios. S. R. Williams and A. P. Philipse, Phys. Rev. E 67, (2003). P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).

20 MC-like compression L/D=0 L/D=0.5 L/D=3 L/D=10

21 MC-like compression The orientational pair distribution function g 2 (r) is used to measure the degree of order.

22 MCM 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, (2003).

23 MCM 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, (2003).

24 MCM 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, (2003). n

25 MCM Mechanical Contraction Method [*] This method was developed by Philipse and Williams. Each particle is moved away from its overlapping particles with a speed: r S. R. Williams and A. P. Philipse, Phys. Rev. E 67, (2003).

26 MCM Mechanical Contraction Method Initial configuration

27 MCM Mechanical Contraction Method Initial configuration Compression

28 MCM Mechanical Contraction Method Initial configuration Compression Calculations

29 MCM Mechanical Contraction Method Initial configuration Compression Calculations Movements

30 MCM Our approach: MCM until loose packing has been reached. Monte Carlo-like compression.

31 MCM Packing fractions of spherocylindres for different aspect ratios. S. R. Williams and A. P. Philipse, Phys. Rev. E 67, (2003). P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).

32 MCM L/D=0.5 L/D=2.0 L/D=5.0 L/D=10.0

33 MCM The orientational pair distribution function g 2 (r) is used to measure the degree of order.

34 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

35 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?

36 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.? The same hybrid model is used to study these mixtures. L/D=5 L/d 1 How the packing fraction changes with different mixtures of spheres and spherocylinders?

37 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

38 Mixtures Spheres and Spherocylinders L/D=5.0, d=l. hs =0.057 hs =0.110 hs =0.202

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

40 Thanks to: Dr. Jeroen van Duijneveldt JSvD Group ACRC, University of Bristol CONACYT And thank you for listening!