Simulation of model biaxial particles

1. Simulation of model biaxial particles A.J. Masters School of Chemical Engineering and Analytical Science , University of Manchester, UK

2. Thermodynamics 2013 - Manchester, 3-6 September https://www.meeting.co.uk/confercare/ thermodynamics2013/ Abstract deadline: 1 April, 2013 Invited speakers: Keith Gubbins; Daan Frenkel; Ross Taylor;Carol Hall;Alejandro Gil-Villegas; Peter Monson; Aline Miller; Paola Carbone; Geoff Maitland

3. Rods and discs • Most liquid-crystal forming particles (molecules or colloidal particles) can be regarded as either rods or discs • Axially symmetric rods: • Isotropic - nematic (+) - smectic A - crystal • Axially symmetric discs: • Isotropic - nematic (-) - columnar - crystal

4. What else can you get? • Look at some other possibilities that might arise from simple shapes • Studies are of hard particles - no attractive forces, no flexibility • A quick scamper through V-shapes and fused hexagons!

5. V-shapes and the Biaxial Nematic Phase • A liquid crystal phase characterized by molecular alignment along three orthogonal axes while maintaining random positional behaviour • Gives rise to three distinct optical axes • Uniaxial nematic  biaxial nematic transition can lead to novel ferroelectric & optical devices • The theoretical possibility of such a phase was first discussed in 1970*. * Ref: M. J. Freiser, Phys. Rev. Lett., 1970, 24, 104

6. Experimental state-of-play • Observed by Yu and Saupe (1980) in a lyotropic system (potassium laurate/1-decanol/water) • Observed in colloidal suspension of goethite - a board-like particle (van den Pol et al, 2009)

7. Bent-Core Molecules and Biaxiality • Biaxial nematic phase requires molecules withoutcylindrical symmetry for alignment along multiple axes • “V-shaped” or bent-core molecules have correct symmetry to allow biaxial nematic phase, and have experimentally viable shapes B.R. Acharya, A. Primak and S. Kumar, Phys. Rev. Lett., 92, 145506 (2004)

8. Idealized Phase Diagram Disc-like nematic Rod-like nematic Biaxial nematic Density Isotropic Narrowing internal angle P.I.C. Teixeira, A.J. Masters and B.M. Mulder, Mol. Cryst. Liq. Cryst. 167, 323 (1998) G.R. Luckhurst, Thin Solid Films, 393, 40 (2001)

9. Onsager limit? • I think (!) that in the Onsager limit (large L/D), that all virials higher than second order can be neglected • Tested against 3rd virial calculations but nothing higher • Biaxial phase is truly stable in this limit • Can we see it in a simulation/experiment?

10. Simulation studies on bent-core models • Phase transitions for a bent-core model • Dependence on bond angle and arm length • Binary mixtures of bent-cores • House rules - we will obtain all phases by compressing the isotropic. We are not allowed to start from an assumed crystal structure! Y. Lansac et al, Phys. Rev. E, 67, 011703 (2003) • Dewar and P.J. Camp, Phys. Rev. E, 70, 011704 (2004)

11. Molecular model • Multi-site model of soft, repulsive Weeks-Chandler-Andersen potentials • Rigidly linked particles at separation σ – no bond flexibility • Two arms of equal length, with a shared atom at apex • Bend angle defined as θ=180° linear, θ=90° perpendicular •  = kT ij ij ij ij ij θ=170° θ=140° θ=110°

12. Initial Methodology • Parameter space of bond angle and pressure, N=512 molecules • Starting at low-density isotropic liquid phase, perform a series of time-stepped NPT-MD (constant pressure, constant temperature) simulations at incremental pressure steps • Use order parameters, configurational energy,pair correlation function g(rij) and snapshots to examine phase behaviour and transitions

13. N=512, n=11 potentials, θ=140° P*=0.5 P*=1 P*=2.5

14. N=512, n=11 potentials, θ<135° θ=110°, P*=2.5 θ=130°, P*=2.5

15. Help needed! • Can someone who understands simulation please either tell us what to do or do it for us?

16. N=4096, n=11, θ=150°, P*=1.4

17. n=7 potentials • Theoretical limit is for bent-core moleculesin Onsager limit (L >> D) • Examine the effects of the length of themolecule arms on phase behaviour • Equivalent parameter space sweep as for n=11 potentials

18. Arm length dependence: n=7 @ P* = 4 θ=170° θ=140° θ=160°

19. Give up - how about binary mixtures? • Incommensurate particles will not sit comfortably together in a smectic layer • Maybe we can find a uniaxial/biaxial nematic transition on compression. • Just consider 50:50 mixtures in terms of particle numbers

20. Binary mixture: n=7 & n=11 θ=150°, P*=4.2

21. Binary mixture: n=5 & n=11 θ=160°, P*=1.9 θ=160°, P*=1.7

22. Summary of binary mixtures • On increasing the pressure, a smectic precipitates out. • We never see a biaxial nematic • Similar issues for binary mixtures where we vary bend angle • Effect of higher polydispersity? Christine Stokes on Friday!

23. Other molecule shapes (in progress) “Symmetric” “Asymmetric” “Y-Shaped”

24. Boards and hexagons Resembles mono-disperse goethite (van der Pol) If C/B ~ B/A - self-dual point, biaxial nematic predicted (and, indeed, found!)

25. The Model Rod • Rodlike nematic • Smectic • Crystal Disc • Discotic nematic • Columnar • Crystal Also checked large discs

26. System Parameters Rigid shapes Spheres interact via the repulsive Weeks-Chandler-Andersen potential. NpT molecular dynamics. N dependence checked. Some NsT simulations.

27. Particle structures

28. Disc system Small discs should give no liquid crystal phases.

29. Columnar Phase (no nematic seen) P*=1.6 T*=1

30. 5 Disc system As , should be rod-like.

31. 5 Disc systems First phase transition is from isotropic to nematic. P*=0.8 Coloured according to primary director Coloured according to secondary director Centres of mass are random Uniaxial nematic

32. Smectic A Phase Layered nematic alignment to the primary director only Coloured to the normal director P*=0.2 T*=1 P/T=0.2 Random positioning of centres of mass within layers.

33. Smectic C phase Same as before but with a tilt. P*=0.4 Getting close to a crystal phase

34. Crystalline Phase Coloured to the primary director Rigid system with no free movement in the layers P*=2 T*=2 P/T=1 Coloured to the secondary director Perfectly fixed and packed system

35. Conclusion 5 disc system shows all rod phases. Expected as .

36. 2 Disc system , Expect disc like behaviour

37. 2 disc systems Overall isotropic behaviour at low pressure. P*=1.3

38. Discotic nematic Coloured normal to face Coloured to the secondary director Global discotic phase alignment. Random alignment of molecules Coloured to primary director Centres of mass are random P*=1.8

39. Discotic smectic phase P*=2 T*=1 P/T=2 Coloured to the primary director Coloured to the secondary director Discotic alignment, layers are one molecule thick. No columns found.

40. 2 Disc conclusion Isotropic Uniaxial discotic nematic Uniaxial layered smectic A

41. 3 Disc system Near the dual point, A/B ~ B/C

42. Discotic nematic systems Coloured along the primary axis Coloured along the normal axis P*=1 Shows a Discotic nematic phase (possibly biaxial?) Centres of mass are random

43. Weakly biaxial smectic P*=0.8 Ordering along long axis Ordering along the normal. Ordering along third axis

44. 3 Disc conclusion Phase sequence appears to be: Isotropic Discotic nematic (maybe weak biaxial? ) Biaxial layered smectic (weakly biaxial but significant in our humble opinions - )

45. 4 Disc system Now , should be rod like

46. 4 Disc system Uniaxial alignment along the primary director Centres of mass are still randomly arranged P*=1.3 4 Discs are large enough to show uniaxial nematic phase preference over discotic.

47. Biaxial nematic phase P*=1.5 Strong uniaxial nematic alignment with the primary director. Good discotic nematic alignment with the secondary director. Centre of mass is still random

48. Biaxial smectic phase P*=1.6 Alignment of primary director. Alignment of secondary director. Smectic arrangement of center of mass. Looks like a biaxial smectic phase.

49. 4 Disc order parameters

50. 4 Disc conclusion Phase sequence is: Isotropic Rod-like uniaxial nematic (we think) Biaxial nematic Biaxial rod-like smectic