1. LIQUID-CRYSTALLINE PHASES IN COLLOIDAL SUSPENSIONS OF DISC-SHAPED PARTICLES Y. Martínez (UC3M) E. Velasco (UAM) D. Sun, H.-J. Sue, Z. Cheng (Texas A&M) Aqueous suspensions of disc-like colloidal particles (diameter  m) Same thickness (nm) Polydisperse in diameter

2. Anisotropic colloids rod-like (prolate) disc-like (oblate) ORIENTED PHASES PARTIAL SPATIAL ORDER Non-spherical colloidal particles (at least in one dimension) Give rise to mesophases rods prefer smectic discs prefer columnar But there is another factor: POLYDISPERSITY discotic colloids

3. But all synthetic colloids are to some extent polydisperse in size polydispersity parameter Polydispersity could destabilise non-uniform phases, since it is difficult to accommodate range of diameters in an ordered arrangement FRACTIONATION parent phase coexisting phases

4. Effect of polydispersity in discotics thickness polydispersity: destabilization of smectic diameter polydispersity: destabilization of columnar smectic phase columnar phase

5. Platelets made of gibbsite  -Al(OH) 3 steric stabilisation with polyisobutylene (PIB) (C 4 H 8 ) n before fractionation  R =25% after fractionation  R =17% van der Kooij et al., Nature (2000) Gibbsite platelets in toluene: a hard-disc colloidal suspension I+N N N+C C C (without polarisers)  =0.19 0.28 0.41 0.47 0.45 Suspensions between crossed polarisers "hard" platelet 200nm

6.  platelet volume fraction phase sequence: I-N-C of monodisperse discs with and GEL SMECTIC?  R =25%  R =17% 18% 14% But what happens at higher/lower diameter polydispersity? Can the smectic phase be stable? Role of thickness polydispersity?

7. Zirconium phosphate platelets TEM of pristine  -ZrP platelets TEM of  -ZrP platelet coated with TBA  -Zr(HPO 4 ) 2 · H 2 O

8. PROCESS OF EXFOLIATION OF LAYERED  -Zr(HPO 4 ) 2 ·H 2 O aspect ratio diameter optical lengths COLUMNAR thickness X rays SMECTIC

9.  = platelet volume fraction = volume occupied by platelets total volume Optical images: white light and crossed polarisers I I+N N N+S

10. ISOTROPIC-NEMATIC phase transition non-linearity in the two-phase region: some fractionation RR II + NN extremely large volume- fraction gap: In gibbsite

11. Small Angle X-ray scattering NEMATIC SMECTIC large variation in smectic period with  (almost factor 3) long-range forces? sharp peaks with higher- order reflections (well- defined layers) smectic order, with weak N to S transition

12. Isotropic-nematic Restricted-orientation approximation: Hard interactions treated at the excluded-volume level (Onsager or second-virial theory) where is a Schultz distribution characterised by  R minimum Distribution projected on Cartesian axes:

13. CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT  RR RR

14. number of particles at r in a volume d 3 r with diameter between D and D+dD Nematic-smectic-columnar perfect order Second-virial theory not expected to perform well : complicated distribution function Simplifying assumption: SMECTIC COLUMNAR Fundamental- measure theory for polydisperse parallel cylinders

15.  R =0.52  S =0.452 RR

17. Attractive polydisperse platelets free-energy functional: L

18. Phase diagrams (Gaussian tail distribution)  R = 0.294 = 1 = 2

19. Microfractionation in the coexisting smectic phase  R = 0.294,  = 2,  = 1.665

20. Improve and extend experiments larger range of polydispersities (in particular lower) overcome relaxation problems Improve and extend theory. Include polydispersity in both diameter and thickness Terminal polydispersities in diameter (columnar) and thickness (smectic)? Better understanding of platelet interactions better modelling of interactions Future work

21. THE END

22. CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT

23. Theory: some ideas Potential energy: pair potential will contain short-range repulsive contributions + soft interactions (vdW, electrostatic, solvent-mediated forces,...?) We treat soft interactions via an effective thickness L eff (  ) of hard discs Criteria:   in correct range in smectic phase approximate theory of screened Coulomb interactions?