1. LIQUID-CRYSTALLINE PHASES IN COLLOIDAL SUSPENSIONS OF DISC-SHAPED PARTICLES E. Velasco (UAM) Y. Martínez (UC3M) 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. dispersions of particles of size 1nm-1  m large surface-to-volume ratio: large interactions "human" time and length scales "model" molecular systems and more flexible interactions (tuning), engineered particle shapes (self-assembly) Present in natural environments and industrial applications Colloidal fluids: basic properties Present in natural environments and industrial applications: paints, food, pharmaceutical products, cosmetics, paper, oil production, cement,...

3. 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

4. POLYDISPERSITY AND HARD SPHERES  = sphere volume fraction = volume occupied by spheres total volume  Hard spheres: good model for some colloidal spheres (silica, latex,...)

5. But all synthetic colloids are to some extent polydisperse in size Hard-sphere crystal cannot exist beyond   =0.06  polydispersity parameter This is because the lattice parameter of the crystal is otherwise the crystal should melt into a (more stable) fluid Polydispersity should destabilise crystal, since difficult to accommodate range of diameters in a lattice structure

6. Fluid and crystal exhibit FRACTIONATION For still higher   system phase separates into crystals with different size distributions FRACTIONATION Size distribution more sharply peaked in both crystals than in parent crystal parent phase two coexisting phases

7. When   even higher, collection of different, coexisting crystallites, possibly in coexistence with fluid Fasolo & Sollich (PRL 2003) FRACTIONATION provides method of purification (decreasing polydispersity)

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

9. Discotic colloids (of inorganic compounds) Obtained from exfoliation of layered compounds: synthetic clays, gibbsite, Ni(OH) 2, CuS or Cu 2 S, niobate,... Typical problems: Hard to exfoliate (strong interlayer interactions) Layers not chemically stable in common solvents Hard to synthesise (reactant heated to high T) Too large polydispersities (in solution form gels easily) Non-uniform thicknesses  -ZrP colloids: Easy to synthesise and exfoliate Exfoliate to monolayers Discs mechanically strong, chemically stable

10. Platelets made of gibbsite  -Al(OH) 3 steric stabilisation with polyisobutylene (PIB) (C 4 H 8 ) n before fractionation  D =25% after fractionation  D =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

11.  platelet volume fraction phase sequence: I-N-C of monodisperse discs with and GEL SMECTIC?  D =25%  D =17% 18% 14%

12. columnar smectic? gel Small angle X-ray diffraction Conclusions: Spatially ordered phases possible Discs promote columnar phase Columnar phase stands high degree of diameter polydispersity But what happens at higher/lower diameter polydispersity? Can the smectic phase be stable? Role of thickness polydispersity?

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

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

15. Polydispersity: diameter distribution diameter polydispersity parameter monodisperse in thickness! as obtained from Dynamic Light Scattering & direct visualisation by TEM

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

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

18. 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

19. 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?

20. 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  D minimum Distribution projected on Cartesian axes:

21. CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT  DD DD

22. 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

23.  D =0.52  S =0.452 DD

24. 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 (soft interactions, avoid mapping on hard system) Future work

26. THE END

27. CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT

28. Some applications of discotic colloids clays: drilling fluids, injection fluids, cements (oil exploration and production) fluid properties depend on particles because of high surface to volume ratio nanocomposite fillers to tune mechanical, thermal, mass diffusion and electrical properties of materials (polymer matrices: composites of epoxy use nanodiscs of a-ZrP, clay, graphene sheets to enhance material performance) Surface chemistry: surface active agents (asphaltenes form Pickering emulsions) high-efficiency organic photovoltaics epoxy (Araldite): resina termoestable basada en polímero que se endurece cuando se mezcla con un catalizador. Se usa como protección contra corrosión, mejora de adherencia de la pintura, decoraciones de suelos también se modifican para que sean adhesivos, los más resistentes del mundo para hacer piezas industriales muy resistentes para aislar electricamente componentes electrónicos, transformadores,... encapsulado de circuitos integrados, reparaciones en naútica

29. epoxy nanocomposites based on a-ZrP advantage: a-ZrP platelets have very high ion exchange capacity adding 2 vol% tensile modulus of epoxy increases by 50% loss of ductility

30. Colloidal fluids: basic properties dispersiones partículas 1nm-1  m large surface-to-volume ratio: large interactions "human" time and length (visible light) scales => human molecular systems and more flexible interactions (tuning) Some examples Colloidal spheres: well studied/understood anisotropic colloids not so much Give rise to liquid-crystalline phases or mesophases Mesophase: orientational order + partial spatial order rod-like versus discotic colloids (smectic versus columnar phases) Some applications of discotic colloids Polidispersidad: conceptos generales con esferas duras Effect of diameter polydispersity in discotics: destabilization of columnar Effect of thickness polydispersity in discotics: destabilization of smectic Gibbsite: a hard-disc colloid Nuestro sistema: zirconium phosphate