LIQUID-CRYSTALLINE PHASES IN COLLOIDAL SUSPENSIONS OF DISC-SHAPED PARTICLES

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 mm) • Same thickness (nm) • Polydisperse in diameter

2. Colloidal fluids: basic properties dispersions of particles of size 1nm-1mm • 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: paints, food, pharmaceutical products, cosmetics, paper, oil production, cement,... Present in natural environments and industrial applications

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

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

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

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

7. When ds 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 columnar phase smectic phase

9. Obtained from exfoliation of layered compounds: synthetic clays, gibbsite, Ni(OH)2, CuS or Cu2S, niobate,... Discotic colloids (of inorganic compounds) 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 a-ZrP colloids: Easy to synthesise and exfoliate Exfoliate to monolayers Discs mechanically strong, chemically stable

10. Gibbsite platelets in toluene: a hard-disc colloidal suspension van der Kooij et al., Nature (2000) Platelets made of gibbsite a-Al(OH)3 200nm "hard" platelet steric stabilisation with polyisobutylene (PIB) (C4H8)n Suspensions between crossed polarisers f=0.19 0.28 0.41 0.47 0.45 I+N N N+C C C before fractionation dD=25% after fractionation dD=17% (without polarisers)

11. SMECTIC? 14% 18% GEL dD=17% dD=25% phase sequence: I-N-C of monodisperse discs with <L> and <D> f platelet volume fraction

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

13. Zirconium phosphate platelets a-Zr(HPO4)2· H2O TEM of pristine a-ZrP platelets TEM of a-ZrP platelet coated with TBA

14. PROCESS OF EXFOLIATION OF LAYEREDa-Zr(HPO4)2·H2O 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. Optical images: white light and crossed polarisers I I+N N N+S f = platelet volume fraction volume occupied by platelets = total volume

17. ISOTROPIC-NEMATIC phase transition I I + N N non-linearity in the two-phase region: some fractionation extremely large volume-fraction gap: dD In gibbsite

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

19. pair potential Theory: some ideas Potential energy: will contain short-range repulsive contributions + soft interactions (vdW, electrostatic, solvent-mediated forces,...?) We treat soft interactions via an effective thicknessLeff (f) of hard discs • Criteria: • fIN in correct range • in smectic phase • approximate theory of screened • Coulomb interactions?

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

21. f dD dD CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT

22. Nematic-smectic-columnar Fundamental-measure theory for polydisperse parallel cylinders Second-virial theory not expected to perform well : complicated distribution function Simplifying assumption: perfect order SMECTIC COLUMNAR number of particles at r in a volume d3r with diameter between D and D+dD

23. dD=0.52 dD fS=0.452 fS=0.452

24. Future work • 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)

26. THE END

27. CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT

28. 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 Some applications of discotic colloids

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-1mm 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