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

dispersions of particles of size 1nm-1m

• 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

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 smecticdiscs prefer columnar

But there is another factor:

POLYDISPERSITY

discotic colloids

POLYDISPERSITY AND HARD SPHERES

= sphere volume fraction

=volume occupied by spheres

total volume3

6

VN

Hard spheres: good model for some colloidal spheres (silica, latex,...)

But all synthetic colloids are to some extent polydisperse in size

Hard-sphere crystal cannot exist beyond =0.06

2

0

20

2

polydispersity parameter

This is because the lattice parameter of the crystal is 10.1aotherwise the crystal should melt into a (more stable) fluid

Polydispersity should destabilise crystal, since difficult to accommodate range of diameters in a lattice structure

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 phasetwo

coexisting phases

When even higher,

collection of different, coexisting crystallites, possibly in coexistence with fluid

Fasolo & Sollich

(PRL 2003)

FRACTIONATION provides method of purification (decreasing polydispersity)

Effect of polydispersity in discoticsthickness polydispersity: destabilization of smectic

diameter polydispersity: destabilization of columnar

smectic phase columnar phase

Discotic colloids (of inorganic compounds)

Obtained from exfoliation of layered compounds:synthetic clays, gibbsite, Ni(OH)2, CuS or Cu2S, niobate,...

Typical problems:Hard to exfoliate (strong interlayer interactions)Layers not chemically stable in common solventsHard to synthesise (reactant heated to high T)Too large polydispersities (in solution form gels easily)Non-uniform thicknesses

-ZrP colloids:Easy to synthesise and exfoliateExfoliate to monolayersDiscs mechanically strong, chemically stable

Platelets made of gibbsite -Al(OH)3

steric stabilisation with polyisobutylene (PIB) (C4H8)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 0.45Suspensions between crossed polarisers

"hard" platelet

200nm

platelet volume fraction

phase sequence: I-N-C

of monodisperse discs with <L> and <D>

GEL

SMECTIC?

D=25%D=17%

18%

14%

columnarsmectic?

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?

Zirconium phosphate platelets

TEM of pristine -ZrP

platelets

TEM of -ZrP

platelet coated

with TBA

-Zr(HPO4)2· H2O

PROCESS OF EXFOLIATION OF LAYERED -Zr(HPO4)2·H2O

aspect ratio 740

7.22000

• diameter optical lengths COLUMNAR• thickness X rays SMECTIC

20

20

2

D

DDD

Polydispersity: diameter distribution

diameter polydispersity

parameter monodisperse in thickness!

%32D

%0L

as obtained from Dynamic Light Scattering & direct visualisation by TEM

= platelet volume fraction

=volume occupied by platelets

total volume

Optical images: white light and crossed polarisers

I I+N N N+S

ISOTROPIC-NEMATIC phase transition

non-linearity in the two-phase region: some fractionation

D

I I + N N

%100

extremely large volume-fraction gap:

%7In gibbsite

Small Angle X-ray scattering

NEM

ATI

CSM

ECTI

C 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

Theory: some ideasPotential energy:

i ij

jiij eerU )ˆ,ˆ,(

)'ˆ,ˆ,( eer

pair potential

'ee r

)'ˆ,ˆ,( eer

will contain short-range repulsive contributions + soft interactions (vdW, electrostatic, solvent-mediated forces,...?)We treat soft interactions via an effective thickness Leff () of hard discsCriteria: • in correct range• in smectic phase• approximate theory of screened Coulomb interactions?

)(2.1 effLd

zyxe ˆ,ˆ,ˆˆ

Isotropic-nematic

Restricted-orientation approximation:

);,,(],,[ Dzyxzyx FF

Hard interactions treated at the excluded-volume level (Onsager or second-virial theory)

)(),(),( DDD zyx ),ˆ( De

)()( )0( DhD jj )(Dhwhere is a Schultz distribution characterised by D

minimum

xy

z

Distribution projected on Cartesian axes:

D

D

Nematic-smectic-columnar

ze ˆˆ perfect order

Second-virial theory not expected to perform well

),ˆ,( Der

: complicated distribution function

Simplifying assumption:

),( DzSMECTICCOLUMNAR),( Dr

Fundamental-measure theory for polydisperse parallel cylinders

D=0.52

S=0.452 S=0.452D

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

THE END

CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT

Some applications of discotic colloidsclays: drilling fluids, injection fluids, cements (oil exploration and production) fluid

properties depend on particlesbecause 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 photovoltaicsepoxy (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 suelostambién se modifican para que sean adhesivos, los más resistentes del mundopara hacer piezas industriales muy resistentespara aislar electricamente componentes electrónicos, transformadores,... encapsulado

de circuitos integrados, reparaciones en naútica

epoxy nanocomposites based on a-ZrPadvantage: a-ZrP platelets have very high ion exchange capacityadding 2 vol% tensile modulus of epoxy increases by 50%loss of ductility

Colloidal fluids: basic propertiesdispersiones partículas 1nm-1mlarge surface-to-volume ratio: large interactions"human" time and length (visible light) scales => human molecular systems and more flexible

interactions (tuning) Some examplesColloidal spheres: well studied/understoodanisotropic colloids not so muchGive rise to liquid-crystalline phases or mesophasesMesophase: orientational order + partial spatial orderrod-like versus discotic colloids (smectic versus columnar phases)Some applications of discotic colloidsPolidispersidad: conceptos generales con esferas durasEffect of diameter polydispersity in discotics: destabilization of columnar Effect of thickness polydispersity in discotics: destabilization of smecticGibbsite: a hard-disc colloidNuestro sistema: zirconium phosphate