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 smectic
discs prefer columnar
But there is another factor:
POLYDISPERSITY
discotic colloids
POLYDISPERSITY AND HARD SPHERES
= sphere volume fraction
=volume occupied by spheres
total volume
3
6
V
N
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 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
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 0.45
Suspensions 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%
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?
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
7407.2
2000
• diameter optical lengths COLUMNAR• thickness X rays
SMECTIC
20
20
2
D
DDD
Polydispersity: diameter distribution
diameter polydispersity
parametermonodisperse 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
NE
MA
TIC
SME
CT
IC 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 ideas
Potential 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:
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
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
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
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
Colloidal fluids: basic propertiesdispersiones partículas 1nm-1m
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/understoodanisotropic 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 durasEffect 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
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