Transcript LIQUID-CRYSTALLINE PHASES IN COLLODIAL SUSPENSIONS …

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
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
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
POLYDISPERSITY AND HARD SPHERES
Hard spheres: good model for some
colloidal spheres (silica, latex,...)
f = sphere volume fraction
=
volume occupied by spheres
total volume

 N 3
 
6 V 

But all synthetic colloids are to some extent polydisperse in size

d
d 
 2   02
 02
polydispersity
parameter
Polydispersity should destabilise crystal, since difficult to
accommodate range of diameters in a lattice structure
Hard-sphere crystal cannot exist beyond d=0.06
This is because the lattice parameter of the crystal is a  1.10
otherwise the crystal should melt into a (more stable) fluid
Fluid and crystal exhibit FRACTIONATION
For still higher d 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
When d 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 discotics
thickness 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
a-ZrP colloids:
Easy to synthesise and exfoliate
Exfoliate to monolayers
Discs mechanically strong, chemically stable
Gibbsite platelets in toluene: a hard-disc colloidal suspension
Platelets made of gibbsite a-Al(OH)3
van der Kooij et al., Nature (2000)
200nm
"hard"
platelet
steric
stabilisation with
polyisobutylene
(PIB) (C4H8)n
Suspensions between crossed polarisers
f=0.19 0.28
I+N
N
0.41
0.47
0.45
N+C
C
C
(without
polarisers)
before fractionation
dD=25%
after fractionation
dD=17%
SMECTIC?
14%
18%
GEL
dD=17%
dD=25%
phase sequence: I-N-C
of monodisperse discs
with <L> and <D>
f platelet volume fraction
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
a-Zr(HPO4)2· H2O
TEM of
pristine
a-ZrP
platelets
TEM of
a-ZrP
platelet
coated
with TBA
PROCESS OF EXFOLIATION OF LAYERED a-Zr(HPO4)2·H2O
aspect 2000

 740
ratio
2 .7
• diameter
• thickness
optical lengths
COLUMNAR
X rays
SMECTIC
Polydispersity: diameter distribution
diameter
polydispersity
parameter
dD 
D 2  D0
D0
2
2
d L  0%
monodisperse in thickness!
d D  32%
as obtained from
Dynamic Light
Scattering & direct
visualisation by TEM
Optical images: white light and crossed polarisers
I
I+N
f = platelet volume fraction
=
volume occupied by platelets
total volume
N
N+S
ISOTROPIC-NEMATIC phase transition
I
I+N
N
non-linearity in the
two-phase region:
some fractionation
dD
extremely large volumefraction gap:
f
f
 100%
In gibbsite 7 %
smectic order, with weak
N to S transition
Small Angle X-ray scattering
SMECTIC
sharp peaks with higherorder reflections (welldefined layers)
large variation in
smectic period with f
(almost factor 3)
NEMATIC
long-range forces?
Theory: some ideas
Potential energy:
pair potential
eˆ

r
eˆ '


U   (rij , eˆi , eˆ j )
(r , eˆ, eˆ' )
i j i

(r , eˆ, eˆ' ) will contain short-range repulsive contributions + soft
interactions (vdW, electrostatic, solvent-mediated forces,...?)
We treat soft interactions via
an effective thickness Leff (f)
of hard discs
Criteria:
• fIN in correct range
• in smectic phase d  1.2Leff (f )
• approximate theory of screened
Coulomb interactions?
zˆ
Isotropic-nematic
Restricted-orientation approximation:
eˆ  xˆ, yˆ , zˆ
xˆ
yˆ
Distribution projected on Cartesian
axes:
 (eˆ, D)
 j ( D)   j h( D)
( 0)
 (D),  (D),  (D)
x
y
z
where h(D ) is a Schultz distribution
characterised by dD
Hard interactions treated at the excluded-volume level (Onsager
or second-virial theory)
F[x ,  y , z ]  F (x ,  y , z ;d D )  minimum
dD
f
dD
Nematic-smectic-columnar
Second-virial theory not expected to perform well

 (r , eˆ, D): complicated distribution function
Simplifying assumption: perfect order eˆ  zˆ

 (r , D) COLUMNAR
SMECTIC
Fundamentalmeasure
theory for
polydisperse
parallel
cylinders
 ( z, D)
dD=0.52
dD
fS=0.452
fS=0.452
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)
THE END
CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT
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,
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 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