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

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

• Y. Martínez (UC3M)
• E. Velasco (UAM)
• D. Sun, H.-J. Sue, Z. Cheng (Texas AM)

• Aqueous suspensions of disc-like
• colloidal particles (diameter mm)
• Same thickness (nm)
• Polydisperse in diameter

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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
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But all synthetic colloids are to some extent
polydisperse in size
parent phase
coexisting phases
FRACTIONATION
polydispersity parameter
Polydispersity could destabilise non-uniform
phases, since it is difficult to accommodate
range of diameters in an ordered arrangement
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• Effect of polydispersity in discotics
• thickness polydispersity destabilization of
  smectic
• diameter polydispersity destabilization of
  columnar

smectic phase
columnar phase
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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
f0.19 0.28 0.41 0.47 0.45
IN N NC C C
before fractionation dR25
after fractionation dR17
(without polarisers)
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GEL
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SMECTIC?
dR17
dR25
phase sequence I-N-C
f platelet volume fraction
of monodisperse discs with ltLgt and ltRgt

• But what happens at higher/lower diameter
  polydispersity?
• Can the smectic phase be stable?
• Role of thickness polydispersity?

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Zirconium phosphate platelets
a-Zr(HPO4)2 H2O
TEM of pristine a-ZrP platelets
TEM of a-ZrP platelet coated with TBA
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PROCESS OF EXFOLIATION OF LAYERED a-Zr(HPO4)2H2O
aspect ratio

• diameter optical lengths
• COLUMNAR
• thickness X rays
• SMECTIC

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Optical images white light and crossed
polarisers
I IN N
NS
f platelet volume fraction
volume occupied by platelets

total volume
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ISOTROPIC-NEMATIC phase transition
I
I N
N
non-linearity in the two-phase region some
fractionation
extremely large volume-fraction gap
dR
In gibbsite
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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
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Isotropic-nematic
Restricted-orientation approximation
Distribution projected on Cartesian axes
where is a Schultz distribution
characterised by dR
Hard interactions treated at the excluded-volume
level (Onsager or second-virial theory)
minimum
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f
dR
dR
CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT
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Nematic-smectic-columnar
Fundamental-measure theory for polydisperse
parallel cylinders
Second-virial theory not expected to perform well
complicated distribution function
perfect order
Simplifying assumption
SMECTIC
COLUMNAR
number of particles at r in a volume d3r with
diameter between D and DdD
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dR0.52
dR
fS0.452
fS0.452
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Attractive polydisperse platelets
free-energy functional
L
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Phase diagrams (Gaussian tail distribution)
l 2
l 1
dR 0.294
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Microfractionation in the coexisting smectic
phase
dR 0.294, l 2, be 1.665
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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

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• THE END

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CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT
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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
thickness Leff (f) of hard discs

• Criteria
• fIN in correct range
• in smectic phase
• approximate theory of screened
• Coulomb interactions?