Transcript LIQUID-CRYSTALLINE PHASES IN COLLODIAL SUSPENSIONS …

LIQUID-CRYSTALLINE PHASES IN COLLOIDAL
SUSPENSIONS OF DISC-SHAPED PARTICLES
Y. Martínez (UC3M)
E. Velasco (UAM)
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
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
But all synthetic colloids are to
some extent polydisperse in size
parent phase
R 
R 2  R0
R0
R
coexisting
phases
2
2
FRACTIONATION
polydispersity
parameter
Polydispersity could destabilise non-uniform phases, since it is
difficult to accommodate range of diameters in an ordered
arrangement
Effect of polydispersity in discotics
thickness polydispersity: destabilization of smectic
diameter polydispersity: destabilization of columnar
smectic phase
columnar phase
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
R=25%
after fractionation
R=17%
GEL
14%
18%
SMECTIC?
R=17%
R=25%
phase sequence: I-N-C
of monodisperse discs
with <L> and <R>
f platelet
volume
fraction
• 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
 R  32%
aspect 2000

 740
ratio
2 .7
• diameter
• thickness
optical lengths
COLUMNAR
X rays
SMECTIC
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
R
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?
zˆ
Isotropic-nematic
Restricted-orientation approximation:
eˆ  xˆ, yˆ , zˆ
xˆ
yˆ
Distribution projected on Cartesian
axes:
 (eˆ, R)
 j ( R)   j h( R)
( 0)
 (R),  (R),  (R)
x
y
z
where h(R ) is a Schultz distribution
characterised by R
Hard interactions treated at the excluded-volume level (Onsager
or second-virial theory)
F[  x ,  y ,  z ]  F (  x ,  y ,  z ; R )  minimum
R
f
R
Nematic-smectic-columnar
Second-virial theory not expected to perform well

 (r , eˆ, R): complicated distribution function
Simplifying assumption: perfect order eˆ  zˆ

 (r , R)
COLUMNAR
SMECTIC
Fundamentalmeasure
theory for
polydisperse
parallel
cylinders
 ( z, R)
R=0.52
R
fS=0.452
fS=0.452
Attractive polydisperse platelets
free-energy functional:
L
r  R / R0
F    Fref    Fatt  
Fref  : hardpolydisperse platelets


 
1
Fatt     dR1  dR2  (r1 , R1 ) (r2 , R2 )Vatt (r1  r2 , R1 , R2 )
2
2
   r / R    z / L 2 1


  e 
,

2
2
r / R   z / L 
Vatt r , z, R1 , R2   


0

R R R
1
2
z  L and r  R
or z  L
otherwise
Phase diagrams (Gaussian tail distribution)
  s r 2
h0 (r )  C r e
=1
R = 0.294
=2
Microfractionation in the coexisting smectic phase
R = 0.294,  = 2,  = 1.665
d
h( z , r ) 
 z, r 

 dr z, r 
0
p(r ) 
 dz z, r 

0
d
 dr dz z, r 
0
0
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
THE END
CHARACTERISTICS OF SMECTIC PHASE FROM EXPERIMENT
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?