Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions Liquid crystal colloids: a 2d picture Nuno M. Silvestre CFTC - University of Lisbon April 14th, 2010 Collaboration: P. Patr´ ıcio (ISEL/CFTC) M. M. Telo da Gama (UL/CFTC) NM Silvestre CFTC Seminar - April 14th 2010 Liquid crystal colloids: a 2d picture 1/27
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Liquid crystal colloids: a 2d picture
Nuno M. Silvestre
CFTC - University of Lisbon
April 14th, 2010
Collaboration: P. Patrıcio (ISEL/CFTC)M. M. Telo da Gama (UL/CFTC)
NM Silvestre CFTC Seminar - April 14th 2010
Liquid crystal colloids: a 2d picture 1/27
Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Outline
IntroductionMean field approachColloid-colloid interactions
Quadrupolar interactionsDipolar interactions
Key-LockSoft ColloidsConclusions
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Introduction
Figure: Blood
Figure: Fish oil droplets
Figure: Ink
Figure: Fog at 25th of April bridge
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
What’s a colloid?
Figure: Colloid
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Liquid crystal colloids
Figure: Water droplets dispersed in nematic liquid crystal drops.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Liquid crystal colloids
Figure: (a) and (b) Self-assembling colloidal particles in 5CB LC. (c) Bindingpotential measured in kBT . M. Skarabot et al, PRE 77, 031705 (2008).
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Important?
1. Self-assembly
2. Colloidal optical materials
3. Super-capacitors
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Quadrupolar interactions
Quadrupolar inclusions in Smectic-C films
Figure: Inclusions in Smectic C film with parallel anchoring and surface defects.P. Cluzeau et al, JEPT Letters 76, 351 (2002).
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Quadrupolar interactions
Quadrupolar inclusions in Smectic-C films [NMS et al, Mol. Cryst.
Liq. Cryst. 495, 618 (2008)]
Figure: Energy profiles for severalanchoring strangths ωR/k = 0.1, 1,10, 100.
Figure: a) Equilibrium separationsmin and b) equilibrium orientationαmin as functions of anchoringstrength ωR/k
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Dipolar colloidal particles [in collab. with J. Maclennan and N. Clark,
Boulder, Colorado]
Figure: Chiral colloidal particles in a freely standing smectic film. Depolarizedreflected light microscope images of a smectic C∗ film of racemic MX8068showing (a) two colloidal particles with same handedness and (b) two colloidalparticles with opposite handedness. Equilibrium director field around twoislands with (c) the same handedness and (d) opposite handedness.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Behond the one-constant approximation
Chiral Smectic C∗:
one-elastic-constant approximation
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Behond the one-constant approximation
Chiral Smectic C∗:
one-elastic-constant approximation NOT VALID
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Behond the one-constant approximation
Chiral Smectic C∗:
one-elastic-constant approximation NOT VALID
Spontaneous polarization ~P (~x) Additional contribution to bendelastic constant k3.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Behond the one-constant approximation
Chiral Smectic C∗:
one-elastic-constant approximation NOT VALID
Spontaneous polarization ~P (~x) Additional contribution to bendelastic constant k3.
Important to consider: κ = k3/k1
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Homochiral inclusions
Figure: Colloid-defect geometry and interaction energies U(D)/(k1d) obtainedfrom computer simulations yielding dipole chains with homochiral colloid pairs,for various κ = k3/k1.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Homochiral inclusions
Figure: Dipolar chain. Bar: 20 µm. P.Cluzeau et al, PRE 63, 031702 (2001)
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Heterochiral inclusions [ NMS et al PRE 80, 041708 (2009)]
Textures of heterochiral colloidalparticles interacting on a film of25% chirally doped MX8068. (a)The quadrupolar structures is inequilibrium when the particlesalmost touch. (b) The equilibriumseparation between the defectsincreases as the particles areseparated using optical tweezers.(c) When the separation issufficiently large, the quadrupolarsymmetry is broken. (d) When theislands are forced even furtherapart, the quadrople evolves intotwo separate dipoles.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Heterochiral inclusions [ NMS et al PRE 80, 041708 (2009)]
Figure: Colloid-defect geometry and interaction energies U(D)/(k1d obtainedfrom computer simulations yielding quadrupoles with heterochiral pairs, forvarious κ = k3/k1.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Heterochiral inclusions [ NMS et al PRE 80, 041708 (2009)]
Figure: Equilibrium vertical separation S between defects as a function of thecolloid center-to-center separation D in the quadrupolar configuration regime,for racemic and 25% chirally doped films of MX8068, compared with the resultsof numerical calculations for systems with elastic anisotropies κ = 0.2, 1.0, 2.4
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Dipolar interactions
Heterochiral inclusions [ NMS et al PRE 80, 041708 (2009)]
How important are the thermal fluctuations?
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Capturing colloidal particles
Figure: FR Hung et al, J. Chem. Phys. 127,124702 (2007)
Figure: NMS et al, PRE69, 061402 (2004)
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Capturing colloidal particles [NMS et al, PRE 69, 061402 (2004)]
¯
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Capturing colloidal particles [NMS et al, PRE 69, 061402 (2004)]
Figure: Left: Equilibrium interaction free energy F = F/k for depthd/R = 0.01 as a function of the width of the cavity. Right: Equilibriumposition of the colloidal particle as a function of the width of the cavity.
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Capturing colloidal particles [NMS et al, PRE 69, 061402 (2004)]
Figure: Interaction energy F = F/k profile parallel to the wall, for severaldistances s/R.
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Deforming colloids
Figure: P.V. Dolganov et al, EPL 78,66001 (2007).
Figure: NMS et al, PRE 74, 021706(2006).
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Deforming colloids
Figure: Aspect ratio H/hversus major axis H . h -minor axis. P.V. Dolganovet al, EPL 78, 66001(2007).
Figure: Optimal eccentricity,e =
p
1 − (h/H)2 versus σ = γR/k. γ is thesurface tension. NMS et al, PRE 74, 021706(2006).
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Deforming colloids
Figure: Shape diagram: lines of constant eccentricity. σ = γR/k versus ωR/k.NMS et al, PRE 74, 021706 (2006).
NM Silvestre CFTC Seminar - April 14th 2010
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Introduction Mean field approach Colloid-colloid interactions Key-Lock Soft Colloids Conclusions
Conclusions
Self-assembling of liquid crystal colloids is driven by long-range
anisotropic attractions
Equilibrium colloidal structures are stabilised by short-range
repulsions that appear in the presence of topological defects
Elastic anisotropy influences the behavior of the topological
defects surrounding the colloidal particles.
Colloidal particles can be captured by self-similar surfaces
The shape of colloidal particles strongly depends on the elasticity