DEFECT-MEDIATED DYNAMICS IN SOFT MATTER
Jordi Ignés-Mullol
Departament de Química Física, UB.
OUTLINE
1. Topological Defects. TD in Soft Matter.
2. Experiments with monomolecular films.
3. Different scenarios of defect dynamics (including coupling with external field).
4. Analysis of defect dynamics to yield material parameters.
5. Conclusions, Acknowledgements.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
INTRODUCTION. Topological Defects.
Structures that locally break a continuous symmetry
Screw dislocation at the
surface of a crystal
Dislocation pairs in a 2-d hexagonal lattice.
Example: magnetic bubbles on garnet film .
Point defects on the surface of a nematic liquid
crystals. Observed between crossed polarizers.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
INTRODUCTION. Soft Matter.
Simple components, weak interactions, collective effects.
s
A
S
Membranes and vesicles
y
l
e
Examples:
b
m
l
e
f
s
Polymer gels
Thermotropic LC
Sensitive to perturbations (labile) + Great adaptability
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
INTRODUCTION. Topological Defects in Soft Matter.
Example: defects arising in LC cell under E-field for material with negative ea with homeotropic
anchoring.
An
Vrms ~
Pol
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Monolayers with Smectic-C Order.
8Az3COOH
trans
1 mM chloroform
solution
hn
hn
UV
vis
Photo-stationary mixture
trans
(mesophase)
Ordered textures
described with XY
model.
cis
200 mm
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
cis
EXPERIMENTS. Monolayers with Smectic-C Order.
8Az3COOH
trans
1 mM chloroform
solution
hn
hn
UV
vis
Photo-stationary mixture
trans
(mesophase)
cis
We have identified several motifs,
a combination of bend and splay
deformation modes (XY model)
200 mm
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
cis
EXPERIMENTS. Different scenarios of defect dynamics.
Domain coalescence leads to scenarios of formation, interaction and annihilation of different
defect structures:
1.- Domain coalescence is promoted by reduction of line tension.
2.- There may be steric impediments to coalescence, since ordered fields merge.
3.- Constant-angle boundary conditions imply a +1 topological charge in closed domain: new
defects are created during coalescence.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
Domain coalescence leads to scenarios of formation, interaction and annihilation of different
defect structures:
1.- Domain coalescence is promoted by reduction of line tension.
2.- There may be steric impediments to coalescence, since ordered fields merge.
3.- Constant-angle boundary conditions imply a +1 topological charge in closed domain: new
defects are created during coalescence.
+1
+1
-1/2 ?
+1
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
DIFFERENT EXAMPLES OF STRUCTURES AND
DYNAMICS ARISING FROM DEFECT INTERACTION
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Defect dynamics may couple with symmetry-breaking flow.
1.- Formation of domains with a pure bend texture
Spread a pure cis monolayer (isotropic). Irradiate with
visible light: formation of trans form and phase
separation.
50 mm
Formation of elliptical domains with quasi-uniform inner molecular orientation. The shape
reveals an anisotropic line tension.
Constant-angle boundary conditions + elliptical
shape corresponds to XY field with one +1/2
point defect at each pole.
+1/2
+1/2
Close inspection reveals a real and a virtual defect: crucial for the dynamics!
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Defect dynamics may couple with symmetry-breaking flow.
1.- Formation of domains with a pure bend texture
Spread a pure cis monolayer (isotropic). Irradiate with
visible light: formation of trans form and phase
separation.
Domains with a given chirality arise from the
coalescence of two complementary achiral domains
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
T=298K
EXPERIMENTS. Defect dynamics may couple with symmetry-breaking flow.
1.- Formation of domains with a pure bend texture
Domain chirality is biased by a vortical flow as long as the proposed mechanism is allowed by
experimental conditions.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
2.- Coalescence of pure bend domains with opposed chirality.
Minimal steric hindrance favors coalescence.
Initial defect recombination leads to a final
asymmetric dynamics of semi-integer boundary
defects
T=310K
-1/2
+1/2
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
p (mN/m)
p (mN/m)
3.- Coalescence of bend-splay domains. Formation of integer defects and disclinations.
Hexatic (non labile)
10
10
25
25
35
35
T (ºC)
T (ºC)
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
3.- Coalescence of bend-splay domains. Formation of integer defects and disclinations.
Line tension overcomes steric hindrance: opposite molecular
fields entre into contact.
We can study the dynamics of a ±1 defect pair linked by a
shrinking disclination line.
T=313K
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
ANALYSIS. Material parameters from defect dynamics.
ANALYSIS OF DEFECT DYNAMICS TO EXTRACT MATERIAL PARAMETERS
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
ANALYSIS. Material parameters from defect dynamics.
Asymmetric dynamics of semi-integer boundary defects
20
4.0
-20
Asymmetric
Dynamics
3.5
3.0
-40
v + / v-
L+, L - (mm)
0
-60
2.5
2.0
1.5
-80
1.0
-30
L-
-10
-20
t-t0 (s)
0
-10
-8
-4
-6
t-t0 (s)
-2
Attractive force (elastic energy reduction). Symmetric.
Dynamics:
L+
Rotational viscosity
Dissipation
Backflow
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
ANALYSIS. Material parameters from defect dynamics.
Asymmetric dynamics of semi-integer boundary defects
Elastic free energy:
·
¸
Z
KS
KB
F =
d2 x
(r ¢n) 2 +
(r £ n) 2
2
2
Motion asymmetry  elastic anisotropy:  
n+
n-
KS  KB
KS  KB
In the absence of backflow, and under local-dissipation conditions:
m  ( ) v  F ,   m  ( ) v
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
ANALYSIS. Material parameters from defect dynamics.
Dynamics of defects linked by disclination lines
+1 (mobile)
2p disclination
of length d
-1 (pinned)
Simplified dynamics for mobile +1 defect:
viscous elastic defect Line energy per
dissipation attraction
unit length
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
ANALYSIS. Material parameters from defect dynamics.
Dynamics of defects linked by disclination lines
14
t0 - t (s)
12
10
8
6
D = A/m
4
d = A/l
2
0
20
40
60
d (mm)
80
We can get l from knowledge of KS, KB, and the profile of molecular field across disclination:
350
300
200
200
150
150
100
100
50
0
20
40
60
80
x (mm)
100
120
140
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
160
j (deg)
graylevel
250
CONCLUSION AND PERSPECTIVES.
•Topological defects determine the structure and dynamics of soft materials.
•Labile two-dimensional layers feature a rich variety of structures and dynamics.
•The semi-quantitative study of these monolayers yields material parameters from the
analysis of (non-equilibrium) defect dynamics.
•Defect-mediated dynamics determine the transformations arising from the coupling with
external macroscopic forces: control defect dynamics and you will control the structure.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
ACKNOWLEDGEMENTS
Research Group:
Self-Organized Complexity & Self-Assembled Materials
(F. Sagués)
Contributors: M. A. Vallvé, N. Petit, J. Claret, R. Albalat, F. Sagués, J. I.-M.
Collaborators: J. Casademunt, J. Brugués (ECM).
Funding: FIS-2006-03525, 2005SGR00653.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009