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DEFECT-MEDIATED DYNAMICS IN SOFT MATTERDEFECT-MEDIATED DYNAMICS IN SOFT MATTER
Jordi Ignés-MullolDepartament de Química Física, UB.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
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.
Screw dislocation at the surface of a crystal Dislocation pairs in a 2-d hexagonal lattice.
Example: magnetic bubbles on garnet film .
Structures that locally break a continuous symmetry
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.
S
e l f
A
s
s
e
m b
yl
-
Simple components, weak interactions, collective effects.
Examples:
Membranes and vesicles 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 a with homeotropic anchoring.
~Vrms
Pol
An
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Monolayers with Smectic-C Order.
h
transcis
UV
vis
transcis
8Az3COOH
h
200 m
1 mM chloroform solution
Photo-stationary mixture
200 m
trans
cis
(mesophase)Ordered textures described with XY
model.
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Monolayers with Smectic-C Order.
h
transcis
UV
vis
transcis
8Az3COOH
h
200 m
1 mM chloroform solution
Photo-stationary mixture
200 m
We have identified several motifs, a combination of bend and splay deformation modes (XY model)
trans
cis
(mesophase)
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.
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.
Spread a pure cis monolayer (isotropic). Irradiate with visible light: formation of trans form and phase separation.
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!
50 m
1.- Formation of domains with a pure bend texture
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Defect dynamics may couple with symmetry-breaking flow.
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
1.- Formation of domains with a pure bend texture
T=298K
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Defect dynamics may couple with symmetry-breaking flow.
Domain chirality is biased by a vortical flow as long as the proposed mechanism is allowed by experimental conditions.
1.- Formation of domains with a pure bend texture
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
-1/2
+1/2
Minimal steric hindrance favors coalescence.
Initial defect recombination leads to a final asymmetric dynamics of semi-integer boundary defects
2.- Coalescence of pure bend domains with opposed chirality.
T=310K
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
EXPERIMENTS. Different scenarios of defect dynamics.
(m
N/m
)
T (ºC)
10
25 35
Hexatic (non labile)
(m
N/m
)
T (ºC)
10
25 35
3.- Coalescence of bend-splay domains. Formation of integer defects and disclinations.
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.
T=313K
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.
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
L-
L+
4.0
3.5
3.0
2.5
2.0
1.5
1.0
v + /
v-
-10 -8 -6 -4 -2t-t0 (s)
-80
-60
-40
-20
0
20
L+
, L -
(m
)
-30 -20 -10 0t-t0 (s)
Dynamics:
Attractive force (elastic energy reduction). Symmetric.
DissipationRotational viscosity
Backflow
Asymmetric Dynamics
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
F =Zd2x
·K S
2(r ¢n)2+
K B
2(r £ n)2
¸Elastic free energy: n+ n-
Motion asymmetry elastic anisotropy:BS
BS
KKKK
In the absence of backflow, and under local-dissipation conditions: vFv )()( ,
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)
-1 (pinned)
2 disclination of length d
Simplified dynamics for mobile +1 defect:
viscous dissipation
elastic defect attraction
Line energy per 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 lines14
12
10
8
6
4
2
0
t 0 -
t (s)
80604020d (m)
D = A/
d = A/
We can get from knowledge of KS, KB, and the profile of molecular field across disclination:350
300
250
200
150
100
50
(deg
)
200
150
100
gra
yle
vel
160140120100806040200x (m)
Defect-mediated dynamics in Soft Matter. Jornada Científica ECM, 06/02/2009
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:
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.
Self-Organized Complexity & Self-Assembled Materials (F. Sagués)