DEFECT-MEDIATED DYNAMICS IN SOFT MATTER Jordi Ignés-Mullol Departament de Química Física, UB

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.


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.


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


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


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.


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)


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.



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



DIFFERENT EXAMPLES OF STRUCTURES AND DYNAMICS ARISING FROM DEFECT INTERACTION


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



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


T=298K



Domain chirality is biased by a vortical flow as long as the proposed mechanism is allowed by experimental conditions.




-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



(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.



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.


ANALYSIS. Material parameters from defect dynamics.

ANALYSIS OF DEFECT DYNAMICS TO EXTRACT MATERIAL PARAMETERS



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



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 )()( ,



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



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)


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.


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)

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DEFECT-MEDIATED DYNAMICS IN SOFT MATTER Jordi Ignés-Mullol Departament de Química Física, UB