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

2. 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.

3. 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.

4. Defect-mediated dynamics in Soft Matter.Jornada Científica ECM, 06/02/2009 INTRODUCTION. Soft Matter. S e lf A s s e m b y l - Simple components, weak interactions, collective effects. Examples: Membranes and vesiclesPolymer gelsThermotropic LC Sensitive to perturbations (labile) + Great adaptability

5. 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. ~ V rms Pol An

6. Defect-mediated dynamics in Soft Matter.Jornada Científica ECM, 06/02/2009 EXPERIMENTS. Monolayers with Smectic-C Order. h trans cis UV vis trans cis 8Az3COOH h 200  m 1 mM chloroform solution Photo-stationary mixture 200  m trans cis (mesophase) Ordered textures described with XY model.

7. Defect-mediated dynamics in Soft Matter.Jornada Científica ECM, 06/02/2009 EXPERIMENTS. Monolayers with Smectic-C Order. h trans cis UV vis trans cis 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)

8. 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. 

9. 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 -1/2 ? +1

10. 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

11. 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 Close inspection reveals a real and a virtual defect: crucial for the dynamics! 50  m 1.- Formation of domains with a pure bend texture Self-assembly + Minimization of interfacial (inter-line) energy = shape and inner field of minimum energy!

12. 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 Close inspection reveals a real and a virtual defect: crucial for the dynamics! 50  m 1.- Formation of domains with a pure bend texture

13. 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

14. 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

15. 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

16. Defect-mediated dynamics in Soft Matter.Jornada Científica ECM, 06/02/2009 EXPERIMENTS. Different scenarios of defect dynamics.  (mN/m) T (ºC) 10 2535 Hexatic (non labile)  (mN/m) T (ºC) 10 2535 3.- Coalescence of bend-splay domains. Formation of integer defects and disclinations.

17. 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.

18. 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

19. 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- L+L+ Dynamics: Attractive force (elastic energy reduction). Symmetric. Dissipation Rotational viscosity Backflow Asymmetric Dynamics

20. 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: n+n+ n-n- Motion asymmetry  elastic anisotropy: In the absence of backflow, and under local-dissipation conditions:

21. 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

22. 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 D = A/  d  = A/ We can get from knowledge of K S, K B, and the profile of molecular field across disclination: 350 300 250 200 150 100 50  (deg)

23. 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.

24. 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)