1. Kyongok Kang (FZ-Juelich) A (short) introduction to colloids Electric-field induced phase transitions, dynamical states and non-equilibrium critical behaviour in concentrated suspensions of rods From David pine’s webpage Jan Dhont ICS-3

2. Introduction to Colloids Colloidal particles are “aggregates” with linear dimensions in the size range of 1 nanometer – 20 microns What are Colloids ? colloids are much larger than fluid molecules colloids exhibit vivid thermal motion sphere diameter 500 nm “hydodynamic interactions” “Brownian motion”

3. Introduction to Colloids Colloidal particles are “aggregates” with linear dimensions in the size range of 1 nanometer – 20 microns What are Colloids ? colloids exhibit vivid thermal motion sphere diameter 500 nm colloid water molecules

4. Introduction to Colloids Colloidal particles are “aggregates” with linear dimensions in the size range of 1 nanometer – 20 microns What are Colloids ? colloids exhibit vivid thermal motion sphere diameter 500 nm colloid water molecules Same laws of Thermodynamics and Statistical Physics Phase transitions You don’t have to learn anything new to understand colloids (in principle) Brownian motion is nothing but thermal motion

5. r V(r) - - - - - - - - - - -- - - - - - - - - -- - Direct interactions can be tuned “at will” Crystallization (FCC) Glasses Liquid-gas coexistence Aggregation Gels Crystallization (FCC and BCC) Electric fields

6. Crystallization of “hard spheres” P.N. Pusey, E. Zaccarelli, C. Valeriani, E. Sanz, W.C.K. Poon, M.E. Cates, Phil.Transactions A, 367, 4993 (2009); arXiv:0908.1663v1 [cond-mat. Mtrl-sci]

7. fluid gel H. Verduin, J.K.G. Dhont, J. Coll. Int. Sci. 172, 425 (1995) “sticky spheres” (taken from Eric Weeks webpage) binodal spinodal

8. M.E. Leunissen et al., Nature 437, 235 (2005) Mixture of charged and uncharged colloids NaCl-type crystal NiAs-type crystal - - - - - - - - - - -- - - - - - - - - -- -

9. Other shapes : rod-like colloids fd virus : L = 880 nm D = 7 nm P = 3000 nm

10. Sphere diameter 100 nm Rod length 900 nm Adams et al., Nature,1998 Mixtures of rods and spheres

11. F.M. van der Kooij, M. Vogel, H.N.W. Lekkerkerker, Phys. Rev. E 62, 5397 (2000) disks patchy colloids From David pine’s webpage star-like polymers (like DNA-colloids) from David Pine’s webpage transient, non-equilibrium forces

12. - COOH - COO- H+H+ H+H+ H+H+ H+H+ H+H+ H+H+ H+H+ Electric double layer / layer of condensed ions : no dissociation : low S low U dissociation : high S high U minimization of F=U -TS - COOH - COO- - COOH - COO- - COOH - COO- - COOH - COO- - COOH - COO- - COOH - COO- - COOH - COO- - COOH - COO- H+H+ H+H+ H+H+ H+H+ H+H+ H+H+ H+H+ H+H+ 1 nm-10 micron

13. Debye length screening length Electric double layer charge density

14. diffuse electric double layer thin layer of “condensed” ions

15. At sufficiently low frequencies (< 10 kHz) : - double layers are polarized - the layer of condensed ions is polarized - field-induced association-dissociation of condensed ions - electro-osmotic flow is induced - - - - - - - - - - - - - ++++ + + + ++ + ++ - - - - ----- -- - - + ++ + +++++ + + + Field-induced colloid-colloid interactions : - electrostatics - hydrodynamics E Electric-field induced phases, dynamical states, and critical behaviour in suspensions of rod-like charged colloid

16. fd virus : L = 880 nm D = 7 nm P = 3000 nm - 0.16 mM TRIS/HCl buffer (Debye length is 27 nm) - fd concentration is 2.0 mg/ml = within the isotropic-nematic two-phase region - At high ionic strength, the nematic phase is a cholesteric

17. polarizer analyzer 10 x G sample function generator light source DIC CCD L = 1.5 mm K. Kang, J.K.G. Dhont, Soft Matter 6, 273 (2010) Concentration : 2.0 mg/ml two-phase, isotropic-nematic coexistence = 26 c* isotropic nematic

18. Nematic + Isotropic 200 micron

19. Nematic + Chiral-nematic 200 micron a chiral nematic is also found at high ionic strengths and at higher f-concentration without an electric field

20. 200 micron Uniform homeotropic alignment

21. 200 micron Uniform homeotropic alignment order parameter (S=0.48) and diffusion coefficients are independent of field strength and frequency no charge-polarization

22. 200 micron Melting and forming of nematic domains

23. E 0 dissociation of condensed ions increase of ionic strength aligned state is unstable decay towards the isotropic state association of condensed ions decrease of ionic strength de-aligned state is meta-stable or unstable orientational order increases rotation of the director towards the external field (i) (ii) (iii) (iv) (v) Origin of the dynamical state:

25. Critical behaviour: - Domain size diverges - Characteristic time for melting/forming diverges 200 micron

26. I t characteristic time for melting/forming “video-image correlation function”:

27. d : power-law : power-law d : logarithmic : power-law : logarithmic d : finite E N* D H

28. Polarization for parallel orientation only important when : Hydrodynamic interactions are instantaneous when : Long rods : time to diffuse over the length of the rod frequency of the external field diffusion coefficient of salt ions time for a shear wave to propagate of a distance specific mass shear viscosity

29. polarization (neglect hydrodynamic interactions) hydrodynamic interactions (neglect polarization)

30. Theory low frequencies - polarization of a single particle (cooperation with Jerry Manning) - calculation of the pair-interaction forces - include these forces in the Smoluchowski equation (no HI: ) - account for the field-induced association-dissociation of condensed ions high frequencies (cooperation with Bogdan Cichocki) - flow induced by a single, unperturbed equilibrium double layer - “active” hydrodynamic interaction functions - analyze the Smoluchowski equation + “active” hydrodynamic + unperturbed direct interactions pdf for positions and orientations hydrodynamic interactions direct interactions rotation operator gradient operator Smoluchowski equation: (or : “the overdamped Liouville equation”) diffusion-migration on a surface

31. movies are 10 times accelerated 200 um N*-formation kinetics after a frequency quench from the H-phase

32. Thank you for your attention 200 um movies are 10 times accelerated