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

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”

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

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

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

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: v1 [cond-mat. Mtrl-sci]

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

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

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

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

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

- 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

Debye length screening length Electric double layer charge density

diffuse electric double layer thin layer of “condensed” ions

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

fd virus : L = 880 nm D = 7 nm P = 3000 nm 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

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

Nematic + Isotropic 200 micron

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

200 micron Uniform homeotropic alignment

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

200 micron Melting and forming of nematic domains

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:

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

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

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

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

polarization (neglect hydrodynamic interactions) hydrodynamic interactions (neglect polarization)

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

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

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