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 coexistenceAggregationGels

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:0908.1663v1 [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 nmRod 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

-COOH

-COOH

-COOH

-COOH-CO

OH

-COOH

-CO

OH

-CO

OH

-CO

OH

-CO

OH

-COOH

-COOH

-COOH-COOH -COOH -C

OO

H

-CO

OH

-CO

O-

-CO

O-

-COO-

-COO-

-COO-

-COO-

-COO-

-COO--CO

O-

-COO-

-CO

O-

-CO

O-

-COO-

-COO-

-COO- -COO- -CO

O-

-CO

O-

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

-COOH

-COO--CO

OH

-COO-

-CO

OH

-CO

O-

-CO

OH

-CO

OH

-COO-

-COOH

-COO--COOH -COO- -C

OO

H

-CO

O-

H+

H+

H+

H+

H+

H+H+H+

1 nm-10 micron

Debye lengthscreening length

Electric double layer

ionconcentratsalt/1~1

r

r}exp{~

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

- 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

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

polarizer

analyzer

10 x

G

sample

function generator lightsource

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

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

Nematic + Isotropic

200 micron

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

Nematic + Chiral-nematic

200 micron

a chiral nematic is also found at high ionic strengthsand at higher f-concentration without an electric field

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

200 micron

Uniform homeotropic alignment

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

200 micron

Uniform homeotropic alignment

order parameter (S=0.48) and diffusion coefficients are independent of field strength and frequency

no charge-polarization

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

200 micron

Melting and forming of nematic domains

E0

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:

100 101 102 1030

2

4

6

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

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

200 micron

I

t

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

CV

time [s]

3.26 V/mm

3.78

4.09

5.77

( ) expV

tC t

2

( ( ) ( ) ) ( (0) (0) )( )

( (0) (0) )V

I t I t I IC t

I I

100 101 102 1030

2

4

6

characteristic time for melting/forming

“video-image correlation function”:

d : power-law : power-law

d : logarithmic

: power-law

: logarithmic

d : finite

E

1.39E 0.18 1.29E

d 0.15

0.65 0.15

N*

DH

kHzL

kHzD

L

H

D

10001

11

2

2

L

Polarization for parallel orientation only important when :

Hydrodynamic interactions are instantaneous when :

1/

1

Ld

LLong 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 L

specific mass

shear viscosity

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

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

ˆˆˆ PP

PPHP

t ,

pdf for positions and orientations

hydrodynamic interactions

direct interactions

rotation operator

gradient operator

Smoluchowski equation: (or : “the overdamped Liouville equation”)

rD

uuIDH

0

0ˆˆˆ,

0 E

diffusion-migration on a surface

movies are 10 times accelerated200 um

N*-formation kinetics after a frequency quench from the H-phase

100 101 102 1030

2

4

6

E[V/mm]

[Hz]

*N

N

HD

Thank you for your attention

200 um movies are 10 times accelerated