Colloids

•What’s a colloid?•Colloidal Interactions and Colloidal Crystals•Hard Spheres and thermodynamics•Packings and the Liquid-Crystal Transition•Hard Ellipses•Role of Gravity•Sedimentation Dynamics•Sedimentation Equilibria•Microgravity Experiments•Crystallization Kinetics•Phonons in hard Sphere Crystals

Colloids?

Encyclopaedia Britanica 1948

Colloidal Interactions

Range Strength

Van der Waals Attractive 0.3-10nm 0-100kBT

Electrostatic AttractiveRepulsive

0.3-1000nm 0-1000 kBT

Depletion Attractive 10-300nm 0-20 kBT

Brushes Hard repulsionSoft repulsionSoft-repulsion

Reversible attraction

5-50nm 0-50 kBT

DNA RepulsionSpecific attractionReversible

10-5000nm 0-100 kBT

mgh k TB=Gravitational Height

Van der Waals and excluded volume

PNk T

V NbNk T

VB B

C=

−=

−( )1 φ φ

Exact in 1D

Exact asymptotic form in any dimension

PC

∝−

11( )φ φ

Φ.64 .74

P

( )

( )( )S Nk V Nb

Nk VB

B C

= −

= −

ln

ln 1 φ φ

liquid

solid

Hard Sphere Equilibrium Phase Diagram

Phase Diagram by 1g Experiment

Pusey & van Megen, Nature, 320 (1986) 340

325 nm PMMA/decalin/CS2

0.4780.5020.5120.5280.5530.5780.5950.6210.637LiquidCoexistenceFully

crystallizedCrystal

HeterogeneousGlassMainly

0.50 0.502 0.504 0.512 0.516 0.518 0.524 0.537

CDOT 1998

0.5470.549 0.561 0.591 0.618 0.619 0.633 0.6340.605

Mullins – Sekerka InstabilityPlanar Instability similar to dentritic instability

Bulge sharpens concentration gradient, flux increases, bulge grows faster

v

Quasi-steady Solution

Perturbation unstable

J. S. Langer

• Bragg Scattering• Dynamic Light Scattering• Static Light Scattering• Rheology

30 40 500

40

80

120

160

7.5 days

Time in Seconds Just after melting B183 B198 B213 B228 B244 B259 B274 B289 B304 B836 B650106

Angle (degree)

Coun

ts p

er s

econ

d (

/ Exp

osur

e tim

e)

FCC{111}

FCC{200}

t

φ = 0.552

Do ellipsoids pack denser than spheres?

.6361+/-.001

Ball bearings

.672.672.6791.91+/-.005

M&m minis

.669.671.6761.89+/-.005

Regular m&m’s

0.5 litre1 litre5 litreAspect ratio

Multi-speckle Cross-correlation Spectroscopy: Phonons in an Entropic Crystal

Controlled Growth of Hard Sphere Crystalsin a temperature gradient

Scattering Problems and solutions with a CCD•Multiple scattering.. Cross-correlate in a single scattering speckle•Non ergodicity.. ensemble average speckles with ~ same q

Phonon Spectrum for RCHPhard sphere single crystals

Steps:•Grow large hard sphere single crystal•Get rid of multiple scattering•Ensemble average non-ergodic sample•Separate Incoherent (δr2(t)) from coherent phonons•Worry about what phonons mean in a

completely anharmonic crystal

CCD

Density and Index Matched Hard Spheres

Single Crystal Crystallite

Heater

Bragg Spots

10 cm

Sample

Single scattering

MultipleMultipleScatteringScattering

Incident Beam

Multiple Scattering Speckle

Single Scattering Speckle

Pixels

Pairs of Pixels ~ 60µ separationSingle Scattering correlated Multiple Scattering uncorrelatedfor

Bill Meyer’s Trick - Cross Correlate to eliminate Multiple Scattering

µλ

ξ 120~~sinbeam

gle dr

µλ

ξ 15~~photon

multiple lr

glepixelmultiple d sinξξ <<

CCD

100 pixels~1.5mm

Ensemble Averaging

~150mm

δθ~10-2Well defined scattering vector

over 100x100 arrayδq/qBragg~.02

part of CCD

Separation of pixels~50µ

100 pixels~1.5mm

Speckle size ~75µ

Typically average 20x20 specklesx20 translations⇒ ~1% error

Two Contributions to Correlation Function

Coherent Scattering from Phonons

λω /1

2

~ tqeg −

1

0t

q

Incoherent Scattering from Polydispersity/Polyindexivity

0

1

trqeg22

~1δ−

t

Can get self diffusion fromlarge angle scattering