Transcript Structure, dynamics and manipulation of colloidal systems in real-space Roel Dullens

Structure, dynamics and manipulation
of colloidal systems in real-space
Roel Dullens
Physical and Theoretical Chemistry Laboratory
Department of Chemistry
University of Oxford
Outline
Introduction
• Colloids in real life and as model systems
Crystal-Fluid interface of hard spheres
• Core-shell PMMA colloids
• 3D single particle imaging
Manipulating colloids
• Optical tweezers: deforming 2D colloidal crystals
• Magnetic colloids: dipolar fluids and ‘explosions’
quarks protons &
neutrons
10-15
1 fm
atoms &
molecules
10-12
1 pm
10-9
1 nm
COLLOIDS
What are colloids?
10-6
1 μm
10-3
1 mm
1
1m
103
1 km
106
International Union of Pure and Applied Chemistry
“The term colloidal refers to a state of subdivision, implying
that the molecules or polymolecular particles dispersed in a
medium have at least in one direction a dimension roughly
between 1 nm and 1 mm.”
Colloids in nature: milk
Colloids in nature: blood
7 mm
Colloids in nature: clay
1 mm
Natural and synthetic colloids: latex
Colloids as atoms
Jean Perrin (1870 – 1942)
Albert Einstein (1874 – 1942)
Same statistical thermo  Similar phase behaviour
Colloids as atoms
“The same equations have
the same solutions.”
Richard Feynman (1918-1988)
…so what is new?
Colloidal model systems
1. Tunable shape
2. Tunable interactions
energy
Hard
Soft repulsive
0
distance
Attractive
new and fascinating behaviour!
3. Colloids are larger and slower than atoms
Outline
Introduction
• Colloids in real life and as model systems
Crystal-Fluid interface of hard spheres
• Core-shell PMMA colloids
• 3D single particle imaging
Manipulating colloids
• Optical tweezers: deforming 2D colloidal crystals
• Magnetic colloids: dipolar fluids and ‘explosions’
Simplest system: hard spheres
Phase diagram*
Fluid
Fluid +
Crystal
0.494
Glass
Crystal
0.545
quench
0.58

*Computer Simulations: Alder & Wainwright (1957), Wood & Jacobson (1957)
Experimental hard spheres: Colloids
Sterically stabilized PMMA colloids in optically matching solvent
Fluid
0.494
Fluid + Crystal
Crystal
0.545
Pusey and van Megen, Nature, 320, 340 (1986)
Glass

Crystal-fluid interface
Core-shell colloids
z
x
y
Confocal
microscope
40 x 40 μm2
RPAD, D.G.A.L. Aarts & W.K. Kegel, PRL 97, 228301 (2006)
Colloids are seeable and slow
Structure and dynamics at single particle level
Structure
Dynamics
Correlations in single images
Correlation in subsequent images
Crystal-fluid interface
z
x
y
Confocal
microscope
40 x 40 μm2
40 x 40 x 70 μm3
RPAD, D.G.A.L. Aarts & W.K. Kegel, PRL 97, 228301 (2006)
Outline
Introduction
• Colloids in real life and as model systems
Crystal-Fluid interface of hard spheres
• Core-shell PMMA colloids
• 3D single particle imaging
Manipulating colloids
• Optical tweezers: deforming 2D colloidal crystals
• Magnetic colloids: dipolar fluids and ‘explosions’
Colloidal materials are soft
Softness of materials  Young’s modulus E:
stress
F A
energy
E 


strain L L volume
Young’s modulus E
Atomic materials
eV
Eatom ~ 3 ~ 100 GPa
Å
Colloidal materials
kT
Ecolloid ~ B 3 ~ 0.01 Pa
mm
Colloids are easy to manipulate and deform!
Optical tweezers
Optical tweezers
Optical tweezers
Time-sharing laser-beam
• Multiple quasi-static traps
• Control symmetry, density, …
Manipulation: optical tweezers
Dynamic optical tweezing
• control trap as a function of time
170 x 130 μm2
Example: micro-mechanics
Optical tweezers: microscopic deformation  Dragging particles through crystals
170 x 130 μm2
V = 0.25 μm/s
Displacement from trap
Dissipated energy  stiffness of crystal
1.2
250
2.5
200
2.0
Utrap (kBT)
r = |rimp-rtrap| (mm)
3.0
Ftrap (pN)
1.0
1.5
0.8
0.6
0.4
0.2
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
150
r (mm)
100
1.0
50
0.5
0
0.0
0
100
200
300
time (s)
400
500
600
-3
-2
-1
0
r (mm)
1
2
3
Δrsteady-state = direct measure for
dissipated energy (and force)
V = 0.25 μm/s
Orientational stiffness of 2D crystals
θ = 60˚
θ = 30˚
(11)-direction
r = |rimp-rtrap| (mm)
2.2
2.0
1.8
1.6
1.4
1.2
θ = 0˚
(10)-direction
1.0
0
5
10
15
20
 (degrees)
• high symmetry  low force (energy)  low stiffness
• low symmetry  high force (energy)  high stiffness
• variation in U ~ 100 kBT (!!!)
25
30
V = 0.25 μm/s
Effect on crystal: Strain-field
Determination of strain tensor1
80
ideal
60
real
εxx
40
20
-0.05000
-0.04500
-0.04000
0
Bond-vectors:
ri
Ri
y (mm)
-0.03500
-20
-0.03000
-40
-0.02500
-0.02000
-60
-0.01500
-80
-0.01000
-125
-100
-75
-50
-25
0
25
50
75
100
125
150
-0.005000
0
0.005000
80
0.01000
60
0.01500
εyy
40
0.02000
0.02500
Lattice spacing  g(r)
20
0
0.03500
Orientation  angle distribution
-20
0.04000
0.03000
0.04500
-40
0.05000
-60
Determine strain tensor ε by
minimizing mean-square diff.
 r
i
1
i
  Ri

-80
-125
-100
-75
-50
-25
0
25
x (mm)
50
75
100
125
x-profiles of εxx and εyy
Falk and Langer, PRE 57, 7192 (1998) & Schall et al., Nature 440, 319 (2006)
150
V = 0.25 μm/s
x-profiles of εxx and εyy
80
εxx
40
20
expansion
0.02
60
-0.05000
0.01
-0.04500
-0.04000
0
0.00
-0.03500
-20
y (mm)
-40
-60
-80
-125
-100
-75
-50
-25
0
25
50
75
100
125
150
strain 
-0.03000
-0.02500
-0.01
-0.02000
-0.01500
-0.01000
-0.02
xx
compression
-0.005000
0
yy
-0.03
0.005000
80
0.01000
60
0.01500
εyy
40
20
-0.04
0.02000
0.02500
0.03000
-0.05
0
0.03500
-20
0.04000
0.04500
-40
0
20
40
60
80
0.05000
x' (mm)
-60
-80
-125
-100
-75
-50
-25
0
25
x (mm)
50
75
100
125
150
Angular dependence of εxx and εyy?
100
120
140
V = 0.25 μm/s
Angle-dependent strain
-0.020
0.02
strain yy
strain xx
-0.025
-0.030
-0.035
-0.040
0.01
0.00
-0.045
-0.050
-0.01
-0.055
0
5
10
15
20
25
30
 (degrees)
• high symmetry  high strain (εxx)
0
5
10
15
25
30
 (degrees)
• increasing angle  increasing strain (εyy)
• low symmetry  low strain (εxx)
θ = 0˚
20
θ = 30˚
Outline
Introduction
• Colloids in real life and as model systems
Crystal-Fluid interface of hard spheres
• Core-shell PMMA colloids
• 3D single particle imaging
Manipulating colloids
• Optical tweezers: deforming 2D colloidal crystals
• Magnetic colloids: dipolar fluids and ‘explosions’
Magneto-rheological fluids
Paramagnetic colloids in external magnetic field
repulsion
Structure formation
m0 m2
U 
4 r 3
B
• band- and chains
• formation kinetics
attraction
B
2m0 m
U
4 r 3
2
B
m0: permeability constant
m:
magnetic moment
Tune interactions using
external magnetic field
170 x 130 μm2
Repulsive quench: explosions
B
partice-trajectories
highly non-equilibrium (non-diffusive, driven colloids)
Zigzag-instability in lines
Experiment
simulation
Arthur Straube and Ard Louis
Rotating fields ...
Summary
• Colloidal systems, confocal microscopy and optical
tweezers are a very nice playground!
• Structure of hard sphere crystal-fluid interface
• Orientational stiffness of 2D colloidal crystals:
high symmetry  low force  high strain
low symmetry  high force  low strain
• Magnetic colloids:
tunable interaction potential
great model system for self-assembly
Acknowledgements
Utrecht:
Volkert de Villeneuve
Willem Kegel
Andrei Petukhov
Maurice Mourad
Maria Claesson
Henk Lekkerkerker
Oxford:
Dirk Aarts
Stuttgart:
Clemens Bechinger
Stefan Bleil
Christopher Hertlein
Jens Harting
Rudolf Weeber
The end
2D colloidal model system
• small melamine spheres:
σs = 2.9 µm
• large polystyrene spheres:
σb = 15.5 µm
• screening of charges:
(almost) hard sphere interactions
Effective size-ratio ≈ 4
Example: micro-mechanics
Dragging a large probe particle through a 2D crystal
Variables
θ = 30˚
θ = 0˚
• orientation
• speed
Characterization of 2D crystals
snapshot
Voronoi construction
Np ≈ 1890, 170 x 130 μm2
170 x 130 μm2
Nearly defect-free 2D crystal
Characterization II
radial distribution function
angle distribution
9
8
9
8
7
7
g(r)
g(r)
5
p() (a.u.)
6
6
5
4
3
4
2
1
3
0
2
4
6
8
2
10
12
r (mm)
14
16
18
20
1
0
0
20
40
60
80
100
120
-180
-120
-60
0
60
120
r (mm)
 (degrees)
• sharp well-defined peaks
• 6 peaks  single crystal
• Lattice-spacing: 3.5 μm
• Crystal orientation: 18˚
180
V = 0.25 μm/s
Velocity of probe particle
4.5
0.30
0.25
Vx
Vy
II
0.15
I
0.10
P(v) (a.u.)
V (mm/s)
0.20
III
4.0
Vx
3.5
Vy
3.0
2.5
2.0
1.5
0.05
1.0
0.00
0.5
0
200
400
600
800
time (s)
1000
1200
0.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
V (mm/s)
Three regimes
• indentation (I)
• steady-state (II)
• relaxation (III)
Gaussian P(vx) and P(vy)
0.6
0.8
Tuning buoyancy of particles
“close to and away from equilibrium”
Increasing mass
non-density-matching
(non-equilibrium)
density difference
4
4
3
3
3
2
1
0
-20
d3ρ(z)
4
d3ρ(z)
d3ρ(z)
density-matching
(equilibrium)
2
1
-10
0
z’/d
10
20
0
-20
2
1
-10
0
10
20
0
-20
-10
z’/d
0
z’/d
Interfacial broadening! What’s happening?
Local bond order algorithm: identify crystallites
10
20
Visualisation of crystal-fluid interface
Particles that are part of crystalline cluster
A
Solvent 1
B
Solvent 2
C
Solvent 3
• Crystal nulceation and growth  increasing roughness of interface
• Dynamic broadening of interface away from equilibrium
Core-shell PMMA colloids
X-linked
PMMA
11.5 x 11.5 mm2
PHS
~ 1 μm
X-linked PMMARAS core
•
Rcore = 200 nm (fluorescent)
•
Rtotal = 650 nm,  = ~ 4 %
•
Density and refractive index matched
•
Hard sphere interactions
RPAD et. al., Langmuir 19, 5963 (2003) & Langmuir, 20, 658 (2004)
Velocity dependence: defect structures
V = 0.05 μm/s
V = 0.10 μm/s
V = 0.25 μm/s
V = 0.40 μm/s
V = 1.00 μm/s
V = 4.00 μm/s
V = 8.00 μm/s
V = 16.0 μm/s
Elastic
increasing
Plastic
txtal < tdrag
velocity
txtal > tdrag
500
60
400
55
W_|_ (mm)
W// (au)
“Defect lengths”
300
200
100
50
45
40
35
0
30
0
5
10
15
20
25
30
35
V (mm/s)
Further work:
• relation defect structure and strain
• correlation with dissipated energy
0.1
1
V (mm/s)
10
txtal ≈ tdrag
V = 0.25 μm/s
Displacement vs. strain
probe particle
r = |rimp-rtrap| (mm)
2.2
2.0
1.8
1.6
1.4
2.0
1.2
0
5
10
15
20
 (degrees)
25
30
|R|
1.0
1.5
-0.020
strain xx
-0.025
1.0
0.020
-0.030
0.025
-0.035
-0.040
-0.045
-0.050
host crystal
-0.055
0
5
10
15
20
 (degrees)
25
30
0.030
0.035
|xx|
0.040
0.045
0.050
Number density profile
4
(almost) density matching solvent
d3ρ(z)
3
2
(almost) stationary interface:
equilibrium interface
1
0
-20
-10
0
10
20
z’/d
Interfacial width*: W10-90(d) = 8
*10-90
width W10-90: Davidchack and Laird, JCP (108), 9452 – 9462 (1998)
Cornerstones of colloids
I. Chemistry
size, shape, interactions, fluorescence
I
III
III. Manipulation
light forces, optical
tweezers, magnetic and
electric fields
II
II. Time and
length scales
microscopy, scattering,
dynamics