Slide: 1
Soft Matter Studies with X-rays
Theyencheri Narayanan
European Synchrotron Radiation Facility
Structure from Diffraction Methods, Eds. D.W. Bruce, D. O’Hare & R.I.
Walton, (Wiley, 2014)
Soft-Matter Characterization, Eds. R. Borsali & R. Pecora (Springer, 2008)
Slide: 2
Outline
• What is Soft Matter?
• Some general features
• Different X-ray techniques employed
• Self-assembly & complexity
• Out-of-equilibrium phenomena
• Summary and outlook
Slide: 3
What is Soft Matter?
Matière molle » Madeleine Veyssié
Soft matter is a subfield of condensed matter comprising a variety of
physical states that are easily deformed by thermal stresses or thermal
fluctuations. They include liquids, colloids, polymers, foams, gels,
granular materials, and a number of biological materials. These materials
share an important common feature in that predominant physical
behaviors occur at an energy scale comparable with room temperature
thermal energy. At these temperatures, quantum aspects are generally
unimportant. Pierre-Gilles de Gennes, who has been called the "founding
father of soft matter,"[1] received the Nobel Prize in physics in 1991 for
discovering that the order parameter from simple thermodynamic
systems can be applied to the more complex cases found in soft matter,
in particular, to the behaviors of liquid crystals and polymers.
Slide: 4
Soft Matter: Encounter in everyday life
Sustainable development and supply of consumer products
Slide: 5
Soft matter science is an interdisciplinary field of research where
traditional borders between physics and its neighboring sciences
such as chemistry, biology, chemical engineering and materials
science disappear.
Soft Matter studies seek to address the link between microscopic
structure/interactions and macroscopic properties.
What is Soft Matter?
Materials which are soft to touch – characterized by a small
modulus (energy/characteristic volume), typically 109 – 1012
times lower than an atomic solid like aluminum.
A significant fraction of consumer products fall in this category.
Slide: 6
Soft Matter Characteristics
Dominance of entropy
Strong influence of thermal fluctuations (~ kBT)
Characteristic size scale or microstructure ~ 100 – 1000 nm
Shear modulus, G ~ Energy/Free volume » 109 – 1012 smaller
Low shear modulus (G) » soft and viscoelastic
Soft implies: (1) high degree of tailorability
(2) lack of robustness
Multi-scale out-of-equilibrium systems
Slide: 7
Soft Matter Triangle
3 main ingredients of soft matter
Harder side
Flexible side
Selective side
Slide: 8
Soft Matter: Increasing levels of complexity
Elucidating the pathways of self-assembly O. Ikkala and G. Brinke, Chem. Commun., (2004)
Slide: 9
Impact of Soft Matter in Condensed Matter Physics
• Critical Phenomena (static and dynamic)
• Freezing, glass transitions, etc.
• Fractal growth (e.g. colloid aggregation)
• Self-organized criticality (granular matter)
Over the last 40 years
Soft Matter constitutes a significant fraction of modern day Nanoscience/Nanotechnology.
Slide: 11
Synchrotron Radiation Studies of Soft Matter
• High spectral brilliance or brightness
Real time studies in the millisecond range, micro/nano focusing and high q resolution
Time-resolved SAXS, WAXS, micro-SAXS, USAXS, etc.
High detectivity for studying extremely dilute systems (f < 10-6)
• Partial coherence
Equilibrium dynamics using the coherent photon flux (for concentrated systems)
Photon correlation spectroscopy (XPCS)
• Continuous variation of incident energy
Contrast variation of certain heavier elements, e.g. Fe, Cu, Se, Br, Rb, Sr, etc.
Anomalous SAXS
• Complementary imaging techniques
X-ray microscopy, micro and nano tomography, etc.
Slide: 12
Small-Angle X-ray Scattering (SAXS)
l q
detector sample
)2/sin(4
ql
q
beamstop
vacuum
Measured Intensity:
i0 - incident flux
Tr - transmission
e - efficiency
DW - solid angle
Differential scattering
cross-section WDW
d
dTiI rS
e0
W
W
d
d
Vd
dqI
Scat
1)(
Beamline – ID02
Slide: 13
10-3
10-2
10-1
100
101
102
103
104
105
106
q-4
I(q)
(mm
-1)
q (nm-1)
Silica particles (f ~ 0.01, size ~ 600 nm, p ~ 2%)
Model (RMean
=303 nm, R=6.2 nm & Dq=0.001 nm
-1)
SAXS from dilute spherical particles
Porod
Guinier region
Slide: 14
)()()( qSqFNqI
SAXS from spherical colloidal particles
N – particle number density,
F(q) – single particle scattering function,
S(q) – structure factor of interactions
)()()( * qAqAqF
drrqr
qrrrqA me
2
0
sin])([4)(
(r) – radial electron density
re – classical electron radius
=2.82x10-15 m
)()()()( 2* qSqPVNqI DV – volume of the particle
P(q) – form factor
***
mS D contrast
Ser *scattering length density for homogeneous particles
Calculation of S(q) involves approximations (e.g. Percus-Yevick closure)
Thomson scattering
Slide: 15
Microworld
0.1 nm
1 nan
om
eter (nm
)
0.01 mm
10 nm
0.1 mm
100 nm
1 micro
meter (m
m)
0.01 mm
10 mm
0.1 mm
100 mm
1 millim
eter (mm
)
1 cm
10 mm
10-2 m 10-3 m 10-4 m 10-5 m 10-6 m 10-7 m 10-8 m 10-9 m 10-10 m
Visible
Nanoworld
1,000 nan
om
eters =
Infrared
Ultraviolet
Microwave Soft x-ray
1,000,000 nan
om
eters =
Size scales probed by SAXS & related techniques
q2
Colloids
Polymers
Surfactants
Liquid crystals
Etc.
Slide: 16
Microworld
0.1 nm
1 nan
om
eter (nm
)
0.01 mm
10 nm
0.1 mm
100 nm
1 micro
meter (m
m)
0.01 mm
10 mm
0.1 mm
100 mm
1 millim
eter (mm
)
1 cm
10 mm
10-2 m 10-3 m 10-4 m 10-5 m 10-6 m 10-7 m 10-8 m 10-9 m 10-10 m
Visible
Nanoworld
1,000 nan
om
eters =
Infrared
Ultraviolet
Microwave Soft x-ray
1,000,000 nan
om
eters =
Size scales probed by SAXS & related techniques
q2
Colloids
Polymers
Surfactants
Liquid crystals
Etc.
Slide: 17
10-2
10-1
102
103
104
105
0.0 0.2 0.4 0.6
0.0
0.2
0.4
0.6
f [S
(q)
PY]
fC [I(0)]
I(q)
(m
m-1
)
q (nm-1)
Form & Structure Factors
)()()()( 2* qSqPVNqI MD
Experimental P(q), polydisperse & S (q) within Percus-Yevick (PY) approximation
Differential scattering cross-section
per unit volume
10-2
10-1
10-3
10-2
10-1
100
101
102
103
Form Factor
Fit
I(q)
(mm
-1)
q (nm-1)
f < 0.001
Slide: 18
10-2
10-1
102
103
104
105
0.0 0.2 0.4 0.6
0.0
0.2
0.4
0.6
f [S
(q)
PY]
fC [I(0)]
I(q)
(m
m-1
)
q (nm-1)
Form & Structure Factors
)()()()( 2* qSqPVNqI MD
Experimental P(q), polydisperse & S (q) within Percus-Yevick (PY) approximation
Differential scattering cross-section
per unit volume
10-2
10-1
10-3
10-2
10-1
100
101
102
103
Form Factor
Fit
I(q)
(mm
-1)
q (nm-1)
f < 0.001
Crystalline order
Slide: 19
Beamline – ID10
Silica microspheres in water
d=0.49±0.02mm, q=0.09 nm-1
X-ray Photon Correlation Spectroscopy (XPCS)
2
01 qDC
Slide: 22
x y
z
ai
af qf qy
qz
fi
fiff
fiff
q
aa
qaqa
qaqa
l
sinsin
sincossincos
coscoscoscos2
zy,x,
Grazing Incidence Small-Angle X-ray Scattering (GISAXS)
Beamline – ID10
Slide: 23
Soft Interfaces Scattering
gas-liquid
liquid-liquid
liquid-solid
b
a
b y
Z
b
a
b y
- Surface structure of simple and complex fluids (colloid, gel, sol,…)
- Morphology and crystalline structure of thin organic and inorganic films
- 2D organization of molecules, macromolecules and nanoparticles
- Bio-mimetic systems & Bio-mineralization
Langmuir films
P, A, T
Buried interfaces
Slide: 24
Soft Interfaces Scattering
Complex fluids
Elements distribution
α / αC
Dαi < 0.1αi
bulk
surface
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
102
103
Pen
etr
ati
on
dep
th,
1/A
Grazing angle, a/ac
Water @ λ=1.55 Å
Pen
etra
tion
dept
h Λ
, Å
αi 0.1˚
at 8 keV
α β Λ(ρ, α)
SUBSTRATE
)1(
fdFILM
)2(
fd
Varying the penetration depth
Slide: 25
Micro-diffraction (ID13)
Correlate the local nanostructure to
the fiber mechanical properties.
Skin-core morphology of high performance fibers
E.g. Kevlar
Elucidating the local
nanostructure
R. Davies et al., APL (2008)
Slide: 26
10-2
10-1
100
101
10-3
10-2
10-1
100
crystalline
amorphous
crystalline
amorphous
SAXS
WAXS
I(q
) (m
m-1
)
q (nm-1)
SAXS/WAXS from Semi-crystalline polymers
Slide: 27
Scanning Micro-diffraction on HDPE spherulites
• high density poly-ethylene • spherulites under polarized light banded structures indicating long range order
12.5 keV, 1.5 micron spot
Rosenthal M. et al., Angewandte Chemie, (2011)
• SAXS/WAXS patterns • line scans across the center reveal information on crystallite orientation
Slide: 28
Micro-diffraction on HDPE spherulites
• 35° tilt between c-axis and the normal of
the base plane of crystalline lamellas
• orientation of b-axis aligned with
growth direction
• chirality can be determined
Azimuth/Intensity vs Distance from the center in mm
Slide: 29
Coherent X-ray Diffractive Imaging (CDI) 2D and 3D imaging of non-crystalline objects, biological samples with
nanometers resolution
Lensless imaging technique
Thick or small samples (single molecules)
3D reconstruction SEM image
Reconstruction
pixel 24 nm
Slide: 30
H. Jiang et al., PNAS (2010)
Phases encoded by over sampling of the diffraction pattern
3D reconstruction
CDI of Biological Specimen
Slide: 32
Lipid-DNA complex Micelles Cell
Kinetics of self-assembling systems understanding of properties and
functionalities – material stability, cell trafficking (drug delivery), detergency, etc.
How are these complexes formed: kinetic pathways to (non-)equilibrium?
Vesicles
How can these complexes be tuned and manipulated to new materials
(e.g. biomedical/pharmaceutical applications) ?
Motivation: understanding self-assembly in nature
Complexity
Slide: 33
Spontaneous self-assembly of micelles and vesicles
Kinetic pathway: stopped-flow rapid mixing & time-resolved SAXS
Self-assembly of micelles and vesicles
Rate-limiting steps » predictive capability
?
spherical
micelles
vesicle
anionic
cationic
E.g. surfactants, lipids or block copolymers
Large variety of equilibrium structures
Dynamics of formation is very little explored
?
monomers micelles
Slide: 34
Stopped-Flow Mixing Device
• Rapid mixing of reactants in turbulent flow through a mixer
• Solenoid valve at the exit to stop the flow of the mixture
• Deadtime ~ a few millisecond
Beamline ID02@ESRF
Slide: 35
Poly(ethylene-propylene) -
poly(ethylene oxide)
? Unimer
Micelle
DMF
DMF/water
Spontaneous self-assembly of block copolymer micelles
Rapid jump in solvent selectivity /
Interfacial tension
R. Lund, et al., PRL, 102, 188301 (2009)
» mean aggregation number, Pmean
0.01 0.02 0.030
10
20
30
40
50
60
70
80
90
100
I(Q
)
14.5 ms
24.5 ms
194.5 ms
994.5 ms
2914.5 ms
240 s
Unimer Reservoir
Model fits
Q [A-1]
0 100000 200000 300000 4000000
5
10
15
20
25
30
P
time [milli seconds]
Slide: 36
Self-assembly of unilamellar vesicles
10-1
100
10-5
10-4
10-3
10-2
10-1
M2
< 4 ms
M1
M2
< 4 ms
M1
I(q)
(m
m-1
)
q (nm-1)
M1
M2
M1+M
2
50 mM
disk-like
Transient disk-like micelles are formed within the mixing time (< 4 ms)
< 4ms
M1
M2
• disk-like objects with:
R = 7.5nm; H = 4.8nm
• size of initial disks:
670 2 x size rod-like micelle
T.M. Weiss et al., PRL (2005)
Langmuir (2008)
Slide: 37
10-1
100
10-4
10-3
10-2
10-1
100
101
102
103
2.68 s
0.88 s
0.58 s
0.24 s
0.06 s
0.01 s
I(q)
(m
m-1
)
q (nm-1)
Growth of disk-like micelles
2R
C
1
disk area
Radius of curvature
4
1 2
2
R
CRC
& - bending moduli
L - line tension
4
12
2
2
R
CRCEedge L RCEbend 24
Bending energy vs Edge energy
At the closing state:
L
24maxR
T.M. Weiss et al., PRL (2005)
Langmuir (2008)
Slide: 38
10-1
100
10-4
10-3
10-2
10-1
100
101
102
103
2.68 s
0.88 s
0.58 s
0.24 s
0.06 s
0.01 s
I(q)
(m
m-1
)
q (nm-1)
Growth of disk-like micelles
2R
C
1
disk area
Radius of curvature
4
1 2
2
R
CRC
& - bending moduli
L - line tension
4
12
2
2
R
CRCEedge L RCEbend 24
Bending energy vs Edge energy
At the closing state:
L
24maxR
T.M. Weiss et al., PRL (2005)
Langmuir (2008)
ln(F/A
[kT/nm2])
Vesicles
Disk,
lense
Free energy of a bend bilayer
Slide: 39
gas-liquid
liquid-liquid
liquid-solid
b
a
b y
Z
b
a
b y
qZ
β α
I0 I
qX
Beam travel path 70 mm
oil
water
Soft matter self-assembly at interfaces
Interfacial cavities for reaction
Slide: 40
Formation and Ordering of Gold Nanoparticles at
the Toluene-Water Interface
M.K. Sanyal et al., J. Phys. Chem. C, 112, 1739 (2008)
cluster-cluster separation, d1=180 Å
particle-particle separation, d2 = 34 Å
Each cluster consists of 13 NPs with Ø 12 Å & 11 Å thick organic layer
Slide: 41
Formation and Ordering of Gold Nanoparticles at
the Toluene-Water Interface
M.K. Sanyal et al., J. Phys. Chem. C, 112, 1739 (2008)
Each cluster consists of NPs with Ø 12 Å & 11 Å thick organic layer
Slide: 43
Diffusive to ballistic dynamics
near glass transition
Multi-speckle XPCS analysis
q
2q
q [nm-1]
(a)(b)
Dynamics of tracer particles in a glass-forming liquid
Silica particles in
propylene glycol
C. Coronna et al.,
PRL (2008)
This type of dynamics studies can be
performed in the sub-millisecond range
Slide: 45
Soft Matter: out-of-equilibrium dynamics
Probing the dynamics of ageing: related to shelf-life of products
Crossover of dynamic behavior – large scale reorganization
Gel
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20
Time (h)
H(t
) /
Ho
Colloid-polymer mixture two-time
correlation function
A. Fluerasu, A. Moussaid, et al., PRE(R) (2007)
Slide: 46
SAXS/WAXS/USAXS
Multiple detectors
Energy range: 720 keV
Dq: 5x10-4 nm-1 (FWHM)
q – range: 10-3 – 50 nm-1
Time res. – 10 ms
Sample-detector distance: 0.6 - 30 m
2014
32 m long and 2 m diameter
UPBL9a: TRUSAXS Beamline
Slide: 47
SAXS/WAXS/USAXS
Multiple detectors
Energy range: 720 keV
Dq: 5x10-4 nm-1 (FWHM)
q – range: 10-3 – 50 nm-1
Time res. – 10 ms
Sample-detector distance: 0.6 - 30 m
2014
32 m long and 2 m diameter
UPBL9a: TRUSAXS Beamline
2/q (nm)
10-1 100 101 102 103 104
Tim
e (
s)
10-5
10-4
10-3
10-2
10-1
100
101
102
103
USAXS
WA
XS
SAXS
Stroboscopic
Slide: 48
• High brilliance X-ray scattering is a powerful method to elucidate
the non-equilibrium structure & dynamics of soft matter.
• Time-resolved scattering experiments in the millisecond range can
be performed even with dilute samples.
• Combination of nanoscale spatial and millisecond time resolution
makes synchrotron techniques unique in these studies.
• Challenges lie in the ability to investigate complex polydisperse
systems with competing interactions.
• Experiments can be performed in the functional state of the system.
• The emphasis will be on quantitative studies made possible by the
high detection capability and reduced radiation damage, and
complemented by advanced data analysis.
Summary & Outlook