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: 10

Synchrotron Techniques used in Soft Matter

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: 20

Multi-speckle XPCS

Slide: 21

Combination with shear flow

Couette cell

X-ray beam

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: 31

Spontaneous self-assembly

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: 42

Out-of-equilibrium Dynamics

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: 44

Multi-speckle XPCS

Soft Matter: out-of-equilibrium dynamics

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