Structure Analysis using Small-Angle X-ray Scattering
Bruker AXS Korea / Carbon Nanomaterials Design Lab.
@ X-선 회절 측정클럽, 한국표준과학연구원, 2013. 08. 27.
Bruker AXS Korea([email protected]) / 서울대학교 재료공학부 CNDL ([email protected])
김 세 훈
2013.08.27. X-선 회절 측정클럽 WORKSHOP @한국표준과학연구원
SAXS
Small-angle X-ray Scattering
Scattering vs
Diffraction
Small-angle vs
Wide-angle
Introduction
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Introduction : Various structure levels in materials (aramid fiber)
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Introduction : X-ray Diffraction/Scattering Equipments
Source
: Properties of X-ray
Sample
: Interaction between X-ray & Materials
Detection
: X-ray Patterns
• X-ray Diffractometer (XRD/D8 Advance) • Small-angle X-ray Scattering (SAXS/Nanostar)
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• Angle Range of SAXS - Length Scale of Small Angle Scattering : 10 – 2000 Å - Information on relatively large r is contained in I(q) at relatively small q - Bragg’s Law - Sample contains a scattering length density inhomogeneity of dimension
larger than 10Å (1nm), scattering becomes observable in small angle region.
d2sin
d = few Å = 1Å 2 = 20
d = 100 Å = 1Å 2 = 0.6
• Nano-structural Paramaters obtained from SAXS - Mean Size, Size Distribution - Shape (sphere, cylinder, etc.) - Orientation, Degree of Orientation - Mean distance between particles
SAXS determines the site, site distribution, orientations and structure arrangement of macromolecules or precipitants
in bulk materials. (Ref. http://www.bruker-axs.de)
Introduction
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• Small Angle vs Wide Angle (scattering vs diffraction)
Introduction
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Introduction
• Transmission SAXS vs. GI (Grazing Incidence) SAXS
- Transmission : X-rays are incident normal to the surface of the sample (liquid dispersion, gels, powders, sheets, etc.) - GI : Incident angle close to the critical angle (0.1 to 1 degree) (semiconductor quantum dot/island, porous films on substrate, condensed powder, nanoparticle embedded in polymer)
Transmission SAXS GI-SAXS
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Introduction
• Transmission SAXS vs. GI (Grazing Incidence) SAXS
Transmission SAXS GI SAXS
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Introduction
• Statics and Kinetics
• Statics - Relatively Low Intensity (Lab SAXS) - DNA Cage - SDS micelles and protein-SDS complexes
• Kinetics - High Intensity (Synchrotron) - Fibrillation of glucagon (polypeptide) - SDS-a-synuclein complexes and fibrillation - Nanoporous silica synthesis directed by polymer
Phase transformation of Girl Group
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Introduction
• Classification 1 : SAXS Experimental Setup / Smaple-to-Detector Distance
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Introduction
• Classification 1 : SAXS vs. WAXS Example : Silver Behenate (AgBh) for system calibration
SAXS
WAXS
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X-ray Sources : Synchrotron Radiation
• The European Synchrotron Radiation Facility (ESRF) • http://www.esrf.eu/
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Detection : Bruker’s Commercial Detectors
LYNXEYE XE High-Resolution Energy-Dispersive 1-D Detector
Vantec 500 2-D Gas Detector
Vantec 2000 2-D Gas Detector
with large 14 x 14 cm2 active area
Platinum 135 135mm CCD Detector
APEX II CCD Detector
Vantec 1 Super Speed 1-D Gas Detector
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SAXS in Korea
1. SAXS 4C1, 4C2 @Pohang Accelerator Laboratory : Synchrotron radiation / Open
2. Nanostar @HOMRC, Seoul National University : X-ray tube type / Open
3. SAXS w. GADDS @NICEM, Seoul National University : X-ray tube type / Open
4. Nanostar @Dong Woo Fine Chem : Incoatec Microfocus Source + VANTEC Detector + GI-SAXS Sample Stage / Not open
5. Anton Paar @KIST / @RIC, Wonkwang University
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Introduction
The Soluble Blend System
The Dilute Particulate System
The Nonparticulate
Two-Phase System The Periodic System
Four Models adopted in analysis
of SAXS data
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Introduction
1. The Dilute Particulate System - Particles of one materials are dispersed in a uniform matrix of a second material. When the concentration is sufficiently dilute, the position of individual particles, far from from each other, are uncorrelated. - When the conc. is not sufficiently dilute, the interference effects becomes an important concern of the analysis
2. The Nonparticulate Two-Phase System - Two different materials are irregularly intermixed and neither of them is considered the host matrix or the dispersed phase. - The analysis leads to determination of parameters characterizing the state of dispersion of the materials - The correlation length, the specific interphase boundary area and the thickness of the phase boundaries
3. The Soluble Blend System - A single phase material in which two components are dissolved molecularly as a homogeneous solution - Miscible polymer blend, block copolymer in a disordered state and polymer solution
4. The Periodic System - Semicrystalline polymers consisting of stacks of lamellar crystals - Block copolymers having ordered, segregated microdomains - Micellar aggregates of organic and inorganic substances
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Two-Phase System
Dilute Particulate System
Guinier Law
Porod’s Law
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SAXS : Dilute Particle System
• SAXS – Smaller sample vs Larger sample
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SAXS : Dilute Particle System
• Even when the shape is unknown, or irregular and not describable in simple terms, the scattering function still follows a certain universal form, in the limit of small q, that is given by
where I(q) is the intensity of independent scattering by a particle
which called the Guinier law, -> allows determination of the radius of gyration of a particle
• The Guinier law is valid provided that - q is much smaller than 1/Rg - the system is dilute, so that the particles in the system scatter independently of each other - the system is isotropic as a result of the particles assuming random orientations - the matrix in which the particles are dispersed is of constant density and is devoid of any internal structure that can by itself give scattering in the interested range of q
)3
1exp()( 2222
0 gRqvqI
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SAXS : Dilute Particle System
• The Guinier law suggests that
when the logarithm of I(q) is plotted against q2, the initial slope gives .
• For the purpose of determining the radius of gyration it suffices to have the intensity determined in relative units.
• If, on the other hand, the intensity is measured in absolute units by means of
an instrument suitably calibrated, it is possible to determine the value of
as well.
• Since the value of , the average scattering length density in the particle, is
usually known from its chemical composition, this provides the means of
evaluating the particle volume .
• Knowledge of both the radius of gyration and the particle volume
provides a clue about the shape of the particle.
22
03
1ln2)(ln qRvqI g
2
3
1gR
22
0 v
0
v
gR v
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SAXS : Dilute Particle System
• Pair-Distance Distribution Function
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SAXS : Dilute Particle System
• Examples of Rg of well-defined geometric shape, - for solid sphere of radius R - for solid ellipsoid of half axes a, b, c - for solid rod with length L, radius R - for thin rod of length L - for disk of radius R
RRg5
3
2
1
222 )(5
1cbaRg
212
222 RL
Rg
12
LRg
2
RRg
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SAXS : Dilute Particle System
Case Study : Au Nanoparticles in Liquid Suspension
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SAXS : Dilute Particle System
Case Study : Au Nanoparticles in Liquid Suspension
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SAXS : Dilute Particle System
Case Study : Curve Simulation by Dummy Residue Model
pH = 7.2 PH = 5.4
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SAXS : Dilute Particle System
Case Study : Curve Simulation by Dummy Residue Model
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SAXS : TWO Phase System
• Definition of ideal two-phase system
(1) The system contains only two different regions (or phases),
each of constant scattering length density or .
(2) The boundary between these two regions is sharp with no measurable thickness.
(3) These two phases are irregularly intermixed,
so that the system as a whole is isotropic and there is no long range order.
• If the scattering length densities of the two phases are known from knowledge of their
chemical compositions, the experimental value of Q can be used provide the relative
amounts of the two phases.
1 2
2211
211
122
21
2
2
2
21
2
1
2 )()( VVVQ
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SAXS : TWO Phase System
2
4
2
4
222
654
222
6
22
32
44&02cos2)(
largefor)2cos1(
8)(
2cos12sin2)2cos1(8)(
)(
)cos(sin9
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4)()(
RNRSqRq
S
qRRN
q
qR
q
qRR
q
qRRN
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qRqRqRRNqI
Intensity of scattering from a system containing N solid spheres of radius R
Intensity of scattering from a solid spheres of radius R
6
22
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0
2
3
3
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0
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)(
)cos(sin9
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qR
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drqrrq
drqr
qrrrqA
R
Rrfor
Rrforr
0)(
0
R
0
Porod Law
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SAXS : TWO Phase System
Two phase system with finite boundary
pl
rV
V
SV
SrVr
1
4
11
4)(
2
2
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2
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21
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8
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l
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p
p
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p
4
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qasq
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2)(2)(
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SAXS : TWO Phase System
4
2 2)()(
q
SqI
Intensity of scattering from a system containing N solid spheres of radius R
Ideal two phase system
1l
2l
1l
2l
2l4
21
4
2
12)(
)(2)(
qV
S
Q
qI
qasq
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11
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lll
V
Sl
V
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p
Porod’s length of inhomogeneity
Sl
V
dr
rd
pr
2
2
04
1)(
pl
pl
rVr exp)( 2
VdrrrQ 2)0()()(
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SAXS : TWO Phase System
Case Study : Glassy Carbon (Porous Material)
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SAXS : TWO Phase System
Case Study : Pore Characterization (Two-Phase) by microbeam SAXS
• Characterization of pore distribution in activated carbon fibers(ACFs) by microbeam SAXS D . Lozano-Castello et al., Carbon, 40, 2002, 2727
• The experiments done with CO2 and steam ACFs have demonstrated the suitability of this technique to characterize a single ACF. The experiments show that scattering intensity increases with the burn-off degree, which agrees with SAXS experiments carried out using bigger amounts of fibers.
• The use of an X-ray microbeam of 2 μm diameter allows the characterization of different regions of the same fiber with microscopic position resolution.
• CO2 ACFs : the scattering is high in different regions across the fiber diameter, confirming that CO2 activation takes place within the fibers, generating a quite homogeneous development of porosity.
• Steam ACFs : the scattering is much higher in the external zones of the fibers than in the bulk, which means that steam focuses the activation in the outer parts of the fibers.
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SAXS : TWO Phase System
Case Study : Pore Characterization (Two-Phase) by microbeam SAXS
• Two phases : the carbonaceous matrix and the pores. -> an increase in the scattering corresponds to an increase in the porosity
• Before plotting the curves, it must be taken into account that the fibers have cylindrical shape and, volume correction is needed.
• The results indicate a higher concentration of pores in the outer zone.
• One useful parameter for the analysis of porous materials is
Porod Invariant (PI), defined as
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Dimension / Mass Density
Surface Fractal
Mass Fractal
Surface Roughness (2D)
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SAXS : Fractal Dimension Analysis
Fractal objects : Definitions
• At large q the intensity I(q) of scattering from a sphere decays as q-4,from a thin disk as q-2, and from a thin rod as q-1. related to the dimensionality of the scattering object
• The inverse power-law exponents can be explained in terms of the concept of a fractal.
• A fractal possesses a dilation symmetry, that is, it retains a self-similarity under scale transformations. In other words, if we magnify part of the structure, the enlarged portion looks just like the original.
The Koch curve
The Sierpinski triangle
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SAXS : Fractal Dimension Analysis
Fractal objects
• A fundamental characteristic of a fractal is its fractal dimension.
Mass fractal
• Suppose we draw a sphere of radius r around a point in the object.
• If the fractal object is a line, the mass M(r) within the sphere will be proportional to r. If it is a sheet, then proportional to r2 and if a solid three-dimensional object, proportional to r3.
• In a fractal, where d is the fractal dimension : 1 < d < 3
• Since the volume of the sphere is proportional to r3, the density of actual material embedded in it is
drrM )(
3)(~ drr
)(~ r
rrM )( 2)( rrM 3)( rrM
open structure
close structure
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SAXS : Fractal Dimension Analysis
Surface fractal
• Some object possess a surface that is rough and exhibit fractal properties.
• Imagine we cover the island completely with square tiles of edge length l, and we mark those tiles that at least partially overlap the coastline.
• N(l ) : the number of marked tiles
• If the coastline is smooth and nearly straight, N(l ) will be proportional to l -1.
• If the coastline is irregular and fractal, N(l ) depends more strongly on l , and is proportional to l -ds where ds is a number larger than 1.
• The length L(l ) of the coastline : l N(l ) or
• ds : the fractal dimension of two-dimensional surface fractal.
• In a three-dimensional surface fractal, where S(r) is the surface area measured with a tool of area r2
sdllL
1
)(
sdrrS
2)(
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SAXS : Fractal Dimension Analysis
Case Study : Surface Fractal Dimension
• Fractal dimension analysis of polyacenic semiconductive (PAS) materials
K . Tanaka et al., Carbon, 39, 2001, 1599– 1603
• The fractal dimensions D of the pristine and the Li-doped PAS materials have been analyzed by SAXS and compared with that of graphite.
• D of the PAS powder increases according to decrease in [H]/[C] molar ratio -> the dehydrogenation process with the raise of pyrolysis temperature.
• Introduction of binder for the fabrication of the battery electrode generally makes D smaller. The D value depends on the binder species.
• Li doping into the PAS sheet causes smaller D, which signifies the existence of Li atoms makes the nanoporous structure more plane-like at least from the fractal aspect.
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SAXS : Fractal Dimension Analysis
Case Study : Surface Fractal Dimension
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SAXS : Periodic System
Scattering from Ideal two-phase lamellar structure
• Let us first consider an ideal two-phase lamellar structure in which lamellae of phase A, of thickness da and uniform scattering length density ρa, alternate with lamellae of phase B, of db and ρb.
• The scattering length density profile :
• a one-dimensional lattice of period d (=da+db)
• The density distribution within a single period can be represented by
)/(*)()( dxzxx u
n
nxxz )()( :)/( dxz
abu dxx /)( ba
2
10
2
11
xfor
xforx
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SAXS : Periodic System
Scattering from Ideal two-phase lamellar structure
• By taking the absolute square of the Fourier transform of , the intensity of scattering I1(x) is obtained as
• With , we obtain
• Bragg peaks occur at a series of q values satisfying or , and that the height of (or, more exactly, the integrated area under) the nth order peak is proportional to , where is the volume fraction of phase A.
• From the measurement of the relativity heights of successive peaks, the relative volumes of the two phases can be determined.
• When the volumes of the two phases are equal, all even order peaks are reduced to zero heights.
)(x
)2/()()(2
dqzqFqI
)(xu 2
2
2
22sin
4)(
qda
qqF
ndq 2/ dnq /2
22 /sin nn a
)/( ddaa
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SAXS : Periodic System
Case Study : Liquid Crystal (Plulonic P84 / Water / p-xylene)
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SAXS Case Study : Ordered Porosity (Two Phase System)
• SAXS and EM Investigation of Silica and Carbon Replicas with Ordered Porosity Francoise Ehrburger-Dolle, et al, Langmuir, 19, 2000, 4303
• SAXS investigations of ordered porous carbon materials Francoise Ehrburger-Dolle, et al, Proceeding of Carbon Conference, 2003
• Ordered nanoporous carbons can be prepared by a replica technique starting from an organized silica template, SBA-15, which contains an hexagonal array of mesopores interconnected by micropores.
• Two routes for introducing carbon into the pores of the silica matrix, liquid impregnation by a solution of sucrose followed by carbonization and chemical vapor infiltration (CVI) of propylene.
• After dissolution of the silica template by hydrofluoric acid treatment, a carbon material is obtained.
High-resolution image (HRTEM) of pores with hexagonal symmetry for the silica SBA-15 (left) and the carbon replica R15AC-52 (right)
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SAXS Case Study : Ordered Porosity (Two Phase System)
• The SAXS intensity curve obtained for the ordered mesoporous silica SBA-15 clearly shows three Bragg peaks. -> hexagonal packing
• In the low q domain (q < 2×10.2 nm.1), the data can be fitted (red line) by the Guinier relation I = I0 exp[-(qRG )
2/3]. RG = 180 ± 10 nm.
• For long cylindrical particles of uniform density and small cross section, this corresponds to a length L equal to (12)1/2RG=623 nm, which is comparable to the sizes observed on TEM images.
• In the intermediate q domain, I(q) scales as q-4, as expected from the Porod law. This result also indicates that the external surface of particles is smooth.
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SAXS Case Study : Time Dependency of Scattering Curves (Kinetics)
Moitzi, Ch., Guillot, S. Fritz, G., Salentinig, S. Glatter, O. Advanced Materials (2007) 19, 1352-1358
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SAXS Case Study : SAXS on Microfluidic Analysis
Thomas Pfohl, Department Chemie, Universitat Basel
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Tahseen Kamala, Soo-Young Park, et. Al. Polymer (2012) 53, 3360-3367
SAXS Case Study : An in-situ simultaneous SAXS and WAXS survey
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SAXS Case Study : GI-SAXS from Liquid to Solid Surface
P. Siffalovic, Institute of Physics SAS, Slovakia
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SAXS Case Study : Particle Aggregates and Surface
• Characterizing dispersion and fragmentation of Fractal, Pyrogenic silica nanoagglomerates by SAXS, Langmuir 23 (2007) 4148-4154
• 압력을 가해 nanoagglomerate를 분산시키는 과정에서 primary particle size, surface area, polydipersity 등을 SAXS를 통해 구하고 TEM과 비교함으로써 분산 거동을 살펴봄
• 이때 기존의 Guinier law의 modification을 통해 보다 정확한 값을 구해냄
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f
D
Gp
G
D
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1
2
1
3
2
2
1
2
2
2
2
2
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3exp
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1G
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