Pohang, Korea - Cheiron2007

�

Polymer Synthesis and Physics Laboratory

Moonhor ReeDeputy Director of Pohang Accelerator Laboratory (PAL)Professor of Chemistry Department and Polymer Research InstitutePohang University of Science & Technology (POSTECH)Pohang, KoreaTel: +82-54-279-2120; Fax: +82-54-279-3399E-mail: [email protected]://www.postech.ac.kr/chem/mreehttp://pal.postech.ac.kr

Small Angle X-ray Scattering and Applications in Structural Analysis

Small Angle X-ray Scattering and Applications in Structural Analysis

2


Outline1. Introduction – POSTECH & Pohang Light Source2. Optics, Beamlines and Equipments of SAXS3. Data Collection and Samples4. Fundamentals of SAXS5. Fundamentals of Conventional, Transmission SAXS (TSAXS)

(1) Single Molecule (or Particle)(2) Multiple Molecules (or Particles) and Their Assemblies

6. Fundamentals of Grazing Incidence SAXS (GISAXS)(1) Static GISAXS(2) In-Situ GISAXS

1. Conclusions – I, II2. References3. Introduction – M. Ree’s Group at Postech4. Acknowledgments

33

4 4

5

5

6

6

7






8


Optics of Small Angle X-ray Scattering (SAXS)

Optics of Small Angle X-ray Scattering (SAXS)

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

9


SAXS SAXS BeamlinesBeamlines

X-rays at the sample• Photon flux (monochoromatic, focusing) :

1011 − 1018 photons/sec/mm2 at 8 keV

• Beam size : < 0.8 × 0.8 mm2

Main Slit Monochoromator

Slit SlitSlitFocusing

Mirror

Sample

Vacuum Chamber Detector

Scintillation Counter

Storage ring

Experimental Station

e-

I/C

��


22--D CCD XD CCD X--Ray DetectorRay Detector

Roper Scientific MAR research

11


Device for Temperature Jumping

Temperature A Temperature B

Sample

Sensor

12


Other Devices for Samples

1. Mechanical Tester2. Rheometer3. DSC4. Liquid Cell5. Liquid Flow Cell6. Fiber Spinner7. Magnets8. Many Other Devices

depending on what you want

13






14


TXS

Beamstopx

yz

qx

qyqz

2θ

φ

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

Data Collection Time and

Sample Thickness (Volume)in

SAXS Measurements

Data Collection Time and

Sample Thickness (Volume)in

SAXS Measurements

15


Optimization of Collection Time (Error Analysis)

P N nt eN

N nt

( ) ( )!

=−

Poisson distribution

nt: average valueP(N) ; probability of having N count in a given time t

±N

NRelative error possessed in the count N

1000.3100,000

101.010,000

13.21,000

collection time (sec)standard deviation (%)number of pulses counted

16


I ~ t e-μt

Io Ioe-μt

2θ

t, μ : Thickness, Linear Absorption Coefficient

I s t eobst( ) ~ ⋅ −μ

topt =1μ

Optimum Sample Thickness (transmission geometry)

17






18


Fundamentals of Small Angle X-ray Scattering (SAXS)

Fundamentals of Small Angle X-ray Scattering (SAXS)

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

19






20


Fundamentals:Conventional

Small Angle X-ray Scattering (SAXS)

Transmission Small Angle X-ray Scattering (TSAXS)

Fundamentals:Conventional

Small Angle X-ray Scattering (SAXS)

Transmission Small Angle X-ray Scattering (TSAXS)

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

21


AFM

Sample sizeStructure size

Structuresize

Length Scales in Structure

22


Hierarchical Structure of Polymer Crystalsspherulite fibrillar branching helical lamellar structure

within fibrils1mm 1µm

500 Å

L

crystal lattice individual lamellar stacks

1 Å 100 Å

Experimental techniquesfor the lengthscales involvedare indicated in Red

opticalmicroscopy(OM)

light scattering (SALS)

SAXS

WAXS TEM & SEMSAXS

Hierarchical Structure of Polymer Crystalsspherulite fibrillar branching helical lamellar structure

within fibrils1mm 1µm

500 Å

LLL

crystal lattice individual lamellar stacks

1 Å 100 Å

Experimental techniquesfor the lengthscales involvedare indicated in Red

opticalmicroscopy(OM)

light scattering (SALS)

SAXS

WAXS TEM & SEMSAXS

23


X-Ray Scattering from Single Molecule (or Particle)

X-Ray Scattering from Single Molecule (or Particle)

24


X-Ray Scattering from One Molecule (Particle)

X-ray

2θ

Scattered wave

Incident wave

M (Induced Dipole Moment)

Molecule(Scatterer)

α (Polarizability)

Ei = Eoeiωt

Es

Det

ecto

r

X-ray

2θ

Scattered wave

Incident wave

M (Induced Dipole Moment)

Molecule(Scatterer)

α (Polarizability)

Ei = Eoeiωt

Es

Det

ecto

r

M = αE(M = ql)Ψ

l : displacement

ω : light frequencyt : time

c : light speedr : sample-to-detector

distance

Ψ∂∂

= cos)/(2

22

rctEs

M

tioeEE ωαα ==M

tioeEt ωαω 22 )/( −=∂∂ M2

Ψ−

= cos2

2

rceEE

tio

s

ωαω

*sss EEI ⋅= (scattered wave intensity)

2*oooo EEEI =⋅= (incident wave intensity)

25

Light scattering

X-RayScattering

(because ω is very high.)

>>

e : charge of an electron k : force constantm : mass of an electron


26


Scattering vector

d=2π/q

z

y

O

r

O

Q P

R

2θsos1

2θs1

so

s

q

qso

The phase difference δ, from O and P is equal to the inner vector product, q.r.

so s1δ = 2πλ QP - OR( ) = r - r)= q r. .2π

λ( .so s1δ = 2π

λ QP - OR( ) = r - r)= q r. .2πλ

( .

2dsinθ = nλ n = 1,2,3...( ) ⇒ d =nλ

2sinθ=

2πq

n = 1( )Bragg’s eq.: lattice spacing d

2dsinθ = nλ n = 1,2,3...( ) ⇒ d =nλ

2sinθ=

2πq

n = 1( )Bragg’s eq.: lattice spacing d

Scattering vector

Wave number

= ez , = eysin2θ + ez cos2θ

= =[ ]k = 2π /λ

so s1

s so − s1 eysin2θ−ez 1− cos2θ( )

s = = sin2 2θ+1− cos2θ( )2[ ]1/2

= 2 sinθs

q = 4πλ

sinθk s =q = k s

(modulus of wave vector)

q

27

Is : Scattering Intensity

F : Form Factor

Phase Factor δ = q r.q r.

Ψ−

= cos2

2

rceEE

tio

s

ωαω

∑ −Ψ−

=i

ikxi

tio

sie

rceEE αω ω

cos2

2

∑ −=i

ikxi

ieF ρ

∑ ⋅−=i

iii

ieF )()( rqr ρ

)( iss FKE r=

Ψ−

= cos2

2

rceEK

tio

s

ωω

*sss EEI ⋅=

)}()({ *iiss FFKI rr ⋅=


28

0

(interdistance of a pair of scatters)

rij

Q P

R

2θsos1

q

qso

Dete

ctor

(ri)

(rj)O

0 0(homogeneous)

(no correlation between the fluctuation of

a volume element and its distance away from another)

rij = ri - rj

∑ ⋅−=i

iiii

ieF )()()( rqrr ρ ioi ρρρ Δ+=)(r

∑ ⋅−=j

ijjj

jeF )()()( rqrr ρ joj ρρρ Δ+=)(r

(a generalized scattering equation))()()()( rqrrq ⋅−ΔΔ= ∑∑ i

jii j

ss eKI ρρ

)}()({ *iiss FFKI rr ⋅=

)()( ji i

jj

i

iis eeK rqrq ⋅⋅− ∑∑= ρρ

}{ )()()()(2 ijijijij iji

ijo

iio

io

i js eeeeK rqrqrqrq ⋅−⋅−⋅−⋅− ΔΔ+Δ+Δ+= ∑∑ ρρρρρρρ

)( ijiji

i jss eKI rq⋅−ΔΔ= ∑∑ ρρ

29

Structure analysis by Scattering andConcept of Real and Reciprocal Spaces

X-ray (or light, neutron)

sampletransimittedwave

scattering vector q : q = (2π/λ) s

incident wave

|q| = (4π/λ)sinθ2θ

wavelength l

PQ

rij

r = jiij rrr −=

Scattering amplitudeF(q)

reciprocal space (q or s)

Scattering Intensity: I(q)

Contrastρ(r)

real space (r)

Correlation function γ(r)

[Patterson function Q(r) = ρ(r)⋅ρ(-r)]

Fourier Tr. ℑ

30


How to find Scattering Amplitude [F(r)] from Scattered Intensity?

I(q) = Ks [F(r)⋅F*(r’)]

(1) Correlation Function Approach

(2) Fine Structural Model Approach- sphere- Gaussian sphere- core/shell sphere- rod- cylinder- discetc

Correlation functionγ(r)

- Correlation function γ(r)

)()()()( rqrrq ⋅−ΔΔ= ∑∑ iji

i jss eKI ρρ

31


(1) Correlation function Approach

[ ] rr

rrrd

2

∫∞Δ

−ΔΔ=

0)(

)(*)()(ρ

ρργ∫∫

∞

∞

ΔΔ

+ΔΔ=

0

0

)()(

)()(

uuu

uuru

d

d

ρρ

ρρ

{ }V

1Iobs 21

)()()(

ργ

Δ⋅ℑ= − qr

Auto-Correlation Function (Patterson Function)AutoAuto--Correlation Function (Patterson Function)Correlation Function (Patterson Function)

For an isotropic system rq == rq ,

( ) ( )( )

( )∫

∫=

Δℑ=

⎭⎬⎫

⎩⎨⎧−

dqIqdqqr

qrIq

VuI

q

qqr

obs

obsobs 2

2

21

sin

)}({1

ργ

Pair Distance Distribution Function (PDDF) p(r) = r2 γ(r)

( ) ( )0

ρρρ −=Δ rr

γ(r)

32


ρ r( )

Scattering intensity

Correlation function

Density distribution

Fourier transform

r = r – r’

γ(r)

I q( ) = KV

γ r( )∫ exp iq ⋅r( )dr

Correlation ofpaired scatters

Correlation function versus Scattering intensity

γ r( )= ρ r '( )ρ r − r '( )dr '∫ / ρ2 r'( )dr '∫

33


( ){ }qq QI ℑ=)(

{ } { }CI ℑ+−ΔΔℑ= )(*)()( rrq ρρ

Cd +∫ +ΔΔ= uuru )()( ρρ

( ) ( )∫ +=−= uururrr dQ )(*)()( ρρρρ

uurur dQ 000))()()(()( ρρρρ ++Δ+Δ= ∫

∞

( ) ( )0

ρρρ −=Δ rr

{ })()()( rrq −Δ∗Δℑ= ρρobsI

( ){ }qr IQ 1)( −ℑ=

( ) ( ) ( ) ( ){ }qrrq obsobsIQQI 1 −ℑ=Δ⇔Δℑ=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

ρρ

Patterson FunctionPatterson Function

)(rρ )(qF

)(rQ )(qI

ℑ

ℑ)(rγ

34


ρρ

( )rinsideoutside

=⎧⎨⎩

⎫⎬⎭0r

u

γ

γ

( )

( ) ( )

r r R

r rR

rR

= >

= − +

0 2

1 34

116

3

u and r + u

(outside the particle): 0)( =rγ

(inside the particle): 1)( =rγ

Correlation function of sphere of radius R

γ depending on particle shape and size, representing the probability of finding of a point u + r within the particle

Meaning of Correlation Function

∫∫

∞

∞

ΔΔ

+ΔΔ

0

0

)()(

)()(

uuu

uuru

d

d

ρρ

ρρ

r + uru+

PDDF)r(r)r( 2γ=p

( )3

2

3

161

431

22

21

21

3/4)(

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−=

⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛ −=≡

Rr

Rr

Rr

Rr

RrVr

πγ

Volume V(r)of the shaded part

35


p(r) = r2γ(r)

Pair Distance Distribution Function (PDDF)and Correlation Function

Probability finding scattering elements separated by r

36

Pair Distance Distribution Function P(r )

Distribution of distances of atoms from centroid1-D: Only distance, not direction20:1 ratio qmin(π/dmax):qmaxusually okp (r ) gives an alternative measure of Rg and also “longest cord”

( ) ( )2 2) ( )r r r u r u duγ ρ ρ= = ⋅ Δ Δ +∫P(r)

37


Particle Scattering Pattern and PDDF

F2(q)

��


r(nm)

0 10 20 30 40

p(r)

(a.u

.)

0.00

0.05

0.10

0.15

0.20

0.25

0.30RT.70oC80oC90oC100oC

S.-Y. Park et al., Macromolecules, 40, 3757-3764 (2007)

39


Scattering amplitude (i.e., Scattering Function = Structure Function);Scattering intensity

ρ r( )

Scattering intensity

Scatt. amplitude

Density distribution

Fourier TF = summation withphase difference

F q( )= Ks

Vρ r( )∫ exp iq ⋅ r( )dr

ρi r( )

r = r – r’

(2) Fine Structural Model Approach

I q( ) = KV ∫ exp iq ⋅r( )drρj r( )∫

40


∫ ⋅=rV

i deF rqq rq )()()( ρ

- X-ray scattering from the electron density distribution in sample- Small angle scattering for the large distance

{ }2)()( xI ρℑ=q

d1sin2

==λθs

)()()( * qqq FFI ⋅=

transformFourier :(functionPatterson:)rQ(

functiondensityElectron:IntensityScattered:

ray-XscatteredofAmplitude:

ℑ−∗ ))()(

)()()(

rrrqIrF

r ρρρ( ){ }rq QI ℑ=)(

( ){ }qr IQ 1)( −ℑ=

λθπ sin4

=q

)(rρ )(qF

)(rQ )(qI

ℑ

ℑ)(rγ

41


Example of FFTy = y1 + y2 + y3 + y4 + y5

y1 = cosr, y2 =12

cos2r, y3 =13

cos 3r ,

y4 =14

cos 4r, y5 =15

cos5r, yq' = aq ' cos q'r( )

Y (q) = aq =1

2πyexp iqr( )

0

2π∫ dr = 1

πycos qr( )

0

π∫ dr

1. FT of even functions areFourier cosine transform.

2. FT of a cosine function isa delta function.

3. The amplitude of each functiongives a spectrum.

1.0

0.8

0.6

0.4

0.2

0.0

a q

10Hz86420q

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

y

6543210r (rad)

y=y1+y2+y3+y4+y5 y=y1 y=y2 y=y3 y=y4 y=y5

FFT

Real space Fourier space

42


1 limit q → 0electron density contrastdensity fluctuationsmolecular weights

2 Guinier rangeparticle size

3 particle shapelarge scale structures

4 Porod rangeparticle surfaceSurface/volume

5 Intermolecularordering

1 2

3

4 5

400 nm 0.2 nm

I(q)

q

Scattering Angle Region versus Length Scale in Structural Information

43


λθsin2== Ss

Inhomogeneous Density Distribution over Large Distance (nm scale)

s = 1/d (or q = 2π / d) (Å-1)s = 0.001 - 0.1 Å-1 d (10~ 1000 Å)2θ = 0.008-8, λ = 1.542 Å

Scattering at Low AnglesScattering at Low Angles

- Morphological information of multiphase system: Domain (Particle) Size, Distribution, Surface Area, Interface Thickness

- Density Fluctuation- Supramolecular Ordered Structure

sq π2== q

44

Various types of plots

1.0

0.8

0.6

0.4

0.2

I(q)/a

.u.

0.100.080.060.040.020.00

q/?-1

intermediate q region; q ≈ Rg-1 model dependent region (RPA eqs. for BP and blends) Mw, χ, Rg

low q region; q < Rg-1 Guinier plot ... Rg (logI vs. q2) Zimm plot ... Rg, A2, Mw (I-1 vs. q2) Ornstein-Zernike plot ... ξ (I-1 vs. q2) Debye-Bueche plot (two phase) (I-1/2 vs. q2) ... chord length

I q( )~ exp −R g2q2 /3[ ]

KC / I q( ) = M−1 1+ Rg2q2 /3 + ..[ ]+ 2A2C

I q( )= I 0( )/ 1+ a2q2[ ]2I q( )= I 0( )/ 1+ ξ2q2[ ]

large q region; q > Rg-1 Porod law (two phase)

I q( )~ q −4

I q( )~ q −1 / ν

scattering exponent (logI vs. logq)

q 2 I q( ) ~ zq 4 R g

4 exp − R g2 q 2[ ]− 1{ }− 1

a 2

wide range of q Kratky plot (q2I vs. q)... segment length, a

(Debye fun.)

Methods to analyze I(q)

linear plot (I vs. q)

45


Integration of Intensity

[ ]

r V,V

I

deIdI

22

obs1

i2obsobs

0)()0()(

)(

)()(

0 0

=Δ=⋅Δ

ℑ

=

−

∞ ∞ ⋅∫ ∫

ργρ

π

s

ssss rs

Integration of intensity =average density difference * scattering volume

InvariantInvariant

46






47


X-Ray Scattering from Multiple Molecules (or Particles)

X-Ray Scattering from Multiple Molecules (or Particles)

Molecules (or Particles) and Their AssembliesMolecules (or Particles) and Their Assemblies

48


Convolution { } ∫∞

∞−

−≡ uurur dSFSF )()()(*

{ } { } { }SFSF ℑ⋅ℑ=ℑ *

∫∞

∞−

+≡− uurur dSFSF )()()}(*{

= ⊗Packing order ?

(Positional order?)

Singlemolecule(particle)

X-Ray Scattering from Multiple Molecules (Particles)

F S

49


= ⊗

X-Ray Scattering from Multiple Molecules (Particles)

Packing order ?(Positional order?)

( ) ( ){

( ){

( )

2

1 for dilute solution

p p

Form StructureFactor Factor

I N P q S q

S q

ρ= Δ

≈

F2 2

F S

50


( ) ( ){

( ){

( )

2

1 for dilute solution

p p

Form StructureFactor Factor

I N P q S q

S q

ρ= Δ

≈

2F2

50

51


F(q)

F2(q)

X

)(rρ )(qF

)(rQ )(qI

ℑ

ℑ)(rγ

)(rρ )(qF

)(rQ )(qI

ℑ

ℑ)(rγ


(Positional order?)



(Positional order?)


F S

52


*)(xZ *)(xZ *)(xZ *)(xZ*)()( xZx =ρAρ

*)()( xZx =ρAρ

{ }2)()( xsI ρℑ=

)()( ndxxZn

−≡ ∑+∞

−∞=

δ dd

ds 1sin2

==λ

θπ

{ } { }{ } { }

)()()()(

)()()(

)()()(

SZSFxZx

xZxx

xZxx

A

A

A

⋅=ℑ⋅ℑ=

∗ℑ=ℑ

∗=

ρ

ρρ

ρρ

dAρ

Aρ

Aρ

dAρ

dAρ

AρAρ

AρAρ

Various Shapes of Molecules (Particles) and Their Packing

{ } { } { }SFSF ℑ⋅ℑ=ℑ *{ } { }{ } { }

)()()()(

)()()(

)()()(

sSsFxSx

xSxx

xSxx

A

A

A

=ℑℑ=

∗ℑ=ℑ

∗=

ρρρ

ρρ{ } { }{ } { }

)()()()(

)()()(

)()()(

sSsFxSx

xSxx

xSxx

A

A

A

=ℑℑ=

∗ℑ=ℑ

∗=

ρρρ

ρρ

ρ(x) = S(x) * S(x) * S(x) *ρA ρA

S(x)

53


{ } { }{ } { }

)()()()(

)()()(

)()()(

sSsFxSx

xSxx

xSxx

A

A

A

=ℑℑ=

∗ℑ=ℑ

∗=

ρρρ

ρρ

( ))()()( 22 sSsFsIobs ⋅=

)(2 sF)(2 sS

1/DF sL

2 ( )

Z s2 ( )

*

)(2 sS

Rod Rod Array (or Packing)

54


)}({)( xZSZ ℑ=

0I

L1~d

1

s

0I

L1~d

1

s

L

Aρ

s

s

)}({)( xSF Aρℑ=)(xZ

d

S(x)SS(s) F(s)

)()( SFSZ ⋅

0

I

d1

)()( SFSZ ⋅

0

I

d1

S(s) ⋅ F(s)

��


SAXS SAXS SAXS

SAXS SAXS

��


T < 50��C T~ 75��C 75��C < T < 140��C T~140��C 140��C < T

WAXS patterns

Chain packing

H.H. Song et al., Macromolecules, 36, 9873 (2003)

57


Oriented Lamellar Patterns (WAXS)

��


1/q2Long spacing- 1/q1

�

Tilt angle : ��

Long spacing- 1/q1

Maximum intensity

q2

��

��

1/q2Long spacing- 1/q1

�

Tilt angle : ��

Long spacing- 1/q1

Maximum intensity

q2

��

��

H.H. Song et al., Macromolecules, 36, 9873 (2003)

59


Nanostructures

60


(100))(xZ

(110)

(100))(xZ

(110)

AρAρ

0I

0I

S(x)

61


0.062361

0.060093

0.055277

0.052705

0.05

0.057735

0.05

0.04714

0.040825

0.037268

0.033333

0.028868

0.02357

0.016667

s

16.04 √140.00389123

16.64 √130.00361023

18.09 √110.00306113

18.97 √100.00278013

20.00 √90.0025003

17.32 √120.00333222

20.00 √90.0025122

21.21 √80.00222022

24.49 √60.00167112

26.83 √50.00139012

30.00 √40.00111002

34.64 √38.33E-04111

42.43 √25.56E-04011

60.00 12.78E-04001

dorders2lkh

0.062361

0.060093

0.055277

0.052705

0.05

0.057735

0.05

0.04714

0.040825

0.037268

0.033333

0.028868

0.02357

0.016667

s

16.04 √140.00389123

16.64 √130.00361023

18.09 √110.00306113

18.97 √100.00278013

20.00 √90.0025003

17.32 √120.00333222

20.00 √90.0025122

21.21 √80.00222022

24.49 √60.00167112

26.83 √50.00139012

30.00 √40.00111002

34.64 √38.33E-04111

42.43 √25.56E-04011

60.00 12.78E-04001

dorders2lkh

Sphere cubic packing

2

222

2

1a

lkhd

++=

(a=60Å)

62


0.00 0.05 0.10 0.15 0.20 0.25 0.3010

100

1000

10000

roots7s

roots3s

1s=0.0201(49.75 angstroms)

Log

Inte

nsity

(a.u

.)

s

Hexagonal cylinder

63


Columnar hexagonal packing

0.133333

0.117063

0.101835

0.088192

0.07698

0.1

0.083887

0.069389

0.057735

0.066667

0.050918

0.03849

0.033333

0.019245

s

7.50 √480.017778044

8.54 √370.013704034

9.82 √280.01037024

11.34 √210.007778014

12.99 √160.005926004

10.00 √270.01033

11.92 √190.007037023

14.41 √130.004815013

17.32 √90.003333003

15.00 √120.004444022

19.64 √70.002593012

25.98 √40.001481002

30.00 √30.001111011

51.96 10.00037001

dorders2lkh

0.133333

0.117063

0.101835

0.088192

0.07698

0.1

0.083887

0.069389

0.057735

0.066667

0.050918

0.03849

0.033333

0.019245

s

7.50 √480.017778044

8.54 √370.013704034

9.82 √280.01037024

11.34 √210.007778014

12.99 √160.005926004

10.00 √270.01033

11.92 √190.007037023

14.41 √130.004815013

17.32 √90.003333003

15.00 √120.004444022

19.64 √70.002593012

25.98 √40.001481002

30.00 √30.001111011

51.96 10.00037001

dorders2lkh 2

2

2

22

2 )(341

cl

akhkh

d+

++=

(a=60Å)

64


0.094281

0.083333

0.074536

0.068718

0.066667

0.070711

0.060093

0.052705

0.05

0.04714

0.037268

0.033333

0.02357

0.016667

s

10.61 √320.008889044

12.00 √250.006944034

13.42 √200.005556024

14.55 √170.004722014

15.00 √160.004444004

14.14 √180.005033

16.64 √130.003611023

18.97 √100.002778013

20.00 √90.0025003

21.21 √80.002222022

26.83 √50.001389012

30.00 √40.001111002

42.43 √20.000556011

60.00 10.000278001

dorders2lkh

0.094281

0.083333

0.074536

0.068718

0.066667

0.070711

0.060093

0.052705

0.05

0.04714

0.037268

0.033333

0.02357

0.016667

s

10.61 √320.008889044

12.00 √250.006944034

13.42 √200.005556024

14.55 √170.004722014

15.00 √160.004444004

14.14 √180.005033

16.64 √130.003611023

18.97 √100.002778013

20.00 √90.0025003

21.21 √80.002222022

26.83 √50.001389012

30.00 √40.001111002

42.43 √20.000556011

60.00 10.000278001

dorders2lkh

Columnar quadratic packing

2

222

2

1a

lkhd

++=

(a=60Å)

65


A

Bρ

ρ0ρ = 0

a

b

a b

ρο

ρ

Model of two phase system (A) and electron density distribution follow up line a-b (B).

Two Phase System

Sharp boundary

66


η ρ φ φ2 21 2= Δ

Condensed Multi-phase

Δρ ρ ρ= −1 2

{ } { })()()( 1222 rr γφφργη ℑ⋅Δ=ℑ= VVIobs s

{ })()()( 212 rγφφρπ ℑ⋅Δ= VIobs 2s

Invariant

)0( )()()( =∫⋅

∫ = rr sssss di2eIdI obsobsπ

0 , )()( 212 =Δ rrγφφρ V

Surface Area

′ = −γφ φ

( )0 14 1 2

AV

fractions volume matrix and particle of densities

:,:,

21

21

φφρρ

density average 22110 φρφρρ +=

orr ρρη −= )()(1ρ

2ρ

67


Aρ

ρ0

0

ρ ρ− 0

0

B

C

0

− −( )ρ ρ0

Babinet’s Reciprocity Principle

All produces identical Iobs

68


0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.1610

100

1000

10000

6s5s4s3s

2s

1S=0.0217 (46 angstroms)

Log

Inte

nsity

(a.u

.)

s

Lamella

λθsin2

=s

69


Polymer Crystals (Lamellae)

C

A

D

0

ρ c

ρ A

D = C + ACA

I s s I sobs obs124( ) ( )= π

70


Correlation FunctionCorrelation Function

A

Br

( )ρρηηη - , BA =

( ) ( )221 )(

ηηη

η

ηηγ BA

duuurr =

+= ∫

∫∫=

ds)s(I

rsds2cos)s(I)r(

1

11

πγ

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0- 0 .5

0 .0

0 .5

1 .0 0 k G y 1 0 0 k G y 2 5 0 k G y 5 0 0 k G y 7 5 0 k G y 1 M G y

γ 1,r/Q

r (Å )

L CM

71


Porod Law (for high scattering angle, Porod region)

I s8

Asobs

03 4( ) =

−ρ ρπ

I s8

4 Rs

1s

4Rs

sin4 Rs 4 as

1s

cos4 Rsobs0

3

2

4 6 5

2

4 6( ) =−

+ + + −⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

ρ ρπ

ππ

π ππ

π

when s is large

For spherical particle

A is surface area of the particle

Satisfies regardless of particle shape, size and concentrationSurface area A can be obtained from the plot of s vs. sIs obs

4 )(

This is also used for intensity fit at high angles

72


ρ ρdiffuse sharpr r h r( ) ( ) * ( )=

Interface Thickness

ρ sharp r( ) h r( ) ρ diffuse r( )

( )h r 1

2exp r

23

2

2( ) ( )= −πσ σ

{ }2sharpdiffuse hII )()()( rℑ= ss { } 222 s42 eh σπ−=ℑ )r(

I s I s ediffuse sharp4 s2 2 2

( ) ( )= − π σ ))((~ 222sharp s41sI σπ−

)()(~)( 2224

2diffuse s41

sA

81sI πσρπ

−Δ Porod region

h(r)

Here,

73


Guinier Approximation

log

I

Guinier plot of cellulose nitrate in acetone solution of 0.5 %.

I s N V e

43

R sobs

2 2

2g

2

( ) =−

ηπ 2

lnI s lnNV43

R sobs2 2 2

g2 2( ) = −η π

volume g scatterin: V

gyration of radius : Rg

Rg from the slope

I 0 2( ) = NV 2 η

Applicable only at very small anglesMust be sufficiently dilute

74


ln[q

4 I(q)

]

75


Density Fluctuation

Fl VN N

N( )

( )=

− < >

< >

2

Fl V I sV

s dsVr( ) ( ) ( ( ))= ∑∫1 1

0

2

ρRuland (1975)

Fl I( ) ( )∞ =1 0

0ρ

Fl T T( )∞ = ρκ β

76


Correlation and Interface Distribution Functions Analysis on Lamellar Structure

Correlation and Interface Distribution Functions Analysis on Lamellar Structure

Examples of various arbitrary models

∫∞

∞→ ⎥⎦⎤

⎢⎣⎡ −=

0

4422 cos)()(lim

)2(2)(" qrdqqIqqIq

rrZ

qe π

77


Ideal Two Phase ModelIdeal Two Phase ModelIdeal Two Phase Model

ρ(r)

r

la lc

ρc

ρa

lc=100Å, la=30Å, finite no. of lamellae in the stack is 20

( )idealidealidealI ρρ ∗ℑ=

78


ρ(r)

r

la lc

ρc

ρa

li

lc=100Å, la=30Å, li=12Å

The ideal two phase model with a finite crystal amorphous transition zone

Model With Interface (I)Model With Interface (I)Model With Interface (I)

79


ρ(r)

r

ρa

ρc

Distribution of lamellar and amorphous layer sizes

12mc

Mcmodel

12mc

Mcmodel

w wfor LLL

w wfor LLL

≥≤=

≤≥= 2 ; thicker phasew; width of the thickness distributionLmodel; average long spacing in the model

lc=90Å, wc=10Å, la=25Å, wa=10Å, li=15Å, wi=1Å

Model With Interface (II)Model With Interface (II)Model With Interface (II)

80


Primary Lamellar Stack Primary Lamellar Stack

Secondary Lamellar Stack

Dual Lamellar Stack ModelDual Lamellar Stack ModelDual Lamellar Stack Model

Stack 1 lc=90Å, wc=10Å, la=25Å, wa=10Å, li=15Å, wi=1Å

Stack 2 lc=60Å, wc=10Å, la=25Å, wa=10Å, li=15Å, wi=1Å

12IMc

mc

12Imc

Mc

w wfor LL L

w wfor L LL

≥≥≥

≤≥≥

LL ,LL ImcI

Mc ≥≥

81


ExamplesExamplesExamples

Correlation function Interface distribution function

82


Biological SystemsBiological Systems

Å μmnm mm m

crystallographyspectroscopy

imaging techniquemicroscopy

Characteristic length

SAXS

Proteins Viruses Subcellular structures

��

Solution SAXS versus Single Crystallography

(a) Crystal structure of Escherichia coli RseBat a resolution of 0.24 nm

The solution models of RseB (b) and RseA121–216/RseB complex (c) restored from the SAXS data at a resolution of 1.25 nm. The ribbon diagram of the RseB is overlapped onto the solution model of RseB for the comparison of overall shape and dimension.

(a) (b) (c)

RseA binding site

RseA binding site

RseA binding induced-conformational change

D.Y. Kim, K.S. Jin, E. Kwon, M. Ree, K. K. Kim, Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 8779-8784.


��

��

86






87


Grazing Incidence Small Angle X-ray Scattering

(GISAXS)

Grazing Incidence Small Angle X-ray Scattering

(GISAXS)GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

88


Grazing Incidence X-ray Scattering (GIXS)

Internalstructure

αi ≤ αc

αi ≥ αc

αi > αc Surfacestructure

>>

<<

Surfacestructure

Surfacestructure

Internalstructure

+

Internalstructure

Internalstructure

αi ≤ αc

αi ≥ αc

αi > αc Surfacestructure

>>

<<

Surfacestructure

Surfacestructure

Internalstructure

+

Internalstructure

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

0.0 0.1 0.2 0.3 0.4 0.5100

1000

10000

100000

1000000

Λi (Å

)

α i (deg)

Penetration depth profile

Critical angle of film- Surface- Interfaces- Sub-layers- Electron density- etc.

89

0.0 0.1 0.2 0.3 0.4101

102

103

104

105

Pen

etra

tion

dept

h (Å

)

Incidence angle (degree)

( ) )(4

12 222222

cici ααβααπλζ

−−+−×=

jjj

ωρμρ

πλ

πλμβ ∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛×==

44

μ: linear absorption coefficient: mass density of the sample

ω: weight fractionγe: classical radius of electron

ρ

αi : incidence angleαc : critical angle of the sample

M. Tolan, X-ray Scattering from Soft-Matter Thin films. (1999) Springer, NY.

221,

2 2c

e eαδ δ γ λ ρ

π= =

90


Nanostructures

Bulk Specimens

Supporter(Substrate)Supporter(Substrate)

Nanostructures

Nanoscale SpecimensNanotechnology

Era (21st Century)

Nanotechnology

Era (21st Century)

Challenges in Characterization of Nano-Products

Transmission: WAXD, SAXS, WAND, SANSSALS

Reflection: WAXD, SAXSReflectivity

TEM, SEMAFM

Spectroscopiesetc.

Analytical Techniques

Scatterings ? GIXSGINS

Reflectivity X-rayNeutron

Microscopies ?Spectroscopies ?etc.

Analytical Techniques

One of Major Issues:How to characterize?

MaterialsFabricationsCharacterizations

small mass, volume weak signal

91


Concerns and Complexity in GIXSand

GIXS Theory Developmentfor

characterizing Nanostructures in nanoscale specimens

supported with substrates

92


Con

cern

s - Any possible scattering from substrate

- Transparency of substrate to X-ray beam

- High energy and high flux X-ray beam

- Scattering from surface structure - Scattering from internal structure

* Scattering from reflected beam* Scattering from transmitted beam

- Refraction effect involved • Need a special setup• Need new scattering theory

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

TXS

Beamstopx

yz

qx

qyqz

2θ

φ

Mer

it - Easy measurement- Easy analysis

- Strong intensity- Easy preparation of samples- More informations

TSAXS vs GISAXS for Characterizing Nanotructure on Substrate

Si

93


GIXS Analysis of Nanotructure in supported with SubstrateC

once

rns

- Scattering from internal structure• Scattering from reflected beam• Scattering from transmitted beam

- Refraction effect involved

Ree, et al., Macomolecules (2005) 39, 3395; (2005) 39, 4311.Nature Materials (2005) 4, 147.Adv. Mater. (2005) 17, 696.

Other Groupsetc.

- Scattering from internal structure• Scattering from reflected beam• Scattering from transmitted beam

- Refraction effect involved

Ree, et al., Macomolecules (2005) 39, 3395; (2005) 39, 4311.Nature Materials (2005) 4, 147.Adv. Mater. (2005) 17, 696.

Other Groupsetc.

Sinha, et al., Phys. Rev. B. (1988) 38, 2297.Rauscher, et al., Phys. Rev. B (1995) 52, 16855.etc.

- Scattering from surface structureSinha, et al., Phys. Rev. B. (1988) 38, 2297.Rauscher, et al., Phys. Rev. B (1995) 52, 16855.etc.

- Scattering from surface structure

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GISAXS

94


Nanostructure on SubstrateC

once

rns

- Scattering from surface roughness : diffuse scattering* usually very weak,

but depending on the degree of roughness or surface structure.

(This is not discussed in this presentation. Further information available: Sinha, et al., Phys. Rev. B. (1988) 38, 2297, etc.)

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

95


once

rns

- Scattering from surface roughness : diffuse scattering* usually very weak,

but depending on the degree of roughness or surface structure.

(This is not discussed in this presentation. Further information available: Sinha, et al., Phys. Rev. B. (1988) 38, 2297, etc.)

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

96



once

rns

- Scattering from internal structure* Scattering from reflected beam* Scattering from transmitted beam

αf = αi

αf = -αi

X-Rayαf = αi

αf = -αi

X-Ray

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

transparentsubstrate

GISAXS

97


Con

cern

s - Scattering from internal structure* Scattering from reflected beam* Scattering from transmitted beam

αf = αi

αf = -αi

X-Rayαf = αi

αf = -αi

X-Ray

Nanostructure on Substrate

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

non-transparentsubstrate

GISAXS

98


Nanostructure on Substrate

Con

cern

s - Scattering from internal structure* Scattering from reflected beam* Scattering from transmitted beam* Refraction effect

PS-b-PI(37/63) film(HPL; ρe = 360 nm-3 )

2θf (deg.)

α f (d

eg.)

αf = αc,s

αf = αc,f

(108)

(107)

(101)

(105)(104)

(102)

0.00 0.25 0.50- 0.25- 0.500.00

0.20

0.40

0.60

0.80

1.00

1.20

( )

B

A

C

D

2θf (deg.)

α f (d

eg.)

αf = αc,s

αf = αc,f

(108)

(107)

(101)

(105)(104)

(102)

0.00 0.25 0.50- 0.25- 0.500.00

0.20

0.40

0.60

0.80

1.00

1.20

( )

B

A

C

D

2θf (deg.)

α f (d

eg.)

αf = αc,s

αf = αc,f

(108)(108)

(107)(107)

(101)(101)

(105)(105)(104)(104)

(102)(102)

0.00 0.25 0.50- 0.25- 0.500.00

0.20

0.40

0.60

0.80

1.00

1.20

( )

B

A

C

D

0.00 0.02 0.04 0.06

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Reflected beam

Transmitted beam

αi = 0.21o

λ = 1.54 Å

α f (deg

.)

qz (Å-1)

0.00 0.02 0.04 0.06

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Reflected beam

Transmitted beam

αi = 0.21o

λ = 1.54 Å

α f (deg

.)

qz (Å-1)

After correction for refraction effect)

After correction for refraction effect Before

correctionfor refraction

effect

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GISAXS

99


Scattering process

GIXS Intensity : DWBA

||rz

dMedium 1

23

||rz

dMedium 1

23

GIXS Theory

2 20 1( ) 0k V∇ + − Ψ =

3 ' 1 102( ) ( , ) ( ) ( , )

4scik r d r V

rπΨ = − Ψ − Ψ∫ ' ' '

f ir r k r r k

(V = V1 + V2 )

2 2

1, , ,

2 , , ,

3 , , ,

4 , , ,

x y

z z f z i

z z f z i

z z f z i

z z f z i

q q q

q k k

q k k

q k k

q k k

= +

= −

= − −

= +

= − +

αf

qαi

αf

qαi

Ri , Ti : incoming waveRf , Tf : outgoing waveF : amplitude of scattering

from the internal structureI1 = FF* ; intensity

tindependenffGIXS II ⋅≅ 2161)2,(π

θα

ioiz n α22, coskk −=

fofz n α22, coskk −=

λπ /2=ok

(DWBA) 2

,4||

,3||

,2||

,1||

)Im(2

2

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161)2,(

zfi

zif

zfi

zfi

z

q

ffGIXS

qqFRR

qqFRT

qqFRT

qqFTT

qeI

z

+

+

+

⋅−

⋅=⋅− d

πθα

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅=⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z

π

100


drqrSqrFrrncI )(|)(|)()( 2

0

21 ∫

∞= υ

(1) Spherical structures:

2

2

22

)/ln(

2/21)( σ

σσπ

orr

o

eer

rn−

=

I1, scattered intensity from scatters in nanoscales

222

32)()(

1 )1(

))(1(8

ξ

ξρρφπφ

qI scatteremediumfilme

+

−−=

(2) Random two-phase structures:

)()()(1 qqq PSI ⋅=

(3) Structures in Crystal lattices:

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z d

πffGIXSI ≅1

)2,( θα

Ree, et al., Macomolecules (2005) 38, 3395 Macromolecules (2005) 38, 4311.Nature Materials (2005) 4, 147Adv. Mater. (2005) 17, 696

drqrSqrFrrncI )(|)(|)()( 2

0

21 ∫

∞= υ

(1) Spherical structures:

2

2

22

)/ln(

2/21)( σ

σσπ

orr

o

eer

rn−

=

I1, scattered intensity from scatters in nanoscales

222

32)()(

1 )1(

))(1(8

ξ

ξρρφπφ

qI scatteremediumfilme

+

−−=

(2) Random two-phase structures:

)()()(1 qqq PSI ⋅=

(3) Structures in Crystal lattices:

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z d

πffGIXSI ≅1

)2,( θα

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z d

πffGIXSI ≅1

)2,( θα

Ree, et al., Macomolecules (2005) 38, 3395 Macromolecules (2005) 38, 4311.Nature Materials (2005) 4, 147Adv. Mater. (2005) 17, 696

101


2D GIXS Pattern measured for a nanopous dielectric thin film

2D GIXS Pattern(experimental data)

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

αf(d

eg.) 1

αf(d

eg.) 1

2θf (deg.)2θf (deg.)

αf(d

eg.) 1

αf(d

eg.) 1

2θf (deg.)2θf (deg.)

50 nm50 nm50 nm

SubstratePMSSQ

Nanopore

TEMTEM

50 nm50 nm50 nm

SubstratePMSSQ

Nanopore

TEMTEM

* AFM found: Surface is very smooth (<0.5 nm)!* Nanospcimen thickness: ca. 100 nm.

102


(1) Data Analysis with GIXS of Spherical Structures (Pores)

(In-plane)2θf (In-plane)2θf

( ) 2

20

2

2)/ln(

5.002

1 σ−

σσπ=

rr

eer

rn

( ) ( ) ( )( )

( )

2

2

3

23 cossin3

4⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ π= ∫ drqrS

qrqrqrqrrrnI1 ( ) ( ) ( )

( )( )

2

2

3

23 cossin3

4⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ π= ∫ drqrS

qrqrqrqrrrnI1

Pore sizeSize distributionsShape Porosity …

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z

πffGIXSI ≅)2,( θα

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


0.1 1

100

101

102

I (a.

u.)

qy (nm-1)

B Sphere

Sphere Form Factor: ( ) ( ) ( )[ ]( )3

cossin3,qr

qrqRqrrqFsphere−

=

0.322.17σr0 (nm)

0.322.17σr0 (nm)

* AFM found: Surface is very smooth (<0.5 nm)!* Nanospcimen thickness: ca. 100 nm.

103


(2) Data Analysis with GIXS of Ellipsoidal Structures (Pores)


( ) 2

20

2

2)/ln(

5.002

1 σ−

σσπ=

rr

eer

rn

) ( ) ( )2

223

34π

elliposid drqrSFrrnq ⎟⎟⎠

⎞⎜⎜⎝

⎛= ∫I1) ( ) ( )

2

223

34π

elliposid drqrSFrrnq ⎟⎟⎠

⎞⎜⎜⎝

⎛= ∫I1


⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


I(a

.u.)qy (nm-1)

ε = 0.9 (best fit)ε = 0.8ε = 0.7ε = 0.6ε = 0.5ε = 0.4ε = 0.3ε = 0.2ε = 0.1

0.1 1

100

101

102

I(a

.u.)qy (nm-1)

ε = 0.9 (best fit)ε = 0.8ε = 0.7ε = 0.6ε = 0.5ε = 0.4ε = 0.3ε = 0.2ε = 0.1

0.1 1

100

101

102

( ) ( )2 2

0, , , , , sinellipsoid sphereF q R F q r R d

πε ε α α α= ⎡ ⎤⎣ ⎦∫

( ) 2 2 2, , sin cosr R Rε α α ε α= +

(ε : aspect ratio)

r

R

εR

long axes

short axes

r

R

εR

long axes

short axes

r

R

εR

long axes

short axes

0.33

σ

0.90ε

2.20

r0 (nm)

0.33

σ

0.90ε

2.20

r0 (nm)

104


(3) Data Analysis with GIXS of Cylindrical Structures (Pores)


( ):, LRn

) ( ) ( )drqrSFVLRnq cylinder, 22∫=


⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


I(a

.u.)

qy (nm-1)

L/R = 1.49 (best fit)L/R = 1L/R = 2L/R = 4L/R = 6

0.1 1

100

101

102

( ), ,cylinderF q R L =

I1

lognormal function

( ) ( ) 22 1

0

2 sin sin cos / 2sin

sin cos / 2B qR qL

dqR qL

π α αα α

α α⎡ ⎤⎢ ⎥⎣ ⎦

∫R : radius, L : lengthB1 : first order Bessel function)

2.81R0 (nm)

4.20L (nm)

0.33σ

2.81R0 (nm)

4.20L (nm)

0.33σ

105


This Series of GIXS Analyses gives Conclusions:

• Nanopore shape: “Sphere (hard sphere)”• Packing order: “None”

(randomly dispersed in the film plane)

(In-plane)2θf

106


(4) Structural Information in the Out-of-PlaneOut-of-plane

αfOut-of-plane

αf

( ) 2

20

2

2)/ln(

5.002

1 σ−

σσπ=

rr

eer

rn

( ) ( ) ( )( )

( )

2

2

3

23 cossin3

4⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ π= ∫ drqrS


( )( )

2

2

3

23 cossin3

4⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ π= ∫ drqrS

qrqrqrqrrrnI1

0.1 1

102

103

104

10

106

107

6

20 wt%I(a.

u.)

αf (deg.)

5

0.1 1

102

103

104

10

106

107

6

20 wt%I(a.

u.)

αf (deg.)

5

-0.3 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.11E-24

1E-61E-51E-41E-30.010.1

110

1001000

10000100000

1000000

dσ/dΣ(αf)

|T2|

|R2|

αf (deg.)

I

-0.3 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.11E-24

1E-61E-51E-41E-30.010.1

110

1001000

10000100000

1000000

dσ/dΣ(αf)

|T2|

|R2|

αf (deg.)

I

αc (film)αc (Si)

πρλα ee

cr= πρλα ee

cr=

Electron densityPorosityThicknessOrientation

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z


107


In- and Out-of-Plane GIXS Profiles Analysis gives Conclusions:

• Nanopore shape: “Sphere (hard sphere)”• Packing order: “None”

(randomly dispersed within the thin film)

* Further, We have verified these GIXS Analysis Results by the TXS Measurement and Data Analysis!

M. Ree et al., Macromolecules 39, 8991 (2005)

GIXS TXS

(In-plane)2θf

(out-of-plane)

108


Pore structures and properties of nanoporous PMSSQ filmsimprinted with PCL4 porogen

gR a (nm) Porogen loading (wt%)

Cure temp. (°C) GIXS TXS

eρ b (nm-3)

P c (%) n d k e

0

400

-

-

399

-

1.3960

2.70

PCL4

10

20

30

30

400

400

400

200

5.3(0.01)

10.0(0.02)

>40 g

-

4.4 (0.06)

11.3 (0.10)

>40 g

>40 g

373

338

302

398

6.5

15.3

24.3

-

1.3587

1.3207

1.2795

-

2.44

2.16

1.85

- aAverage radius of gyration estimated from the radius r and number distribution of pores obtained by the analysis of

SAXS profile. b Electron density determined from the out-of-plane GISAXS profile. c Porosity estimated from the electron density of the film. d Refractive index measured at 633 nm using spectroscopic ellipsometry. e Dielectric constant measured at 1 MHz using an impedance analyzer. f Standard deviation in the determined gR value. g Not detected due to the out of the detection limit (ca. 40 nm).

Comparison of GIXS and TXS Analysis

M. Ree et al., Macromolecules 39, 8991 (2005)

109


(5) 2D GIXS Simulation

Simulated GIXS pattern

Experimental data

( ) 2

20

2

2)/ln(

5.002

1 σ−

σσπ=

rr

eer

rn

( ) ( ) ( )( )

( )

2

2

3

23 cossin3

4⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ π= ∫ drqrS


( )( )

2

2

3

23 cossin3

4⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ π= ∫ drqrS

qrqrqrqrrrnI1

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z

πffGIXSI ≅1

)2,( θα

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z

πffGIXSI ≅1

)2,( θα

Ree et al.,Nature Materials (2005) 4, 147Adv. Mater. (2005) 17, 696Patents filed

110


Surface Structures of a Nano-Template on Substrate

PS-b-PMMA Film (25-90 nm thick)

1. Spin-Coating PS-r-PMMA solution (toluene)

2. Drying

Si wafer

1. Spin-Coating PS-b-PMMA(0.25)/PMMAsolution (toluene)

2. Drying & Anealing at 170°C for 2 days

UV-Etching

Neutral Brush

PMMA blockPS block

PMMA homopolymer

1. Spin-Coating PS-r-PMMA solution (toluene)

2. Drying

Si waferSi wafer

1. Spin-Coating PS-b-PMMA(0.25)/PMMAsolution (toluene)

2. Drying & Anealing at 170°C for 2 days

UV-Etching

Neutral Brush

PMMA blockPS block

PMMA homopolymerNeutral Brush

PMMA blockPS block

PMMA homopolymer

100 nm

Surfaceroughness:<0.5 nm

AFM

100 nm100 nm

SEM

(1) Rcylinder & Distribution ?

(2) Lcylinder & Distribution ?

(3) Cylindrical Pore Depth & Its Quality ?

*Co-worked with Prof. Jin Kon Kim(Postech)

?

?Ree et al.,J. Appl. Cryst. 40, 305 (2007)

111


Parameters in calculating 2D GIXS pattern:αi = 0.20°L = 86.1 nm R = 11.7 nm σr = 2.90 nmDsp = 34.0 nm ρe(film)=261nm-3

Parameters in calculating 2D GIXS pattern:αi = 0.20°L = 78.8 nm R = 11.8 nm σr = 2.95 nmDsp = 34.0 nm ρe(film)=348 nm-3

0.5

1.0

1.5

0.0

2θf (degree)-1.0 -0.5 0 0.5 1.0

αf

(d

egre

e)

0.5

1.0

1.5

0.0

2θf (degree)-1.0 -0.5 0 0.5 1.0

αf

(d

egre

e)

Before UV-Etching After UV-Etching

2θf (degree)-1.0 -0.5 0 0.5 1.0

αf

(d

egre

e)

0.5

1.0

1.5

0.0

2θf (degree)-1.0 -0.5 0 0.5 1.0

αf

(d

egre

e)

0.5

1.0

1.5

0.0

2θf (degree)-1.0 -0.5 0 0.5 1.0

αf

(d

egre

e)

0.5

1.0

1.5

0.0

2θf (degree)-1.0 -0.5 0 0.5 1.0

αf

(d

egre

e)

0.5

1.0

1.5

0.0

g=0.048 g=0.0362θf (degree)

-1.0 -0.5 0 0.5 1.0

αf

(deg

ree)

0.5

1.0

1.5

0.0

<Exp. Data>

<Calc. Data>

GIXS

Calculated

Measured

112


⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z

πffGIXSI ≅1

)2,( θα

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+

+

⋅−

⋅⋅−

))Re(,(

))Re(,(

))Re(,(

))Re(,(

)Im(21

161

,4||1

2

,3||1

2

,2||1

2

,1||1

2

d)Im(2

2

zfi

zif

zfi

zfi

z

q

qqIRR

qqIRT

qqIRT

qqITT

qe z

πffGIXSI ≅1

)2,( θα

)2/exp()2/sin()(2),,( 12 iqLqLqRqRJLRLRqF −= π

)()()( 21 qZqFqI =

∏=

=1

)()(d

kk qZqZ

222 / jj aag Δ=

⎥⎦

⎤⎢⎣

⎡ −−= 2

2

2)(exp

21)(

RR

RRRGσσπ

+⋅−

−=

⎭⎬⎫

⎩⎨⎧−+

= 2

2

)cos(21

1)(1)(1)(

kkk

k

k

k

FqaF

FqFqFreqZ

∏=

⎥⎦⎤

⎢⎣⎡−=

−=2

1

22 )(21exp)(

)exp()()(

jjk

kkk

qagqF

iqaqFqF

θ Dsp

L

R

n

θ Dsp

L

R

n

Rcylinder=11.5 nmL = 25 – 100 nmRcylinder=11.5 nmL = 25 – 100 nm

g: paracrystal distortion factor

Internal Structure of a Nano-Template on Si SubstratePS-b-PMMA Film (25-90 nm thick)

113


Structural and property characteristics of thin films of the PS-b-PMMA/PMMA mixtures before and after UV-etching

Structural parameters Properties

Sample t a (nm) Lb

(nm)R c

(nm)σR

d (nm)

dspe

(nm) g f

αc g

(deg.) eρ

h

(nm-3) Pe i (%)

Before etching

Film-1 28.5

28.5

11.0

3.01

34.0

0.053

0.156

348

−

Film-2 78.8 78.8 11.4 3.00 34.0 0.048 0.156 348 − After UV-etching

Film-3 25.0

25.0

11.8

2.95

34.0

0.040

0.136

265

25.3

Film-4 86.1 86.1 11.7 2.90 34.0 0.036 0.135 261 26.6a Film thickness. b Length of the cylindrical pores. c Pore radius determined from the peak maximum of the radius r and the number distribution of pores. d Standard deviation of the pore radius. e Center-to-center distance of the cylindrical pores (d-spacing of the hexagon). f Paracrystal distortion factor g Critical angle of the film determined from the out-of-plane GIXS profile. h Electron density determined from the critical angle of the film. i Porosity estimated from the electron density of the film with respect to the electron density of PS.

114


Self-Assembled PS-b-PMMA DiblockCopolymer on Substrate

AFM

2.0 μm × 2.0 μm

PS-b-PMMA Film (200 nm thick)

Fractionated (FM)(wtPMMA = 0.345)

or or ?*Co-worked with

Prof. Taihyun Chang(Postech)

Macromolecules, 38, 10532 (2005)

rms roughness: 0.1-0.3 nm

115


2.0 μm × 2.0 μm

PS-b-PMMA Film (200 nm thick)

Fractionated (FM)(wtPMMA = 0.345)

HPL

009

003

003006

006009

009

101

105108

107

102105

104

102

from reflected beam

(Measured)(Calculated)

Ree et al.,Macromolecules, 38, 4311 (2005)Macromolecules, 38, 10532 (2005)Macromolecules, 39, 684 (2006)Macromolecules, 40 (2007), ASAPJ. Appl. Crystal. (submitted)αc ≤ αi ≤ αs

116


PS-b-PI (wtPI=0.634) film (1254 nm thick) rms roughness: 0.1-0.3 nm

αf (deg.)

2θf (deg.)

(Measured) αc ≤ αi ≤ αs

Self-Assembled PS-b-PI DiblockCopolymer on Substrate

117


αc ≤ αi ≤ αs

117

118


αf (deg.)

αf (deg.)2θf (deg.)

2θf (deg.)

(Measured)

(Calculated)

αc ≤ αi ≤ αs

Ree et al.,Macromolecules, 38, 4311 (2005); Macromolecules, 38, 10532 (2005)Macromolecules, 40 (2007), ASAP; J. Appl. Crystal. (in press)

119


(B)140 oC (C)160 oC

Phase Transition of HPL phase to Gyroid

(A) 120 oC

PS-b-PI (wtPI=0.634) film (1254 nm thick)

GIXS

•Gyroid-structured microdomains perfectly oriented along the {121} plane parallel to the in-plane of a film.

HPL

*Co-worked with Prof. Taihyun Chang(Postech)

HPL Gyroid

αc ≤ αi ≤ αs

rms roughness: 0.1-0.3 nm

HPL+

Gyroid

Gyroid

Ree, Chang, et al.,Macromolecules, 38, 10532 (2005)Macromolecules, 40 (2007), ASAP

120120

121






122


In-Situ GIXS Measurements

123


Matrix Porogen

- Coating- Dry

Thermal process

solvent

400-430°C

H O Si

CH 3

O Si

CH 3

OC 2H5

O O

Si Si

CH 3 CH 3

O O OHC2H5

n

PMSSQ Precursor10,000 Mw

H O Si

CH 3

O Si

CH 3

OC 2H5

O O

Si Si

CH 3 CH 3

O O OHC2H5

n

PMSSQ Precursor10,000 Mw

O

O

O

O

O

OO

O

O

OOO

On

nn

n

H

H H

H

O

O

O

O

O

OO

O

O

OOO

On

nn

n

H

H H

H

PCL4 Porogen

in-situ GIXSMeasurementsconducted

TEM 50 nmTEM 50 nm50 nm

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

GIXS

x

yz

qx

qy

qz

2θf

αfαi

Beamstop

Ree et al.,J. Phys. Chem. B, 110, 15887 (2006) J. Mater. Chem. 16, 685 (2006) Nanotechnology 17, 3490 (2006)Macromolecules 38, 8991 (2005) Macromolecules 38, 3395 (2005)

In-situ GIXS - Nanopous dielectric thin films: Low-k nanofilms

124


In-situ GIXS Measurements: PCL4/PMSSQ film

0.1 1.0qy (nm-1)

I(a

.u.)

400°C370°C330°C290°C200°C

103

102

101

100

10-1

101

100

I(a

.u.)

200°C

170°C

150°C145°C

50°C

0.1 1.0qy (nm-1)

I(a

.u.)

400°C370°C330°C290°C200°C

103

102

101

100

10-1

101

100

I(a

.u.)

200°C

170°C

150°C145°C

50°C

0.1 1.0qy (nm-1)

I(a

.u.)

400°C370°C330°C290°C200°C

103

102

101

100

10-1

101

100

I(a

.u.)

200°C

170°C

150°C145°C

50°C

10 wt% PCL4

n(r

)0 5 10 15

r (nm)

150°C

170°C400, 370, 330°C200, 290°C

n(r

)0 5 10 15

r (nm)

150°C

170°C400, 370, 330°C200, 290°Cn

(r)

0 5 10 15r (nm)

150°C

170°C400, 370, 330°C200, 290°C

PCL4/PMSSQ precursorThin Film (25°C) (400°C) PCL4/PMSSQ

Thin Film2°C/minvacuum

2°C/minvacuum (25°C)

in-plane

2θf

αf

125


In-situ GIXS Measurements: PCL4/PMSSQ film

PCL4/PMSSQ precursorThin Film (25°C) (400°C) PCL4/PMSSQ

Thin Film2°C/minvacuum

2°C/minvacuum (25°C)

out-of-plane

2θf

αfout-of-plane

2θf

αf

αc,f

αc,f

200°C

400°C

0.15 0.20 0.25αf (degree)

I(a

.u.)

145°C150°C170°C

5.0°

C i

nter

val

αc,f

αc,f

200°C

400°C

0.15 0.20 0.25αf (degree)

I(a

.u.)

145°C150°C170°C

5.0°

C i

nter

val

126





1. Conclusions – I, II2. References – TSAXS, GISAXS3. Introduction – M. Ree’s Group at Postech4. Acknowledgments

127


Conclusions – TSAXS

▪ SAXS Optics and Sample Stage Related Equipments Reviewed.

▪ Theoretical Fundamentals of TSAXS Reviewed.

▪ TSAXS is Very Powerful to Analyze Single Particles (Molecules) and Their Assemblies in Solutions and Solids.

▪ TSAXS is Very Powerful to Analyze Proteins and Other Biomacrmolecules in Nature.

▪ TSAXS is Very Powerful to Characterize Structural Changes in Time-Resolved Mode.

▪ GIXS is the Nondestructive analysis technique.

128


Conclusions – GISAXS

▪ GISAXS Optics, Theory and Data Analysis Methods Reviewed.

▪ GISAXS is Very Powerful to Analyze Structures in NanoscaledSamples and Products.

▪ GISAXS is Very Powerful to Characterize Structural Changes in Time-Resolved Mode.

▪ GISAXS is the Nondestructive analysis technique.

��


References – TSAXS1) D. Y. Kim, K. S. Jin, E. Kwon, M. Ree, K. K. Kim, Proc. Natl. Acad. Sci. USA,

104, 8779-8784 (2007).

2) J. M. Choi, S. Y. Kang, W. J. Bae, K. S. Jin, M. Ree, Y. Cho, J. Biol. Chem., 282, 9941-9951 (2007).

3) D. S. Jang, H. J. Lee, B. Lee, B. H. Hong, H. J. Cha, J. Yoon, K. Lim, Y. J. Yoon, J. Kim, M. Ree, H. C. Lee, K. Y. Choi, FEBS Letters, 580, 4166-4171 (2006).

4) K. Heo, J. Yoon, K. S. Jin, S. Jin, G. Kim, H. Sato, Y. Ozaki, M. Satkowski, I.Noda, M. Ree, J. Appl. Crystallography, 40, s594-s598 (2007).

5) B. Lee, T. J. Shin, S. W. Lee, J. Yoon, J. Kim, M. Ree, Macromolecules, 37, 4174-4184 (2004).

6) B. Lee, T. J. Shin, S. W. Lee, J. Yoon, J. Kim, H. S. Youn, K.-B. Lee, M. Ree, Polymer, 44, 2509-2518 (2003).

7) B. Lee, T.J. Shin, S.W. Lee, J.W. Lee, M. Ree, Macromol. Symp., 190, 173 (2002).

8) T.J. Shin, B. Lee, H.S. Youn, K.-B. Lee, M. Ree, Langmuir, 17, 7842 (2001).

9) S. I. Kim, T.J. Shin, S.M. Pyo, J.M. Moon, M. Ree, Polymer, 40, 1603 (1999).

10) J. K. Kim, H. H. Lee, M. Ree, K.-B. Lee, J. Park, Macromol. Chem. Phys., 199, 641 (1998).

11) M. Ree, K. Kim, S. H. Woo, and H. Chang, J. Applied Physics, 81, 698-708(1997).

12) M. Ree, T. L. Nunes, J. S. Lin, Polymer, 35, 1148 (1994).

13) H. H. Song, M. Ree, D. Q. Wu, B. Chu, M. Satkowski, R. Stein, J. C. Phillips,Macromolecules, 23, 2380 (1990).

14) H. H. Song, D. Q. Wu, M. Ree, R. S. Stein, J. C. Phillips, A. LeGrand, B. Chu,Macromolecules, 21, 1180 (1988).

15) R.-J. Roe, Methods of X-Ray and Neutron Scattering in Polymer Science. Oxford Univ. Press, N. Y., 2000.

16) L. E. Alexander, X-Ray Diffraction Methods in Polymer Science. Wiley-Interscience, N. Y., 1969.

��


References – GISAXS (1)1) K. Heo, J. Yoon, S. Jin, J. Kim, K.-W. Kim, T. J. Shin, B. Chung, T. Chang, M.

Ree, J. Appl. Cryst. (in press, 2007).

2) G.-W. Lee, J. Kim, J. Yoon, J.-S. Bae, B. C. Shin, I. S. Kim, W. Oh, M. Ree, Thin Solid Films (in press, 2007).

3) S. Jin, J. Yoon, K. Heo, H.-W. Park, T. J. Shin, T. Chang, M. Ree, J. Appl. Crystallography, 40, 950-958 (2007).

4) K. Heo, S.-G. Park, J. Yoon, K. S. Jin, S. Jin, S.-W. Rhee, M. Ree, J. Phys. Chem. C. 111, 10848-10854 (2007).

5) J. Yoon, K. S. Jin, H. C. Kim, G. Kim, K. Heo, S. Jin, J. Kim, K.-W. Kim, M.Ree, J. Appl. Crystallography, 40, 476-488 (2007).

6) J. Yoon, S. C. Choi, S. Jin, K. S. Jin, K. Heo, M. Ree, J. Appl. Crystallography, 40, s669-s674 (2007).

7) K. S. Jin, K. Heo, W. Oh, J. Yoon, B. Lee, Y. Hwang, J.-S. Kim, Y.-H. Park, T.Chang, M. Ree, J. Appl. Crystallography, 40, s631-s636 (2007).

8) K. Heo, K. S. Oh, J. Yoon, K. S. Jin, S. Jin, C. K. Choi, M. Ree, J. Appl. Crystallography, 40, s614-s619 (2007).

9) T. J. Lee, G.-s. Byun, K. S. Jin, K. Heo, G. Kim, S. Y. Kim, I. Cho, M. Ree, J. Appl. Crystallography, 40, s620-s625 (2007).

10) W. Oh, Y. Hwang, T. J. Shin, B. Lee, J.-S. Kim, J. Yoon, S. Brennan, A. Mehta, M. Ree, J. Appl. Crystallography, 40, s626-s630 (2007).

11) J. Yoon, S. Y. Yang, K. Heo, B. Lee, W. Joo, J. K. Kim, M. Ree, J. Appl. Crystallography, 40, 305-312 (2007).

12) Y. Kim, J. Nelson, J. R. Durrant, D. D. C. Bradley, K. Heo, J. Park, H. Kim, I. McCulloch, M. Heeney, M. Ree, C.-S. Ha, Soft Matter, 3, 117-121 (2007).

13) K. Heo, K. S. Jin, J. Yoon, S. Jin, W. Oh, M. Ree, J. Phys. Chem. B, 110, 15887-15895 (2006).

14) J. Yoon, K. Heo, W. Oh, K. S. Jin, S. Jin, J. Kim, K.-W. Kim, T. Chang, M. Ree, Nanotechnology, 17, 3490-3498 (2006).

15) K. Heo, J. Yoon, M. Ree, IEE Proc. Bionanotechnology, 153, 121-128 (2006).

��


References – GISAXS (2)16) Y. Kim, S. Cook, S. M. Tuladhar, S. A. Choulis, J. Nelson, J. R. Durrant, D. D. C.

Bradley, M. Giles, I. McCulloch, C.-S. Ha, M. Ree, Nature Materials, 5, 197-203 (2006).

17) Y. Hwang, K. Heo, C.H. Chang, M.K. Joo, M. Ree, Thin Solid Films, 510, 159-163 (2006).

18) M. Ree, J. Yoon, K. Heo, J. Mater. Chem., 2006, 16, 685-697.

19) B. Chung, M. Choi, M. Ree, J. C. Jung, W. C. Zin, T. Chang, Macromolecules, 39, 684-689 (2006).

20) I. Park, B. Lee, J. Ryu, K. Im, J. Yoon, M. Ree, T. Chang, Macromolecules, 38, 10532-10536 (2005).

21) B. Lee, W. Oh, J. Yoon, Y. Hwang, J. Kim, B. G. Landes, J. P. Quintana, and M.Ree, Macromolecules, 38, 8991-8995 (2005).

22) J.-S. Kim, H.-C. Kim, B. Lee, M. Ree, Polymer, 46, 7394-7402 (2005).

23) B. Lee, I. Park, J. Yoon, S. Park, J. Kim, K.-W. Kim, T. Chang, M. Ree, Macromolecules, 38, 4311-4323 (2005).

24) B. Lee, J. Yoon, W. Oh, Y. Hwang, K. Heo, K. S. Jin, J. Kim, K.-W. Kim, M.Ree, Macromolecules, 38, 3395-3405 (2005).

25) B. Lee, W. Oh, Y. Hwang, Y.-H. Park, J. Yoon, K. S. Jin, K. Heo, J. Kim, K.-W. Kim, M. Ree, Adv. Mater., 17, 696-701 (2005).

26) B. Lee, Y.-H. Park, Y.-T. Hwang, W. Oh, J. Yoon, M. Ree, Nature Materials, 4, 147-150 (2005).

27) K. Omote, Y. Ito, S. Kawamura, Appl. Phys. Lett., 82, 544-546 (2003).

28) R. Lazzari, J. Appl. Crystal., 35, 406 (2002).

29) M. Rauscher, T. Salditt, H. Spohn, Phys. Rev. B., 52, 16855 (1995).

30) S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, Phys. Rev. B., 38, 2297-2311(1988).

31) M. Tolan, X-ray Scattering from Soft-Matter Thin films. Springer, NY, 1999.

32) V. Holy, U. Pietsch, T. Baumbach, High-resolution X-ray scattering from thin films and multilayers. Springer-Verlag, Berlin, 1999.

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