ソフトマターの時空間階層構造と

ＥＲＬへの期待

篠原佑也（SHINOHARA Yuya）

東京大学大学院 新領域創成科学研究科

雨宮研究室

ERL サイエンスワークショップ 2009年7月10日 於 KEK

/42

Topics

• ソフトマターの時空間階層構造• 小角Ｘ線散乱法の重要性• 小角X線散乱法の応用例 -- 次世代光源 での展開• 極小角散乱• X線光子相関分光• マイクロビームX線散乱

2

/42

Collaborators

• 雨宮慶幸（東大院新領域）、雨宮研の学生のみなさん

• 岸本浩通（住友ゴム工業（株））

• 八木直人、鈴木芳生、竹内晃久、上杉健太朗、太田昇、井上勝晶（JASRI）

3（敬称略）

/42

Hierarchical Structure of Soft Mattert/s

10-12

10-9

10-6

10-3

100

103

10-15

側鎖運動

主鎖運動

マクロ相分離

ミクロ相分離合成高分子絡み合い効果

セグメント運動

生体高分子ものと生き物のクロスオーバー

膜細胞

生物

10010-110-2 101 102 103 104 105 106 107

r/nm

100101102 10-1 10-2 10-3 10-4 10-5 10-6 10-7

s/nm-1

電子顕微鏡

10-3

10-6

10-9

10-12

10-15

E/eV

（多体中の）単分子 分子集合体 相分離構造 vs 組織構造

10-0

X線トモグラフィー共焦点レーザー顕微鏡

レオメーター

動的光散乱

核磁気共鳴

4

/42

ソフトマターの特徴

5

ソフトマター高分子、液晶、コロイドガラス、粉流体など

電場

磁場

光

流動場

階層的なダイナミクス

小さな外場で大きな構造変形非常にゆっくりとした緩和ダイナミクス

t/s

10-12

10-9

10-6

10-3

100

103

10-15

側鎖運動

主鎖運動

マクロ相分離

ミクロ相分離合成高分子絡み合い効果

セグメント運動

生体高分子

膜細胞

生物

10010-110-2 101 102 103 104 105 106 107

r/nm

どの階層が？どのように？

非晶性・非対称・不均一な構造

/42

非周期的・非対称な構造のダイナミクス :!(r, t)

階層構造の動的構造解析

回折・散乱（逆空間像の観察）結晶性試料、unit cell

イメージング（実空間像の観察）マクロスコピック

Small-Angle X-ray Scattering : SAXS非晶性試料、結晶の不均一な分布 S(q,!)

0.1 nm 1 nm 10 nm 100 nm 1 !m 10 !m 100 !m実空間

逆空間 10 nm-1 1 nm-1 0.1 nm-1 10-2 nm-1 10-3 nm-1 10-4 nm-1q = 2! / d

広角散乱 小角散乱 極小角散乱 イメージング

6

S(q,!)

/42

小角X線散乱: Small-Angle X-ray Scattering

X-ray

Scattered

Transmitted: wavelength!

2!

small angle large structure(1 - 100 nm)

散乱X線と透過X線の分離平行度が高くビームサイズも小さいX線

7

/42

小角Ｘ線散乱が対象とする非晶性試料

100 nm

ゲル

典型的な小角散乱像

ナノコンポジット

溶液中でのタンパク質（Dr. Svergun, EMBL）

8

/42

小角散乱の解析法

! モデルとなる電子密度分布を仮定して散乱強度を計算

9

r

q

! (r) I (q)

Fourier変換＆絶対値の２乗

/42

粒径分布の影響

10

Scat

terin

g In

tens

ity

6x10-2543210

q / Å-1

0.1 % 1 % 3 % 5 % 7 % 10 % 15 % 20 % 30 %

Gauss 分布を仮定して計算

完全な球でも、粒径分布の影響で散乱像の解釈が困難になる

粒子形状にも分布がある場合は？

分布が大きく

/42

凝集体からの散乱

11

10-2

10-1

100

101

102

103

104

105Sc

atte

ring

Inte

nsity

2 4 6 80.001

2 4 6 80.01

2 4 6 80.1

q /Å-1

凝集体の大きさ

さらに大きな階層の構造

凝集塊の大きさ

凝集塊の質量フラクタル次元 dm

凝集体/単粒子の表面フラクタル次元 ds

I(q) ~ q-(6-ds)

I(q) ~ q-dm

BL20XU & BL40B2, SPring-8

/42

USAXS of model sphere

12

Rubber !lled with mono-disperse spherical silica particles

x =

F(q): form factorDave = 282.9 nm

S(q): structure factor I(q): intensity

Form factor (sphere): knownStructure factor (distribution of spheres): unknown

BL20XU & BL40B2, SPring-8

/42

RMC による解析結果

防衛大：萩田克美講師、荒井隆教授

試料：単分散球形シリカ充填ゴム

13

高輝度・高コヒーレンスなX線を用いた可視化

単パルス

/42

明確な形状をもたない場合

14

電子密度 散乱強度

Debye-Bueche

Ornstein-Zernike

I(q) =1

1 + !2q2

I(q) =1

(1 + !2q2)2

相関関数

!(r) = exp!!r

"

"

!(r) ="

rexp

!!r

"

"

two phase system

polymer chain etc.

Autocorrelation Fourier trans.高輝度・高コヒーレンスなX線を用いて

相関関数ではなく電子密度の可視化

/42

Non-crystallineSample

Hierarchical Structure

Inhomogeneity of nano-structure

Element-specific structure

Surface/Interface Structure

Dynamics Structure vs Properties

Scanning !-beam SAXS

XPCS

Anomalous SAXS (ASAXS)

NFS/USAXS/SAXS/WAXS

Grazing-incidence SAXS (GI-SAXS)

KineticsTime-resolved

Multi-probe

15

/42

Reinforcement of rubber

increase of elasticity

increase of hysteresis loss

16

100nm

addition of filler (carbon black & silica)

Mechanism of reinforcement effect ?TEM Image of Carbon Black

6

4

2

0

Str

ess

/M

Pa

3002001000

Strain /%

unfilled

filled

/42

階層構造の小角散乱

primary particleaggregateagglomerate

surface fractalmass fractal

階層構造と物性との相関を解明する例）ナノ粒子充填ゴム

●　マクロな変形に対して階層構造の変化は？ --> 破壊強度 etc.

●　動的な構造変形に対する階層構造の応答は？ --> 摩耗特性 etc.

時間分割極小角・小角・広角X線散乱測定による階層構造変化のその場測定

XPCS によるナノ粒子揺らぎの測定

17

/42

USAXS @ SPring-8

sample

detector~ 160 m

18

/42

粒子が球形・単分散の場合球形シリカを充填したゴム

5

4

3

2

1

0

Str

ess

[M

Pa]

200150100500strain [%]

応力歪み曲線の履歴に対応して、散乱像も履歴を示す。

延伸方向

Y. Shinohara et al., J. Appl. Cryst., 40, s397 (2007). 19

/42

RMC による解析結果

0% 50% 100% 150%

防衛大：萩田克美講師、荒井隆教授

試料：単分散球形シリカ充填ゴム

20

/42

USAXS @ SPring-8

sample

detector~ 160 m

21

高輝度光 + 高空間分解能カメラ

↓

通常のビームラインでのUSAXS

広い階層構造の測定を１つのビームラインで！

/42

ゴム補強効果の研究

22

?

USAXS-SAXS XPCS

Reinforcement Effect

Structural Change of Aggregatesin Deformed Sample

Microscopic Dynamics of Aggregates in Rubber

TEM & X-ray CT observation in real space

Dynamical Viscoelasticity

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Rubber

Rubber filled with filler

Energ

y L

oss

Wet Grip Rolling Resistance

~ 10 Hz104 - 106 Hz

Temperature / ˚C

/42

ナノ粒子充填ゴムの動的物性

Rolling Resistance

~ 10 Hz

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RubberRubber filled with nano-particles

Energ

y L

oss

Wet Grip Rolling Resistance

~ 10 Hz104 - 106 Hz

Temperature / ˚C

60 km/h

Tire’s grip

~ 104 - 106 Hz

@ brake, wet road surface

Input Frequency from road surface

100 nm

carbon black (CB)

Addition of nano-particles

- Wet grip "

- Fuel Efficiency #

Dynamical Properties of

nano-particles in rubber?

(Fuel Efficiency)

23

/42

X-ray Photon Correlation Spectroscopy: XPCS

! X-ray Photon Correlation Spectroscopy: XPCS! 散乱Ｘ線の強度揺らぎの測定 -> 内部の構造揺らぎ!"#$%&'()&*+,(-'$,,./&#*((0(!)-(1

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relaxation time in system

Autocorrelation

Fluctuation of intensity

5

4

3

Sca

tter

ing

Inte

nsity

200150100500Time /s

1.030

1.020

1.010

1.000Auto

corr

ela

tion

12 4 6 8

102 4 6 8

1002

Time /sec

コヒーレントX線を用いた高時間分割小角Ｘ線散乱

g(2)(q, !) =!I(q, 0)I"(q, !)#!I(q)#2

24

/42

XPCS の位置づけ

10-1 100 101 102 103 104 105

101 100 10-1 10-2 10-3 10-4 10-5

r/nm

q/nm-1

100

103

10-6

10-9

10-12

10-15

10-3

X-ray Photon Correlation Spectroscopy

Light Scattering

BrillouinRaman

Photon Correlation

Inelastic X-ray Scattering

NSENeutron Scattering

WAXS SAXS USAXS

BS

"cold"

TOF

E /eV

t/s

100

10-3

10-6

10-9

10-12

10-15

25

/42

動的光散乱によるソフトマター研究例! コロイドの流体力学的粒径の測定! 高分子鎖の揺らぎの測定! ゲル中の構造揺らぎの測定

!

D : diffusion constant

: friction constant

mdvdt= F(t) ! !v + f "

希薄溶液中におけるBrown運動

m

v!

g(1)(q, !) = exp!!Dq2!

"Intermediate Scattering Function:

R =kT

6!"D

R : radius

Stokes-Einstein’s relation

26

/42

マイクロレオロジーとしての XPCS

• 一般論：揺動散逸定理（第１種）• 外力に対する応答関数と外力がないときの揺らぎとは関係している。

複素アドミッタンス

マイクロレオロジーへの応用Intermediate scattering

function

系の複素弾性率（Laplace 領域）

27

/42

XPCS を用いたゴム中のナノ粒子ダイナミクス観察

100nm

nano-particles in rubber speckle pattern fluctuation of scattering intensity

coherent x-ray

1.030

1.020

1.010

1.000Auto

corr

ela

tion

12 4 6 8

102 4 6 8

1002

Time /sec

Dynamics of Filler in Rubber

Dependence of dynamics on...

- Volume fraction of nano-particles

- Vulcanization (cross-linking)

- Type of nano-particles

- Temperature etc.

5

4

3

Sca

tter

ing

Inte

nsity

200150100500Time /s

28

/42

100 nm < d < 1 µm

５枚/秒を３０倍速で再生中...

29

/42

散乱強度揺らぎの温度依存性

Inte

nsity

/a.u

.

200150100500Time /s

150˚C

120˚C

90˚C

60˚C

30˚C

30

/42

加硫過程の XPCS 測定S

catt

erin

g I

nte

nsi

ty

35302520151050Time /min

Time /min

Tem

pera

ture 150 ˚C

30 ˚C

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Y. Shinohara et al., Jpn. J. Appl. Phys., 46, L300 (2007). 31

/42

XPCS の位置づけ

10-1 100 101 102 103 104 105

101 100 10-1 10-2 10-3 10-4 10-5

r/nm

q/nm-1

100

103

10-6

10-9

10-12

10-15

10-3

X-ray Photon Correlation Spectroscopy

Light Scattering

BrillouinRaman

Photon Correlation

Inelastic X-ray Scattering

NSENeutron Scattering

WAXS SAXS USAXS

BS

"cold"

TOF

E /eV

t/s

100

10-3

10-6

10-9

10-12

10-15

32

次世代光源で狙う領域

/42

!t

X-ray delay unit

sample

XFEL pulse

splitted XFEL pulse

area detector

Fig. 1. Schematics of the split-pulse technique. A delay line unit consisting of mirrors

and beam-splitters produces two equal intensity pulses travelling along the same path but

delayed in time. Each pulse produces a speckle pattern and the sum is recorded on an area

detector and analyzed in terms of speckle contrast.

in XPCS experiments is the intensity autocorrelation function g 2(!) = < I(t)I(t + !) > / <I(t) >2. Assuming Gaussian fluctuations the intensity autocorrelation function can be rewritten

with the help of the Siegert relation [1] as

g2(!) = 1+ | f (!)|2, (1)

where f (!) is the intermediate scattering function reflecting the dynamics of the sample.

XPCS has developed into a valuable tool for measuring slow dynamics (typically 10!2 to

106 Hz [2]) in the time domain as X-rays provide several advantages when compared to optical

light such as, e.g., short wavelength, high penetration power, surface sensitivity and element

specificity. However, the access to ultrafast dynamics on nanometer length scales is being ham-

pered by the limited photon flux at 3rd generation synchrotron sources and the relatively long

readout time of area CCD detectors.

In contrast to today’s x-ray sources single-pass free-electron lasers based on self-amplified

spontaneous emission (SASE) will provide uniquely intense, coherent, polarized, short-pulse

radiation in the X-ray regime. At the European XFEL, for example, up to 3000 pulses will be

delivered with a temporal spacing of 200 ns between each pulse and an overall repetition rate of

10 Hz [3]. This peculiar time structure of SASE-based sources excludes the classical sequential

way of measuring intensity autocorrelation functions with arbitrary lag times ! . Therefore a

different scheme based on a split-pulse technique has been proposed [4]. The concept of this

technique is to split each x-ray pulse into two equal-intensity pulses separated in time, but

propagating along the same path. The time separation is achieved via a delay path similar

to delay line units used in optical laser technology (see Fig. 1). The scattering from the two

pulses will then be collected during the same exposure on an area detector making ultrafast

time resolution of area detectors unnecessary. Instead an analysis of the speckle contrast of the

recorded image as a function of the delay time yields direct information about the intermediate

scattering function of the sample.

Here we show with the help of coherent X-ray data taken at a 3rd generation synchrotron

(C) 2009 OSA 5 January 2009 / Vol. 17, No. 1 / OPTICS EXPRESS 56

#101144 - $15.00 USD Received 5 Sep 2008; revised 14 Nov 2008; accepted 17 Nov 2008; published 22 Dec 2008

Measuring temporal speckle correlations

at ultrafast x-ray sources

C. Gutt1!, L.-M. Stadler1, A. Duri1, T. Autenrieth1, O. Leupold1, Y.

Chushkin2, G. Grubel1

1Hasylab at DESY, Notkestrasse 85, D-22603 Hamburg, Germany,

2European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex, France

Corresponding author: christian.gutt@desy.de

Abstract: We present a new method to extract the intermediate scatte-

ring function from series of coherent diffraction patterns taken with 2D

detectors. Our approach is based on analyzing speckle patterns in terms of

photon statistics. We show that the information obtained is equivalent to the

conventional technique of calculating the intensity autocorrelation function.

Our approach represents a route for correlation spectroscopy on ultrafast

timescales at X-ray free-electron laser sources.

© 2008 Optical Society of America

OCIS codes: (320.7100)Ultrafast measurements; (300.6480) Spectroscopy, speckle;

(140.2600) Free-electron lasers (FELs)

Measuring temporal speckle correlations

at ultrafast x-ray sources

C. Gutt1!, L.-M. Stadler1, A. Duri1, T. Autenrieth1, O. Leupold1, Y.

Chushkin2, G. Grubel1

1Hasylab at DESY, Notkestrasse 85, D-22603 Hamburg, Germany,

2European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex, France

Corresponding author: christian.gutt@desy.de

Abstract: We present a new method to extract the intermediate scatte-

ring function from series of coherent diffraction patterns taken with 2D

detectors. Our approach is based on analyzing speckle patterns in terms of

photon statistics. We show that the information obtained is equivalent to the

conventional technique of calculating the intensity autocorrelation function.

Our approach represents a route for correlation spectroscopy on ultrafast

timescales at X-ray free-electron laser sources.

© 2008 Optical Society of America

OCIS codes: (320.7100)Ultrafast measurements; (300.6480) Spectroscopy, speckle;

(140.2600) Free-electron lasers (FELs)

References and links

1. J. Goodman, Statistical Optics, (John Wiley & Sons, New York, 1985).

2. G. Grubel and F. Zontone, ”Correlation spectroscopy with coherent X-rays,” J. Alloys Compd. 362, 3-11 (2004).

3. M. Altarelli, Editor, XFEL: Technical Design Report 2006, DESY 2006-097.

4. G. Grubel, G. B. Stephenson, C. Gutt, H. Sinn, T. Tschentscher, ”XPCS at the European X-ray free electron laser

facility,” Nucl. Instrum. Methods. B 262, 357-367 (2007).

5. P. K. Dixon and D. J. Durian, ”Speckle Visibility Spectroscopy and Variable Granular Fluidization,”

Phys. Rev. Lett. 90, 184302 (2003).

6. S. Streit-Nierobisch, C. Gutt, M. Paulus, M. Tolan, ”Cooling rate dependence of the glass transition at free

surfaces,” Phys. Rev. B 77, 041410 (R) (2008).

7. T. Seydel, A. Madsen, M. Sprung, M. Tolan, G. Grubel, ”Setup for in situ surface investigations of the liquid/glass

transition with coherent x rays,” Rev. Sci. Instrum. 74, 4033-4040 (2003).

8. D. Lumma, L.B. Lurio, S. G. J. Mochrie, and M. Sutton, ”Area detector based photon correlation in the regime

of short data batches: Data reduction for dynamic x-ray scattering,” Rev. Sci. Instrum. 71, 3274-3289 (2000).

1. Introduction

Complex dynamics on nanometer length scales is an omnipresent phenomenon which is inves-

tigated at the frontier of condensed matter research. Many systems display dynamic features

on ultra-fast time scales and nanometer length scales. Systems of interest range from domain

switching in correlated electron materials, crystalline phase transitions, magnetic dynamics,

protein folding towards glassy non-equilibrium dynamics. As the time scales involved range

from femtoseconds to seconds the method of choice to investigate the dynamic features is X-

ray photon correlation spectroscopy (XPCS) using ultrafast X-ray sources.

XPCS utilizes a coherent X-ray beam to illuminate a disordered sample which results in a

speckle pattern in direct relation to the sample’s exact electron density distribution. Fluctuations

within the sample cause this speckle pattern to fluctuate accordingly and the measured quantity

(C) 2009 OSA 5 January 2009 / Vol. 17, No. 1 / OPTICS EXPRESS 55

#101144 - $15.00 USD Received 5 Sep 2008; revised 14 Nov 2008; accepted 17 Nov 2008; published 22 Dec 2008

33

/4234

Speckle Visibility Spectroscopy5

0

2

0

2

0

2

0

2

0 256 512 768 1024

I i/<I>

pixel number, i

T = 2x10-5

s

T = 2x10-4

s

T = 2x10-3

s

T = 2x10-2

s

FIG. 3: Intensity vs pixel number, ie the profile of the specklepattern in the plane of the CCD camera, for the same colloidalsuspension and optical configuration as in Figure 1. The expo-sure durations T di!er by successive factors of ten, as labelled.Since the speckles change with time, as shown in Fig. 2, theirvisibility is smaller for longer exposures. This is the essenceof SVS.

tocorrelation function g1(!). A subsequent connectionwith scattering site dynamics can then be made as perusual DLS practice in either single- or multiple scatteringlimits.

Before carrying out the theoretical aspects of this pro-gram, we note that our method is not without precedent.Perhaps the first is a calculation [36] and experimentalverification [37] of the distribution for the photocurrentas measured by one detector as a function of integra-tion time. Another precedent is “laser-speckle photog-raphy” [29], in which the blurring of speckle in a laser-illuminated scene is taken as a signature of motion [6, 7].The latter is now being applied to cerebral blood flow,in particular [38, 39, 40, 41]. One aspect of our con-tribution here is to simplify and generalize the work ofRefs. [36], and to correct a mistake in the widely-citedwork of Ref. [29].

A. Variance

The variance of intensity across the pixels is a sim-ple way to quantify the visibility of the speckle patternformed at the imaging array. For a given exposure, eachpixel reports a signal that is proportional to the totalnumber of photons it receives. Thus the signal at pixel iis proportional to the time-average of the intensity traceIi(t):

Si,T =

! T

0Ii(t

!)dt!/T, (4)

where t = 0 defines the beginning of the exposure and Tis the duration of the exposure. The data returned by thecamera, for a single exposure, consists of the set {Si,T }where the index i ranges from 1 to the total number N of

pixels. All quantities of interest are to be computed fromthe N members of this set. For example the nth-momentof the distribution of pixel signals is

!In"T =N

"

i=1

(Si,T )n/N, (5)

where the subscript T is a reminder that the result de-pends on the exposure duration. Note that these mo-ments represent an ensemble average over pixels for afixed time interval.

To compute the variance we focus on the first two mo-ments of the signal distribution. The first moment issimply the average intensity, !I" =

#Ni=1 Si,T /N , which

is independent of the exposure duration. The second mo-ment is the average over pixels of the quantity

(Si,T )2 =

! T

0

! T

0Ii(t

!)Ii(t!!)dt!dt!!/T 2. (6)

Since this is an ensemble average, the Siegert relationEq. (3) may be invoked: !Ii(t!)Ii(t!!)" = !I"2{1+"[g1(t!#t!!)]2}, giving an intermediate result for the second mo-ment as

!I2"T = !I"2! T

0

! T

0{1 + "[g1(t

! # t!!)]2}dt!dt!!/T 2. (7)

The first term in the integral is one; the second term canbe reduced to a single integral by recognizing that g1(t)is usually an even function. We now define a normalizedvariance, and finish the calculation:

V2(T ) $1

"

$

!I2"T /!I"2 # 1%

,

=

! T

0

! T

0[g1(t

! # t!!)]2dt!dt!!/T 2,

=

! T

02(1 # t/T )[g1(t)]

2dt/T. (8)

This is the fundamental equation of SVS. The top line isa definition; it quantifies speckle visibility on a scale of0#1 in terms of the first two moments of the distributionof pixel signal data, {Si,T }, returned for a given exposureof duration T . The middle line is an intermediate stepthat holds even if g1(t) is not even. The bottom line iswhere contact usually is to be made between measure-ment and the underlying normalized electric field auto-correlation. Evidently the variance is a weighted-averageof [g1(t)]2 over the exposure interval 0 < t < T , withheavier weighting for shorter t. This weighting reflectsthe distribution of possible time di!erences within an ex-posure.

B. Higher-Order Moments

The distribution of pixel signals is typically skewed to-ward higher values, as seen for example in Fig. 3; there-fore, it is not Gaussian and cannot be fully specified by

5

0

2

0

2

0

2

0

2

0 256 512 768 1024

I i/<I>

pixel number, i

T = 2x10-5

s

T = 2x10-4

s

T = 2x10-3

s

T = 2x10-2

s

FIG. 3: Intensity vs pixel number, ie the profile of the specklepattern in the plane of the CCD camera, for the same colloidalsuspension and optical configuration as in Figure 1. The expo-sure durations T di!er by successive factors of ten, as labelled.Since the speckles change with time, as shown in Fig. 2, theirvisibility is smaller for longer exposures. This is the essenceof SVS.

tocorrelation function g1(!). A subsequent connectionwith scattering site dynamics can then be made as perusual DLS practice in either single- or multiple scatteringlimits.

Before carrying out the theoretical aspects of this pro-gram, we note that our method is not without precedent.Perhaps the first is a calculation [36] and experimentalverification [37] of the distribution for the photocurrentas measured by one detector as a function of integra-tion time. Another precedent is “laser-speckle photog-raphy” [29], in which the blurring of speckle in a laser-illuminated scene is taken as a signature of motion [6, 7].The latter is now being applied to cerebral blood flow,in particular [38, 39, 40, 41]. One aspect of our con-tribution here is to simplify and generalize the work ofRefs. [36], and to correct a mistake in the widely-citedwork of Ref. [29].

A. Variance

The variance of intensity across the pixels is a sim-ple way to quantify the visibility of the speckle patternformed at the imaging array. For a given exposure, eachpixel reports a signal that is proportional to the totalnumber of photons it receives. Thus the signal at pixel iis proportional to the time-average of the intensity traceIi(t):

Si,T =

! T

0Ii(t

!)dt!/T, (4)

where t = 0 defines the beginning of the exposure and Tis the duration of the exposure. The data returned by thecamera, for a single exposure, consists of the set {Si,T }where the index i ranges from 1 to the total number N of

pixels. All quantities of interest are to be computed fromthe N members of this set. For example the nth-momentof the distribution of pixel signals is

!In"T =N

"

i=1

(Si,T )n/N, (5)

where the subscript T is a reminder that the result de-pends on the exposure duration. Note that these mo-ments represent an ensemble average over pixels for afixed time interval.

To compute the variance we focus on the first two mo-ments of the signal distribution. The first moment issimply the average intensity, !I" =

#Ni=1 Si,T /N , which

is independent of the exposure duration. The second mo-ment is the average over pixels of the quantity

(Si,T )2 =

! T

0

! T

0Ii(t

!)Ii(t!!)dt!dt!!/T 2. (6)

Since this is an ensemble average, the Siegert relationEq. (3) may be invoked: !Ii(t!)Ii(t!!)" = !I"2{1+"[g1(t!#t!!)]2}, giving an intermediate result for the second mo-ment as

!I2"T = !I"2! T

0

! T

0{1 + "[g1(t

! # t!!)]2}dt!dt!!/T 2. (7)

The first term in the integral is one; the second term canbe reduced to a single integral by recognizing that g1(t)is usually an even function. We now define a normalizedvariance, and finish the calculation:

V2(T ) $1

"

$

!I2"T /!I"2 # 1%

,

=

! T

0

! T

0[g1(t

! # t!!)]2dt!dt!!/T 2,

=

! T

02(1 # t/T )[g1(t)]

2dt/T. (8)

This is the fundamental equation of SVS. The top line isa definition; it quantifies speckle visibility on a scale of0#1 in terms of the first two moments of the distributionof pixel signal data, {Si,T }, returned for a given exposureof duration T . The middle line is an intermediate stepthat holds even if g1(t) is not even. The bottom line iswhere contact usually is to be made between measure-ment and the underlying normalized electric field auto-correlation. Evidently the variance is a weighted-averageof [g1(t)]2 over the exposure interval 0 < t < T , withheavier weighting for shorter t. This weighting reflectsthe distribution of possible time di!erences within an ex-posure.

B. Higher-Order Moments

The distribution of pixel signals is typically skewed to-ward higher values, as seen for example in Fig. 3; there-fore, it is not Gaussian and cannot be fully specified by

検出器の露光時間を変える --> Visibility が変わるERL と組み合わせることでマイクロ秒領域の XPCS

Phys. Rev. Lett. 90, 184302 (2003).Rev. Sci. Instrum. 76, 093110 (2005)

D. J. Durian et al.,

/42

XPCS の位置づけ

10-1 100 101 102 103 104 105

101 100 10-1 10-2 10-3 10-4 10-5

r/nm

q/nm-1

100

103

10-6

10-9

10-12

10-15

10-3

X-ray Photon Correlation Spectroscopy

Light Scattering

BrillouinRaman

Photon Correlation

Inelastic X-ray Scattering

NSENeutron Scattering

WAXS SAXS USAXS

BS

"cold"

TOF

E /eV

t/s

100

10-3

10-6

10-9

10-12

10-15

35

次世代光源で狙う領域

/42

Microbeam SAXS

! scanning --> structural heterogeneity

! time-resolved measurement --> local structural development

36

! = 2d sin " : Bragg’s law

Scanning microbeam SAXS/WAXS => inhomogeneity in hierarchical structure

Time-resolved SAXS/WAXS => development of hierarchical structure

SAXS/WAXS => hierarchical structure

Polarization Optical Microscope

(POM)

Small-Angle X-ray Scattering

(SAXS)Wide-Angle X-ray Scattering

(WAXS)

crystalline

non-crystalline

Molecular packing

0.1 ~ 1 nm

Lamella

1~100 nmSpherulite

1 ~ 10 µm

高分子球晶の偏光顕微鏡像

200 µm

Microbeam SAXS/WAXS: distribution of nano- & subnano-structure

/42

Microbeam SAXS に必要なスペック

sample

x-ray (1 Å) 2$

transmitted x-ray

scattered x-ray

detector

scattering vector:

安全係数

X線ビーム発散

X線ビームサイズ＠試料

cf. 10 pm!rad @ ERL

マイクロビーム小角X線散乱で要求されるX線ビームのエミッタンス

37

/42

通常ビームでの 測定に必要なスペック

sample

x-ray (1 Å) 2$

transmitted x-ray

scattered x-ray

detector

scattering vector:

安全係数

X線ビーム発散

X線ビームサイズ＠検出器

cf. 3 nm!rad @ SPring-8 ID

通常ビームでの小角X線散乱で要求されるX線ビームのエミッタンス

38

/42

PF

SPring-8

エミッタンスでの比較（イメージ）

USAXS測定

XPCS測定・マイクロビーム SAXS 測定

通常の SAXS 測定

ERL

39

/42

まとめ

• ソフトマターの時空間階層構造• 非晶・不均一・非対称性• 膨大な未開拓領域• 次世代光源を用いた展開• 実空間の可視化（位相回復）• 広い階層構造を１つのビームラインで測定• XPCS の時間領域の拡大（短時間測定が可能）• マイクロビーム SAXS の時分割測定・走査測定のハイスループット化

40

/4241

t/s

10-12

10-9

10-6

10-3

100

103

10-15

側鎖運動

主鎖運動

マクロ相分離

ミクロ相分離合成高分子絡み合い効果

セグメント運動

生体高分子ものと生き物のクロスオーバー

膜細胞

生物

10010-110-2 101 102 103 104 105 106 107

r/nm

100101102 10-1 10-2 10-3 10-4 10-5 10-6 10-7

s/nm-1

電子顕微鏡

10-3

10-6

10-9

10-12

10-15

E/eV

（多体中の）単分子 分子集合体 相分離構造 vs 組織構造

10-0

X線トモグラフィー共焦点レーザー顕微鏡

レオメーター

動的光散乱

核磁気共鳴

/42

XPCS の位置づけ

10-1 100 101 102 103 104 105

101 100 10-1 10-2 10-3 10-4 10-5

r/nm

q/nm-1

100

103

10-6

10-9

10-12

10-15

10-3

X-ray Photon Correlation Spectroscopy

Light Scattering

BrillouinRaman

Photon Correlation

Inelastic X-ray Scattering

NSENeutron Scattering

WAXS SAXS USAXS

BS

"cold"

TOF

E /eV

t/s

100

10-3

10-6

10-9

10-12

10-15

42

次世代光源で狙う領域