JRR-3

MLF

JRR-3

J-PARC

(3Gev )

(20MW)J-PARC: Japan Proton Accelerator Research ComplexMLF: Materials and Life Science FacilityJAEA: Japan Atomic Energy AgencyJRR-3: Japan Research Reactor No. 3 (1990 - )

2009.7.7

d2

q, 2

d

7Å

40 ~ 800Å

2 0.5° ~ 10°

•

•

•

•

•

•

3

4

experiment

Solid sample Open beam; Iopen(q)

Block beam; IB4C(q)

Sample; Isample(q) Tsample/open

Standard Sample; Istandard(q) Tstandard/open

Liquid sample Cell; Icell(q) Tcell/open

Solvent; Isolvent(q) Tsolvent/open

Open beam; Iopen(q)

Block beam; IB4C(q)

Sample; Isample(q) Tsample/open

Standard Sample; Istandard(q) Tstandard/open

From left to right: Open, Sample, cell, D2O, B4C

1 cm

6

I q( ) =1

TSample/Open

I Sample q( ) IB4C q( )[ ] IOpen q( ) IB4C q( )[ ]

I q( ) =1

TSample/Open

ISample q( ) IB4C q( )[ ]1

TCell/Open

ICell q( ) IB4C q( )[ ]

TA/BはAのBに対する透過率、 IA(q)はA(=Sample, cell, B4C, Open beam)の散乱強度である。 B4Cはガンマ線や宇宙線、装置の電気的ノイズなどの バックグラウンド散乱を測るための試料である。 また、絶対強度に換算するために、標準試料の散乱強度を 測る必要がある。SANS-Uの場合、ポリエチレン標準試料(Lupolen)を用いて、 ILupolen(q)を測定している。 したがって、試料の他に最低３つ（液体試料では４つ）の測定を 行わなければならない。

= +a xy b

X

a

x

b

-(CH2-CH)200-(CH2-CH)400-

O

Et

O

O

Me

O

pEOVE-pMOVE

T 17 °C; T 20 °C;

d

dI q( ) = ( )

2nV

2P(q)S(q)

nN

V

9

P(q)2J1(qRsin )

qRsin

sin(qHcos )

qHcos

= 0

2

2

sin d

2R

2H

P(q) = 2qR( ), qR( ) =

3 sin qR( ) qR cos qR( )[ ]qR( )

3

Rg

2R

1

6. ( X )

7.

8.

10

11

R = rn

n=1

N

R2

= rn

rm

m=1

N

n=1

N

=

Na2

...

N2a

2

P R,N( ) =3

2 Na2

3 / 2

exp3R

2

2Na2

rn

rm

=nm

R2

= Na2

N;

a;

R

3

R

12

R G =1

NR

n

n=1

N

Rg

2 =1

NR

nR

G( )2

n=1

N

Rg

2 1

2N2

Rm

Rn( )

2

m=1

N

n=1

N

(N >> 1)

Rn

Rm( )

2n m b

2

Rg

2 =a

2

2N2

n m

m=1

N

n=1

N

=Na

2

2x

2dx0

1

=Na

2

6

Rg

2=

Na2

6Rg

2=

3

5R

2 R

13

gn r( ) = r R m R n( ){ }m=1

N

g r( ) =1

Ngn r( )

n=1

N

=1

Nr R m R n( ){ }

m=1

N

n=1

N

g q( ) = dreiq r

g r( ) =1

Nexp iq Rm Rn( )[ ]

m=1

N

n=1

N

exp iq Rm Rn( )[ ] = dreiq r 3

2 n m a2

3 / 2

exp3r

2

2 n m a2

= exp iq Rn Rm( )[ ]

= exp1

2q

2Rn Rm( )

= exp

m n

6a

2q

2

g q( ) =1

Nexp iq Rm Rn( )[ ]

mn

=1

Nexp

m n

6a

2q

2

mn

= NgD qRg( )2

gD qRg( )2

gD x( ) =

2

x2

ex 1+ x( )

gD q( ) =N 1 q

2Rg

2/3( ), qRg <<1

2N /q2Rg

2, qRg >>1

gD x( ) =2N

x2

ex

1+ x( ), x Rg

2q

2

q = 0

PD (q) =gD x( )

N=

2

x2

ex

1+ x( ), x Rg2q

2

m n

PD q( ) =11

3Rg

2q

2 + ...

14

I (q) = ( )2v2 NPD (q)

N; v2;

;

dPEG = 1.129 [g/cm3]

PEG = 6.39 x 109 [cm-2] (NIST Table)dD2O =1.10 [g/cm3]

D2O = 6.36 x 1010 [cm-2] (NIST Table)mD2O = 20 [g/mol]mPEG = 44.05 [g/mol]b = 11 [Å] (Rubinstein’s book)Mw = 20,000 [g/mol]N = 454.03<Rg

2> =Nb2/6 = 9156.27 [Å2]

( )2

=b

PEG

dPEG

bD2O

dD2O

2

vPEG = VPEG/NA = 6.48 x 10-23 [cm3]

I(0) =(6.39x109 - 6.36x1010)2 x 6.48x10-23

x 0.01 x 454 x 1 = 0.9629 [cm-1]

(PEG)

1%I(0) 1cm-3.

N

sc 0.52bcc 0.68fcc 0.74

, *,

overlap

(<< 1%)

I (q) = ( )2v2 NP(q)S q( ) =

( )2v2 NP q( )

1+ vex /v1( ) NP q( )

S q( ) = 1vex

v1

NP q( )[ ] +

vex

v1

2

NP q( )[ ]2

vex

v1

3

NP q( )[ ]3

+ ... =1

1+ vex /v1( ) NP q( )

vex; v1;

v1

v1

16

b2v

1/v

2b

1( )2

NAc

I q( )m2=

1

zmPD q( )+

NAvex

m2

c

=1

MPD q( )+ 2A

2c

A2

=N

Av

ex

2m2

=N

Aa

3

2m2

1 2( )

b2v

1/v

2b1( )

2NAc

I q( )m2=

1

M1+

1

3Rg

2q

2 + ...

+ 2A

2c

(Zimm equation)

m; , NA; , vex; , M; , c;b2; b1

PD(q);

X

17

g r( ) ~1

rexp

r

E

I q( ) =I 0( )

1+E

2

q2

Ornstein-Zernike

18

I(q) =bD bH( )

2

v0

(1 )NPD (q)

=bD bH( )

2NA

ˆ v 0

(1 )NPD (q)

I(q = 0) = (106.63 1013

[cm]) (23.34 1013

[cm]){ }2

0.52 6.022x10

23

100[cm3]

1000

=104.4[cm1]

: 50/50 N = 1000)

P(q) = PD,11(q) = PD,22

(q) = PD,12(q)

PD(q)

19

( )2

v0I q( )=

1

vA A NA PD q;NA( )+

1

vB B NB PD q;NB( )2

v0

v0

vAv

B

H2O

D2O

I(q) = (C S

)2S

CC(q)

+ (P S

)2S

PP(q)

+ 2(C S

)(P S

)SCP

(q)

3

SCC(q), SPP(q)

21

I(q) = (C S

)2S

CC(q)

+ (P S

)2S

PP(q)

+ 2(C S

)(P S

)SCP

(q)

SCC

(q), SPP

(q)

Sij q( ) = nV2P(q)S(q)

10x10-6

8

6

4

2

0

scat

tering length

densi

ty /

Å-2

43210

D2O

H2O

NIPA

clay

I(q) = P S ( P S )2SPP

I(q) = P S ( P S )2SPP + C S ( C S )

2SCC

+ 2 P C ( P S )( C S )SPC

(C), (P), (S) Sij ;

S=

C

H 2O:

D2O= 0.34 : 0.66if

Mix

(SCC, SPP).

i

10-3

10-2

10-1

100

101

I(q)

/ cm

-1

5 6 7 8 9

10-2

2 3 4 5 6 7 8 9

10-1

2

q /Å -1

fD2O

0 %

25 %

50 %

66 %

80 %

100 %

in H2O

in D2O

16

14

12

10

8

6

4

2

0

I(0

) /

cm

-1

100806040200

fD2O / vol%

fD2O,min

68.4 % (obsd.)66.0 % (cald.)

Clay4Contrastmatched

I(0) = C S C S fD2O( ){ }2

SCC(0)

C C S fD2O( ){ }2V

SCC

SPP

SWW

SCW

SPWSCP

Self Terms ;

Cross Terms ;

, Sii

, Sij

SCP

NC

I(q) = (C S

)2S

CC(q)

+ (P S

)2S

PP(q)

+ 2(C S

)(P S

)SCP

(q)

I1(q)

I2(q)

I3(q)

1.

0.01

0.1

1

10

I(q)

/ cm

-1

7 8 90.01

2 3 4 5 6 7 8 90.1

q / Å-1

D2O = 0 D2O = 0.56 D2O = 0.66 D2O = 0.76 D2O = 1.0

NC1-M0.4

0.01

0.1

1

10

I(q)

/ cm

-1

7 8 90.01

2 3 4 5 6 7 8 90.1

q / Å-1

D2O = 0 D2O = 0.56 D2O = 0.66 D2O = 0.76 D2O = 1.0 reconstructed

NC1-M0.4

3.

1 C

2

1 P

2

21 C 1 P

2 C

2

2 P

2

22 C 2 P

3 C

2

3 P

2

23 C 3 P

1

=

SCC

(q)

SPP

(q)

SCP

(q)

2. I(q) Sij(q)(singular value decomposition)3. ; Sij(q)

10-24

10-23

10-22

10-21

Sij

/ cm

3

7 8 90.01

2 3 4 5 6 7 8 90.1

q / Å-1

self-term SCC(q) SPP(q)

cross-term SCP(q)

NC1-M0.4

Clay-polymer has strong correlation.

Fpl(q) = ( pl pn )Fcyl plFcyl

Fcyl = 2Vsin(qH cos )

qH cos

J1(qRsin )

qRsin

SCC(q) =NC

2Fcyl

2sin d

= 0

SCP(q) =NC

2FcylFplsin d

= 0

SPP(q) =NC

2Fpl

2sin d

= 0+

S0(0)

1+2q

2

2H R

SCC NC

SCC

10-24

10-23

10-22

10-21

10-20

Sij /

cm3

7 8 90.01

2 3 4 5 6 7 8 90.1

q / Å-1

Scc fit_Scc

NC

SCP RP, HP, and pl

SCP

7 8 90.01

2 3 4 5 6 7 8 90.1

q / Å-1

Scp fit_Scp

NC, RP, HP, pl

SPP

SPP

7 8 90.01

2 3 4 5 6 7 8 90.1

q / Å-1

Spp fit_Spp polymer layer of Spp network polymer of Spp

Interaction

20Å

455Å

Water = 0.75

Water = 0.95

= 164Å10Å40Å

380Å

300Å

164Å

D70 8m_ = 5

D70 8m_ = 7

D70 8m_ = 9

=

5

=

7

=

9

Mechanical properties of NC15800

600

400

200

0

Str

ess

/ kP

a

12108642

Stretching Ratio,

NC15N=182

NC2

NC4

NC6

800

600

400

200

0

Str

ess

/ kP

a

12108642

Stretching Ratio,

NC15N=182

NC2

NC4

NC6

800

600

400

200

0

Str

ess

/ kP

a

12108642

Stretching Ratio,

NC15N=182

NC2

NC4

NC6

total=

0+ =

E

3L

1{( 1) / Z}

Scc

Sww

Scw

Spw

Scp

Spp

Macromolecules, 40, 4287 (2007).

Macromolecules, 41, 5406 (2008).

In preparation.

2Scc

Spp

Scp

Biomaromolecules, 8, 693 (2007).

d

dI q( ) = ( )

2nV

2P(q)S(q)

nN

V

•

•

•

33

34

b bmolecule

= rib

atom,i

i

bbenzene = 6bH + 6bC

= 6 ( 3.739 1013

) + 6 (6.646 1013

)

= 17.442 1013

cm[ ]

http://www.ncnr.nist.gov/resources/n-lengths/

C6H6

35http://www.ncnr.nist.gov/resources/sldcalc.html

http://www.ncnr.nist.gov/resources/n-lengths/

Iinc

=HI

inc,H

0+

DI

inc,D

0

HI

inc,H

0

Iinc = Iobs q( ) Itheory q( )

TItr

I0

= exp tot t( )

d

d

inc

=1

4

1 T

Tt

透過率 T

非干渉性散乱強度, (d /d )inc

J. Appl. Cryst., in press.