J-PARC MLF JRR-3shibayama.issp.u-tokyo.ac.jp/BioSoftDownload/file/2_Shi...JRR-3 MLF JRR-3 J-PARC...
Transcript of J-PARC MLF JRR-3shibayama.issp.u-tokyo.ac.jp/BioSoftDownload/file/2_Shi...JRR-3 MLF JRR-3 J-PARC...
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.