/ JP9611322
KEK Proceedings 95-13 February 1996 M
KEK-PROC—95-13 JP9611322 — 9 7 *- 9 's 3 "j 7°
Proceedings of the Workshop on Small Angle Scattering Data Analysis - Micelle related topics -
December 13-14, 1995 KEK, Tsukuba, Japan
C/jX i" oto r Nto j' O r-
edited by T. Yamaguchi, M. Furusaka and T.Otomo
NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS National Laboratory for High Energy Physics, 1996
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Technical Information & Library National Laboratory for High Energy Physics 1-1 Oho, Tsukuba-shi Ibaraki-ken, 305 JAPAN
Phone: 0298-64-5136 Telex: 3652-534 (Domestic) (0)3652-534 (International) Fax: 0298-64-4604 Cable: KEK OHO E-mail: [email protected] (Internet Address) 'hftmir- 9 Ilf7 - 9 '> 3 y 7” < f-
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13 0 (*) • 7-^73 'y7 (^A) 3 WINK T- (#%#) 12 WINK ^e%Am (m#) 24 SAN (D$ft^^r-9 rn^7 A (Sj£) 37 Small-Angle X-ray Scattering Data Analysis Program (SAXS) (0A) 48 14 0 (A) ¥H*&A (£XA) 84 • ##fy7 /d^7A 0-/(0 ver 1.0 XEB%A (£XA) 96 (g^MA) 105 rr> h yx h h" • WINK COFJ A^:#^& (KEK) 147 • KENS/J'^tfcSL^S^^tCOV'f *K)M (KEK) 152 itirMA LliPic^ TEL:092-87 1 -663 lext6224, FAX:092-865-6030, E-mail: YAM AGUCH @ SUNSP1 .SC.FUKUOKA-U. AC. JP ke^ib]) ^A • a [email protected] ¥B £xa • [email protected] urn fm^A • a yamaguchi@ sunsp 1 .sc.fukuoka-u.ac.jp n b f@MA ■ a 4-# X$ mA • m» [email protected] suzuya @ schnee. tokai.j aeri.go.j p m^a#A•ax [email protected] TfelS ##A • x [email protected] % BA [email protected] H PAX sea •ax [email protected] fgRI fmMA • a SB • a SB ^XA • X mgA KEK [email protected] AA KEK otomo @ kekvax.kek.jp 7 — ir '> a 7 7°C0±bB itS4 (KEK) — 1 — SAN/WINK Workshop Workshop ’C't'o $A,sm o 1. < -t IV (~IM13$ L tz Analysis % b° 7 $ t* 9 LTV>* 3^ f o LtzbKT# 3 fr =$7 4 77 ’J -it 2. Wink 5-E? t- (i k" 9 L£ t i *Hard Ware Low-angle > Mid-angle > High-angle *Soft Ware Data reduction> Data analysis 3. S AN/Reflectometer 1996 # 10 M 1-lWT * h"<7) beam line ! ~ *h"A^ST' install "t* b) 5 ^PX7JI-V3 c) 3?l:fll*JU5K>l» 9H3 ^12^25" N-0 ^12^25" SO4" Na+ ch 3 dodecyldimethylamine oxide sodium dodecyl sulfate (C12DAO) (SDS) total concentration Ct = 80 raM mole fraction X = [SDS]/([Ci2DAO]+[SDS]) NaCl concentration Cs = 0, 50 mM l(Q) O N) G) small-angle neutron scattering intensity l(Q) = np[ particle scattering factor for prolate ellipsoid - pj +(p, - Cj = CizDAO/SDS = S2((a + P2 + (£+ ^)2(l - P2))2 o in o 80 H = cos 6 [/c = 2(aVJ + tJ(l-nf mM, sin X - X cos X J,(X)-3x C s : O, OmM; interparticle structure factor mixtures a rescaled mean spherical approximation (RMSA) by Hansen and Hayter [Molec. Phys. 46, 651 (1982)] , • ° ro co 50mM g(r) = 1 + (1/12* nr)io"[S(Q)-l]QrsinQrdQ g(r) - 1 = h(r) = c(r) + npR3 $ h( I r-r' I )c(r')dr' c(r) = -V(r)/kBT r>R h(r) = -1 rS R V(r) = re £q s Rz*o zexp[-x (r-R)]/r r>R V(r) = °° r5R rho = zm/ it £p £ R(2 + k R) C TABLE 1 12 1—' o o o o o o O O | DAO X o CO ■sj on £> w fO I—* 1 II: 1 and 1 1 Parameters o o o o o o O o SDS the L_i phase in a 1 in un crv C\ ON in In ON 1 VO o o »-• VO VO O 1 dodecyldimethylamine oxide (C^DAO) U» o «0 ro U1 N) CO 1 in /hexanol/water ternary system 1 the H- u* h-* H i—• 1 CO CO CO CD CD 00 CO CO O' > Obtained 1 Absence in in in in in in in in in 1 C-C12DAO ~ 20, 50 mM 2 1 X = [hexanol]/([Ci DAO]+[hexanol]) >-* H-* u* to ro ro ro H* M (a 1 N “ 0, 0.29, 0.44 U in in w w vo cr of o o in o GO •o o in in from 1 NaCl. 1 1 SANS in in in ON in in in in vo i-* u ON o CD CD in M I 1 > Q M «o ON O *o vo ON 1 1 Analysis 1 H-* »-* M H t-» 1 VO w in vo -O -J 3 CO CJ w vo in vo 4* CD O 1 1 1 for o o o o o O O o O 1 o o o o o O O o O 1 cj tO ro to ro to to to ro U> 1 Mixed -O vo CO CO •o CO CO vo o • ON -o ,5. ■o w «o in •O 1 TEM of Li phase in 1 Solutions CO -O •o CN ON O n ON o “ 1 SOmMC-^DAO/hexanol *-* CD to VO *o vo VO w to 1 (X=0.29)/water. bar=200nm. I / 1 1 o O o O o o o O I N M f*—i O o o o o of ro o CO 'O •o CO ON »—1 1 o in vo in l 3 I(Q} (cm-!) 100 0.1 100 0.1 100 0.1 ’ 10 10 0 1 1 V 1 b R R No C p 0 i m m n q n s . : n : : : : : the the the the the 0.005 the •' polydisperse R %) the g 1(0.) x=0.44 , x-0.29 volume sum radius n minimum coherent molar -(3/5)R -^SiNCbm radius = 0.01 Q} of ^ of concentration the (A-2) of C of n N of 0.015 neutron aggregation N(b monomer coherent gyration N-mer - m spherical p - s [C p V 0.02 s scattering m V sphere 12 ) m of 2 in neutron exp(-R^Q. of f DAO] exp(-Rg N-mer number a - 0.025 N-mer particle 7 - particle length scattering 2 particle N /5) particle Q. = 2 / 3) 50 density system length mM of (3) ( ( 2 1 ) ) the of R a 100 solvent n 5(8) monomer (A) x=0.29 x=0.44 2: 150 | 200 2 solvent, | ' scattering the respectively function values dcos0 1/2 and neutron ')] axes, Intensity QRg Q /3) 0 2 2 equation) Bessel Q 2 -* 2 ~1 P(Q) small G cos x particle p (3ji(u)/u) - n at at 1 x)/x S(Q) coherent Guinier semiminor particle (1 = So the Factor 2 - a at (a b exp(-R | fl cos spherical Scattering 2 > and of of '+ 2 ) x 2 System 1 ) s | fl mean )/5 s - 2 = 2 gyration x particles 2b solution /3 of F(Q) the 2 cos + (p-p volume I (p-p (sin density 2 2 2 : Structure first-order < semimajor 2 Neutron V = (a p dilute V : s 3Ji(x)/x n 4rtab Q[a radius total p = a = = b the = = = respectively 2 i(x) g length : u Ellipsoidal V for j the R the and Monodisperse and : P(Q) : P(Q) l(Q) a g V a p R ji(x) Prolate for Intraparticle Small-angle CH=CH-COOI-I dioctadecyldimethylammonium chloride (2C18DAC) Rigid rod particles QP(Q) = 7t V At (0-0 s)2 [2ji(QRt)/QRt]z V — LAt = ft Rt2L QP(Q) = ;t V At (0- 0 s)2 exp(-RG,c2Q2/2) Rg.c = RtAT2 at small QRq.c values Lamellar layers with a periodic multilamellar At ; an area of the transversal cross-section of rod structure of infinitely extended bilayers Rt : radius of the transversal cross-section L : length of a cylindrical structure L > Rt Q2P(Q) = (27t/np) (t2/D)( p - p s)2[sin(Qt/2)/(Qt/2)]2 D = tV* = 27t/Qmax Rq,c : the radius of gyration for the transversal cross-section Q2P(Q) = (2zt/np) (t2/D)(p- 0S)2 exp(-RGiC2Q2) Rg,c = t//" 12 at small QRg.c values Vesicles with a unilamellar spherical shell t : the width of the scattering length density profile D : the repeat distance of the bilayers P(Q) = (0-0 s)2 [3V0j1(QRo)/QRo - 3VJ1(QRi)/QRi] t' : the bilayer thickness, that is, the width Vj = 4«R,3/3 of the mass-density profile, t' ^ t V0 = 47tR03/3 : the volume fraction of the component molecules ax : the first-order Bragg peak position Q2 P(Q) - ?7t(A/V)(0-0s)2(Ro - Ri)2 c : the radius of gyration of the thickness t Rg2 = 3(Ro5 - RiS)/5(Ro3 - Rj3) V = V0 - Vj A = 47t(Ro2 + Rj2) at the large QRq values Ri and R@ : inner and outer radii, respectively Vj and V0 : volumes of spheres with radii Rj and R0, respectively Ci2DAO/cinnamic Q?I(QJ 1(0) (cm') 0.003 0.003 0.002 0.001 0.002 0.001 0 0 0.05 0.05 Q. 0.1 0.(A-1> Q. 0.1 (A-1 (A-1) ) acid/water X X = 0.15 X 0.15 = 0.29 = 0.5 0 0.2 0.2 (cm1 ' ) I(Q) (cm1) - CieDAO/cinnamic 0.003 0.002 0.001 0 0 0.05 Q 0.1 Q. — Q.(A-i) (A-i) 0.1 (A-1 rrnin acid/water ) X X X - - 0.15 - 0.31 0.17 0.5 0.2 0.2 C^DAO/cinnamic acid/water CieDAO/cinnamic acid/water X = 0 30A ■■ 53" 58A lamellar layer ellipsoidal micelle 50A X = 0.2 Si Si 44 A <------> 104A rodlike micelle ellipsoidal micelle <0m> -30A or 35-36 A multilamellar vesicle multilamellar vesicle — 11 — • WINK t'- 9 (###) -12- PET 88°C Annealing Process WINK measurement 30min 2 min 60min 10 min J__l l 1 Mil J_l l i_U 11 0.01 0.1 1 10 Q/A' -13- Intensity 0.01 i PET i i i 0.1 11 WINK 88°C 360 240 Q/A' 120 — Annealing measurement 14 min min min — 1 Process 720 1310 min min 10 wn W/i (l /4. Qmit* Qewui f IQ 3 0.0106 0.1696 0.0270 0.4314 10 4 0.0132 0.2107 smzso.o'i 0.5038 10 5 0.0180 0.2517 #m#o °yj o.576i {106 0.0200 0.2927 0=6405 °-°l 0.6483 007 0.0240 0.3337 0.0450 o.oj 0.7202 10 8 0.0270 0.3746 0.0495 0.7919 0 9 0.0234 0.3764 0.0540 0.8634 0 10 0.0234 0.3764 (fc©584 oj e’ 0.9346 "IX 11 0.0183 0.2927 0=8270 oA 0.4314 1 IX 12 0.0209 0.3337 o.o'i 0.5038 .lx 13 0.0234 0.3746 6=6966 0.5761 0 14 0.0 0.0 0.0000 10.0000 [10 15 0.0183 0.2927 0.0000 10.0000 hoi6 0.0209 0.3337 0.0000 10.0000 ll 0 17 0.0234 0.3746 0.0000 10.0000 0 18 0.0 0.0 0.0000 10.0000 f Ox 19 0.0270 0.4314 0.0270 0.4314 1 0 20 8=8955 ' -<’r 0.5038 0.0315 0,5038 1 o 21 -6=6360 o.of> 0.5761 0.0360 0.5761 7 Oo 22 6=6465 o.o^o.6483 0.0405 0.6483 \ IQ 23 0t6450 °-otr0.7202 0.0450 0.7202 1 Q 24 0:649 5 0.7919 0.0495 0.7919 1 p 25 #6540 ^,0 0.8634 0.0540 0.8634 ;0 X26 0.0584 0.9346 0.0584 0.9346 A o 27 0.0270 0.4314 0.0270 0.4314 1 o 28 0,6315 ojds- 0.5038 0.0315 o.diy 0.5038 1 o 29 0.0360 o,e>£ 0.5761 0.0360 °yis 0.5761 1 o 30 0.0405 »x»7 0.6483 0.0405 0.6483 1 ° 31 0.0450 o.oH0.7202 0.0450 0.7202 0 X32 0.0495 0.7919 6=6495 °x°7r 0.7919 10 33 0.0540 0.8634 #6340 0.8634 1 o 34 0.0584 o.ofl 0.9346 #6584°. ^0.9346 1 o 35 0.0270 ".or 0.4314 0.0978 1.5644 1 o 36 0.0315 osi 0.5038 &&66oJ> 1.7048 1 o 37 0.0360 ^0.5761 6rM52 ®sT 1.8432 0 X38 0.0405 0.6483 0.1233 1.9796 0 x39 0.0450 0.7202 6^462-1 2.1138 0 X40 0.0495 0.7919 0.0000 10.0000 0 x41 0.0540 0.8634 0.0000 10.0000 [0 x 42 0.0584 0.9346 0.0000 10.0000 0 x 43 0.0270 0.4314 6=646-Ko 4.330 0X44 0.0315 0.5038 #430 lx^ 5.372 1 0 45 06330ostr 0.5761 #521 o.7 7.131 0 X 46 0.0405 0.6483 97657 0-7 8.207 1 0 47 06456 o^y>0.7202 07739 9.233 lo 48 0.0495 ©.^0.7919 0.818 10.228 Ox 49 0.0540 0.8634 M98 14.981 1°50 979584 ojO 0.9346 0.0 10.0 H - U'M 7 'K '• Ti xv/v/v Y h/t^j D-PET 2750min Annealed at 88°C WINK ; 2.5 HIT - 1.5 3 j_i_i—_ i i i i i i i i 0/A" D-PET 2750min Annealed at 88°C WINK HIT i i i i ml 0.01 0.1 1 10 0/A" — 16 — AlW/dQ • L I(«> /t T J r/t 1. &a. A . I(Q) iTMOWitJ* /tat* C c«wn£ fi ) 4 A. dtfoob 1* q/IZA, r t# tjUfoctr *> e ditbcfcn* A - Aa*»- (cm1) t- ' S+njd* Tf)Tck-*4*4 few ) "T T T -- • +ff c- f - (5"a, : a.L5orptf»n qro&f sec-tw^ ^ '- : $ct.iien«j I(Q ) *• “1 -Tl *) ^ 1 4f $, TcC grp -17- Se-Ce* ihiy $V*a lio) MWr ctr Ts_ JiJf(o) Altai/cHQ 1 M«f d -T ~u ^■s(p ) Me****^ l*t TCxt'ty /f" S-rtu-J+d $at»f>)e *tS As 1 7 ft ic-le-nser t>jr SrarJ^d P**'fJ e' Ts : TrMfw;sri,i o/- 5* •ian*lm( &* **&£■ StOrA&d * A./ V»u^ -18- I). ])yu*£ . *H e. counter /U ^ i; 2. -A ) Van^ftm C ''-'b""< ,c (Tt.k 01** (M* (b*r*s ) v <\oi 7 4.7? 4.?7 » multiple S'catfch’i*^ ^ ^ o sur-f^cc Scattering ( Surface to volume ratio 1 1(8) -- I.M («/r‘)W?»)/Jal'T *1 ZCQ)/ol& * f<% /f^ (* f ticr,/^)) ^ °f-uA <1 ( 0.1 < t < l.pt» ) ^ -t ^.y: K j&r i% Kt 5 »fle i* i t . ^ "tl°A * a? (in *a-> f°it-W(-fn,t) 1 Ur,- ^6f-foit; [ Z- ty(-fcr>t)] -19- ' b ) y*sa~te tr ( in coherent -Ir** H } 07 AC C kxrnJ ) H U75T* 79.7 £>..? $ I(Q) = £l,/l »8.U 7 * *ff (-P <-t < 2»» Ifqv I, *££ Lu-rV^l^ g : -cfitet *i A| cIas-D'c- je* 5'u> -- (/- -w^ ^ 2-c.) M*neel>sf>ir'sc *z fQ;/7^2 - Xp XH )2//2^/>f q ) P(Q ) ' f*rtn {a&t,r eff P/r[jrtUT M*Ue»le. Table 2. Measurement of KN = el0Aa for 2 5 cm diameter slit Calibration technique/standard Ks = zl0da Water using g = 15 838 Vanadium single crystal (t = 0-44 cm)* 867 Partially labeled polystyrene using 893 GPC values for 2 Partially labeled polystyrene using 846 RJMl!1 = 0-21 A g* ,/2 AI-5 using dl(0)/dn= 175 cm"1 826f * Corrected for multiple scattering (7-8%) via equation (9). f Independent calibration via density measurements and vanadium; see Hendricks el al. (1974), Fig. 5. -20- jl'tfuyizmLT .^I_. Tr = 5.73X10 V LL= D“ dQ D : Tr: b 7 > X i y 's 3 > .«L. . - D Tr dQ &sWf5o y-'y'?Jl(D D • -^2- • Tr \% " t*LL 2 tL u ymmm$ ts Ll yl/^ly>CDS-DggS Ls ib>X;u©s-Dgiit j!2_= dQ D • Tr ^[U(i Poly(styrene-h 8 ) Poly(styrene-d 8 ) 1 X = 6.4 A , S-DSg# = 8 m , t: - AIM X = 8 mm 0 background £dI^> 1 II#Pet!^7c <9 ©^Oy h Liz ( Figure 1 ) q > 0.01(A -21- Figure 1 Luporen <1 >=5.606 40x1 0 2 Polystyrene CD$IJ/£ X = 6.4 A, S-DggH = 8 m , tf- AIM X = 5 mm 0 background t 31 ^ > 1 Fel^j/c <9 Guinier PlotUM ( Figure 2 ) Guinier fitting [HisSANS (96.7A) 6UT:t#:L/c^ (97 .2A) Polystyrene (Rg=97A) ln=5.59 Guinier plot a 5.5 - 5.0 - 4.5 — 140x10 -22- <11>= 5.61 tUO, oeim, S-DPmtlyl'^ Xf-U y^iZ 1 B#E> 8m TfrZ)(D T =D • -i- -Tr = ^k IC-eft-eflftAUT D ■ lo" "Tr= 700 1q~ =109 (cm") tfc&o -^2- = x (l-x) (aH - aD)2 NA——— Mw dS2 Mm2 X Poly(styrene-dg)(Z)#:#^# aH> aD styrcnc-hyStyrcnc-dgOf&S'LJx: Na T^’Kd E Pp ■t/ t—IfI'fitD^ypjS Mw ^ V '7 — (Dfr-f-M Poly(styrene-dg)®{$#^}# 0.50 < #&### #) H#\ D#:ty-7-®#gLmC^M^2.34xl0^10.7x Mw = 112000 6% (% (125000)66 610.6%omi^# c m -r-m u-cua^E^-cmuo ^±0j: 9 c, a c 6c -23- • WINKf'-f ## (WM) — 24 — unit ru M a -, ^ m S 5 [U a )4 3| dim 4-J 5 ti- y> CN I K? j> m 1? V IS £ y «/ -> i* AD E * i X) WS y % a. T$ I# * A AJ t\ * tK R 1C Ll. I W S\ Jl I )T\ f 1 iN < I A\ *AJ s -A ,\ 5t v S X 1 m K I ,X » fe{ w -A ■H & ^ % Ha "f § 53 Sw' w K> & A Q r< 4A O £ S A m % )A q y a ir\ 6 W § *A t_ if £ S' I 4\ | if 4\ -R -26- ( 3 - 1 £.1 ) 'K K MI s (A, d) K? 0 c< v> CD JO c< CD O h — 1 m m i # i •w 5 CO Q 0 o j I Aj K? z -H ✓—s +4 m \o 4£ -28- line ffcglU f <5) %5'^r^A_ /•S+'J^A £\i, Z (3-8) Wo IfrU H20«I±s WL<0 3 0 D , Hmf li |$Wz»#$t!mSLm£%tt*tv\, ttz, mmmma \t bound atom KtttZ>i> 'C* D x bound atom cross section l±s A&f^t/i/f— ttffttt’bo-CV'i, oi 0, (3-9) Lt5'<), COi 9 ot < * [2] 0 Lfc^-C, (3-5) ~ (3-7) 4H2OJCJ: SAN LTV' 3 Z 0 tB V'l 6 AtTOTf'BW i n k frv*t b ti*„ tZ?, Wink VH 2 0 t&m LM * m o A 6 « j K> -o 4 5 -•*! -R z$ E # i i ) 0 E 0 AJ I - -V o AJ o «j fO CO K? K? £ (3 +* cd YU P 4 m t u Q 00 sc -: it ■>p YU AJ CL & i£> * ni I I tx >J H e 0 o * FT 0 Y@ 0 H l # -H *o O +4 P a AJ ('P H- 5a < K? „/ AJ •H l 1 S& 4 W & 5 Stf -K % -B- 5a K? m n a j , 4Q H- 3$$ i j £8 « ► 4 y • % Tr fc -' WS i Y@ o 1?C AJ - . ^ P K -H as ■^r'Tm * J _.I["(^1_ 45> v AJ • 4 CN -J p y -R i4 * ■tfO 31_1 J3 O H ^4: l Sf ted H-1 * . 6 W m 5a 4M t C m ■b- X & 4* H < 8i “ o o u ■a- «R ■s U_ (X) YU T -M 4&\ H |# r Q 0 A Tr u s jrt A K? *2 O • k < O ia Q .iA \ ( I ^ M l >> tf a> 5a -O K O CM II ih = H CM V' *N = r$ CO Q •R X « K? T X *to o u H »H ■w AJ X o O V CM I u. CM u >J •*H 5 X IF it r 5 -30- -31- zvRvtmfrbommjs. 0-3) 0-6) rvi i\z&mt s JJ K> h(? 1 ) m r m — 4 m Co 1 — 1 -32- % ■K- > co CO to 53 in ■R ■D 4\ ■H ifl!i «a y YU £ $5 » e B -»e ,\ 1 y I 0 j J u ■« m « E -XJ 5a 4$ co * I 1 1 0 j o s ig ei iM AJ $* •y ft B a jj O' X3 m r~ II 1 X > CD a •o X*4ic-sin6 Messung des differcnticlicn Wirkungsquerschnittes 431 U/ . was fiir g = t bis in zweiter Ordnung von (E — E0)/E0 korrekt ist, so ergibt sich nach Integration iiber Q (r ^ (6) <3*. Der Faktor (1 — £) korrigiert bezuglich der Vielfach-Streuung. > o Streuwinkd ■& Fig. 4 {>.:'• t=> Fig. 3 und 4. DifferentieUer Streuquerschnitt von H,0 fiir verschiedene EinfaUsenergicn E, und Proben- temperaturen T in Einbeiten von o,/4 n (Streuwinkelverteilung). Der fiir die Wasserkurven in die Figur eingetragene statistische MeQfehler "gilt aiich fiir die iibrigen Kurven T" • Mit solchen Transmissionsversuchen gewinnt man keine sehr genaue Aussage iiber das logarithmische Energiedekrement. Das hat drei I') r-- -33- I( A ) (arbitrary units) 1E+2 Oq W I MI ------= » “• » IB O 5 * #'Ll » * * at a -H 35 K B I Sl. =» •• B , pi (5 » ss at a. DH W \T a ' *7 it t& M S * iff > i.*W Ml' » 2 0 w % r> a -B- * at ... o> m 4< H ^ * 6 8- °t> toi/o»cv) o o CD HWf»T*-(A) it 2 tu# ? e * *v 16 A Io> I# o x^** e--<611 ^ to % ittL. (WitiV-lj n$ I l&ft iY>,») = ® h^Hl- < #r*tK^ ri* . ^^0 k": * %y t3 WWvk 4»A <— VV check I >%& tho, %Z -35- tA ■» e. + w L iL * s*. comA16*^' w>/™-e) - IgCa,w)] de,«fw L slASti'c i — -36- • SAN dSrLv^T-^ -37- 1, SAN (Small-Angle Neutron Scattering Instrument) O time-of-flight (TOP) type small-angle neutron scattering instrument O O wave length of utilized neutron : 3-11 A —p | ^ \2-A -fO covered Q range : 0.006 ^ Q ^ 0.4 A'1 lm pos. : 0.02 ^ Q ^ 0.4 A'1 3~pos. : 0.01 ^ Q ^ 0.2 A": 5m pos. : 0.006 ^ Q ^ 0.1 A1 O sample position from a moderator : 19 m O 2D detector : consist of 32 lD-PSDs of 1/2 inch, in diameter. O spatial resolution : 10" x 12v mm2 CeU Metkwof Straight Ovids Tube Dent Guide Ct vinlng n*cJ 1 Dlmcnstond Tube Solkr Sill Jeitcten EXfccio# Tell Cutler Simple foilde* Sewering w# Chamber wg B—0- * ‘"1 0J« 9.4m m -3 m- ”11 m- ol Cwemlng Fixed Simple rwhlee 3 Olmcnilenil Sewering Seller SIU Dtiepers Deswer Owebv SAN !Lojr®iiil PoYfftOh* -38- O data acquisition is carried out by mac + VME O position : 8b:t (max : 256 ch) O time : ]%%bit (max : 65536 ch) /£ igl#'p<>^w x 1*** so PSDOr-fCDffitl D-KI *(D/(A + D))-K2 FIFO> v tieK't'o l’) 'VME CPU SCSI \ X Macinioshll or VAXstation -39- total I (X,9) = I0(X) Ss-ts-p ,~jjf (X,0)T rsa) Ai3 del-,? (X)del ■!-/fla9)-Tr,a) 1 total (-*, 0) *9> 9- 3 /<)(■*) S. ‘s Ps da s d£2 (A, 0) 7>/A) K# (B.G. Sr-g-tf) del P (A )d=t 3 # 9 y /8 (A, 6») /< 9 y KiJ' b 1 rs\A) = / 0(A ) S ,-f , p (A, e ) AC2 d„ 77 (A )dM bt£%>. —40— ttz, TkhzMLX 1 wjotal a,e) a, 8) (A,0) water T r„a,jx) B_water (3) ds = / 0(^ >S water'* water P water~^?L 0 ) ^ del7! U )dct (2), (3) 5% J: %, do s dQ a,e) ^ 5 ^ ) *-* water'7 water P water dO water I water (^> @ ^ j'P j (4) dQ (A,0) water (X, #) = tvafer = COHJf dQ 4^ (5) iot, r*K dcr 7 * 0- sin ‘ (%F )) ^(6) dQ water 7 water P water dX (6) water 7 sin"' (|^ )) S s'* s'P s 4;r ^mln —41 — 3.1.a 7jc ^ ^ a, m& "C li Jacrot \Z X.%> @8^^ (C g(A) = [l- exp(-0.6-Au0.5'5)]m-1 1 wjotal (A, ^ ) ^ r.^XA) 1 I water (^’ ^ ) D water (h & ) 1 “ T rlw,„(A) g0 1) -• / o(A )-S water ^ water AQ dct' )dct 1 4 n-t water tmztiz. z?>-£*R}\,'Tm®-comL&i£zm&'iki-z>t d(J ' , n „ x ^ 5 (^» 9 ) ^ water t water 1 (K9) = dQ /wc/A,*) 4*-f water b%2>. -42- READ rawdata ( DetectorNo, PosCh, TimeCh ) • Radial Average & b & rawdata ( DetectorNo, PosCh, TimeCh) , {32 x 64 x 50) I_S ( Radial_Index, TimeCh ) , {128 x 50} I_BG (Radial_Index, TimeCh) , {128 x 50} - Normalizing factor 2D ditector S_Norm = Sample_trs x S_Monitor BG_Norm = BG_trs x BG_Monitor • BG component (DM I ^ Srad (Radial_Index, TimeCh) = I_S (Radial_Index, TimeCh) I_BG (Radial_Index, TimeCh) S_Norm BG_Norm —43 — • 7jWT- ^ KM LX i) IsJSt- LT, Wrad (Radial_Index, TimeCh) = I_W (Radial_Index, TimeCh) IJBG (Radial_Index, TimeCh) W Norm BGNorm • ^ KM' 1 Tch_sum (Radial_Index ) = 22 Wrad (Radial_Index, TimeCh) TimeCh Rad_sum (TimeCh) = 2) Wrad (Rad_Index, TimeCh) Rad index Rad_sum (t) Tch_sum (r) tel tc2 tc3 Tch sum (Rad Index) x Rad sum (TimeCh) Wrad (Rad_Index, TimeCh) = 22 Tch_sum (Radjkdex) Rad_index —44— • StftOtfcgLSSjS Srad 17jC(7)fi$L^S Wrad CD jfc%7$Ub& Srad (Rad_Index, TimeCh) —► Srad (QJndex, TimeCh) Wrad { RadJfadex, TimeCh) —► Wrad (QJndex, TimeCh) Srad (QJndex, TimeCh) Sq (QJndex, TimeCh) Wrad (QJndex, TimeCh) I (Q_index) = X Sq (Q_index, TimeCh) TimeCh T b ivrv^v' 0#62;Mi & S £>& tz *b K £M & Z. t (bTIS) • EIt<0fi.vvJc<7)T-9 ("TIB?) i ©M$v1k -45- 3,4 t®# ®7jc(D7- SAN 7- ^S#7"D ^7*7 A (0{M rawdata ( DetectorNo, PosCh, TimeCh ) , {32x64x50} V I_S ( Q_index, 0_index, TimeCh) , {100 x 1 x 50} OJctcoJtfc t ■ detector efficiency OWTEffi'j&W • incident beam monitor cOiSS^-SIE/i^jil'lE m#T # 3. • y--)Vi:y $ -Z> £ i: tc J; <0 , PfiMW range <7) $j!: £ 'SHte K ffi V' 3> i # 3 (i CO 7"n ^ 7 A Tii, TimeChW V7, ^ 7 7 d- [ran, cm,a.- p ] Vti"11- 4. 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T-"'9 t ^"4 52;' it. @4 iSl •K-M * &. => 6=v,'C i-fctU-zuSr-* 7 fe4,emr^ It'* a 4iA jfeHU*/ 4.1 —♦ 6e*tic 2-»i ^ 1= L -7 •?. • 'ixtXM&wiHSl** A 'frltj| (4, Z*'5 $ ^XZ-CT»Za J V -49- • <&& a 8MH t"c7 £T. • dleWc^bv^ a Jhd&L°i "^,L^ tt- a A& • aigoUc ^4ev.G»4y ! • 4$RK5tefc*.B 4feflr^ PpUs ^Uc I V — 50— ( y ) x o o o Ol Ol ro bo O co O Trans -i — L i. l _L n > >> V Trans. % a i s J o Trans. pO _L 00 (D -L Ll K) X a (A) Small -Angle X-ray Scattering Data Analysis Program SAXS Version 1.8 User's Guide l % 11 Polymer Engineering Laboratory, Department of Industrial Chemistry, College of Science and Technology, Nihon University 1994 —54— 1 s in ztitffltnvMt)-?$>%>. ttz, K*)x7i:V7 h oTE¥S-eti#x.^tL^v^J:d^E Mmt'<£f%ffliz£fzt\,'z.2>. i-cr, xffii/hftmmmzj: *)&c>tifzr-? tz. 2$ Cfl$?(7)W* ##nm^Tv^ya/7A(SAxs)(i, ?FM-8 ri?2$A£*i£0#K, FB ASICT # ^ fb ^ (D f ^ t V —64KB, MSEIi^EteH >^FDD, 6(:cfL, ow:(i^^i;-64KB-e(imi9^< imtz Z t-?%A,tfrW'9mi& ZttfXZ tz. f <9#, FM-16P<7)#AK#v^ CP/M±COFBASIC (m%, S±ii-eCP/M£^SOS£ LTWc) , £ b MMS-DOS <7)ME'T>E-<7)FBASICHSS£ti£. ^ to -64KB##W'W;t MtitZti, 1 ^/D Vy At LXjt*V-±.lZV- KL i&Bt&Z t im&ttii'itz. itz, ^E-^-<7)MJ$^|6]±tU: 9 r- & /c. Cco^ATBASIC Cornpiler^emf 6 C 7 h ^x.r^M<7)m^X>fztb, m±m%#3> t: ^ f (7)## -55- ^EMttEPC-9801 W4'>iTS:^K)te £twc. a lotvH'ii^, z:<7)n> tijl-snrWz. t Step scan, PSPC<7) n y h n - ju# £ Xfr- f &a fc. C r- * ###(7X$# ±*cff * 9 %tz. mjj, oTv'fc*'; 7 hMiE^y^-y^;vrj'yh-jL -* Jb^mf U£#>Zzll#$Tyn/yA S&tiFORTRANTS^ftTV'Z:Z: *S!l^bXA-xtcS1f-t^^ f Olft li MS-FORTRAN Compiler(Version 3.2)$: f 6 ^ ^ Z: C: b (: Z 6. M®, *SIfg$S (HITAC M-200H)T5#(5 ^LZr (#r, m###3yat7 4Ze^#f. m& Tfi, 32kT7 h#/<-yf;i/3y , PC-9801FA(804871£ffl )T &mo& #l&(Z)/<-y y;i/n y ST, mijtizmtt, ±.B ££#&< &^Zj. FBASICbN88 BASIC^(i|W] CBASICSEb tiv^x., M, #i:Zn y y < y y_hTFBASICt:: \th%> SYMBOL/^N88 BASKX& V'<7MC (i tafrtafr^Z^tziitz (Ztilt, PC-9801 T(7)#m^oT # b % c Z:. *lt*) , iIIN88 B ASIC Compiler £ t TM&tttfi* frbii T ^ . n±^', y n y y asaxsogz'MTh'o , c#mfm##i04mT*a. — 56 — 3S y □ 9 —7"; b'?'/>£PC-9800's1J—Xt L, MS-DOS± l-c/o^a^^^toztizL/z. %m~± ♦S&ILilLSrfTofc. fit, &c7)2o<7)^£+£;£T£. (1) & (2) & v y > |§ £ tti # t" S Compiler £ fig JE t £ C(02o(0^tl:owT, f L $:i>MM3b2> ^ ^<01<01#A^fL6. fit, Iv^oT 3 v> KMf i i: t: l/:. ##0*6^%#, nv> ijiuc#^ i tiim&t & <7) t fflft lr^&. (2) N88 BASIC Compiler"C(d;Run Time Library£'J&Ic t L, Compiler ffct, ?-.t wm v^(0(0-j^%^m§ (C,Pascal,FORTRAN55: ^) ffU3 L'##(0-r- ^ £#o <0"C(d:^v4:-^d:, X 9 vVif> o . #Mf 6me^)##(iC, FORTRAN<502ff$f£ # x. £. &M Z-h, FORTRAN £ t £ Ztiz Lfz. Ztilt, *7n V 7 A&T- Zt^o&ni., #tc/x- K'>JiTCOW<7)^E(d:^ -57- &£, /£■/□ ?7 A (iGENIES 3 V y K#cM£## RUTHERFORD APPLETON LABORATORY*? ffi&ZtitzisAf&'Cib* ), TOP t - * tcffl ftT V' 3. i£, MKENS t: S A $ tiSS L T -58- 4S 7n?'7A©t7 4-1 -fe 7 h 7 7 7pny9ASAXS<7)-fe7 h ^ LIT (7)50697 7-f $fLTw3C 1. SAXS.EXE ya^9AT# 2. SAXSINI.INI ya f 9 A ^%#69%m#m^7 7 ^ 3. HELVE.FON ya ^7A^T#Mt6 7 ^ 7 h 7 7 4^)1/ 4. GICOPY.COM — K 7 kf—^ cot. — 9 -f - 5. SAXS.BAT SAXS ####/< 7 T 7 7 ^ -tr 7 h 7 7 yfi, ±m0 7 7 -f 7 L"-f 6 mtTf. tztzL, SAXSINI.INI t HELVB.FON& Yy^fA SAXS.EXE , GICOPY.COM, SAXS.BATO/^Xfg^^^fo X&lflft'vr'T h V t-f. 4-2 3ffl±(7)$IJE Z -XX^-XiH£9, 512#^ T69T-f^AT7"T#Tf. —59 — 4-3 4m##m##SAXSINI.INI (V X h 1) t&MLT >K 5*rgte7 ,7*;H'<7)K7d'7\ 7f ;iz Y -7-^-^^X. 1 OM#%##;%?4^1/. 1 l^fitiY#(7)7^>f;v, l 2^ffiti ^*7 7»0/’j7 K<7)E^, 1 3tfSt±Xj»^&g|£5eS:fi:oTV'i’t. i 1-c7)-c, tc b-ti tl r r fijffl< Zf$v\ VX H (SeWB#(DSAXSINI. INI<7)1*3 W) 1: ! SAXS startup command file. 2: ! 3: ! 1994.3.17 by S.Shimizu 4: ! 5: set disk b: 6: set directory ¥ 7: set x "q (1/A)" 8: set y "I(q)" 9: set marker 4 10: toggle x linear 11: toggle y linear 12: set grid off 11: set lambda 1.54 4-4 ^(D^u'fyA ZWjfrtfc f±, MS-DOS & %SAXS b* 4 7'1*S /ilfet. ztuy-f h<7)SAXS> — 60— Lfzfr? ztiT, . znvmitzi'vy zvvtm?, 5$ 03 vy KV 77 U^fctBffcStiTV'Snvv KOA^^hE£ * <9 St. y o y y h 2 K& (±, yn /7 tit v\ SAXSINI.INI * £ ^ it HELVB.FON^- hy^f 1/^ h V -t:#£l&v\ 4 - 5 fO# %^o/<-ya yeti, y?7^ y ^o/\- Fnk°-(7)^-T^ VT-f-^y^v- ±tcSB$-ti-rv^t. HfrSfflti, " h7K3'^i-^iJf MS-DOSS^ynyy < yy$i# PC-9801 y 7 7 -r 7 y y • yn y 7 ^ yy ” , (cqmm) #7$e# BSLT -61- 5S =17>K‘J77t/>^ SAXST#mf 6 n:ov'T#W&&frV'2f. i-f, &n-?y 6#K, — tt. (1) #37>KPi, ^ -? tt^ya y : <> ffy 3 y^y*-*7 : { } (2) 37>ni, «r# &mb~LZt. M) DISPLAY Display : A;£ ^ D B&S. (3) A^(i, (4) z^r's F£s*7*-?<7)%.W*)lt£&'Ct. AT^*££KL£1\ -62- 5.1 DISPLAY Display A Wn : n#i<7)7-^x^-x. marker : % 1i «h v- * -<7)^co^jS(iJ^T<7)® <9 -Ct. m # 1 2 3 4 5 6 7 8 9 •7 — j] — O • □ ■ + X 0 • Line color : v-^-cofe^r^i-e^^Li-f. 1^7 i-ecoM'CA* Lit. # # 1 2 3 4 5 6 7 A w v7> v-tfy ? n 6 marker £ color v-# 1, 7# (8A) L, Z. —63— 5.2 EXIT EXit SAXS SAXSZfcJt2>fztb<7)n-?y K£ IT, QuitkfflSWzLi Uz. nv'y KA#£LTIi, C: —64— 5,3 FUNCTION FUNctionA<7 r > 7 v a >^>A«d/Vn1>A«d/Vn2> 7 h tc*tS Ltz, T-? L27. 77'/^y3'4: t t. GUinier In I(q) - q2 CROss : mmm*>£&2>tzib In (I(q)*q) - q2 KRAtky : ^77^“-fuy . I(q)*q 2 - q LORentzian ! n — vyyfuy bffl(DT'— 9 Lt 'f. 1/I(q) - q2 PORod : zh°n- K7"n 7 b f8<7)f*- ? I(q)*q 4 - q4 DEBye : 07 t'fBo-F-f&mKLaf. 1/Vl(q) - q2 Wn, : Wn2 : t, A*T :,-^<7)7-^X^-Xtc±S^ Li t. —65— 5.4 LIMITS Limits / x# (#) y# («) x : x# (#) y : y# (») Xfoiftte. xmin : x#<7)#/T#. xmax : x#<^)#±#. xstep : x m&m . ymin : y ymax : ytt xstep.ystepco xstep=10,ystep=5 f. **£A,. 1.0, 1., 1,0.1, .1,1E10, iE-io#-et. —66— 5.5 LOAD LOad A 7-77^-X n IZ-r-fZ n- Ftz. Wn : (n(iEM5rEt) filename: n-Kt^7 7^fH. 7 7T;H5t;t, K7 T 7*, 77 h V t*7 * ;v he^-ir y YZtitt. &£t7*;1/ Mg <7)^3E^ov^Tti, SETn vy K<7)Jg£#B6 LT < Zf£v\ £(7)3-7 7 KT(iJ^T<7) 3 M <0 <7)A*S^:^nt- 1. LO 7 - 7 7^-7 t 7 7 T )V% V'17rtl<7)^/a‘(C & , A—7(7)3 — Fffi]E1%hZfft>tlfzi§'ultZl£, Data successfully read mAn#^ a LT Photon Factory BL-IOC^^&t^ 3 \zLtLtz. ^7)#^-, 3-77Ffy73> LO/PF A -67- 5.6 MULTIPLOT MUltiplotad A '*7 * -68- 5.7 PLOT Plot A 7~7 7^-7 *77 yC^T^Ltt. £c7)r7v> KtiDISPLAYnvy F?m& l fz?7 7izzt>bzr-7* l tz Wn : n&g marker : -<%>##. lfrbgw&mxAJjLit. % ffi-hv-* *) X't. % # 1 2 3 4 5 6 7 8 9 v — jj — O • □ ■ + X o • Line color : i & & 7 a uif. m#a^-rf. m # 1 2 3 4 5 6 7 A ft m i/7> n 6 markers colorsSQ& 2, f <^A(± 7# (6A) <9 if. -69- 5.8 SAVE SAVe A 7n Wn : /<-;%. (n filename: n - Kt^7r^^. Fy'fr, n is? *i37'7*;uMiS tf>£5Lfcov'-n±, SETn v> KcOJi^rSMLT < Zf£v\ :«37> K-e(imT<7) 3 a»? Ztiit. 1. SAV £ iOS^'CA^J $ (i, 7-77^-7 ilSn^lb d: LT, Macintosh±<7)Excel,KaleidaGrapIrCy — 7 6 «t ? iz Lt Ltz. ZtiZftilZlt, u^y K*7°V3 yt LT7MAC£*t5£LT:T£v\ #) SAV/MAC A ft Jo, Macintosh# "C li Apple File Exchange £ LTT 5 v\ -70- 5.9 SET SETADIRAcrV V9 h v%> ADISKA : 1/7 h V . PyTX& : Bico^^cnn y£ XAJj LX < v\ V — ^7 — X I -9- t X{± 4 ^ £> 8 i xvmm&xt. Sf^T Hi/ : 8 0X3=aT#2&2:&9 2f. Sr Lv^co^^fs : " " -eti^AT-T^vx 2 OX^ XV y K : CC&ONHf 6 t, Xy 7^<7)0#tcXV y 3 em u-cv^ A^f & -71- 5.10 SHOW &m SHow A DEFault : T4 U? h'J, #$*?)£ #<7)1$ as, DAta ! f\ Wn^jta^tvrv^Jif^ti, 77^;^, h;i/j3J: X?T-?(D?'1 -fZ&TFLtt. . Cot #, (d:77 Empty , Sffl Lx^xi>7 7 4 Unknown £ L11. -72- 5.11 TOGGLE Toggle A<#^,# > A #%# : X x# (#^[6]) : lin i;r.7x^--;v^co^ LOG uy^'r- 73- 5.12 Wn= IJSl^o# l [U 1. Wn2=Wn1 : 3Lit. 2. Wn3 : Wn3 :\yj = Wr^+1.30 3. Wn3 :1 yj = Wn-| - Wn2 t> # Wn3 : = Wni -5.48 4. Wn3 : j !> = Wn-j * Wn2 Wn3 : iyj = Wn-j * 10.3 5. Wn3 : 1y| = Wni/Wn2 Wn3 : jy | = Wn-,/2.3 Zf$v\ iZ:, EMUS tcttLTti, x £>2>^teyfjZfr<7)\s'tti<0$lftlztfL<7)-iM&fr:£i%feLT < Zi$v\ -74- 5.13 $ MS-DOSoav'/ rtSS37> Kfit^-c^iTortg ’et^, >::-emiso^^37> k** l X £&tt. (1) r-f l/^ DIR, MKDIR, CHDIR, RMDIR (2) 7r^H^37>F COPY, DEL, REN, TYPE DIR tcov^T Z<7)a^y K^ov^Tli, Ztitt. $t:$DIR^A^LX:#^(i, SH DEF TtfZtiZr'f A?, f^n’Jd'tU w*%ifeLtzmtn-^-& iott. 7 7 ^ ^ * i *? n@^ TFLtz^m&Kte, $D\R/PtAt)LX -75- 5.14 MONIOTOR MONitor{ Ft/v a >}A rj-^y Ff7is3's : ZP Z7 7<7)Mil£*Zy hS^E^LSt" ZM Z7 7(0##^M#CB^L^f Z C Compact camera 60 Z — ^ ^OU^^^E Lii" y£AXL&v^^{i, *Z y -=6-^Hll^7 L-Xv^^-ti, m,jj 7 titi*7 7-r;v<7)S^:ti, migv-fuy br-? MONITORn v y K-eE/Z$-£'C < Zi£ v\ 7 - 7 7.^-7±ii 7 7-f Monitor^ ^oTv^B#(i, 7 7 > K r ,b ttctyit. BA&tr ft tz&Jj 7 7 4 U'VjgfcZ-t-f, ?£tc 7 7 ^ ttZ'D fz^iz f±, SAVEavy FWU< Zf$v\ Z77(7)7Z-;i/^M(±, LIMITS7vy p-efiZ T < Z:$v\ Z MON{ 7vy FtZ>a y} A &jo, ^§-7 -7X^-7(7)Z-7 60 7 ^ Z(±, SHOWn^y p-e##Ef 6 C tt. -76- 5.15 RATIO RATIO{ Kf/v3>}A 37>Ft^/3> : ZP y ZM Z77###^M#cm^L^f Z C Compact camera# 7* —$ ^<7)3 vy < £ &, 4f“^^)7 7^^it!U^ IT < £'£v\ Ratio#& 7 7 T Vi/## $ 1". > Ml, ±f. ) . C#Z-f LOADrtvy KTn - KLT& (C#£§#77-f ;i/S^iiScattering t%*) it) , 7 ^ y RATIO7-7y re^/Tc£«< Zr£v\ v-^^^-^±|:77^;i#^ RATIO{ 77'/ KtTZ a y} A -77- 5.16 ROUND Lit. ROUnd{ n-7'y Ftyv3>}A nv'y Ft7ya> : ZP U-slit £B*S:^3eLtt &l u-siitM te L ^ Z ZPC Compact camera^ 7* — 9 -78- 5.17 REFORM ±r- 9 eDESM, POLYDESM##8#f Y a ?7 *%IZ7 * -w REForm { rr v> \?*7v a >}A<£t-9 3v> k *y'> 3> : & L u-siitfflT-f /C Compact camera^ t*— ^ OB# -79- 5.18 MAIN MAin{ 37V^^>3>} A 377^^>3> : ZP MitcE^Lit ZM Z7 7###^M#(:^Lit Z C Compact camera# f— *7 #0tF 7 4 >#& 77^ L£V'«£-f±, 7 7 ^ ^(DKM^W: t & 0 it. atfj7 7^#7££te( ii^#Zn7 it > Mi, >#a&9 it. ) . LOADrrvy K-en- K LX i> (£#L£#7 7 ^^tiScatteringL&i? it) , 7 7 > $Rli AtofiTvit. l/;^t, 77>Kri^«^li, ^t'-^^MAIN 37> < Zf£ v\ 7-^X^-X±(C7 7 Yy ’l'Ss^Mainf &o Zr^rgic l±, SAVEnvy m£fflLT< Zi$v\ Z7 7#X7--;t/^jEii, LIMITSnv> Ktffot < Zi$v\ f ##, E*>t~7 e n 7 hta#^#, MA< V t — Z> ’C7 Pn 7 h Lit. ##7^-7 (^E-^-JWtl-) ^7pn 7 h LZrf&, #[FE-?- MA{ rtvy Kf tv 3 y} A —80 — 5.19 UNIT Unit{ 37'/ Ft yv s >} A Yt~7'SB xu : Q momentum transfer (A) M m-value (|im) D d-spacing (A) T scattering angle (°) P point <7)5 nMtfvSiZ'Cir. & : vU^-j'cWSifctcoviTtj:, 7o77Atlifxy^^ot^i^. I£ofcAtj£?ToT <> *-<7)fi ») fcglfe LT L S V'i t. 1. M ->Q 1 4 ii I) #bTb&-?1-. *i3, ^<0lt, *v< 7g(cm)£B£, pm# f&TA^LTT$V\ —81 — 5.20 @ 7 7 4 £-£3t*. K7r^H> 37y^7 7^f^ili, i(0-7-a7;K:iei$titv^a-7> K£&£> /^£#b£j<&& 7 T'f JW7>£ £ £^L£1". #!l ! test command file for SAXS i ! file name : testcom ! Nov. 3 1994 ! 01:34 ; 1/y 0 le25 l/xOO.2 set x "Q (A)" sety "I(Q) ' set grid on X t*£, %>tifrZtb-3-7y K77f X ? &B# . r?V> K7 7Ji'Vftf&lXJ-f-'j 7 -82- 5.21 TRANSMISSON TRANSmission { nvy KtT'ya >}A<9- > -?)V 37>Kt/V3'/ : U-slW#^-f (t# /C Compact cameraffl T — ^ <£>B# St#^: -9* > 'ffrtoT- f&Xlfyj U? L, -83- (^I±) tScSLSil (di(Q)/dQ) W£l-I0P(Q)S>(Q) /cm"1 (1) l0:0 5i6jE • • • pf0: sm: je^HWjsH? • • - iSMtlitf PJOfiM liiST’S ( S'(Q) =1 ) q^l. IoP(Q) /cm"1 (2) -85- y 6CMC&U#m#mrnol/l] to 6 ; S (a) fdZfQJ/dqjcDQtt^tt^ ff-#'e^^o -86- S 0.8 10 = 1.3689 [cm"1] 3 0.6 -87- (A) head group counter ion hydrocarbon con Stem layer water molecule Schematic micellar model of an ionic micelle for calculation of P(Q) (A) and S(Q) (B). The scattering length density profile corresponding to P(Q) model is also shown. —88 — Prolate : ~7 y Y yl/gJ -» ; -t?;U Oblate: K5 -V*-® -* 5 -fe;U 6 -89- Guinier Region QR « 1 0.0 0.1 0.2 0.3 0.4 Q [A"1] P(Q) vs. Q plots calculated for model a andZ>. Model (A) : prolate ellipsoid a = 29.1, model (B) : oblate ellipsoid a = 21.8 A with b = 10 A, t = 5 A, p s = -0.4 x 10‘6 A'2, pp = 6.0 x 10-6 x -2 p = _0.4 x 10-6 a-2 and ^ = 15 A. -90- Physical Review A, 1985, Vol.32, No.6, 3807-3810 IOI KOI Hee.lBl OCM case MSA case FIG. 3. Comparison of SMSa (Q) and extracted from the same solution with (LDS) —0.312 Mole/L. J. Phys. Chem, 1987, 91, 1535-1541 2* C..OXYS .IT. lit Figure 7. Inlcrmicellar itructurc factor 5(0 extracted from experiment by MSA (□) for the case of 2 g/dL C|,OXYS micellar solution at T *■ 40 *C. The solid line is the fitted 5((2) using one-component macroion theory (OCM).M I1 The charge of OCM is much higher than that of NaC120XYS 2% MSa- 0 ,-C^ J3 X- *H C..OXVS llTa <0*C Figure 8. Same plot as Figure 7 for the case of 4 g/dL. NaC120XYS 4% — 91 — h;L/6D5SS(d:jy £ ft5 o - IqP(Q)S'(Q) /cm"1 (1) CCT/o teoSfcSL3&!S^ ST<2) <*?£>#;£#& & otfca&& c/0) /0 li $ /0 -/lp10"16[(yOp -Pc)Fc +(A -Pp)Fmf /cm-1 (2) zzp . (C - CMC)Na /cm'3 (3) 1000/z TS£ft5o ::t« (i$ c i cmc B5#; T^DStilitmoll-1 ]^ Na itTtfff Kn$rT£>3( 6.022 x 1023 mol"1 )0 vc, vp feck o' vm i*mt7mm ^ 7 n(^head + (^ ~ ^)^ion * -^S"^solvent) pp (5) ^solvent (1-JhK^ +^H-%l2Q A ” (6) ^solvent ^solvent CCT Flajl {± $ Fsolvenl o##. 2»«aii & s t;[/ 3 % a fn, z^head<■ut bion hi>0 a (i = ■teJls®fflm!&ZbD2ot ^nftiD2o^i h20 -92- ;mm ns (iaro^TE $n-5»o v ^p-"kead*(l-«Kn) _ ^s------%------(9 ) n Ksolvent cct Khead £ Kion {i-en^nsBS^^-r ^ s 0 (1) H Kc -y^ 2-n^ajl (10) Mn-Vc+Vp -y(« + 0(*+0 2 (ID (2) H Vz-^-a 2b-nV^ (12) I'm “ Pc "*■ Ip “y(a + 02(* +1) (13) tteZo rpre;; P(Q)te&T (D^TE £ti3< f(0-j^|F(GWl dix (14) ( 3(sin(QR1) -Q^iCOs(Q^i)), „ _ 3(sin(Q^)-g^cos(g^)) f(l2 p) - * (mr r (ctf , (15) (Pp Pc Fc (16) (/^j Pc)K "*"(ft ~Pp)^m c;t n (2 q 11 -t?;i/CD$A6 -93- (1) BH'omm^rmu,b,b x ctztzLa>b ) (m&iiiAp (Prolate) ^ tzMZM LT(;t /?i t R2 it^tl^rtl ^-[aV+i2(l^2)f2 (17) ^-[(a+t) 2v2 + (b + t)2(l-n 2)f2 (18) X^-ULtl (2) ^bTKSEny^fl,a, b X ) SBSJScD@$^r (Ute^A]) T£> 6 /<£ JIFFS Rf£ (oblate) ; tzMZtt LX it Rl-[a 2(l-i?) + b2n 2]12 (19) Rz "[(« +t)2(l-v2) + (b +r)2^2]1/2 (20) tfcfKiilSf (SY0) itzA(sw) imTofixmztiZo S’(0-1+ (HQ, M)[s(Q) -1] (21) bra ^)2| (22) ±5t43CD S(Q)it Hayter b[l,2](r j: T-^X. LtlXtS <0 n ^ Eft Ltz ; MS® ©SmmZfEffl ^IBiZElT 5 Debye6£ffl^Tlf#T££0 a&m t crcDffliamTofflmmviL^o (1) JE:ESRt£ (Prolate) UTti cr-(2(f + lXa+t)(b + t)2j/3 (23) (2) #^FSRi^ (Oblate) L'TJi CT-(2(/ + l)( CCT -94- 1+ (25) '•(aiferLT <=» T* 3 o a £(jf cx=2(a+t) = 2(b +t )T£> 6 „ Debye# (v) 1/2 f 2000NAe2I /m"1 2 (27) \ £0 £r^B^ . ;:txe (1.602 X 10-12 C)^7 ((Wit [mol/1]) It Boltzmann ^lfc( 1.3806 X 10-23 J K-1 )N 7 *9 0 f0 ^ £r &K£.®WWM( 8.854 x lQ-i2 C2 J-i m-i ) / ~ -CMC + -CMC +-a(C- CMC) (2*) 2 2 2 Tf+S$n^o S(Q)®Vc%OMm* Hayter ^[\,2)(DmX^W,o 1. Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 631. 2. Hayter, J. B.; Penforld, J. Mol. Phys. 1981, 42, 109. —95 — • ffitffy 7 h’? ■=■ ■* 7 t 7°a?'y^ <2-/(0 verl.O ¥B (£XA) $^D^7AH0V'tli, 2FB$/l<7)rra:tCJ; >9 KENS FTP server ±.X’<&fflLXt3»)$ ■fo host : 130.87.132.99 ([email protected] ) username: anonymous path: Document @ gojyokai : Users: SANAVINK: -96- Q-I(Q)ver 1.0 COt't Z.®-7u?=rMZ^ ( 1 : 1 EM5I) © SANS (£/cl±SAXS) ©±£Ifc*)Bt'StemJi (®££JB) (StemS^li, ###, ^ &?Z) 6 6mEUT(,'&-f. a -t?Vl/CDSm Prolate (7>y h^'-Vl/#) £ Oblate ( Tfo S&ffili (dZ(Q)/dO)T-e(D#i6(i[ cm-i ]Tf o P(Q)i S(Q){r^f Fig.l K^LT o titmm i. W£&x.2>'*7 / -?%&TlZ7FL£?o 'Th *) £-t qmin : It#t" 5 Q U y'J(D®tb(Dm #f&(i[A-i] -97- qmax : 9m* % '?©*&©!# St£l;t[A-i] qst : ft&*6 2l/>vP©ai**[A-:] vt: mm*[A 3] bt: ^@^^^©-^©^>fb7j ^/b sAxs ©#*fi:mbt, bh, bci i^o^ot^^AnnifttASto 2. mn 7>a7 ,7J*&7£'b-ttZ£MT®'^J-?&mfcM<<'r£lk-t(DVAtlVTTZl' The Average aggregation number : ^ -bVl/©5F:l~JiK'n‘E The degree of ionization of a micelle : S "brvl/©##^ (a) 0 < a < 1 &UaA<0 Please select Micellar shape. Prolate(p) or Oblate(o) (p/o) : S Prolate p > Oblate K £ 0 To A#£Ha*S<£:M£itUT#£-fo ;nT £At)*Z£ This aggregation number is unsuitable for the selected model, because a < b. The minimum aggregation number of the selected model is OO -98- tmw&T-r s t Q-I(Q) Micelle ver 1.0 Micellar Shape is Oblate. Surfactant concentration [mol/1] = 0.04032 The volume fraction of D20 = 1 The average aggregation number of a micelle = 60 The degree of ionization of a micelle = 0.3 Micellar axis a [A] = 17.3417 Micellar axis b [A] = 16.68 Axis ratio a/b = 1.03967 The polar headgroup layer thicness [A] = 5.5 The average neutron scattering length density of hydrocabon chain *10 A6 [A-2] =-0.451171 The average neutron scattering length density of polar layer *10 A6 [A-2] =5.75045 The average neutron scattering length density of solvent *10 A6 [A-2] =6.33565 The averaged hydration unmber per surfactant polar head (Ns) =13.1573 The macroion diameter [A] = 45.2414 The volume fraction of macroion = 0.0189784 The ionic strength of the solution [mol/1] = 0.00717 The Debye-Huckel screening length [A] = 35.7981 The surface potential [mV] = 90.0877 10 [/cm] = 0.985532 Q[/A] P(Q) S'(Q) I(Q)[/cm] 0.005 0.998339682945639 0.0939972696575474 0.0924835417336836 0.01 0.993373280215487 0.1084147781081695 0.1061382296513638 0.015 0.985144247606727 0.1353180861279676 0.1313791817051663 Teach TEXT \Z U hT-l/T\ gjgExcel KB % tttfT -tiXo 7 77;l/& Excel 7fbT# i)i" tab" OT7 text*Cl% ftfl/TTSt'o t>U 7^r Do you want to change fitting parameters ? (y/n)" 0\> -99- * > % # Sl Fi # null M i 5 * vj- 8 pt 35 rv at » © % # (O * r t Mico^tiifx'y^ LtzCt\$&ty£-&/u(D'(:-mft(Dl%.m$L£&/vo /:/;U Debye van der Waals tHZfrt>J$Usb t&Z.Z> m'&iui-ma&Tauo ctztzLmt^8^3^2 2 gc ^mxf, *ti&& i)#u mm%©^i n 7°d ^5 a (c ui < t (itt b u 0 '<>:©■o t& <9 £ for, r^g-sw ^niiriiST^v^o / ¥B #A (Ob7t OZVt) t466 ^^-SSBSfDKSIsBlTinT M#•WfflEES TEL052-732-2111 Ext.5904 (flf%S) FAX 052-735-5247 e-mail [email protected] M# nx (jo^i^u odA^) TEL 052-735-5212 (Eil) FAX 052-735-5247 e-mail [email protected] —101 — ^0^7^^© Debye 'fu /7AtTli^T SI 'TfW UTl ^ CDT\ Debye tztzL £0 = 8.8541878 X10'12 [C2 J'1 nr1] 4'4b\ yD^7A4>tf*Mo/;toi: sr_|'2000Arl£V| V £0£rkBT / CUT#mUTi'3o ##]):#: 3D-f rn# g^b^E P.50~(n D-r K*£-?-]§SlcDi££fcB^-fiJS) SAN ^ i£©flf2S©MX©'t'fCfi Debye ;E£ V £o£r*c BT) Whai)\ C±T©Sti:McDSV'fr l:@ * ms $ flT & t d\ 4*T%«j:<{Ehn^^6D(CTE© (1) (2) i«l, (3) (4) MKSAS^fc^^BESti:^ (SI) ri%ao CCD-9 -£ (1) ~ (3) TCDSii CGS SmkKU^TEdftao mmt^ t>ftaS:CDm cmftamm^Kftao cDSAto#a^-tc r = Vw WifcStHC^DbftTl'ami3l3f 3X101° cm/s T^a^'o C©f|jlJ(®®7CT> y, % -102- tlZo ( 1 ) r =1, fo = Ao=(l/9) X10-20 s2/cm2 (2) SBS&^Ttex y =1,//0=l %-9 T f0 =(V9)x 10-20s2/cm2 «E>0 (3) £0 = 1, ^ =1 ^-5T Y= 3X10-20s2/cm2 ttZZ* CCDSti^tex tftfXx'Vl'7 j: c ^0Tx ommu: j; ^ T#s^ $ tl £ Z. t && tr 'o (4) MKSA t) ckC^SI Sti£% Tii y =1, //0=4ji x 10* 7 N/A2 % o T l in11 £0 -—z------—ry [C2 N'1 m-2] = 8.8541878 X 10’12 [C2 J*1 nr1] 47r(3xl0 10) -103- (A) head group counter ion hydrocarbon con Stern layer water molecule Fig. 1. Schematic micellar model of an ionic micelle for calculation of P(Q) (A) and S(Q) (B). The scattering length density profile corresponding to P(Q) model is also shown. — 104 — =ry by xbM t" ¥# (mm*.) SANS experiments: A small and medium angle neutron scattering spectrometer WINK at KENS (grange: 0.015-10 A-1, neutron wavelength: 1-12 A) SAXS experiments: A small-angle X-ray scattering spectrometer S AXES at PF (grange: 0.01-0.3 A* 1, X-ray wavelength: 1.49 A) Guinier analysis by using the Guinier equation in the form, /( Distance distribution function p(r) by calculating the Fourier inversion of l{q) with the equation p(r)= ^lrql(q)s\n(rq)dq (2) 0 where the extrapolation of the small-angle data sets by using the least-squares method on the Guinier plot and the modification of the scattering intensity defined as ^ (*?) = /(<7)exP(- (k is the artificial damping factor) were used. Glatter analysis for Rg and /total estimation by using the follwoing equation 'total =j0DmaXp(r)dA (3) and 2 l°ma*p(r)r 2dr Kg = (4) 2 Jq max p(r)dr -106- Modeling Analysis. A particle composed of several shells with different average scattering densities : Structure factor ; n >4h) = P1JP1(r)exp(/qe r)dr + £(^.- P,J ^(OexpC/q • r)dr ", ,=2 *, where p ( is the average scattering density and of / th shell with a shape function /?. (r). Therefore the scattering intensity for an Then, Ellipsoid of rotation composed of shells : /( ■ |3Vi{ Wa/ AqR )'(qR f s+.|(p,- $ j3 *(« w*/ 2 dx where ( } means the spherical average of the scattering intensity /(q) defined as 4(q)4*(q), 2 is the 3/2th Bessel function, and 1/2 R. is defined as where r/ and v/ are the semiaxis and its ratio of / th ellipsoidal shell, respectively. -107- basic scattering functions of the large subunit from E. coli ribosomes distance distributions -108- size distribution probability size distribution -109- radius given (A ) by Gaussian 0.0001 intensity 0.001 polydispersity by size -no- ' * q ' distribution I (1/A) weighted 0.0001 intensity 0.001 0.01 0 - - - 0.1 polydispersity 0.2 by -ill- size q 0.3 distribution (1/A weighted ) 0.4 0.5 0.6 polydispersity weighted by size distribution - -6% • — 8 % - -20% -112- Rg/Rg 1.02 1.04 1.06 i 0 Deviation ______10 for i ______ of hard Rg — i ______113 sphere by — S.D. 20 size-polydispersity i ______ (%) system i ______30 L_ 40 intensity Variation of Hard [from (volume=constant) spherical of ellipsoid -in- scattering to of prolate] rotation function — - - - - -1.05 1.40 1.20 p(r) (arbit. units) of [from Variation hard (volume=constant) oblate -115- ellipsoid of p(r) to of spherical] function rotation — 0.90 axial ratio=0.50 in ten sity Variation of [from hard (volume=constant) oblate of ellipsoid -116- scattering to of spherical] rotation function - — • -0.90 - - 0.70 0.55 Variation of p(r) function of hard ellipsoid of rotation [from spherical to prolate] (volume=constant) axial ratio=1.00 — 1.05 — 1.40 -117- Rg/Rg for hard (volume=constant) Variation ellipsoid -118- axial of ratio of Rg rotation presence probability Shape given (axial -119- by axial ratio) Gaussian ratio distribution - — • • - - SD(20%) SD(1 SD(2.5%) SD(5%) 0%) in ten sity 0 depending Variation of hard on of ellipsoid 0.1 120- scattering shape-polydispersity q ( 1 /A) of rotation function ...... ------ -SD(2.5%) SD(20%) SD(1 SD(5%) SD=0 0.2 0%) Variation of p(r) function of hard ellipsoid of rotation depending on shape-polydispersity SD=0 ---- SD(5%) ---- SD(10%) ...... SD(20%) -121- Rg/Rg Deviation for of (volume=constant) hard Rg -122- ellipsoid by S.D. shape-polydispersity (%) system scattering dens. D-shell with hard [particles smooth sphere boundary with -123- different multi-shell bounaries] ^ D-shell 50 30 with A A * hard ^ core intensity multi-shell double-shell Particles (hard, double-shell, with with with different -124- hard q smooth ( 1 /A) core) • -sphere - boundaries D-shell muti-shell D-shell boundary with with smooth hard bound. core particles with different boundaries ------sphere(50)0.1 - -double-shell(50/30)0.1 ------smooth(50/30)0.1 ...... m ulti-shell( 5 0/3 0)0.1 -125- intensity R=4.493/q q n =tan(q particles i n =50.0 and (shell/core=50A R) with isoscattering -126- different q (A') ----- ...... ----- shell/core=(-l ----- - /30A point - (1.5/0.5) (0.36/-0.64) ( (-0.5/-1 2 contrasts / 1 ) ) .5) /-2) particles with different contrasts (shell/core=50A /30A ) ------hard sphere ------shell/core=(-1 /-2) ------(-0.5/-1.5) ------(0.36/-0.64) ...... (1.5/0.5) ------(2/1) r /A -127- Rg*Rg 1000 2000 1500 2500 3000 -2 0 . I < ------■ Stuhrmann 1 /(contrast) -128- 2 i for ■ spherelcal Rg Plot 0 R=50A 4 =38.73 i ■ particle A 6 i 8 i) 7## 3 x h 7 X (solvent contrast variation method) rii) = (label triangulation method) iii) (iiverse contrast variation method) iii) * transpapent & iv) HSI1IBE&& (triple isotopic substitution method) v) x h° y n y h y 7s h (spin contrast variation method) -129- Scattering densities Neutrons X rays RNA, DNA Proteins 10 f ------Water CM I (CH2 )n E o D20 - dna, rna — Proteins 0 (CH2 )n [B*] 1) X 3 & 2) i(dnp) k** (-eomm, £fft£K* nifcB*) 3) 4-^oHM /hABSUi*(0 Ky 'f >#£&L€Sik #A Schematic Drawing of Contrast -131- 3 y h 5 X hE-ffc&fciotf'S 7k is E * © $ 4- * & ti« © ¥ ® E SI $ $ X-rav scattering RNA protein Neutron scattering glycerol RNA protein lipid-head(PC) lipid-alkyl.(CH2) HzO,______|______, DzO 0 0.5 1 -132- i) solvent contrast variation method P(r) — p(r)solute p(**)solvent • P(r) = ^b n 8(r - r„) - PsoivcmpcO) n 2 />„ - P = — ' P= P-Solvent p(r) = ps(r) + ppc(r) /(Q) = I 5(2) da |/(6) = /.(G) + p/cs(2) + ^/cCe)! f Pc(r) <73r 2 7(0) = p2 :2i/2 R2 = R2 + (a/p) - (p/p2) d3r a = f ps(r)r2 d3r, /?? = J pc(r)r: ^ P = ff ps(r)ps(r')r • r' d3r d3r\ -133- ii) inverse contrast variation method __ _ M P(r) = 2>- §0 - r„) 8(r - r„) />=] n= 1 P(r) = u(r) -f 5'v(r) | /(Q) = /„(C) + b'Iuv(Q) + b'2Iv(Q) /,,(Q)r invariant scattering function ii)* inverse contrast variation method "transparent"method at vanishing contrast p = o /(G) = /.(G) + b'lAQ) + b,2UQ) ” p2/v(0 -134- ii) double isotopic substitution method /(G) = n — 1 m — 1 I */i * m j / X1 sin Qlr„ - rm| + Iv(Q}2j 2 Q|_ _ - I n — 1 n = 1 V£|rn rm| n = 1 m — 1 (2 | **,n I(Q, c)=Ij(Q, c) +It(Q, c) M+tf M+d i, co. ^ = 22 A^‘ n j? m for c=N+M=const. 3 x=M/c 3 I„=0 I (Q, c)/c - xI f(Q)± x*I 2(Q, c) I2(Q, c) = {I(Q. cj- xI 0(Q, c)}/x(l-x) -135- iv) label triangulation method i I(Q)= [/(l) + /(2)] - [/(3) + /(4)] =2(lp 1-p t) (rft-pJAjAjfsjn COrJ/QrJ — 136 — v) triple isotopic substitution method % Pj (rj= fu (r) + Vj (r)} *b (r -rj ...... (a) p 2 (rj= {u(r)+v2 (rJJ *b (r -rj ...... (b) p26r)= {u(r)+v3(r)}*b(r-r 3) ...... (c) yM(r)= (l~b) Vj(r) +bv2(r) [ (a) x(l-b) + (b)xb]- ( +Fy Fj {sin (Qryj)/9r yj JJ Z /y/y? <- * j =Nb (t -b) /, ,.r ,(Q) itl-„(Q) - fv.-r,} fv.-vj' 1 -137- a) A In 40%D20 A In H20 — in D20 i Cl 0 H- 0 UtEET * rRNA In 68%D20 •IOO%D-rRNA 65f?D-rRNA - H-rRNA rRNA H-Pi A in 1C IQ. H -Pi H-P2H Schematic di agram of each method a) solvent contrast variation" b) inverse contrast variation c) transpa rent method+triangulation -138- vi) spin contrast variation method ( spin label method ) Fermi scattering-length operator |A = b +2BI.sj= b + ib/v coherent scattering \F\2 = b2 + \b2Nl2P2 + bbNIP • n Polarization B - -2 by Nuclear Neutron |F|J (Coherent scattering) 0 0/n b1 4ti bll(l + 1) P 0 b1 + \bHiP2 4ti[bll(l 4- 1) - b2„l2P2\ P n b2 + \ b%l2P2 4 bb NP • n 4irlZ*/(/ 4- 1) - b2Nl2P2 - bl!P • n] Parameters of spin-dependent cross-sections of some nuclei (from Glattli and Goldman, 1987) Nucleus I b B (10-12 cm) (10"12cm) Hygrogen 'H 1/2 -0.374 2.912 2H 1 0.667 0.285 Carbon ,2C 0 0.665 0 13C 1/2 0.629 -0.06 Nitrogen ,4N 1 0.937 0.14 Oxygen ,6o 0 0.580 0 (/ + 1) b+ + Ib~ 21 + 1 (b+ -b~) 21+ 1 -139- Pu(r)= Z bjS(T-Tj), j=i Pv(r) = Z — ry) • 7“ I M t U(Q)= I exp[/(Q.r,], 7=1 - * U( Q): invariant y (Q)= I PjIjBj exp [/(Q . r,)] j= i------V(Q): polariz ation-dependent S(Q) = UU* + P„( UV* + VU*) Tt- W* = Su(Q)+P„PSuv(Q)+P2Sv(Q) where — 1 < P < +1 P = (/r)// = (n+-w_)/(«++n_ S(tT) = Su + P„PSt,v + P2Sv Sat) = Su-PnPSuv+P2Sv Suv = [S(tt)-saT)]/(2P„P) 2Su + 2P2Sv=S(n) + Sat) 1/(6) = /»(6) + PIuv(Q) + P2M01 IYgj - 0. r (nm) Fig. 3. Distance-distribution functions, P(r), calculated with the scattering curves obtained by using the extrapolation method and the artificial damping factor. Alphabetical symbols corre spond to various solvents as in Fig. 1. -141- Table 2. Some characteristic parameters of urease in solutions with different surfactants determined using small-angle X-ray scattering. Urease concentration; 5.3 mg/ml. R*, 7*(0), and £>mM are the apparent radius of gyration, the zero-angle scattering intensity normalized by that of native solution (surfactant concentration = 0), and the maximum diameter of solute, respectively. DTAB, dode- cyltrimethylammonium bromide; DM, n-dodecyl /?-D-maltoside. [Surfactant] R* /*(0) An., Peak position of ?(/•) mg/mL nm nm 0 4.76 ± 0.15 1 19.5 3.75 7.3 (SDS) 3.40 ± 0.06 0.46 13.1 4.23 20 (SDS) 2.58 ± 0.10 0.25 7.86 3.75 7.3 (DTAB) 4.43 ± 0.11 0.88 18.6 4.04 7.3 (DM) 7.37 ± 0.28 3.1 22.3 9.23 v Fig. 4. Presumed subunit configurations of hexameric structure for modeling analysis used to examine the structure of the urease molecule illustrated by solid spheres. -142- a. o r (nm) Fig. 5. Distance distribution functions, P(r), corresponding to various model structures as shown in Fig. 4, where a hexanier is assumed to consist of six cylindrical subunits with radius 2.87 nm, and height 4.44 nm, or of six spherical subunits with radius 3.11 nm. Those structural parameters were deduced by the compensation of SDS binding to the native subunit. Alphabetical symbols with the suffix * correspond to the models using cylindrical subunits. -143- AESLfflS (DMtixUti; iXiO/ibo/nj^^w^- z, mfc Q = 4Jtsin0 /X I (Q)=r ^|^(p(r)-ps)exp (iQ*r) dv j p(v): , ps : mi&comufe > Guinier plot | Guinier plot In I (0) = - (Rg 2/3)Q2 + 1 n (pV)2 Rg : urn-m p: b 7% h f P= p Ps 1 p: mmrmm Mai tiling p<> i n L P = Ps V I --'jff-fDMtfil >a DzOiftJg-pV plot Mioimimp omit P =0 CO }l c* P = p s ' Ps = (-0.00562 + 0. 0697% )x lO ^cmA"'1 Plot of pV vs D2O cone. =3> hpC0^)ii ___ jr______Stuhrmann plot Rg2= Rgc2 + a(l/p) ♦ p (l/P )z Rgc : a : mV&E&ftAi* ~ $ 1/p Stuhrmann plot -144- 1. fr-F modeling program " BAUSES (NECttS) " (l) Ovo Transferrintf)l#$li5l$'Lactoferrin Matching'?' 3 (2) Transferrin^±#K (3) M. 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