![Page 1: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/1.jpg)
Chapter 2.Chapter 2.Techniques for studying
polymers
![Page 2: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/2.jpg)
Characterization of Polymersy
Thermal analysis
Microscopy
SpectroscopySpectroscopy
Diffraction or scatteringDiffraction or scattering
Density measurement and etc…y
![Page 3: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/3.jpg)
Thermal analysisy
-Thermal analysis for BULK samples
Differential scanning calorimeter (DSC)Differential thermal analysis (DTA)y ( )
Thermal gravimetric analysis (TGA)Thermal gravimetric analysis (TGA)
![Page 4: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/4.jpg)
![Page 5: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/5.jpg)
-Typical amount of sample for DSC: 1~10 mgTypical amount of sample for DSC: 1 10 mg
-Is it available in thin film analysis? Absolutely NOT
![Page 6: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/6.jpg)
![Page 7: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/7.jpg)
Microscopypy
Optical Microscopy
Scanning Electron Microscopy
Transmission Electron Microscopy
Scanning Prove Microscopy
![Page 8: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/8.jpg)
Electron MicroscopyElectron Microscopy
• SEM – Secondary electron
imicroscopy
• TEMTransmission electron– Transmission electron microscopy
Acquiring surface image(Microscopy)
![Page 9: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/9.jpg)
![Page 10: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/10.jpg)
![Page 11: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/11.jpg)
Scanning Electron Microscopy
![Page 12: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/12.jpg)
![Page 13: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/13.jpg)
Scanning Electron Microscopy (SEM)Scanning Electron Microscopy (SEM)
![Page 14: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/14.jpg)
SEM vs OMSEM vs. OMSEM Optical microscope
Source of light electron beam wavelength: 2000~7500Awavelength : 0.064~
Medium vacuum air
Lens elect on lens optical lensLens electron lens optical lens
Resolution limit 30A~10A visible : 2000Aultra : 1000Aultra : 1000A
Focal depth 30 about 0.1Magnification 10~30 000 10~2000Magnification 10~30,000 10~2000 Kinds of phase secondary&reflec. Transmitted or reflected
![Page 15: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/15.jpg)
Electron beam lithography
20 um
EBL Plasma EtchHSQ resist
g p y
20 um
e- e- e- e- e- 7
Silicon substratespin coat resist trim
e e e e e 7nm
exposure silicon etch10 HOURS!!10 HOURS!!
develop resist strip
80nm line70nm space
11nm 30nmdiameter
![Page 16: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/16.jpg)
Transmission Electron Microscopy
![Page 17: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/17.jpg)
• High e Energy (100~300keV)• Thin specimen (<2000Å)• Thin specimen (<2000Å)• Transmitted beam – bright
fieldfield• Diffracted beam – crystal
structurestructure• Very high resolution (0.15nm)
![Page 18: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/18.jpg)
Thin section preparationThin section preparation
![Page 19: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/19.jpg)
Ion milling법을 이용한 cross section 시료 제작Ion milling법을 이용한 cross-section 시료 제작
![Page 20: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/20.jpg)
![Page 21: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/21.jpg)
![Page 22: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/22.jpg)
Scanning Prove Microscopy
![Page 23: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/23.jpg)
Scanning Probe Microscopy
![Page 24: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/24.jpg)
![Page 25: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/25.jpg)
CNT on electrodesCNT on electrodesCNT on electrodesCNT on electrodes
![Page 26: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/26.jpg)
Scanning Probe Microscopy
![Page 27: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/27.jpg)
![Page 28: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/28.jpg)
Spectroscopyp py
-Analysis for chemical structure identification
-Difference between scattering and spectroscopy?
-Rayleigh scattering
-UV/VIS, IR, Raman scattering
![Page 29: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/29.jpg)
![Page 30: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/30.jpg)
![Page 31: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/31.jpg)
![Page 32: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/32.jpg)
NMR spectroscopy
![Page 33: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/33.jpg)
![Page 34: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/34.jpg)
![Page 35: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/35.jpg)
![Page 36: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/36.jpg)
![Page 37: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/37.jpg)
Scatteringg
-Structure analysis via
Small angle or wide angle x-ray scattering
Neutron scattering
Light scattering
![Page 38: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/38.jpg)
X‐ray Scatteringy g
- Small angle or wide angle x-ray scattering
Wavelength of incident x-ray:
Small angle vs. wide angle:
Not only for bulk materials but also for films
![Page 39: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/39.jpg)
elastic scattering: ki=kfelastic scattering: ki kf
ki kf
dd
2f t ti i t f 2k kfor constructive interference: 2k s k⋅ =
2 sinn dλ θ= 2 sinn dλ θ=
![Page 40: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/40.jpg)
![Page 41: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/41.jpg)
![Page 42: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/42.jpg)
![Page 43: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/43.jpg)
![Page 44: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/44.jpg)
Synchrotron Radiation Facility
![Page 45: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/45.jpg)
Storage ring at PLS
Pohang Light Source
![Page 46: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/46.jpg)
LINAC Storage ring
just before front-end
![Page 47: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/47.jpg)
Neutron Scatteringg
- Elastic vs. inelastic or quasi-elastic scattering
Wavelength:
Unique features of neutron beam:
![Page 48: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/48.jpg)
![Page 49: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/49.jpg)
Spallation Source: IPNS (Argonne National Lab, USA)
![Page 50: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/50.jpg)
![Page 51: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/51.jpg)
Neutron Reactor: NIST (USA)
![Page 52: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/52.jpg)
Confined building
![Page 53: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/53.jpg)
Guide hall
![Page 54: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/54.jpg)
Sample stage
![Page 55: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/55.jpg)
Detector chamber
![Page 56: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/56.jpg)
Detector chamber (1)
![Page 57: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/57.jpg)
Detector chamber (2)
![Page 58: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/58.jpg)
Neutron Scatteringg
- Elastic vs. inelastic or quasi-elastic scattering
Wavelength:
Unique features of neutron beam:
![Page 59: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/59.jpg)
elastic scattering: ki=kfelastic scattering: ki kf
ki kf
dd
2f t ti i t f 2k kfor constructive interference: 2k s k⋅ =
2 sinn dλ θ= 2 sinn dλ θ=
![Page 60: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/60.jpg)
![Page 61: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/61.jpg)
Scattering pattern of nanocrystal
![Page 62: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/62.jpg)
Background of scattering
![Page 63: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/63.jpg)
![Page 64: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/64.jpg)
elastic scattering: ki=kfelastic scattering: ki kf
ki kf
dd
2f t ti i t f 2k kfor constructive interference: 2k s k⋅ =
2 sinn dλ θ= 2 sinn dλ θ=
![Page 65: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/65.jpg)
( ) ( ) ir qA q r e drρ − ⋅= ∫
u( ) ( )* ( )r r z rρ ρ=FT
( ) ( ) ( )A q F q Z q=SLDD Scattering amplitude
∫
IFTForm factor lattice factor
uarin
g
X squ
*
( )( ) ( )
I qA q A q= ⋅
( )I q
![Page 66: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/66.jpg)
for n atomic crystal
( ) ( ) ( )f∑ ∑
for n atomic crystal,
nj j( ) exp( ) exp( )j n
F q f iq r iq R= − ⋅ − ⋅∑ ∑
unit cell structure factor lattice sumPosition determination
2 integernq R π⋅ = ×
∑th i
nexp( ) ~n
iq R N− ⋅∑since
( ) 1i R∑otherwise, nexp( ) ~ 1n
iq R− ⋅∑
![Page 67: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/67.jpg)
Real and inverse lattice
2 integerr q π⋅ = × (Laue condition ~ Bragg Law)
b b b2 32 a ab ×
1 1 2 2 3 3q v b v b v b= + +1 1 2 2 3 3r u a u a u a= + +
i j ij2
when 0
b a
i j
πδ⋅ =
≠
2 31
2 3 1
2ba a a
π=⋅ ×3 12 a ab × when , 0
when , 2i ji j π≠=
3 12
3 1 2
2ba a a
π=⋅ ×
a a×1 23
1 2 3
2 a aba a a
π ×=
⋅ ×
( )1 1 2 2 3 32r q u v u v u vπ⋅ = × + +
![Page 68: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/68.jpg)
3b
a3a
2a
1a
![Page 69: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/69.jpg)
![Page 70: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/70.jpg)
![Page 71: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/71.jpg)
![Page 72: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/72.jpg)
![Page 73: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/73.jpg)
Structure factor for a uniform sphere
[ ]2( ) ( )P F ρ~ 0ρ2 s qπ =
[ ]( ) ~ ( )P q F q ρ2R
( ) ( ) ( )F i d∫( ) ( ) exp( )F q r iq r drρ= − ⋅∫
![Page 74: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/74.jpg)
Structure factors for several structures
Thin rod
At a certain orientations Θ a
4 cos( ) sin( )2
qLF qL
Θ=
Θ
At a certain orientations, Θ
Lcos 2qL Θ L
V=aLV aL
Circular disk
R1(2 )2( ) 1 J qRP q ⎡ ⎤
= −⎢ ⎥F 2 2( ) 1P qq R qR
= ⎢ ⎥⎣ ⎦
F
![Page 75: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/75.jpg)
Structure factors for several structures
Circular disk
R
⎡ ⎤12 2
(2 )2( ) 1 J qRP qq R qR
⎡ ⎤= −⎢ ⎥
⎣ ⎦q q⎣ ⎦
![Page 76: Techniques studying polymers · 2018-01-30 · Scattering-Structure analysis via Small angle or wide angle x-ray scattering Neutron scattering](https://reader034.vdocument.in/reader034/viewer/2022043001/5f7bb124ba32dc1090375da6/html5/thumbnails/76.jpg)
How about this?--synthetic polymer, DNA, protein…synthetic polymer, DNA, protein…
[ ]2( ) ~ ( )P q F q
constant form factor?
Random coil 2 2 2 2exp( ) 1R R+Or Gaussian coil4 4
exp( ) 1( ) ~ 2 g g
g
q R q RP q
q R− − +
g
htt // i t / / / df/ l t t dfhttp://www.ncnr.nist.gov/programs/sans/pdf/polymer_tut.pdf