《 Modern Research Methods in Polymer

Science》Drs. Wei Tian & Yanhui Chen

Sep-Dec. 2014

X-ray diffraction analysis

Fundamental for X-ray diffraction

Wide Angle X-ray Diffraction (WAXD)

Small Angle X-ray Scattering (SAXS)

Modern Research Methods in Polymer Science

Fundamental for X-ray diffraction

Production of X-rays

λ = 0.5 ～ 2.5Å

Cross section of sealed-off filament X-ray tube

Fundamental for X-ray diffraction

Production of in situ Synchrotron X-rays

0.1nm 100nmConfiguration order Crystallization Phase separation Nano self-assembly

BNL NSLSI

Fundamental for X-ray diffraction

Advantages of in situ Synchrotron X-rays• High Flux: high intensity photon beam allows rapid

experiments or use of weakly scattering crystals.

• High Brilliance: highly collimated photon beam generated by a small divergence and small size source (spatial coherence)

• Small Beam Footprint: 2D or 3D studies to sub-mm/micron length scale

• Wavelength Tunability: Choice of energy region (from IR to Hard X-Ray) to suit the problem

Fundamental for X-ray diffraction

Bragg’s Law and DiffractionConstructive interference

Destructive interference

n λ =2dsinθ

Fundamental for X-ray diffraction

Diffraction methods

multicrystal

monocrystal

Photographic method

Diffractometer method

Debye Scherrer method

Focusing method

Pinhole method

Lauemethod

Rotation method

入射X射线

Fundamental for X-ray diffraction

General Application

• Measure the average spacings between layers or rows of atoms

• Determine the orientation of a single crystal or grain

• Find the crystal structure of an unknown material

• Measure the size, shape and internal stress of small crystalline regions

Fundamental for X-ray diffraction

Description

Tiwari, V. K.; Macromolecules 2013, 46 (14), 5595-5603.

Wide Angle X-ray Diffraction (WAXD)

Basic conceptWAXD is an X-ray-diffraction technique that is often used to determine the crystalline structure of polymers. This technique specifically refers to the analysis of Bragg peaks scattered to wide angles (2θ ≥ 6º), which (by Bragg's law) implies that they are caused by sub-nanometer-sized structures.

(a) Random crystals

(b) Partial oriented crystals

(c) Completely oriented crystals

(d) Amorphous phase

Wide Angle X-ray Diffraction (WAXD)

Application

Crystal determination

Crystal parameters: grain size, crystallinity, orientation

Crystal lattice distortion

β-crystals

Wide Angle X-ray Diffraction (WAXD)

Extended Application--in situ detection

Description

Wide Angle X-ray Diffraction (WAXD)

Che, J.; et al. Macromolecules 2013, 46, 5279-5289.

Small Angle X-ray Scattering (SAXS)

Basic conceptSmall-angle X-ray scattering (SAXS) is a small-angle scattering technique where the elastic scattering of X-rays (wavelength 0.1 ~ 0.2 nm) by a sample, which has inhomogeneities in the nm-range, is recorded at very low angles (typically 2 6º) 。

Small Angle X-ray Scattering (SAXS)

Application

Qualitative analysis：(1) Homogeneity or homogeneity of

system electronic density

(2) Dispersibility of scatters

(3) Significance of interphase

(4) Self-similarity of scatters

Systems : colloids of all types, metals, cement, oil, polymers, plastics, proteins, foods and pharmaceuticals and can be found in research as well as in quality control.

0 % 5.8 % 17.6 % 40 % 50 %

Small Angle X-ray Scattering (SAXS)

Quantitative analysis ： Averaged particle sizes

Shapes, distribution

Surface-to-volume ratio

Long period in crystalline system

Application

References

1. 田 威，孔 杰，胡思海 . 高聚物的现代研究方法 [M] ，西北工业大学出版社， 2014.

2. http://en.wikipedia.org/wiki/X-ray_crystallography#Synchrotron_Radiation

3. http://en.wikipedia.org/wiki/Wide-angle_X-ray_scattering

4. http://en.wikipedia.org/wiki/Small-angle_X-ray_scattering