《Modern Research Methods in Polymer Science》 Drs. Wei Tian & Yanhui Chen Sep-Dec. 2014

X-ray diffraction analysis Modern Research Methods in Polymer Science X-ray diffraction analysis Fundamental for X-ray diffraction Wide Angle X-ray Diffraction (WAXD) Small Angle X-ray Scattering (SAXS)

Cross section of sealed-off filament X-ray tube Fundamental for X-ray diffraction Production of X-rays Cross section of sealed-off filament X-ray tube This X-ray tube is usually used in in-house X-ray Diffractometer. X-rays are produced whenever high-speed electrons collide with a metal target, ranging from 0.5～2.5Å. This range is suitable to probe the polymer structures. The recorded X-ray Lines usually have two or three characteristic peaks. The less stronger peaks like Kb and Ka2 will cause extra peaks, and shape changes in XRD pattern should be eliminated by adding filters. λ = 0.5～2.5Å

Production of in situ Synchrotron X-rays Fundamental for X-ray diffraction Production of in situ Synchrotron X-rays BNL NSLSI The other type of X-rays is generated by synchrotron radiation. The process is like this, charged particles (electrons, positrons) are injected in an accumulation ring, accelerated by electric fields around the speed of light and deflected by magnetic fields. The X-rays will emit in certain direction. This is a layout of BNL NSLSI, where I used to work. The in situ synchrotron X-rays can be used to detect from configuration order, crystallization, phase separation to nano self assembly. 电子直线加速器主要作为注入器使用, 建于半地下隧道内以一定的仰角向地面上的储存环内注入电子。注入结束后进入慢加速过程, 使电子最终达到800 MeV 的能量, 并以此能量在储存环内绕闭 合轨道运行。 0.1nm 100nm Configuration order Crystallization Phase separation Nano self-assembly

Advantages of in situ Synchrotron X-rays 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

Destructive interference Fundamental for X-ray diffraction Bragg’s Law and Diffraction Constructive interference Destructive interference When X-ray collides with the atom, it will be reflected in certain direction. In order to obtain the diffraction pattern, we need this constructive interference, where the distance between two X-rays path is equal to n times lammda, the wave length. This is called bragg’s law n λ =2dsinθ

Diffractometer method Fundamental for X-ray diffraction Diffraction methods Debye Scherrer method Photographic method Focusing method multicrystal Pinhole method Diffractometer method 入射 X射线 Laue method monocrystal Afterwards, several diffraction methods were developed. For multicrystal, the most usual crystals, we have one kind of Photographic method, including debye scherrer method, focusing method, pinhole method and the other kind, Diffractometer method. As for the monocrystal, laue method and rotation method can be used. Rotation method

General Application Fundamental for X-ray diffraction 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

Tiwari, V. K.; Macromolecules 2013, 46 (14), 5595-5603. Fundamental for X-ray diffraction Description Tiwari, V. K.; Macromolecules 2013, 46 (14), 5595-5603.

Basic concept Wide Angle X-ray Diffraction (WAXD) WAXD 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 In the following content, the source for wide angle X-ray diffraction and small angle X-ray scattering is in situ synchrotron X-rays.

Application Wide Angle X-ray Diffraction (WAXD) Crystal determination β-crystals Crystal parameters: grain size, crystallinity, orientation Crystal lattice distortion

Extended Application--in situ detection Wide Angle X-ray Diffraction (WAXD) Extended Application--in situ detection

Che, J.; et al. Macromolecules 2013, 46, 5279-5289. Wide Angle X-ray Diffraction (WAXD) Description Che, J.; et al. Macromolecules 2013, 46, 5279-5289.

Basic concept Small Angle X-ray Scattering (SAXS) Small-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)。

Application Small Angle X-ray Scattering (SAXS) 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. Qualitative analysis： (1) Homogeneity or homogeneity of system electronic density (2) Dispersibility of scatters (3) Significance of interphase (4) Self-similarity of scatters

Application Small Angle X-ray Scattering (SAXS) Quantitative analysis： Averaged particle sizes Shapes, distribution Surface-to-volume ratio Long period in crystalline system 0 % 5.8 % 17.6 % 40 % 50 % This is an example from one part of my work, This is SAXS pattern of oriented PP upon different strains. Initially, it has very obvious scattering maxima in the meridian, then slightly moving inside as the strain increases. Based on these pattern ,we can get the one dimensional SAXS curve. Further, we can decompose the long period into two parts, the thickness of crystalline part and amorphous part.

References 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. http://en.wikipedia.org/wiki/X- ray_crystallography#Synchrotron_Radiation http://en.wikipedia.org/wiki/Wide-angle_X-ray_scattering http://en.wikipedia.org/wiki/Small-angle_X-ray_scattering