Small angle X-ray scattering in polymers and polymer composites
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摘要: 在聚合物及其复合材料的合成过程中，实时、动态的观察材料结构的演变并且为性能预测提供启示是当前研究的热点并且面临一定的挑战。小角X射线散射(Small angle X-ray scattering，SAXS)技术作为研究物质微观、亚微观结构的表征手段之一，能够反应出独特的微观构象信息，并且能系统地研究链状、网状、层状高聚物的形貌特征及其形成过程，这对聚合物及其复合材料聚集态结构形成的机制解析、宏观性能预测至关重要。本文从高分子聚合物SAXS研究中常见的峰值观测、模型拟合、环形积分3种方法切入，阐述SAXS在聚合物及其复合材料，特别是天然高聚物材料研究中发挥的实际应用，如动态观测微观结构演变过程、在大范围内获得具有统计学意义的微观结构特征与平均参数。通过对SAXS在聚合物及其复合材料中应用的归纳，总结出SAXS技术在该领域的优势与面临的困难，方便明确不同种类的聚合物及其复合材料研究中SAXS可表征的内容，以期让这一表征技术能够解决更多实际问题。
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关键词:
- 小角X射线散射(SAXS) /
- 聚合物及其复合材料 /
- 演变过程 /
- 形成机制 /
- 微观构象
Abstract: In the synthesis of polymers and polymer composites, it is still a challenge to observe the real-time and dynamic evolution of material structure and provide implications for property prediction. As one of the methods to characterize the microscopic and submicroscopic structures of substances, small angle X-ray Scattering (SAXS) technology can reflect unique microscopic conformational information, and can systematically study the morphological characteristics and formation process of chain-like, network-like, and layered polymers. The analysis of the formation mechanism of the aggregated structure of molecular materials, and their macroscopic performance prediction are very important. In this paper, three common methods for SAXS applications in current polymer materials research were presented, i.e., the peak observation, the model fitting, and the annular integration. Based on the above three methods, this paper introduced the practical functions of SAXS in studying different polymer materials, such as dynamic observation of the microstructural evolution process, and obtaining large-scale and statistically significant microstructural parameters. After comparing and evaluating the application methods and influences of SAXS in different polymer materials, it was concluded that SAXS plays a comprehensive role that is difficult to replicate in the study of complex polymer materials. It was hoped that this paper could serve as a primer to attract researchers' attention to understand SAXS technology, provide alternative research methods for the investigation of complex polymers, and expand the application of SAXS in wider fields to solve more problems. -
图 2 SAXS原理图：(a)穿透样品后的X射线；(b)小角度X射线散射显微图
S0 and S1—Wave vectors of the incident and scattered X-rays; θ—Angle; K point—Electron with the bit vector r from the O point; q—Scattering vector
Figure 2. Principle diagram of the SAXS: (a) X-rays after penetration of the sample; (b) Microscopic diagram of small angle X-ray scattering
图 3
$ \rho {(}{r}{)} $ 、$ \gamma {(}{r}{)、}\;{}{A}{(}{q}{)} $ 和$ {I}{(}{q}{)} $ 之间的转化关系ρ(r)—Electron density; γ(r)—Autocorrelation function of electron density ρ(r); I(q)—Scattering intensity; A(q)—Sum of the amplitudes at each position
Figure 3. Relationships among
$ \rho {(}{r}{)} $ ,$ \gamma{(}{r}{),}\;{}{A}{(}{q}{)} $ and$ {I}{(}{q}{)} $ 
图 4 SAXS图像转化为曲线过程示意图：(a)通过SAXS获得的二维投影；(b)转化后的一维曲线
q—Scattering vector; I(q)—Scattering intensity
Figure 4. Schematic diagram of SAXS image transformation process: (a) SAXS 2D image; (b) Transformed into a 1D curve
图 5 峰值观测法观察的SAXS一维曲线：(a) 不同温度下HDPE的SAXS一维曲线；(b) 不同温度下HDPE的SAXS一维曲线的洛伦兹校正图[31]；(c) 低浓度纤维素乙醇凝胶珠干燥过程的SAXS曲线；(d) 低浓度纤维素水凝胶珠干燥过程的SAXS曲线[32]
HDPE—High density polyethylene
Figure 5. SAXS 1D curves observed by the peak observation method: (a) SAXS 1D curves of HDPE at different temperatures; (b) Lorentz correction of SAXS measurements of HDPE at different temperatures[31]; (c) SAXS 1D curve of low concentration cellulose ethanol gel during the drying process; (d) SAXS 1D curve of low concentration cellulose hydrogel bead gel during the drying process[32]
图 6 环形积分法示意图：(a) 各向异性散射体的形态示意；(b) 各向异性散射体的SAXS散射图像；(c) 环形积分后各向异性散射体的一维曲线
D—Scatterer width; L—Scatterer length; φ—Orientation angle of the scatterer
Figure 6. Schematic diagram of the annular integration method: (a) Existence of anisotropic scatterers; (b) Scattering image of anisotropic scatterers; (c) 1D curve of anisotropic scatterers after circular integration
图 7 脂质聚合膜示意图：(a) 水相中脂质膜的形成过程；(b) 脂质膜与底物接触时的状态；(c) 水相中脂质膜的三维结构示意[49]
Figure 7. Schematic diagram of lipid polymeric membrane: (a) Formation of a lipid membrane in an aqueous phase; (b) State of the lipid membrane when in contact with the substrate; (c) 3D structure of lipid membrane in the aqueous phase[49]
图 9 嵌段共聚物研究中所涉及的概念及设备示意图：(a) 临界堆积参数P的计算方法及P的大小与嵌段共聚物微观形貌间的关系；(b) 原位SAXS测试实验装置[63]；(c) 不同聚合程度的嵌段共聚物微观形貌模拟示意图[62]
P—Critical packing parameter; V—Volume; lc—Length; a0—Effective are
Figure 9. Concepts and equipment diagram of block copolymer part: (a) Critical packing parameter P calculation method, relationship between P and morphology of block copolymer; (b) In situ SAXS experimental device[63]; (c) Schematic diagram of the microstructure of block copolymer at different degrees of polymerization[62]
图 8 水乳液聚合和胶体聚合机制示意图：(a) 水乳液聚合过程中疏水相单体聚合的3个阶段[52]；(b) 氧化铈胶体形成团聚体的形成机制[53]
T—Temperature
Figure 8. Schematic diagram of water emulsion polymerization and colloid polymerization mechanism: (a) Representation of the three main intervals (I, II, and III) that occur during the aqueous emulsion polymerization of a water-immiscible monomer[52]; (b) Formation mechanism of colloidal aggregates of cerium oxide[53]
图 10 多级介晶各级结构示意图：(a) Bi3+、EA和NMP合成的基本结构；(b) 由基础结构经过偶极-偶极相互作用所形成的细长纳米丝；(c) 纳米细丝间通过静电作用形成的Bi-EA介晶结构[64]
Figure 10. Schematic diagram of each level of multistage structure monocrystals: (a) Basic structure of Bi3+, EA, and NMP synthesis; (b) Nanofilaments formed by dipole-dipole interaction of the infrastructure; (c) Bi-EA mesocrystals formed by electrostatic action of the filaments[64]
图 11 纤维素纳米纤维(CNF)模型示意图、模拟和实际测试所得到的SAXS数据：(a) 符合理想假设的CNF模型；(b) CNF横切面上主平面与晶体平面示意图；(c) 实测的单根CNF的SAXS一维曲线、模拟CNF的SAXS曲线及三者对强度的贡献曲线；(d) 实验测量3种组分CNF在广角X射线衍射(WAXD)中对散射强度的贡献情况[66]
Figure 11. Schematic diagram of cellulose nanofibers (CNF) ideal model with simulation and actual experimental data: (a) CNF model schematic diagram; (b) Relation between the principal plane and crystal plane on the CNF cross-section; (c) Measured SAXS 1D curve , the simulated SAXS 1D curve , and the contribution of the three parts to the strength; (d) Experimentally measured wide-angle X-ray diffraction (WAXD) curve and the contribution of scattering intensity in three-part WAXD[66]
图 12 部分天然材料中的组织结构分布图：(a) 毛竹显微CT重建切片影像，1区域为维管束区，2区域为薄壁组织区；(b) 毛竹的SAXS二维散射图，其中Ⅰ区域的散射强度主要由维管束贡献，Ⅱ区域的散射强度主要由薄壁细胞贡献；由区域Ⅰ (c) 和区域Ⅱ (d) 重构的散射分布图[75]；((e)~(h)) 在冻融干燥法制备泡沫结构材料中CNF的实际取向情况，色轮的颜色代表CNF的实际取向，虚线箭头代表了冻结过程开始的主方向[76]
q2—Relative standard deviation of the scattering vector q
Figure 12. Tissue structure distribution of some natural materials: (a) Microscopic CT reconstruction section of phyllostachys edulis, 1 represented the vascular bundle region, 2 represented the parenchyma region; (b) SAXS 2D scattering diagram of Phyllostachys edulis, region Ⅰ was contributed by the vascular bundle and region Ⅱ was contributed by parenchyma cells; Slice of scattering distribution reconstructed from region Ⅰ (c) and region Ⅱ (d)[75]; ((e)-(h)) True orientation of CNF in foam structure materials prepared by freeze-thawing-drying, the colors of the color wheel represents the true orientation of the CNF, the dotted arrows indicate the main direction of the freezing front[76]
图 13 聚烯烃催化剂与钙钛矿纳米片层水凝胶：(a) 聚烯烃催化剂的SAXS一维曲线；(b) 从总散射曲线中分离得到的关于催化剂孔隙的SAXS一维曲线；通过截断高斯场法对催化剂C1 (c) 与催化剂C2 (d) 的三维模型重构[81]；(e) 2.0wt%和3.0wt%钙钛矿纳米片凝胶溶液；(f) 橙色和蓝色钙钛矿纳米片水凝胶[82]
Figure 13. Polyolefin catalyst and perovskite nanosheet hydrogels: (a) SAXS 1D curve of catalyst; (b) SAXS 1D curve of catalyst pores; 3D reconstruction model of catalysts C1 (c) and C2 (d) by correlated Gaussian random filed method[81]; (e) 2.0wt% and 3.0wt% perovskite nanosheet gel solution; (f) Orange and blue perovskite nanosheet hydrogels[82]
图 14 HDPE横截面上的空洞：((a), (b)) 当
${ \varepsilon }_{\text{H}} $ 小于0.5时HDPE内部电镜显示空洞的数量较少且尺寸较小；((c), (d)) 当$ { \varepsilon }_{\text{H}} $ 增大时HDPE内部空洞的数量和尺寸同步增加与扩大[37]εH—True strain defined by Hencky
Figure 14. Cavities on HDPE fracture surface: ((a), (b))When
$ { \varepsilon }_{\text{H}} $ was less than 0.5, the HDPE internal electron microscope showed that the number and size of cavities were small; ((c), (d)) When$ { \varepsilon }_{\text{H}} $ increased, the number and size of HDPE holes increased synchronously[37] -
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