Small-angle X-ray scattering

Short description: Radiation scattering technique

Small-angle X-ray scattering (SAXS) is a small-angle scattering technique by which nanoscale density differences in a sample can be quantified. This means that it can determine nanoparticle size distributions, resolve the size and shape of (monodisperse) macromolecules, determine pore sizes and characteristic distances of partially ordered materials.[1] This is achieved by analyzing the elastic scattering behaviour of X-rays when travelling through the material, recording their scattering at small angles (typically 0.1 – 10°, hence the "Small-angle" in its name). It belongs to the family of small-angle scattering (SAS) techniques along with small-angle neutron scattering, and is typically done using hard X-rays with a wavelength of 0.07 – 0.2 nm. Depending on the angular range in which a clear scattering signal can be recorded, SAXS is capable of delivering structural information of dimensions between 1 and 100 nm, and of repeat distances in partially ordered systems of up to 150 nm.[2] USAXS (ultra-small angle X-ray scattering) can resolve even larger dimensions,[3][4][5] as the smaller the recorded angle, the larger the object dimensions that are probed.

SAXS and USAXS belong to a family of X-ray scattering techniques that are used in the characterization of materials. In the case of biological macromolecules such as proteins, the advantage of SAXS over crystallography is that a crystalline sample is not needed. Furthermore, the properties of SAXS allow investigation of conformational diversity in these molecules.[6] Nuclear magnetic resonance spectroscopy methods encounter problems with macromolecules of higher molecular mass (> 30–40 kDa). However, owing to the random orientation of dissolved or partially ordered molecules, the spatial averaging leads to a loss of information in SAXS compared to crystallography.

## Contents

* 1 Applications
* 1.1 Resonant small-angle X-ray scattering
* 2 SAXS instruments
* 2.1 Point-collimation instruments
* 2.2 Line-collimation instruments
* 3 SAXS instrument manufacturers
* 4 See also
* 5 References
* 6 External links

## Applications

SAXS is used for the determination of the microscale or nanoscale structure of particle systems in terms of such parameters as averaged particle sizes, shapes, distribution, and surface-to-volume ratio.[7][8][9][10] The materials can be solid or liquid and they can contain solid, liquid or gaseous domains (so-called particles) of the same or another material in any combination. Not only particles, but also the structure of ordered systems like lamellae, and fractal-like materials can be studied. The method is accurate, non-destructive and usually requires only a minimum of sample preparation. Applications are very broad and include colloids[11][12][13][14] of all types including interpolyelectrolyte complexes,[15][16][17] micelles,[18][19][20][21][22] microgels,[23] liposomes,[24][25][26] polymersomes,[27][28] metals, cement, oil, polymers,[29][30][31][32] plastics, proteins,[33][34] foods and pharmaceuticals and can be found in research as well as in quality control. The X-ray source can be a laboratory source or synchrotron light which provides a higher X-ray flux.

### Resonant small-angle X-ray scattering

It is possible to enhance the X-ray scattering yield[35] by matching the energy of X-ray source to a resonant absorption edge in as it is done for resonant inelastic X-ray scattering. Different from standard RIXS measurements, the scattered photons are considered to have the same energy as the incident photons.

## SAXS instruments

In a SAXS instrument, a monochromatic beam of X-rays is brought to a sample from which some of the X-rays scatter, while most simply go through the sample without interacting with it. The scattered X-rays form a scattering pattern which is then detected at a detector which is typically a 2-dimensional flat X-ray detector situated behind the sample perpendicular to the direction of the primary beam that initially hit the sample. The scattering pattern contains the information on the structure of the sample. The major problem that must be overcome in SAXS instrumentation is the separation of the weak scattered intensity from the strong main beam. The smaller the desired angle, the more difficult this becomes. The problem is comparable to one encountered when trying to observe a weakly radiant object close to the Sun, like the Sun's corona. Only if the Moon blocks out the main light source does the corona become visible. Likewise, in SAXS the non-scattered beam that merely travels through the sample must be blocked, without blocking the closely adjacent scattered radiation. Most available X-ray sources produce divergent beams and this compounds the problem. In principle the problem could be overcome by focusing the beam, but this is not easy when dealing with X-rays and was previously not done except on synchrotrons where large bent mirrors can be used. This is why most laboratory small angle devices rely on collimation instead. Laboratory SAXS instruments can be divided into two main groups: point-collimation and line-collimation instruments:

### Point-collimation instruments

Point-collimation instruments have pinholes that shape the X-ray beam to a small circular or elliptical spot that illuminates the sample. Thus the scattering is centro-symmetrically distributed around the primary X-ray beam and the scattering pattern in the detection plane consists of circles around the primary beam. Owing to the small illuminated sample volume and the wastefulness of the collimation process—only those photons are allowed to pass that happen to fly in the right direction—the scattered intensity is small and therefore the measurement time is in the order of hours or days in case of very weak scatterers. If focusing optics like bent mirrors or bent monochromator crystals or collimating and monochromating optics like multilayers are used, measurement time can be greatly reduced. Point-collimation allows the orientation of non-isotropic systems (fibres, sheared liquids) to be determined.

### Line-collimation instruments

Line-collimation instruments restrict the beam only in one dimension (rather than two as for point collimation) so that the beam cross-section is a long but narrow line. The illuminated sample volume is much larger compared to point-collimation and the scattered intensity at the same flux density is proportionally larger. Thus measuring times with line-collimation SAXS instruments are much shorter compared to point-collimation and are in the range of minutes. A disadvantage is that the recorded pattern is essentially an integrated superposition (a self-convolution) of many adjacent pinhole patterns. The resulting smearing can be easily removed using model-free algorithms or deconvolution methods based on Fourier transformation, but only if the system is isotropic. Line collimation is of great benefit for any isotropic nanostructured materials, e.g. proteins, surfactants, particle dispersion and emulsions.

## SAXS instrument manufacturers

SAXS instrument manufacturers include Anton Paar, Austria; Bruker AXS, Germany; Hecus X-Ray Systems Graz, Austria; Malvern Panalytical. the Netherlands, Rigaku Corporation, Japan; Xenocs, France.

## See also

* Biological small-angle scattering
* GISAS (Grazing-incidence small-angle scattering)
* Fluctuation X-ray scattering (FXS)
* Wide-angle X-ray scattering

## References

1. ↑ Hamley, I.W. "Small-Angle Scattering: Theory, Instrumentation, Data, and Applications" – Wiley, 2022. ISBN 978-1-119-76830-2.
2. ↑ Glatter O, ed (1982). Small Angle X-ray Scattering. Academic Press. ISBN 0-12-286280-5. http://physchem.kfunigraz.ac.at/sm/Software.htm.
3. ↑ Sztucki, M; Narayanan, T (2007). "Development of an ultra-small-angle X-ray scattering instrument for probing the microstructure and the dynamics of soft matter". Journal of Applied Crystallography 40: s459–s462. doi:10.1107/S0021889806045833. ISSN 1600-5767.
4. ↑ Narayanan, T; Sztucki, M; Van Vaerenbergh, P; Léonardon, J; Gorini, J; Claustre, L; Sever, F; Morse, J et al. (2018). "A multipurpose instrument for time-resolved ultra-small-angle and coherent X-ray scattering". Journal of Applied Crystallography 51 (6): 1511–1524. doi:10.1107/S1600576718012748. ISSN 1600-5767. PMID 30546286. Bibcode: 2018JApCr..51.1511N.
5. ↑ Patil, N; Narayanan, T; Michels, L; Skjønsfjell, ETB; Guizar-Sicairos, M; Van den Brande, N; Claessens, R; Van Mele, B et al. (May 2019). "Probing Organic Thin Films by Coherent X-ray Imaging and X-ray Scattering". ACS Applied Polymer Materials 1 (7): 1787–1797. doi:10.1021/acsapm.9b00324. ISSN 2637-6105. Bibcode: 2019AAPM....1.1787P. https://www.dora.lib4ri.ch/psi/islandora/object/psi:24841.
6. ↑ Burger, Virginia M., Daniel J. Arenas, and Collin M. Stultz. "A structure-free method for quantifying conformational flexibility in proteins." Scientific reports 6 (2016): 29040. DOI: 10.1038/srep29040 (2016).| http://hdl.handle.net/1721.1/108809
7. ↑ Pedersen, JS (July 1997). "Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting". Advances in Colloid and Interface Science 70: 171–210. doi:10.1016/S0001-8686(97)00312-6. ISSN 0001-8686.
8. ↑ Pedersen, JS (2000). "Form factors of block copolymer micelles with spherical, ellipsoidal and cylindrical cores". Journal of Applied Crystallography 33 (3): 637–640. doi:10.1107/S0021889899012248. ISSN 1600-5767. Bibcode: 2000JApCr..33..637P.
9. ↑ Pedersen, JS (1994). "Determination of size distribution from small-angle scattering data for systems with effective hard-sphere interactions". Journal of Applied Crystallography 27 (4): 595–608. doi:10.1107/S0021889893013810. ISSN 1600-5767. Bibcode: 1994JApCr..27..595P.
10. ↑ Gommes, CJ; Jaksch, S; Frielinghaus, H (2021). "Small-Angle Scattering for Beginners". Journal of Applied Crystallography 54 (6): 1832–1843. doi:10.1107/S1600576721010293. PMID 34963770. Bibcode: 2021JApCr..54.1832G.
11. ↑ Hollamby, Martin J.; Aratsu, Keisuke; Pauw, Brian R.; Rogers, Sarah E.; Smith, Andrew J.; Yamauchi, Mitsuaki; Lin, Xu; Yagai, Shiki (2016-08-16). "Simultaneous SAXS and SANS Analysis for the Detection of Toroidal Supramolecular Polymers Composed of Noncovalent Supermacrocycles in Solution" (in en). Angewandte Chemie 128 (34): 10044–10047. doi:10.1002/ange.201603370. Bibcode: 2016AngCh.12810044H. https://onlinelibrary.wiley.com/doi/10.1002/ange.201603370.
12. ↑ Fanova, Anastasiia; Janata, Miroslav; Filippov, Sergey K.; Šlouf, Miroslav; Netopilík, Miloš; Mariani, Alessandro; Štěpánek, Miroslav (2019-08-27). "Evolution of Structure in a Comb Copolymer–Surfactant Coacervate" (in en). Macromolecules 52 (16): 6303–6310. doi:10.1021/acs.macromol.9b00332. ISSN 0024-9297. Bibcode: 2019MaMol..52.6303F. https://pubs.acs.org/doi/10.1021/acs.macromol.9b00332.
13. ↑ Zhang, Xiaohan; Niebuur, Bart-Jan; Chytil, Petr; Etrych, Tomas; Filippov, Sergey K.; Kikhney, Alexey; Wieland, D. C. Florian; Svergun, Dmitri I. et al. (2018-02-12). "Macromolecular p HPMA-Based Nanoparticles with Cholesterol for Solid Tumor Targeting: Behavior in HSA Protein Environment" (in en). Biomacromolecules 19 (2): 470–480. doi:10.1021/acs.biomac.7b01579. ISSN 1525-7797. PMID 29381335. https://pubs.acs.org/doi/10.1021/acs.biomac.7b01579.
14. ↑ Fanova, Anastasiia; Šindelka, Karel; Uchman, Mariusz; Limpouchová, Zuzana; Filippov, Sergey K.; Pispas, Stergios; Procházka, Karel; Štěpánek, Miroslav (2018-09-25). "Coassembly of Poly( N -isopropylacrylamide) with Dodecyl and Carboxyl Terminal Groups with Cationic Surfactant: Critical Comparison of Experimental and Simulation Data" (in en). Macromolecules 51 (18): 7295–7308. doi:10.1021/acs.macromol.8b01161. ISSN 0024-9297. Bibcode: 2018MaMol..51.7295F. https://pubs.acs.org/doi/10.1021/acs.macromol.8b01161.
15. ↑ Leisner, Dietrich; Imae, Toyoko (2003-08-01). "Interpolyelectrolyte Complex and Coacervate Formation of Poly(glutamic acid) with a Dendrimer Studied by Light Scattering and SAXS" (in en). The Journal of Physical Chemistry B 107 (32): 8078–8087. doi:10.1021/jp027365l. ISSN 1520-6106. https://pubs.acs.org/doi/10.1021/jp027365l.
16. ↑ Murmiliuk, Anastasiia; Matějíček, Pavel; Filippov, Sergey K.; Janata, Miroslav; Šlouf, Miroslav; Pispas, Stergios; Štěpánek, Miroslav (2018). "Formation of core/corona nanoparticles with interpolyelectrolyte complex cores in aqueous solution: insight into chain dynamics in the complex from fluorescence quenching" (in en). Soft Matter 14 (37): 7578–7585. doi:10.1039/C8SM01174E. ISSN 1744-683X. PMID 30140809. Bibcode: 2018SMat...14.7578M. http://xlink.rsc.org/?DOI=C8SM01174E.
17. ↑ Dähling, Claudia; Lotze, Gudrun; Drechsler, Markus; Mori, Hideharu; Pergushov, Dmitry V.; Plamper, Felix A. (2016). "Temperature-induced structure switch in thermo-responsive micellar interpolyelectrolyte complexes: toward core–shell–corona and worm-like morphologies" (in en). Soft Matter 12 (23): 5127–5137. doi:10.1039/C6SM00757K. ISSN 1744-683X. PMID 27194585. Bibcode: 2016SMat...12.5127D. http://xlink.rsc.org/?DOI=C6SM00757K.
18. ↑ Sommer, Cornelia; Pedersen, Jan Skov; Garamus, Vasil M. (2005-03-01). "Structure and Interactions of Block Copolymer Micelles of Brij 700 Studied by Combining Small-Angle X-ray and Neutron Scattering" (in en). Langmuir 21 (6): 2137–2149. doi:10.1021/la047489k. ISSN 0743-7463. PMID 15752000. https://pubs.acs.org/doi/10.1021/la047489k.
19. ↑ Filippov, Sergey K.; Chytil, Petr; Konarev, Petr V.; Dyakonova, Margarita; Papadakis, ChristineM.; Zhigunov, Alexander; Plestil, Josef; Stepanek, Petr et al. (2012-08-13). "Macromolecular HPMA-Based Nanoparticles with Cholesterol for Solid-Tumor Targeting: Detailed Study of the Inner Structure of a Highly Efficient Drug Delivery System" (in en). Biomacromolecules 13 (8): 2594–2604. doi:10.1021/bm3008555. ISSN 1525-7797. PMID 22793269. https://pubs.acs.org/doi/10.1021/bm3008555.
20. ↑ Filippov, Sergey K.; Franklin, John M.; Konarev, Petr V.; Chytil, Petr; Etrych, Tomas; Bogomolova, Anna; Dyakonova, Margarita; Papadakis, Christine M. et al. (2013-11-11). "Hydrolytically Degradable Polymer Micelles for Drug Delivery: A SAXS/SANS Kinetic Study" (in en). Biomacromolecules 14 (11): 4061–4070. doi:10.1021/bm401186z. ISSN 1525-7797. PMID 24083567. https://pubs.acs.org/doi/10.1021/bm401186z.
21. ↑ Riabtseva, Anna; Kaberov, Leonid I.; Noirez, Laurence; Ryukhtin, Vasyl; Nardin, Corinne; Verbraeken, Bart; Hoogenboom, Richard; Stepanek, Petr et al. (February 2018). "Structural characterization of nanoparticles formed by fluorinated poly(2-oxazoline)-based polyphiles" (in en). European Polymer Journal 99: 518–527. doi:10.1016/j.eurpolymj.2018.01.007. Bibcode: 2018EurPJ..99..518R. https://linkinghub.elsevier.com/retrieve/pii/S0014305717321055.
22. ↑ Filippov, Sergey K.; Verbraeken, Bart; Konarev, Petr V.; Svergun, Dmitri I.; Angelov, Borislav; Vishnevetskaya, Natalya S.; Papadakis, Christine M.; Rogers, Sarah et al. (2017-08-17). "Block and Gradient Copoly(2-oxazoline) Micelles: Strikingly Different on the Inside" (in en). The Journal of Physical Chemistry Letters 8 (16): 3800–3804. doi:10.1021/acs.jpclett.7b01588. ISSN 1948-7185. PMID 28759235. Bibcode: 2017JPCL....8.3800F.
23. ↑ Suzuki, Daisuke; Nagase, Yasuhisa; Kureha, Takuma; Sato, Takaaki (2014-02-27). "Internal Structures of Thermosensitive Hybrid Microgels Investigated by Means of Small-Angle X-ray Scattering". The Journal of Physical Chemistry B 118 (8): 2194–2204. doi:10.1021/jp410983x. ISSN 1520-6106. PMID 24517119.
24. ↑ Chaves, Matheus Andrade; Oseliero Filho, Pedro Leonidas; Jange, Camila Garcia; Sinigaglia-Coimbra, Rita; Oliveira, Cristiano Luis Pinto; Pinho, Samantha Cristina (July 2018). "Structural characterization of multilamellar liposomes coencapsulating curcumin and vitamin D3" (in en). Colloids and Surfaces A: Physicochemical and Engineering Aspects 549: 112–121. doi:10.1016/j.colsurfa.2018.04.018. https://linkinghub.elsevier.com/retrieve/pii/S0927775718302887.
25. ↑ Di Cola, Emanuela; Grillo, Isabelle; Ristori, Sandra (2016-03-28). "Small Angle X-ray and Neutron Scattering: Powerful Tools for Studying the Structure of Drug-Loaded Liposomes" (in en). Pharmaceutics 8 (2): 10. doi:10.3390/pharmaceutics8020010. ISSN 1999-4923. PMID 27043614.
26. ↑ Zaborova, Olga V.; Filippov, Sergey K.; Chytil, Petr; Kováčik, Lubomir; Ulbrich, Karel; Yaroslavov, Alexander A.; Etrych, Tomaš (April 2018). "A Novel Approach to Increase the Stability of Liposomal Containers via In Prep Coating by Poly[ N -(2-Hydroxypropyl)Methacrylamide with Covalently Attached Cholesterol Groups"] (in en). Macromolecular Chemistry and Physics 219 (7). doi:10.1002/macp.201700508. https://onlinelibrary.wiley.com/doi/10.1002/macp.201700508.
27. ↑ Bressel, Katharina; Muthig, Michael; Prevost, Sylvain; Gummel, Jeremie; Narayanan, Theyencheri; Gradzielski, Michael (2012-07-24). "Shaping Vesicles–Controlling Size and Stability by Admixture of Amphiphilic Copolymer" (in en). ACS Nano 6 (7): 5858–5865. doi:10.1021/nn300359q. ISSN 1936-0851. PMID 22713309. Bibcode: 2012ACSNa...6.5858B. https://pubs.acs.org/doi/10.1021/nn300359q.
28. ↑ Mable, Charlotte J.; Derry, Matthew J.; Thompson, Kate L.; Fielding, Lee A.; Mykhaylyk, Oleksandr O.; Armes, Steven P. (2017-06-13). "Time-Resolved SAXS Studies of the Kinetics of Thermally Triggered Release of Encapsulated Silica Nanoparticles from Block Copolymer Vesicles" (in en). Macromolecules 50 (11): 4465–4473. doi:10.1021/acs.macromol.7b00475. ISSN 0024-9297. PMID 28626247. Bibcode: 2017MaMol..50.4465M.
29. ↑ Filippov, Sergey K.; Bogomolova, Anna; Kaberov, Leonid; Velychkivska, Nadiia; Starovoytova, Larisa; Cernochova, Zulfiya; Rogers, Sarah E.; Lau, Wing Man et al. (2016-05-31). "Internal Nanoparticle Structure of Temperature-Responsive Self-Assembled PNIPAM- b -PEG- b -PNIPAM Triblock Copolymers in Aqueous Solutions: NMR, SANS, and Light Scattering Studies" (in en). Langmuir 32 (21): 5314–5323. doi:10.1021/acs.langmuir.6b00284. ISSN 0743-7463. PMID 27159129.
30. ↑ Cook, Michael T.; Filippov, Sergey K.; Khutoryanskiy, Vitaliy V. (August 2017). "Synthesis and solution properties of a temperature-responsive PNIPAM–b-PDMS–b-PNIPAM triblock copolymer" (in en). Colloid and Polymer Science 295 (8): 1351–1358. doi:10.1007/s00396-017-4084-y. ISSN 0303-402X. http://link.springer.com/10.1007/s00396-017-4084-y.
31. ↑ Sergeeva, Olga; Vlasov, Petr S.; Domnina, Nina S.; Bogomolova, Anna; Konarev, Petr V.; Svergun, Dmitri I.; Walterova, Zuzana; Horsky, Jiri et al. (2014). "Novel thermosensitive telechelic PEGs with antioxidant activity: synthesis, molecular properties and conformational behaviour" (in en). RSC Adv. 4 (79): 41763–41771. doi:10.1039/C4RA06978A. ISSN 2046-2069. Bibcode: 2014RSCAd...441763S. http://xlink.rsc.org/?DOI=C4RA06978A.
32. ↑ Kaberov, Leonid I.; Kaberova, Zhansaya; Murmiliuk, Anastasiia; Trousil, Jiří; Sedláček, Ondřej; Konefal, Rafal; Zhigunov, Alexander; Pavlova, Ewa et al. (2021-06-28). "Fluorine-Containing Block and Gradient Copoly(2-oxazoline)s Based on 2-(3,3,3-Trifluoropropyl)-2-oxazoline: A Quest for the Optimal Self-Assembled Structure for 19F Imaging". Biomacromolecules 22 (7): 2963–2975. doi:10.1021/acs.biomac.1c00367. ISSN 1525-7797. PMID 34180669. https://pubs.acs.org/doi/full/10.1021/acs.biomac.1c00367.
33. ↑ Bernadó, Pau; Svergun, Dmitri I. (2012). "Structural analysis of intrinsically disordered proteins by small-angle X-ray scattering" (in en). Mol. BioSyst. 8 (1): 151–167. doi:10.1039/C1MB05275F. ISSN 1742-206X. PMID 21947276. http://xlink.rsc.org/?DOI=C1MB05275F.
34. ↑ Janisova, Larisa; Gruzinov, Andrey; Zaborova, Olga V.; Velychkivska, Nadiia; Vaněk, Ondřej; Chytil, Petr; Etrych, Tomáš; Janoušková, Olga et al. (2020-01-28). "Molecular Mechanisms of the Interactions of N-(2-Hydroxypropyl)methacrylamide Copolymers Designed for Cancer Therapy with Blood Plasma Proteins" (in en). Pharmaceutics 12 (2): 106. doi:10.3390/pharmaceutics12020106. ISSN 1999-4923. PMID 32013056.
35. ↑ Schuelke, Winfried (21 June 2007). Electron Dynamics by Inelastic X-Ray Scattering. Oxford University Press. ISBN 978-0-19-152328-1.

## External links

* SAXS at a Synchrotron
* A movie demonstrating small-angle scattering using laserlight on a hair

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