Ian W. Hamley - Small-Angle Scattering

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2 Professor Ian Hamley's Book Publications Professor Ian Hamley's Book Publications Authored The Physics of Block Copolymers Introduction to Soft Matter (first and revised edition) Block Copolymers in Solution Introduction to Peptide Science Edited Developments in Block Copolymer Science and Technology Nanoscale Science and Technology (with R.W. Kelsall and M. Geoghegan) Hydrogels in Cell‐Based Therapies (with C. Connon)

3 Title Page Small‐Angle Scattering Theory, Instrumentation, Data, and Applications Ian W. Hamley School of Chemistry, University of Reading, UK

4 Copyright

5 Preface

6 1 Basic Theory1.1 INTRODUCTION 1.2 WAVENUMBER AND SCATTERING AMPLITUDE 1.3 INTENSITY FOR ANISOTROPIC AND ISOTROPIC SYSTEMS AND RELATIONSHIPS TO PAIR DISTANCE DISTRIBUTION AND AUTOCORRELATION FUNCTIONS 1.4 GUINIER APPROXIMATION 1.5 FORM AND STRUCTURE FACTORS1.6 STRUCTURE FACTORS 1.7 FORM FACTORS 1.8 FORM AND STRUCTURE FACTORS FOR POLYMERS REFERENCES

7 2 Data Analysis2.1 INTRODUCTION 2.2 PRE-MEASUREMENT SAMPLE CONCENTRATION AND POLYDISPERSITY MEASUREMENTS 2.3 OVERVIEW: DATA REDUCTION PIPELINE 2.4 CORRECTIONS FOR SAMPLE TRANSMISSION AND OTHERS 2.5 BACKGROUND CORRECTIONS 2.6 DETECTOR CORRECTIONS, MASK FILES, AND INTEGRATION 2.7 ANISOTROPIC DATA 2.8 CALIBRATION OF Q SCALE 2.9 ABSOLUTE INTENSITY CALIBRATION 2.10 ABSORPTION 2.11 SMEARING EFFECTS 2.12 SOLUTION SAXS DATA CHECKS 2.13 POROD REGIME 2.14 KRATKY PLOTS 2.15 ZIMM PLOTS 2.16 INVARIANT AND RELATED INFORMATION CONTENT FROM SAS MEASUREMENTS 2.17 FORM FACTOR FITTING 2.18 SAS SOFTWARE REFERENCES

8 3 Instrumentation for SAXS and SANS3.1 INTRODUCTION 3.2 SYNCHROTRON FACILITIES 3.3 NEUTRON SCATTERING FACILITIES 3.4 SYNCHROTRON SAXS INSTRUMENTATION 3.5 LABORATORY SAXS INSTRUMENTATION 3.6 SANS INSTRUMENTATION 3.7 ULTRA‐SMALL‐ANGLE SCATTERING INSTRUMENTS 3.8 STANDARD SAMPLE ENVIRONMENTS – SAXS 3.9 STANDARD SAMPLE ENVIRONMENTS – SANS 3.10 STANDARD SAMPLE ENVIRONMENTS – GISAS 3.11 MICROFOCUS SAXS AND WAXS3.12 SPECIALIZED SAMPLE ENVIRONMENTS REFERENCES

9 4 Applications and Specifics of SAXS4.1 INTRODUCTION 4.2 PRODUCTION OF X‐RAYS 4.3 SCATTERING PROCESSES FOR X‐RAYS 4.4 ATOMIC SCATTERING FACTORS 4.5 ANOMALOUS SAXS AND SAXS CONTRAST VARIATION 4.6 BIOSAXS: SOLUTION SAXS FROM BIOMACROMOLECULES, ESPECIALLY PROTEINS 4.7 SOLUTION SAXS FROM MULTI‐DOMAIN AND FLEXIBLE MACROMOLECULES 4.8 SOLUTION SAXS FROM MULTI‐COMPONENT SYSTEMS – BIOMOLECULAR ASSEMBLIES 4.9 PROTEIN STRUCTURE FACTOR SAXS 4.10 SAXS (AND WAXS) STUDIES OF SOFT MATTER SYSTEMS 4.11 SAXS AND WAXS FROM SEMICRYSTALLINE POLYMERS 4.12 LIPID PHASES: ELECTRON DENSITY PROFILE RECONSTRUCTION 4.13 SAXS STUDIES OF PEPTIDE AND LIPOPEPTIDE ASSEMBLIES 4.14 SAXS STUDIES OF THE STRUCTURE FACTOR OF COLLOIDS 4.15 SAXS AND SAXS/WAXS STUDIES OF BIOMATERIALS 4.16 FAST TIME‐RESOLVED SAXS REFERENCES

10 5 Applications and Specifics of SANS5.1 INTRODUCTION 5.2 PRODUCTION OF NEUTRONS 5.3 DIFFERENTIAL SCATTERING CROSS‐SECTION 5.4 SCATTERING LENGTHS 5.5 SANS DATA REDUCTION CONSIDERATIONS 5.6 CONTRAST VARIATION 5.7 SINGLE MOLECULE SCATTERING FROM MIXTURES OF PROTONATED AND DEUTERATED MOLECULES 5.8 SANS FROM LABELLED POLYMERS 5.9 KINETIC SANS USING LABELLED MIXTURES 5.10 ULTRA‐SMALL‐ANGLE SANS (USANS) 5.11 SANS AND USANS (AND SAXS AND USAXS) STUDIES ON POROUS STRUCTURES 5.12 SANS ON MAGNETIC MATERIALS 5.13 SPIN‐ECHO SANS (SESANS) 5.14 COMPLEMENTARY SAXS AND SANS REFERENCES

11 6 Grazing‐Incidence Small‐Angle Scattering6.1 INTRODUCTION 6.2 BASIC QUANTITIES: DEFINITION OF ANGLES, REFRACTIVE INDEX, AND SCATTERING LENGTH DENSITY 6.3 CHARACTERISTIC SCANS 6.4 THE DISTORTED WAVE BORN APPROXIMATION 6.5 DATA ANALYSIS 6.6 EXPERIMENTAL EXAMPLES OF GISAS DATA 6.7 EXPERIMENTAL EXAMPLES OF GIWAXS/GIXD DATA REFERENCES

12 Index

13 End User License Agreement

1 Chapter 1 Table 1.1 Sequences of Bragg reflections for common structures. Table 1.2 Expressions for common form factors.

2 Chapter 2Table 2.1 Absorption cross‐sections and mass absorption coefficients for x‐ra...Table 2.2 SAS Software and online calculators.

3 Chapter 3Table 3.1 International synchrotron scattering facilities.Table 3.2 International neutron scattering facilities.Table 3.3 Currently marketed lab SAXS instruments.Table 3.4 Available q range assuming a detector with area 1 m 2for different s...

4 Chapter 4Table 4.1 Characteristic of ATSAS algorithms for rigid body modelling of macr...

5 Chapter 5Table 5.1 Neutron scattering lengths and cross sections for elements/main iso...

6 Chapter 6Table 6.1 Table of scattering length densities and critical angles for GISAXS...

1 Chapter 1 Figure 1.1 Definition of wavevector qand scattering angle 2 θ , related ... Figure 1.2 Ghost particle construction. The overlap volume (shaded) is the a... Figure 1.3 Sketches of pair distance distribution functions for the colour‐c... Figure 1.4 Scattering within particles (from atoms/components shown as black... Figure 1.5 Calculated total intensity I ( q ) = P ( q ) S ( q ) in the monodisperse ap... Figure 1.6 Fluctuations in the layer positions in a lamellar structure that ... Figure 1.7 Representative one‐, two‐, and three‐dimensional structures, with... Figure 1.8 Compilation of SAXS profiles measured for PEO‐PBO [polyoxyethylen... Figure 1.9 Indexation of SAXS reflections observed for the lipid monoolein f... Figure 1.10 Long‐range versus short‐range order showing schematics of real s... Figure 1.11 Schematic of lattice distortions in paracrystals with lattice di... Figure 1.12 Example of fitting of SAS data using the unified Beaucage model,... Figure 1.13 Example of calculated form factor using the generalized Beaucage... Figure 1.14 Example of SAXS data for a bicontinuous microemulsion (Pluronic ... Figure 1.15 Calculated structure factors using the Debye‐Bueche structure fa... Figure 1.16 Parameters for complex form factors. (a) Gaussian bilayer, (b) P... Figure 1.17 Form factors calculated for homogeneous particles along with lim... Figure 1.18 Inter‐relationship between vectors qand rin cylindrical co‐ord... Figure 1.19 Influence of polydispersity on the form factor of a sphere with Figure 1.20 Comparison of form factor of a polydisperse sphere ( R = 30 Å, σ ... Figure 1.21 Debye form factor for a polymer with Rg = 50 Å. Figure 1.22 Comparison of form factor for random walk (Gaussian) chains and ... Figure 1.23 Structure factor for a diblock copolymer melt with f = 0.25 at t...

2 Chapter 2 Figure 2.1 Schematic pipeline for reduction of small‐angle scattering data.... Figure 2.2 SAXS data from 20‐frame solution SAXS measurements showing CORMAP... Figure 2.3 Masking of stripes in 2D SAXS data measured on a modern photon co... Figure 2.4 Integrating anisotropic SAXS data: (a) Sector integration and def... Figure 2.5 Calculated WAXS pattern and peak indexation from para‐bromobenzoi...Figure 2.6 SAXS data measured for lysozyme (4 mg ml −1in buffer, 5 × 5...Figure 2.7 SAXS data measured for RNAse (10 mg ml −1in buffer, 7 × 30 ...Figure 2.8 Guinier plots (data on a logarithmic intensity scale) showing a G...Figure 2.9 Example of raw synchrotron BioSAXS data showing artefacts in the ...Figure 2.10 Schematic showing effect of interparticle interference (structur...Figure 2.11 Non‐superposition of I ( q )/ c curves for solutions of a surfactant...Figure 2.12 Interference and aggregation effects on (a–c) scattered intensit...Figure 2.13 Example of Porod‐Debye plot for a hybrid protein (RAD51AP1‐malto...Figure 2.14 Examples of Kratky plots: black line: polymer coil (calculated f...Figure 2.15 Kratky plots of SANS data for poly(methyl methacrylate) (PMMA) w...Figure 2.16 Example of Zimm plots obtained from a SANS study of the backbone...