Sample Development for Small 

Angle Scattering and Neutron 

Interferometry

KAITLYN ESNEAULT

CAITLYN WOLF -- MENTOR

KATIE WEIGANDT -- MENTOR

NIST SURF PROGRAM 2023
• Small Angle X-Ray Scattering (SAXS)

◦ Scattered by electrons in material

◦ Good for heavy elements with many electrons

• Small Angle Neutron Scattering (SANS)

◦ Scattered by nuclei in material

◦ Much better penetration, but weaker scattering effect

• Difficult to use for heterogenous samples

Small Angle Scattering (SAS)

• Statistical characterization of materials

◦ Reveals interatomic detail smaller than wavelength 

of visible light

◦ Works at length scales of 1nm – 10μm

2

I Q = φ∆ρ

2P Q S(Q)

Q =

4π

λ

sin(

θ

2

)

https://www.nist.gov/image/scatteringgif-0
Neutron Interferometry & INFER

• Characterize materials at multiple length scales simultaneously

◦ Dark field interferometry: 1nm-10μm (same as SAS)

◦ Direct imaging: 50μm-100μm

• SAS information for more complex (heterogenous or hierarchical) materials 

• Data is related to SAS data by a Hankel transform

3

neutron

source

phase gratings

sample

detector

source grating
4

Sample System

• Self-assembling Sodium Dodecyl Sulfate / βCyclodextrin complex (SDS@2β-CD)

• Concentration-dependent phase behavior

Supplementary Figure 1. The general phase diagram of the SDS/β-CD

aqueous solution at room temperature. Yang, S., Yan, Y., Huang, J. et

al. Giant capsids from lattice self-assembly of cyclodextrin complexes. Nat

Commun 8, 15856 (2017). https://doi.org/10.1038/ncomms15856

Figure 1. Stylized view of the lipid-like and protein-like self-assembly. Yang, S., Yan, Y., Huang, J. et al. Giant

capsids from lattice self-assembly of cyclodextrin complexes. Nat Commun 8, 15856 (2017).

https://doi.org/10.1038/ncomms15856
My Objectives

1. Develop a more comprehensive phase space for the 

SDS@2β-CD system using SAS characterization techniques

2. Facilitate the system’s use in testing the accuracy of a 

novel far field interferometer

5
0

10

20

30

40

50

0.3 0.4 0.5 0.6 0.7

Concentration (weight % in H2O)

Molar Ratio (SDS/β-CD)

Sample Distribution

0

10

20

30

40

50

0.3 0.4 0.5 0.6 0.7

Concentration (weight % in H2O)

Molar Ratio (SDS/β-CD)

Sample Distribution

6

Preliminary Samples

• Recreate literature findings

• Dynamic Light Scattering (DLS)

◦ Look for trends in particle radii

• Small Angle X-Ray Scattering (SAXS)

◦ Get structural information from data fitting

Dodecahedra

Tubes

Lamellae
SAXS results

7

Figure 4a. X-ray scattering of the SDS@2β-CD structures. Yang, S., Yan, Y., Huang, J. et al. Giant capsids

from lattice self-assembly of cyclodextrin complexes. Nat Commun 8, 15856 (2017).

https://doi.org/10.1038/ncomms15856 ***Graphs are artificially spaced out along y-axis for clarity***
SAXS results

8

Figure 4a. X-ray scattering of the SDS@2β-CD structures. Yang, S., Yan, Y., Huang, J. et al. Giant capsids

from lattice self-assembly of cyclodextrin complexes. Nat Commun 8, 15856 (2017).

https://doi.org/10.1038/ncomms15856

1.52nm

2π

4.1

≈ 1.52

***Graphs are artificially spaced out along y-axis for clarity***
SAXS results

9

Figure 4a. X-ray scattering of the SDS@2β-CD structures. Yang, S., Yan, Y., Huang, J. et al. Giant capsids

from lattice self-assembly of cyclodextrin complexes. Nat Commun 8, 15856 (2017).

https://doi.org/10.1038/ncomms15856

3.5nm

2π

1.8

≈ 3.5

***Graphs are artificially spaced out along y-axis for clarity***
SAXS results

10

Figure 4a. X-ray scattering of the SDS@2β-CD structures. Yang, S., Yan, Y., Huang, J. et al. Giant capsids

from lattice self-assembly of cyclodextrin complexes. Nat Commun 8, 15856 (2017).

https://doi.org/10.1038/ncomms15856

12-25nm

***Graphs are artificially spaced out along y-axis for clarity***
SAXS results

11

0

10

20

30

40

50

0.3 0.4 0.5 0.6 0.7

Concentration (weight % in H2O)

Molar Ratio (SDS/β-CD)

Sample Distribution

Dodecahedra

Tubes

Lamellae
Data Fitting

12

• SASView (www.sasview.org)

◦ lamellar_stack_paracrystal form factor

◦ Incorporates bilayer form factor and a term to account for interference caused by having lamellar stacks of bilayers

• Key parameters:

◦ thickness – thickness of layers

◦ Nlayers – number of layers

◦ d_spacing – spacing between layers

I Q = φ∆ρ

2P Q S(Q)

1

2

3

4

• Used for lamellar phase and microtube phase
Data Fitting

13

0

10

20

30

40

50

60

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Χ

2

Concentration (weight %)

Goodness of Fit

20.0 wt%

microtubes

27.5 wt%

lamellae
Data Fitting

14

*** Error bars are too small to be visible on these graphs ***

0

2

4

6

8

10

12

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Nlayers

Concentration (mass %)

Number of Layers

0

50

100

150

200

250

300

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

d_spacing (Å)

Concentration (mass %)

Lamellar Spacing
SANS Data

15

***SANS data was collected by Katie Weigandt and Kelsi Rehmann at the Australian Nuclear Science and Technology Organisation (ANSTO) on the Bilby beamline***

Unexpected lamellar peaks

in SANS data
SANS Data

16

***SANS data was collected by Katie Weigandt and Kelsi Rehmann at the Australian Nuclear Science and Technology Organisation (ANSTO) on the Bilby beamline***

layers are closer together

than expected

◦ Samples prepared in D2O rather than H2O
Transformation to Dark Field Intensity

17

Figure 4a. The response of the thermo-reversible microtubes to variations in concentration. Ouhajji, 

Samia, et al. In Situ Observation of Self-Assembly of Sugars and Surfactants from Nanometresto 

Microns. Soft Matter, vol. 13, no. 13, Mar. 2017, pp. 2421–25. pubs.rsc.org, 

https://doi.org/10.1039/C7SM00109F.

?
Transformation to Dark Field Intensity

18

• Add hollow_cylinder form factor to approximate low-Q data from literature values
Conclusions & Future Research

• This system is a good candidate for validating data from the new interferometer

• Areas for further study:

◦ Other cyclodextrins

◦ Effect of D2O

◦ More powerful SAS instrument for lower Q study

◦ Better models for dodecahedral and microtube phases

19
References

1. Landman, J. et al. Inward growth by nucleation: Multiscale self-assembly of ordered

membranes. Sci. Adv. 4, eaat1817 (2018). https://doi.org/10.1126/sciadv.aat1817

2. Strobl, M. General solution for quantitative dark-field contrast imaging with grating

interferometers. Sci Rep 4, 7243 (2014). https://doi.org/10.1038/srep07243

3. Wolf, C. M. et al. Blend Morphology in Polythiophene–Polystyrene Composites from Neutron

and X-ray Scattering. Macromolecules 54 (6), 2960 (2021).

https://doi.org/10.1021/acs.macromol.0c02512

4. Yang, S., Yan, Y., Huang, J. et al. Giant capsids from lattice self-assembly of cyclodextrin

complexes. Nat Commun 8, 15856 (2017). https://doi.org/10.1038/ncomms1585

This work benefited from the use of the SasView application, originally developed under NSF

award DMR-0520547. SasView also contains code developed with funding from the European

Union’s Horizon 2020 research and innovation programme under the SINE2020 project, grant

agreement No 654000.

20
Supplemental Slides

21
lamellar_stack_paracrystal thickness parameter

• Bilayer thickness should be constant

• Further evidence this model may not be the best fit for the microtube phase

• Perhaps an artifact from the curvature of the tubes

• Note the error bar on the 7.5 wt% sample

22

0

5

10

15

20

25

30

35

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

thickness (Å)

Concentration (mass %)

thickness
30 wt% Sample SANS Data

• Suspected issues loading sample – lamellar peaks absent

23
lamellar_stack_paracrystal Model Fitting – Raw Data

sample concentration background error scale error Nlayers error d_spacing error sigma_d error thickness error Χ

2

5A 7.5 3.6318E-06 2.8093E-02 3.9084E-01 1.1141E-03 3.8269E+00 4.4691E-02 2.4934E+02 1.4759E-01 6.2764E-02 3.2191E-03 2.6302E+00 2.8842E+01 8.9507

6A 10 1.7741E-07 3.0989E-03 7.6143E-01 2.4814E-03 5.4764E+00 5.9880E-02 2.2914E+02 8.2188E-02 6.3246E-02 5.1847E-04 1.4399E+01 5.4875E-01 18.652

7A 15 2.8180E-02 2.7798E-04 1.7703E+00 4.5201E-03 6.6491E+00 5.8205E-02 1.7909E+02 4.3471E-02 5.7677E-02 3.5589E-04 2.5379E+01 6.5646E-02 22.91

8A 20 2.5091E-02 3.7408E-04 2.0632E+00 5.6064E-03 1.0457E+01 1.5140E-01 1.5586E+02 3.6304E-02 6.2845E-02 3.5145E-04 2.4295E+01 7.0081E-02 42.746

9A 22.5 4.5582E-02 7.9176E-04 3.2838E+00 1.8328E-02 1.0569E+01 1.2259E-01 1.2689E+02 2.7204E-02 5.1189E-02 4.7271E-04 2.9457E+01 1.2023E-01 56.273

10A 25 3.0886E-02 7.6085E-04 3.8791E+00 1.7334E-02 9.5918E+00 1.5194E-01 1.2982E+02 3.5502E-02 1.7334E-02 4.4086E-04 2.9528E+01 1.0042E-01 25.784

11A 27.5 2.8919E-02 7.1873E-04 3.9127E+00 1.7799E-02 8.5022E+00 8.0421E-02 1.1546E+02 2.4681E-02 5.7803E-02 4.2741E-04 2.9367E+01 1.0050E-01 28.406

12B 30 3.9406E-02 3.9193E-04 2.2963E+00 1.0334E-02 8.4077E+00 8.8577E-02 1.1657E+02 2.8128E-02 5.9877E-02 5.2205E-04 3.0463E+01 9.7483E-02 18.874

13B 35 3.9630E-02 3.2523E-04 1.8982E+00 8.9735E-03 5.7868E+00 7.7784E-02 1.2298E+02 5.2324E-02 9.3762E-02 6.7624E-04 3.0820E+01 1.0243E-01 9.2532

24