Assessing particle orientation in 

small angle neutron scattering

Jack Rooks (jackrook@buffalo.edu), Peter Gilbert

1
Motivation

- Material properties depend on orientation/alignment

2 https://www.slideserve.com/malo/chapter-15-polymers-characteristics-applications-and-processing

https://www.nsf.gov/news/mmg/media/images/spider_silk2_h2.jpg
Motivation

- Material properties depend on orientation/alignment

3 https://www.slideserve.com/malo/chapter-15-polymers-characteristics-applications-and-processing

https://www.nsf.gov/news/mmg/media/images/spider_silk2_h2.jpg
Motivation

- Material properties depend on orientation/alignment

4 https://www.slideserve.com/malo/chapter-15-polymers-characteristics-applications-and-processing

https://www.essentialchemicalindustry.org/materials-and-applications/composites.html
Experimental Setup (Rheometer)

5
Experimental Setup (Rheometer)

6
Experimental Setup (Rheometer)

7
Experimental Setup (Rheometer)

8
Neutron Scattering 

9

- Neutron 

beam
Neutron Scattering

10

- Neutron 

beam
Neutron Scattering

11

- Neutron 

beam

- Scattered 

neutron
Neutron Scattering

12

- Neutron 

beam

- Scattered 

neutron
Neutron Scattering

13

- Neutron 

beam

- Scattered 

neutron
Experimental Setup (Rheometer)

14

p

p
Experimental

• Cylindrical micelles

- 0.03 M Cetrimonium bromide (CTAB)

- 0.24 M Sodium salicylate

• Rheo-SANS

- 10 s−1 shear rate

Obtaining Data

15
Experimental

• Cylindrical micelles

- 0.03 M Cetrimonium bromide (CTAB)

- 0.24 M Sodium salicylate

• Rheo-SANS

- 10 s−1 shear rate

Obtaining Data

16

Theoretical

• Cylindrical rods

- Mean radius of 20 Å

- 5% polydispersity in radius

- Length of 1800 Å
Characterizing Alignment

17
Characterizing Alignment

18
Characterizing Alignment

19
Characterizing Alignment

20
Characterizing Alignment

21

Questions to answer:
Characterizing Alignment

22

Questions to answer:

• How does alignment factor describe 

alignment?
Characterizing Alignment

23

Questions to answer:

• How does alignment factor describe 

alignment?

• What is the best way to calculate it?
Cosine expansion

Differences in Calculation Methods

24 Walker, et. al., Macromolecules 29, 1996 Hayward, et. Al., Rev. Sci. Instrum. 92, 2021

https://doi.org/10.1021/ma951127p https://doi.org/10.1063/5.0040675
Cosine expansion 2nd order Legendre

Differences in Calculation Methods

25 Walker, et. al., Macromolecules 29 (1996) Hayward, et. al., Rev. Sci. Instrum. 92 (2021)

https://doi.org/10.1021/ma951127p https://doi.org/10.1063/5.0040675
Alignment Factor From Series Expansion

26

θθp = 22.5° θθp = 0°

θθp = 90°

Theoretical min (θ=0 ̊)

Theoretical max (θ=90 ̊)
Alignment Factor From Series Expansion

27

θθp = 22.5° θθp = 0°

θθp = 90°

Theoretical min (θ=0 ̊)

Theoretical max (θ=90 ̊)
Alignment Factor From Series Expansion

28

Theoretical min (θ=0 ̊)

Theoretical max (θ=90 ̊)

θθp = 22.5° θθp = 0°

θθp = 90°
Alignment Factor From Series Expansion

29

Theoretical min (θ=0 ̊)

Theoretical max (θ=90 ̊)

θθp = 22.5° θθp = 0°

θθp = 90°
Calculating Alignment Factor – Integrated Axes

30

θθp = 22.5°

Iwase, et. al., Journal of Colloid and Interface Sciences 538 (2019) https://doi.org/10.1016/j.jcis.2018.11.104
31

Calculating Alignment Factor – Integrated Axes

θθp = 22.5°
Experimental

Reminder: Scattering Pattern Shapes

32

Theoretical
Comparison

Theoretical Experimental

33
Summary

Location matters

34

Methods not 

equivalent
Summary

Location matters

35

Methods not 

equivalent Future Plans

- Determine particle 

orientation 

between radial and 

tangential 

configurations

- Which alignment 

factor describes 

particle orientation 

best?

Email: jackrook@buffalo.edu
Supplementary slides

36
Cosine expansion and Legendre polynomial

37

θθp = 22.5°
Cosine expansion and Legendre polynomial

38

θθp = 22.5°
Calculating Alignment Factor – Series Expansion

39

θθp = 22.5°
Cosine expansion

Calculating Alignment Factor – Series Expansion

40

θθp = 22.5°
Cosine expansion

2nd order Legendre

Calculating Alignment Factor – Series Expansion

41

θθp = 22.5°
42

Calculating Alignment Factor – Integrated Axes

θθp = 45°
43

θθff = 45°

Calculating Alignment Factor – Integrated Axes