Particle orientation in soft materials from 

small-angle neutron scattering

JACK ROOKS, PETER GILBERT, YUN LIU, PAUL BUTLER

1
Orientation affects material properties

Material properties depend on orientation/alignment

2 https://www.slideserve.com
Orientation affects material properties

Material properties depend on orientation/alignment

2 https://www.slideserve.com

https://www.nsf.gov/

Spider silk molecular structure
Orientation affects material properties

Material properties depend on orientation/alignment

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Rebar in concrete

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https://www.nsf.gov/
Orientation affects material properties

Material properties depend on orientation/alignment

2 http://www.freeimageslive.co.uk

https://socratic.org/

https://www.slideserve.com

https://www.nsf.gov/

Muscle cells
Orientation affects material properties

Material properties depend on orientation/alignment

https://www.nsf.gov/ 2

Plastic bags

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https://www.arubabag.com
Orientation affects material properties

Material properties depend on orientation/alignment

https://www.nsf.gov/ 2 http://www.freeimageslive.co.uk https://socratic.org/

https://www.arubabag.com
Neutron scattering to measure particles

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3

Neutron scattering to measure particles
3

Neutron scattering to measure particles

Neutron

beam
3

Neutron scattering to measure particles

Neutron

beam
3

Neutron scattering to measure particles

Neutron

beam
3

Neutron scattering to measure particles

Neutron

beam
3

Neutron scattering to measure particles

Neutron

beam
What neutron scattering tells us

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2D Pattern

Mean 

orientation

Small angle neutron 

scattering (SANS)
What neutron scattering tells us

4

• Peak: mean orientation

2D Pattern

Small angle neutron 

scattering (SANS)
What neutron scattering tells us

4

• Peak: mean orientation

• Perpendicular: radius

2D Pattern

Small angle neutron 

scattering (SANS)
What neutron scattering tells us

4

• Peak: mean orientation

• Perpendicular: radius

• Parallel: length

2D Pattern

Small angle neutron 

scattering (SANS)
What neutron scattering tells us

4

• Peak: mean orientation

• Perpendicular: radius

• Parallel: length

2D Pattern

Small angle neutron 

scattering (SANS)
What neutron scattering tells us

4

1D Circular Average

• Peak: mean orientation

• Perpendicular: radius

• Parallel: length

2D Pattern
What neutron scattering tells us

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• Shape: particle morphology

• Position: particle dimensions

1D Circular Average

• Peak: mean orientation

• Perpendicular: radius

• Parallel: length

2D Pattern

Length Radius
Orientation from neutron scattering

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Question:

Can we obtain 

orientation 

information 

from SANS?
Orientation from neutron scattering

All particles 

have mean 

orientation

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Orientation from neutron scattering

Sharp features, 

very straight

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Orientation from neutron scattering

Most particles have mean orientation

Some particles point other directions

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Orientation from neutron scattering

A width parameter 

describes distribution

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Orientation from neutron scattering

Smoothed out 

features. Still 

very straight

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Orientation from neutron scattering

Smoothed out, good 

shape

“Waves” along 

x-axis

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Orientation from neutron scattering

Fixed x-axis

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Orientation from neutron scattering

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Theoretical Experimental
Orientation from neutron scattering

Theoretical Experimental Question:

How do we fit 

theoretical 

distribution to

experimental 

data?

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Comparing experimental and theoretical data

Mean

orientation
Consider directions perpendicular and parallel to 

the mean orientation

Mean

orientation

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Comparing experimental and theoretical data
Comparing experimental and theoretical data

Consider directions perpendicular and parallel to 

the mean orientation

• Perpendicular -> radius

• Parallel -> length

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Sector method

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• Experimental (red)

Figure:

• Sector centered on X-axis

• Total sector angle of 15 ̊

Sector method

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Sector method

Increasing 

distribution 

width

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• Experimental (red)

• Theoretical (black)

Figure:

• Sector centered on X-axis

• Total sector angle of 15 ̊
Sector method

• Experimental (red)

• Theoretical (black)

• Best fitting (blue)

Figure:

• Sector centered on X-axis

• Total sector angle of 15 ̊

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Anisotropy factor method

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p
Anisotropy factor method

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p

୮ (degrees) Intensity (cmିଵ

)
Anisotropy factor method

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Anisotropy factor

୮ (degrees) Intensity (cmିଵ

)
Anisotropy factor method

Anisotropy factor Sector method

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Conclusion

• Orientation distribution

can be obtained from

small angle neutron 

scattering

• Can control orientation

to design materials Theoretical Experimental

jrooks@udel.edu

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Supplementary slides

44
Experimental Setup (Rheometer)

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-Experimental (10 ିଵ shear rate)

- Cylindrical micelles

- Cetrimonium bromide (CTAB)

-Rheo-SANS

Obtaining data

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-Theoretical - Cylindrical rods

- Based on fitting parameters 

from experimental CTAB
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Anisotropy factor – q range

q2 (outer radius) = 

q1 (inner radius) = 

with jଵ,ଵ the first positive 0 of the Bessel 

function of the first kind (≈3.83)
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