Characterizing Spherical Nanoparticles by 

Small-Angle X-ray Scattering to Validate 

New Interferometry Techniques

SURF Summer Colloquium 2021

Daven Shah

Gaithersburg Campus | NIST
Background

Small Angle Scattering (SAS) vs. Far Field Interferometry (INFER)

• Both identify structural features between 1nm – 1μm

Image Credit: Dan Hussey. NCNR Cold Imaging Station. 

Project goals: 

• Construct Library of scattering data for spherical nanoparticles

• Validate INFER data based on scattering data

• Further analyze systems of nanoparticles other than spheres for validation

1

SANS/SAXS Interpretation
Ludox Silica Spherical Nanoparticles

• Well Characterized

• Generally Monodispersed

• Have a charge and counterion

Ludox Listed Radius (nm) Net Charge Counterion

SM 3.5 nm - Na+

LS 6 nm - Na+

CL 6 nm + ClHS40 6 nm - Na+

TM50 11 nm - Na+

2
Small Angle Scattering

QQ =

2ππ

dd

=

4ππ

λλ sin θθ

Neutron/

X-ray 

Beam

2Θ QQ

Sample 2D Detector

Intensity vs Q plot

I(Q) ~ P(Q) S(Q)

P(Q): Form Factor

S(Q): Structure Factor

Lower Q

Larger particle 

size

Higher Q

Smaller particle 

size

3
Understanding The Sphere Form Factor

Ludox Scale Scale 

Uncertainty

Radius 

(nm)

Radius

Uncertainty Polydispersity

SM 4.59E-03 1.02E-05 4.51 0.01 0.292

LS 4.81E-03 1.20E-05 7.94 0.01 0.160

CL 3.80E-03 1.01E-05 7.94 0.01 0.165

HS40 4.52E-03 1.20E-05 6.57 0.01 0.350

TM50 3.96E-03 1.31E-05 13.02 0.03 0.141

4

Ludox Scale Radius (nm) Polydispersity

SM 4.59 x 10-3 ± 1 x 10-5 4.51±0.01 0.292

LS 4.81 x 10-3 ± 1 x 10-5 7.94±0.01 0.160

CL 3.80 x 10-3 ± 1 x 10-5 7.94±0.01 0.165

HS40 4.52 x 10-3 ± 1 x 10-5 6.57±0.01 0.350

TM50 3.96 x 10-3 ± 1 x 10-5 13.02±0.01 0.141

Turnover Regions
LS Concentration Series:

Form Factor 

Parameters

I(Q) ~ P(Q) 

P(Q): Form Factor

% Stock 

Concentration Scale Radius 

(nm) Polydispersity

1 1.306 x 10-3 ± 4 x 10-6 7.925 18.00%

5 4.76 x 10-3 ± 1 x 10-5 7.925 18.00%

10 8.92 x 10-3 ± 3 x 10-5 7.925 18.00%

5
LS Concentration Series:

Form Factor 

Parameters

% Stock 

Concentration Scale Radius (nm) Polydispersity

1 1.306 x 10-3 ± 4 x 10-6 7.925 18.00%

5 4.76 x 10-3 ± 1 x 10-5 7.925 18.00%

10 8.92 x 10-3 ± 3 x 10-5 7.925 18.00%

25 5.3 x 10-1 ± 2 x 10-2 7.925 18.00%

50 3.40 x 10-1 ± 4 x 10-3 7.925 18.00%

75 2.69 x 10-1 ± 2 x 10-3 7.925 18.00%

100 2.32 x 10-1 ± 2 x 10-3 7.925 18.00%

I(Q) ~ P(Q)

P(Q): Form Factor

6
LS Concentration Series:

Structure Factor 

Parameters

% Stock 

Concentration Scale Radius (nm) Polydispersity Volume Fraction Charge (e-)

Salt 

Concentration 

(mM)

1 1.306 x 10-3 ± 4 x 10-6 7.925 18.00% -

5 4.76 x 10-3 ± 1 x 10-5 7.925 18.00% -

10 8.92 x 10-3 ± 3 x 10-5 7.925 18.00% -

25 5.3 x 10-1 ± 2 x 10-2 7.925 18.00% 2.87 x 10-2 ± 8 x 10-4 198.73 5.73

50 3.40 x 10-1 ± 4 x 10-3 7.925 18.00% 6.36 x 10-2 ± 7 x 10-4 198.73 5.73

75 2.69 x 10-1 ± 2 x 10-3 7.925 18.00% 9.60 x 10-2 ± 7 x 10-4 198.73 5.73

100 2.32 x 10-1 ± 2 x 10-3 7.925 18.00% 1.33 x 10-1 ± 1 x 10-3 198.73 5.73

I(Q) ~ P(Q) S(Q)

P(Q): Form Factor

S(Q): Form Factor

7
Conclusions

• Different kinds of Ludox provide diverse fits

• Concentration Effects

• Lower concentrations of Ludox nanoparticles fit best with the sphere form factor

• Higher concentrations of Ludox nanoparticles require both the sphere form 

factor and the Hayter-Penfold structure factor

• Next Steps to further validate INFER approach:

• Observe effects on Hayter-Penfold Structure factor after modifying parameters

• Conducting other dilutions series to verify Hayter-Penfold Structure Factor

• Analyze nanoparticles that require other form factors/structure factors

8
Acknowledgements

• Caitlyn Wolf and Katie Weigandt (Mentors)

• NCNR Directors

• SURF Directors

9