Electronic Supplementary Material
Accurate determination of the size distribution for polydisperse, cationic metallic
nanomaterials by asymmetric-flow field flow fractionation
Julien Gigault, Thao M. Nguyen, John M. Pettibone, and Vincent A. Hackley
National Institute of Standards and Technology, Materials Measurement Science Division,
Gaithersburg, MD 20899
Contacts:
julien.gigault@u-bordeaux.fr
vince.hackley@nist.gov
1. TEM and DLS measurements of SeNPs
Particle size analysis was performed using ImageJ under standard procedures as published on the NIH
website (Reinking 2007). Representative distributions of the analytes present in the solutions were
generated by capturing images at multiple locations that were randomly selected on the TEM grid.
Particle size distribution was determined based on the assumption that particles are spherical in size.
Briefly, a bright field TEM image was initially obtained with even illumination. The scale bar was
calibrated with the scale bar from the TEM image. Next, the threshold of the image was set. The
“Analyze Particles” feature was used to generate a table of particle areas and diameters. The ranges of
particle size were set so that the minimum cut off eliminated background nose and the maximum end
filtered out aggregates. The circularity cut-off was 1.1.
Size characterization by batch-mode DLS was performed following the general guidelines set out in a
NIST-NCL protocol.(Hackley and Clogston 2007) A non-negatively constrained least squares
inversion algorithm, provided by the vendor, was used to generate intensity-weighted hydrodynamic
size distributions. A regularization parameter of 0.01 (corresponding to the “General Purpose” setting
of the instrument) was selected, with data parsed over 70 bins. Measurements were conducted at 20°C
in disposable low volume cuvettes.
This data is provided only for comparative purposes and to show the consistency between two
orthogonal methods of analysis. These results are not used for quantitative purposes in the present
work. The DLS derived particle size distribution is model-dependent, and therefore its exact shape and
breadth should not be taken as highly accurate or independent of the model parameter settings.
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(a)
Fig. S1. TEM images with the corresponding diameter distributions obtained (red histogram, inset)
and hydrodynamic diameter distribution (dH, nm) measured by DLS (blue histogram, inset) for three
representative SeNP populations synthesized with a constant concentration of Na 2SeO3 (25 mmol L-1)
and varying CTAB concentrations: (a) 2.5 mmol L-1; (b) 0.25 mmol L-1 and (c) 0.03 mmol L-1. To
calibrate the A4F system one additional population was synthetized with a CTAB concentration of 1.5
mmol L-1 yielding a nominal size of 40 nm (2nd peak on Figure 1 in the main text).
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2. A4F fractionation of SeNPs
We used both DLS in batch mode and on-line A4F-DLS to compare the hydrodynamic diameter of the
SeNPs. The synthesized SeNPs are highly monodisperse and the fractionation conditions do not
change the size distribution of the NPs (both rH from light scattering and the shape of the peak). In
A4F, the colloidal stability of the NPs in the flow dynamics, especially during the focus time, is one of
the most important conditions required to calibrate A4F methods. Additionally, no aggregation peak
was observed, generally characterized by a second peak or an intense residual peak after elution when
Vc=0 mL min-1.
The diffusion coefficient, D, can be determined based on the retention time, tR, when the effective
spacer thickness, ωeff, is known by:
tR 
 V 
ln 1  c 
6 D  V p 
2
Eq. S1
where Vc and Vp are volumetric cross flow and channel flow, respectively. The effective spacer
determination can be obtained by employing a calibrant with a known or measurable D (e.g., online
DLS). The selectivity, Sd, is defined as:
Sd 
d (ln D)
d (ln R)
Eq. S2
where R is the retention ratio. Increasing values of Sd result in higher resolution (i.e., significant
changes in tR resulting from small variations in analyte D).
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Figure S2: (a) On-line representative fractograms for four SeNP populations showing traces measured
at a UVs wavelength of 254 nm (dotted line) and MALS at 90° (solid line) obtained using the
optimized fractionation conditions outlined in the main text; the hydrodynamic radius measured across
each peak by on-line DLS is shown in blue (dots) with values presented on the right-hand y-axis, (b)
plotted relationship between hydrodynamic radius (rzH) and coefficient of diffusion (D), (c)
relationship between retention ratio (R) and D determined from Figure 2a in main text, and (d)
selectivity (Sd) determination by plotting ln (D) vs ln (R).
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3. Multi-Angle Light Scattering
Figure S3: Zimm and sphere fit formalism at tR=tRmax (maximum of the peak) for the four different
SeNPs analyzed by A4F-UV/Vis-MALS-DLS according to the condition described in the manuscript.
The precision of the determination of rG and r, by using, respectively, the Zimm and sphere formlisms,
depends on the R2 value for the fit. After applying the Zimm and spherical formalisms to the four
SeNP populations analyzed by A4F-UV/Vis-MALS-DLS, there are high-angle light scattering
dependencies at the peak maximum, which allow accurate determination of the radius of gyration (rG).
More detail about the static light scattering formalisms is available in the literature.(Burchard 1983)
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4. Band broadening methodology development
From traditional chromatography, peak broadening is related to the plate height, H, by Eq. 1 in the
main text. In A4F, H can be expressed as different sub-plate height contributions and can be
approximated as:
H  Hd  Hn  H p   Hi
Eq. S3
i
The first term in Eq. (5), Hd, takes into consideration the axial diffusion of the analytes in the A4F
channel:
Hd =
2D
R v
Eq. S4
where <ν> is the average carrier velocity (also expressed as L/t0). Hn is related to the uniformity of the
velocity profile and is expressed as:
Hn =
cw 2 v
Eq. S5
D
where χ is a function of R and ω is the spacer thickness. The contribution of the band broadening
resulting from polydispersity at the end of the channel, Hp, is described in Eq. 2 of the main text. ΣHi
is the summation of all other terms influencing the band broadening due to, for instance, the mobile
phase, membrane nature, sample composition, and other parameters that are not individually
quantified in the current work.
5. On-line autocorrelation function of AuNPs
1.7
Correlation function
1.6
@ peak 2 tR max
1.5
@ LS 90o tR max
1.4
1.3
1.2
1.1
1.0
0.9
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
1e+0
1e+1
 (s)
Figure S4: Autocorrelation functions obtained for the AuNP sample by DLS coupled on-line to the
A4F, where peak 2 corresponds to the peak in the UV/Vis trace centered at 7.9 min and LS 90º
corresponds to the light scattering peak centered near 12 min in Figure 4 of the main text.
References
Burchard W (1983) Static and dynamic light scattering from branched polymers and biopolymers. In: Light
Scattering from Polymers, vol 48. Advances in Polymer Science. Springer Berlin Heidelberg, pp 1-124.
doi:10.1007/3-540-12030-0_1
Hackley VA, Clogston JD (2007) Measuring the size of nanoparticles in aqueous media using batch-mode
dynamic light scattering. NIST-NCL joint assay protocol PCC-1, Washington, D.C.
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Reinking L (2007) http://rsb.info.nih.gov/ij/docs/pdfs/examples.pdf.
http://rsb.info.nih.gov/ij/docs/pdfs/examples.pdf.
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