Manuscript – 2013.On the exposure assessment of engineered nanoparticles in aquatic environments
Multimethod 3D characterization of natural plate-like nanoparticles: shape effects on equivalent size measurements.
Julián Alberto Gallego-Urrea, Julia Hammes, Geert Cornelis, Martin Hassellöv
Department of chemistry and molecular biology, University of Gothenburg
Gothenburg, Sweden
Supplementary information:
XRD crystal structure
Figure S1. XRD pattern of the Illite suspension after drying overnight. Crystal structure was determined using a Siemens Smart CCD diffractometer.
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Table S1. Weight % excluding carbon after sample preparation and EDX analysis (1) / W% (3)Element / A (2) / B (2) / C (2) / D (2) / E (2)
O / 56.23% / 67.52% / 61.56% / 81.03% / 83.79% / 46.04%
Na / 0.18% / 0.38% / 0.22% / 0.47% / 0.57% / 0.00%
Mg / 1.13% / 1.15% / 1.18% / 0.51% / 0.52% / 1.66%
Al / 11.02% / 8.88% / 9.84% / 6.98% / 4.09% / 13.82%
Si / 20.02% / 15.47% / 18.16% / 7.38% / 7.77% / 24.76%
P / 0.16% / 0.18% / 0.17% / 0.18% / 0.00% / 0.04%
S / 0.00% / 0.00% / 0.00% / 0.43% / 0.70% / 0.00%
K / 6.41% / 3.61% / 4.92% / 1.63% / 1.33% / 6.99%
Ti / 0.13% / 0.32% / 0.00% / 0.00% / 0.00% / 0.35%
Fe / 4.72% / 2.49% / 3.95% / 1.22% / 1.24% / 5.97%
Co / 0.00% / 0.00% / 0.00% / 0.00% / 0.00% / 0.00%
Cu / 0.00% / 0.00% / 0.00% / 0.16% / 0.00% / 0.00%
Mn / 0.00% / 0.00% / 0.00% / 0.00% / 0.00% / 0.03%
(1)Sample preparation is described for each column: Sample A, B and C were dried overnight at 80C and put onto a carbon tape; D and E correspond to a carbon tape submerged in an illite suspension of 0.065 g/L for 12 h for C and 6.5 g/L for 2 h for B. Scales are indicated by the white bar: A, B and E 3 um; C and D 1 um.
(2)Scale bars: A, B and E 3μm; C and D 1μm
(3)Weight % from supplier excluding lost on ignition (8.02%)
Manuscript - On the exposure assessment of engineered nanoparticles in aquatic environments
Table S2. Characteristics of the cF3-FLD-MALLS-DLS instrumentation
cF3 system / Postnova CF 2000centrifuge radius / 10.2 cm
channel width / 2 cm
channel length / 57.6 cm
channel temperature / 298 K
channel flow rate / 1 mL min-1
injection volume / 100 μL
void volume a / 2.15 mL
eluent / 5 mM NaCl brought at pH 8 (NaOH)
Parameters for equation (3)
/ 2500 rpm
t1 / 10 min
ta / -25 min
FLD detector / JASCO FP 920
excitation wavelength / 650 nm
emission wavelength / 650 nm
MALLS detector / Postnova PN3621 MALLS
wavelength / 630 nm
measurement angles / 7, 12, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164 degrees
DLS detector / Malvern zetasizer (Nano-S)
wavelength / 532 nm
measurement angle / 173o
a obtained after calibration using spherical latex 200, 300 and 600 nm particles.
Calculation of the hydrodynamic radius for spheroids
The calculations here presented are based on the creeping motion or Stokes equations for slow motion fluids where inertial effects are neglected(Happel and Brenner 1983).The equations for settling of orthotropic bodies have been used. The validity of these equations is therefore for NRe< 0.05– 5 where
(S1)
With
= density, kg/m3
U = fluid velocity,m/s
d = equivalent hydrodynamic length
= viscosity, Pa.s
The drag force for this case is:
(S2)
With
(S3)
Where Ki corresponds to 6.π.Ri and Ri is the Stoke’s radius. The subscripts correspond to the three coordinates as will be described below. This is the expression for averaging the drag force in all possible random orientations.
The following equations are valid for oblate spheroids when the fluid is approaching in the direction represented by the arrow in the corresponding figure; the corresponding equation from Happel(Happel and Brenner 1983) is given:
Eq 5.11.24a=b and φ=c/a <1 / (S4)
Eq. 5.11.20
a=b and φ=c/a <1 / (S5)
Solving for the average value of K using equation S3:
(S6)
Equation S6 gives an expression for the averaged hydrodynamic radius,R̅, under the conditions described earlier.
Other procedure:
The same procedure for determining the hydrodynamic radius can be followed with the equations derived by Perrin (1934):
For a sphere the Stokes friction factor for translational movement is (equivalent to equation 2 but keeping the notation from Perrin; i.e. a=RH):
(S7)
For spheroids:
(S8)
(S9)
If b > a (ellipsoid of revolution (spheroids) oblate ~ discs)
(S10)
Solving for the average in three dimensions for oblate spheroids:
(S11)
Results from DLS analysis
Figure S2. PSD obtained from DLS measurements using CONTIN algorithm (left) and general porpoise algorithm (right). Top: intensity based distribution. Middle: volume based distribution transformed with Mie theory using the Zetasizer software. Bottom: Number based distribution transformed with Mie theory using the Zetasizer software.
MALLS results
Figure S3. MALLS data and infinite thin plate fits of fractions measured at different tr during cF3 runs occurring at low (left) or high (right) field strength.
Calibration of the cF3 and DLS on-line adjustments
Calibration
Figure S4 shows the calibration of the cF3 channel using 200, 300 and 600 nm latex spheres. The void volume of 2.15 mL best fit experimental data using DSEDINT calculations.
Figure S4. Calibration of the cF3 channel.
Effect of flow rate on DLS measurements
Figure S5 shows that, as observed previously (Nicoli David et al. 1991), the effect of flow rate while measuring on-line using DLS is not significant up to flow rates of 2 mL min-1. However, the effect of laser source intensity appears significant as lower source intensity (lower attenuator) leads to underestimation of dh. The laser source intensity is optimized to an as low as possible value that ensures sufficient counts for dh determination, while at the same time minimizes the effect of multiple scattering. More dilute particle suspensions therefore need higher source intensity. The intensity should therefore be altered during a cF3-DLS measurement where the particle concentration varies as a function of time, but the long time needed for such an optimization prevents any practical use, because the particle stream may vary too fast for an optimization to stabilize. In practice, the intensity was set at the maximum value, because the particle suspension is diluted extensively during cF3 fractionation. However, it is not known whether such would introduce overestimation of the Dh determination at the higher diffracted light intensities.
Figure S5. Effect of flow rate and signal amplification on the measured Z-average hydrodynamic diameter. A lower attenuator implies a lower amplification in this case. No optimum attenuator values were obtained for attenuator 6 at flow rates 1.5 and 2 mL min-1.
Optimization of field strength
Two other field strength programs were tested, other than the one presented in the main manuscript, a lower and higher field strength (Table S3). Figure S6 shows the FLD nephelomteric intensity and the dp fitted using MALLS. Although it has been argued that MALLS fitted dp values are not accurate, they serve here qualitatively.
Table S3. Parameters for equation (3) used in two other power-programmed cF3 methods
“Low” field strength / “High” field strength / 1500 rpm / 4500 rpm
t1 / 10 min / 10 min
ta / -25 min / -35 min
Figure S6 shows that the FLD signal of the particles eluting at low tr is high in the case of the low field strength, suggesting a significant particle fraction elutes at these tr. These particles are likely a mixture of very large particles dominating the FLD, MALLS and DLS light scattering signals, and small particles having dv< 10 nm that cannot be separated from the void peak at the given field strength. A higher field strength did not manage to separate these particles, because even more severe deviations from cF3 theory occurred at low tr as can be concluded from the wider low tr range during which particles with a large dp elute. A higher field strength is indeed expected to increase the effects of steric inversion and the entropic contributions (Beckett and Giddings 1997) and thus helps not to fractionate smaller particles from larger ones. There is a wide tr range, however, where no observations occur suggesting steric inversion or an entropic contribution: 2 min <tr< 50 min and 20 min <tr< 50 min for the low and high filed respectively.
Figure S6: FLD intensity and MALLS fitted dp as a function of retention time in the case of the “low” field strength (left) and “high” field strength (right).
Optimization of dilution
When multiple scattering occurs, e.g. when the particle concentration is too high, the dh is underestimated. This is illustrated in Fig S7, where the measured Z-average dh is shown from three different cF3 measurements of differently diluted illite suspensions. The field strength during these preliminary measurements was not optimized and initial field strength was set at 1000 rpm, but the dh measurements indeed increase with higher dilutions. Moreover, the limited change in dh going from 5 times to 10 times diluted suggests most dh measurements of five times diluted illite suspensions are accurate. Larger deviations at higher tr owe also to the lower diffracted intensity of the ten times diluted particle suspensions.
Figure S7. Effect of dilution on DLS measurements during cF3elution
References:
Beckett R, Giddings JC (1997) Entropic contribution to the retention of nonspherical particles in field-flow fractionation. Journal of Colloid and Interface Science 186 (1):53-59
Happel J, Brenner H (1983) Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. Prentice-Hall,
Nicoli David F, Kourti T, Gossen P, Wu J-S, Chang Y-J, MacGregor John F (1991) On-Line Latex Particle Size Determination by Dynamic Light Scattering. In: Particle Size Distribution II, vol 472. ACS Symposium Series, vol 472. American Chemical Society, pp 86-97. doi:10.1021/bk-1991-0472.ch005
Perrin F (1934) Mouvement brownien d'un ellipsoide - I. Dispersion diélectrique pour des molécules ellipsoidales. J Phys Radium 5 (10):497-511
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