Claire Dazon
email: claire.dazon@inrs.fr

Olivier Witschger

Sébastien Bau

Vanessa Fierro

Philip L Llewellyn

Nanomaterial identification of powders: comparing Volume Specific Surface Area, X-Ray Diffraction and Scanning Electron Microscopy methods

Nanomaterials in powder form are widely produced and used in numerous applications

Introduction

Nanomaterials are now a large industry [START_REF] Roco | The long view of nanotechnology development: the National Nanotechnology Initiative at 10 years[END_REF][START_REF] Leong | Nanosafety Issues of Nanomaterials[END_REF][START_REF] Foss Hansen | Nanoproductswhat is actually available to European consumers?[END_REF] . The improvement and increasing control of synthesis processes as well as the new properties of materials developed at the nanoscale suggest that this area is expected to continue to grow.

Whatever the application and the context, the identification of the "nano" nature of substances is an essential step. For example, when implementing the chemical registration dossiers in Europe (REACH regulation) 4 , nanomaterials match the definition of "substances" and therefore, identification and information provisions for them are applicable. Similarly, the responsible management of risks associated to nanomaterials in the workplace requires their identification to propose preventative measures 5, 6 .

Boverhof et al 7 focused on available nanomaterial definitions in the regulatory context worldwide and pointed out a lack of harmonization. By consequence, it is important to indicate the nanomaterial definition used when characterizing any substance. In 2011, the European Commission (EC) issued a recommendation on the definition of nanomaterials related to legal classification , this recommended EC definition, "provides the most specific measurable parameters of nanomaterials compared to other definitions", that is why it appears that several areas rely on this recommendation for the solely nanomaterial identification. A substance is considered as a nanomaterial since at least 50% of the constituent particles in the number size distribution have one or more external dimensions between 1 nm and 100 nm. To determine this distribution, the EC recommends implementing the best available methods and the most appropriate and harmonized protocols as possible. Electron Microscopy (EM) methods are widely harnessed in this view since they let have a direct characterization of particle size and shape 10, 11 . However, these methods are time consuming and require significant human and material resources for both imaging and post-hoc analysis.

Another possibility proposed by EC to identify nanomaterials relies on the determination of the Volume Specific Surface Area (VSSA) when possible. This parameter was suggested as an alternative when defining nanomaterials to overcome disadvantages related to size measurements. The VSSA (equation 1) of a material is calculated from the external specific surface area (A Ex ) and the material's skeletal density ρ:

Based on its VSSA, a substance is considered as a nanomaterial: "when it presents a volume specific surface area greater than 60 m²/cm 3 "

8

. This limit of 60 m²/cm 3 , also named VSSA Cutoff , corresponds to the VSSA of monodisperse spherical non-porous particles with a density of 1 g/cm [START_REF] Foss Hansen | Nanoproductswhat is actually available to European consumers?[END_REF] and a diameter of 100 nm. The VSSA Cutoff has been recently discussed for adapting the threshold value according to the particle shape (40 m²/cm 3 for fiberlike particles or 20 m²/cm 3 for platelets

12

). However, in the absence of consensus, the threshold of 60 m²/cm 3 remains the VSSA Cutoff to consider when applying EC recommendation for nanomaterial identification. Moreover, if a material is identified as non-nanomaterial with its VSSA, particle sizing remains mandatory to confirm the previous statement.

The VSSA method is a particularly attractive approach since it is relatively well adapted for powders. Indeed, for a powder, the A Ex can be determined by the relevant gas adsorption method 13-15 ; and the skeletal density of the material can be obtained by Helium pycnometry [START_REF] Lowell | Density measurement[END_REF] . These two methods are less expensive overall and more readily available than EM. Above all, powders are increasingly encountered in industry and laboratories (synthesis and/or use) as they are included in the composition of products across a very wide range of activity sectors: building, food and agriculture, cosmetics, energy, and so forth. The 2016 public R-Nano report indicates that almost 475,000 tons of nanomaterials were manufactured, distributed or imported in France 17 . Thus, there is an increasing need for nanomaterial identification for regulation purpose, process control, as well as risk assessment. Therefore, the relative easier accessibility of VSSA could be an interesting solution to identify nanomaterials. Although gas adsorption and Helium pycnometry are relatively widely available, precise sample preparation and rigorous data analysis are necessary. Both techniques need a sample outgassing to limit underestimation of measured values 18-22, 34 . The A Ex determination requires an accurate selection of the models (BET for non porous, macroporous or mesoporous powders, t-plot model for microporous powders) as explained by Lecloux [START_REF] Lecloux | Discussion about the use of the volume-specific surface area (VSSA) as criteria to identify nanomaterials according to the EU definition[END_REF] and

Wohlleben et al [START_REF] Wohlleben | Reliable nanomaterial classification of powders using the volume-specific surface area method[END_REF] in their works about the use of VSSA for nanomaterial classification. Besides, skeletal density measured by Helium pycnometry can be validated by comparison with the material's theoretical density, based on its theoretical chemical and crystallographic composition.

To date, the Nanodefine European project [START_REF] Weigel | NanoDefine -An integrated analytical approach to implement the EC definition of nanomaterial[END_REF] allowed advances in the assessment of the relevance of VSSA for the classification of powders as nanomaterials. This project particularly focused on industrial powders representative of the most frequently encountered materials. However, it is still necessary to evaluate the reliability of VSSA for nanomaterial powder identification for promoting this parameter as an alternative approach when EM methods are not available. Besides, in spite of SOPs and guides availability, an operational strategy for VSSA implementation, notably accessible for non-specialists of material characterization, is manifest. Furthermore, it would be interesting to discuss the relative merits of VSSA versus EM methods.

In this context, our study aimed to bring new results supplementing those of the Nanodefine European project for nanomaterial identification. In particular, a detailed operational approach was applied to a series of representative industrial powders to determine their VSSA and state whether they have to be considered as nanomaterials. The relevancy of the classification of powders by VSSA is evaluated by comparing the corresponding equivalent particle size with the Scanning Electron Microscopy (SEM) reference method and with the equivalent particle size derived from X-Ray Diffraction (XRD).

Materials and Methods

Materials

The eight powders used in this study are presented in Table 1. The metal oxides TiO 2 , SiO 2 and CaCO 3 , seven in total, represent the most frequently encountered materials in France according to the latest R-Nano report (2016), with recorded quantities exceeding 1000 tons. That is why we selected them as we considered these materials are representative of powders potentially found in workplaces. These metal oxides are produced at industrial scale and are used in products with applications in engineering, food and agriculture, cosmetics, paints and varnishes, energy and even textiles. In addition of the metal oxides, a powdered activated carbon Maxsorb® which is used for its high specific surface area (> 3000 m²/g) mainly for gas storage by adsorption [START_REF] Otowa | Production and adsorption characteristics of MAXSORB: High-surface-area active carbon[END_REF] was chosen. These powders were selected based on the A t indicated by their de-identified suppliers, which covered a broad range from a few tens of m²/g to more than 3000 m²/g.

Characterization approach

The industrial powders were characterised by the approach schematized in figure 1. This strategy can be broken down into three phases.

Phase 1 (P1)

The first phase consists in implementing the following four characterisation methods in parallel: thermogravimetric analysis (TGA), chemical analysis, XRD and SEM.



TGA allows an optimised outgassing protocol to be selected for sample preparation before the gas adsorption and Helium pycnometry measurements when seeking to calculate the powders' VSSAs.  Chemical analysis by X-ray fluorescence, ICP-MS or ICP-OES, or alternatively the supplier's data allow the material's composition to be included when selecting the theoretical density ρ th to be compared to the ρ measured by Helium pycnometry, for validation of the experimental results.  XRD allows determining the crystal structure of the particles making up the powder as well as their proportions. Moreover, it is possible to calculate a mean particle size d XRD by applying the Scherrer formula (equation 2): Where λ is the wavelength of the X-ray in nm, θ is the Bragg angle for the diffraction peak used for the calculation.

The angle with the greatest radian intensity is generally selected. β is the full-width at half-maximum of the selected diffraction peak, in radians. This formula is based on the hypothesis that the particles are spherical or cubic and monocrystalline and appears to be appropriate for crystal sizes greater than 10 nm 27 . The crystal structure is also considered when selecting the theoretical density of the material to be compared to the density measured by Helium pycnometry for validation of the experimental results.



SEM can be used to determine the main shape of the constituent particles in the powder, making it possible to choose a D factor from which a cutoff VSSA value can be defined (VSSA Cutoff ) as proposed by Wohlleben et al [START_REF] Wohlleben | Reliable nanomaterial classification of powders using the volume-specific surface area method[END_REF] . In addition, SEM can be used to establish the size distribution of the constituent particles in the powder when the number of identifiable and isolated particles on the acquired images is sufficient, i.e., at least 100 to 200 particles 28, 29 . The size of the measured particles corresponds, most of the time, to the mean Feret diameter 29, 30 or to the projected equivalent surface diameter d S of a disc of area S according equation 3 for spherical particles:

For particles in the form of fibres (D = 2), the diameter, rather than the length of the fibre, is measured. For particles in the form of platelets (D = 1), the thickness is measured. In this work, d SEM corresponds to d S for spherical particles, the diameter of a fibre for fibre-like particles or the thickness of platelets.

Phase 2 (P2)

The second step is to determine the VSSA by performing gas adsorption and Helium pycnometry measurements on outgassed samples, prepared by the optimised protocol selected following the thermogravimetric measurements.

Phase 3 (P3)

The third step is data analysis.

Gas adsorption

The gas adsorption isotherms are compared to the typical isotherms proposed by IUPAC 14 so as to apply:



The BET model when a type II (non-porous or macroporous material) or type IV (mesoporous material) isotherm is obtained, for which A Ex = A t . This model is the easiest to apply and the most relevant for these types of isotherm [START_REF] Sing | Classical Interpretation of Physisorption Isotherms at the Gas -Solid Interface[END_REF] .



The t-plot model is applied when a type I (microporous model) isotherm is obtained, it extracts the A Ex from the A t for microporous materials. Rouquerol et al. 32, 33 described how the calculation for the t-plot method should be applied from the values for the Boer "universal t curve" obtained for a non-porous alumina. This reference is the most frequently used to determine the A Ex for microporous materials using the t-plot model and is the one used in this work.

Helium pycnometry

Measurements of the skeletal density ρ by Helium pycnometry were compared to the theoretical values ρ th selected based on the chemical and crystallographic data available for the powders. The measurements were validated by verifying that the relative difference between ρ and ρ th was less than 10%, which corresponds to the uncertainty of the pycnometry measurement.

Determining the VSSA and comparing equivalent particle diameters

The VSSA was calculated (equation 1) from validated A Ex and skeletal density data and compared to the VSSA Cutoff , which was selected on the basis of the particle shapes observed in SEM images (D factor).

The equivalent mean diameter d VSSA of the particles making up the powder was calculated from the value of the VSSA and the D factor (equation 4):

The mean diameters obtained by the three characterisation methods for size measurement: VSSA (d VSSA ), XRD (d XRD ), SEM (d SEM ) were then compared to the size determined by SEM, with an arbitrarily determined relative bias tolerance of ± 15% corresponding to the maximum rounded absolute average bias we obtained in the comparison of VSSA and SEM. As the d SEM is the reference diameter, the ultimate classification of the powder as a nanomaterial or not was based on that value. The comparison of equivalent particle size lets validate the nanomaterial classification based on the solely VSSA value.

Experimental

For each characterisation method in the approach, the experimental details and additional explanations are provided hereafter.

TGA

In this work, thermogravimetric analyses were performed with a thermobalance (Q500, TA Instruments). Samples were heated from room temperature (RT) up to 600 °C with a 10 C/min slope under argon at 100 mL/min. The TGA results directly affected how gas adsorption and Helium pycnometry were implemented during the characterisation approach. As a result, details of the TGA results are presented in the gas adsorption and Helium pycnometry paragraphs. Before performing gas adsorption measurements, it is important to outgas the samples so as to eliminate the chemical species that may be adsorbed on the (external and internal) surfaces of the particles as water or atmospheric pollutants. Otherwise, A t measurements might be underestimated due to the presence of previously adsorbed molecules [START_REF] Rouquerol | Methodology of Gas adsorption[END_REF] . Outgassing is also required prior to measurement of the skeletal density by Helium pycnometry. The appropriate outgassing protocol can be selected by thermogravimetric analysis of the powder, whereby the powder sample is submitted to a temperature range, with addition of a neutral sweeping gas such as nitrogen or argon (to avoid chemical reactions between molecules and the powder). The sample's mass is monitored during the heating programme. The sample is considered "cleaned" when the mass variation as a function of time reaches a plateau that is maintained for at least 30 minutes. Before gas adsorption, powders are generally outgassed for at least 1 hour under a given vacuum, at the temperature corresponding to the one at which the mass variation plateau was attained in thermogravimetry. When elaborating the outgassing protocol before gas adsorption, one can chose for instance, the outgassing temperature corresponding to the beginning of plateau observation obtained with TGA. However, thermogravimetry does not exactly reproduce the vacuum conditions implemented when outgassing powders before gas adsorption. In addition, although recommended, it is important to ensure that the samples are not degraded by the vacuum and the temperature applied during outgassing. A visual inspection is generally sufficient. A change in colour or appearance of the powder indicates that the sample has become degraded and that the outgassing procedure must be reviewed, such as by reducing the degassing temperature or extending its duration.

XRD

XRD measurements were performed with a Siemens-Bruker AXS D5000 diffractometer in Bragg-Brentano configuration (coupled mode θ-2θ) with Cu-Kα radiation (wavelengths K α 1 = 0.15444 nm and K α 2 = 0.15406 nm with a K α 1/K α 2 wavelength ratio = 0.5). The proportions of the phases and the size of the crystalline domains were assessed using FullProf software (version 2015 for Windows, available at https://www.ill.eu/sites/fullprof/) based on the Rietveld method and by applying the Scherrer formula (equation 2).

Chemical analysis

In this work, it was not possible to perform chemical analysis to determine chemical powder compositions. So, we used the chemical compositions in major elements (% weight) given by the various suppliers (see Table 1) were used when selecting the theoretical densities.

SEM

EM images were acquired with a Zeiss Ultra-Plus Scanning Electron Microscope linked to a Bruker Quantacs 400 Energy Dispersive Spectrometer (EDS). Powder samples were deposited on aluminium pins covered with carbon tape (G3347N, Agar Instruments). The pins were then exposed to a metallizer (Denton Desk V) for 45 minutes to deposit carbon in order to make the samples conductive. Between 15 and 20 images were collected at 2 kV with magnifications between x 10,000 and x 500,000. A mean particle size d SEM was calculated as fewer than 50 particles could be counted on all the images obtained for each powder. Images were treated using Image J software (Java version 1.8.0).

Gas adsorption

Gas adsorption measurements were performed with an automatic adsorption equipment (TRIFLEX, Micromeritics) with nitrogen as probe gas, at 77 K. As TGA analyses showed that all the samples were heat-stable over the RT-300 °C interval at atmospheric pressure, and this range is compatible with water and surface pollutants desorption, previously adsorbed onto the received powder materials. The selected outgassing temperature was 150 °C (mean temperature at which the mass variation plateau was measured) under vacuum (10 -2 mmHg) for a minimum of 24 hours. Only activated carbon was heated to 250 °C due to the known (but unquantified) microporosity of carbon. Indeed, microporous powders must be outgassed for longer time and/or at higher temperature to eliminate the species adsorbed in the narrow micropores [START_REF] Rouquerol | Methodology of Gas adsorption[END_REF] . All measurements were performed in triplicate on new samples. The A Ex for powders were then calculated by applying the analytical procedure explained in phase 3 of the characterisation approach.

Comparison of d VSSA vs d SEM and d XRD vs d SEM to evaluate relevancy of VSSA and XRD for nanomaterial identification

Helium pycnometry

The skeletal densities of the powders were determined by Helium pycnometry (Accupyc 1340, Micromeritics) in triplicate, with prior calibration of the measurement cell, as recommended by the manufacturer. Samples were dried in an oven at 105 °C overnight before performing measurements. The system used was incompatible with drying under vacuum, therefore samples were cooled in a desiccator and Helium pycnometry experiments were performed immediately after cooling to limit adsorption of water and other atmospheric gases. Experimental density measurements were validated by comparing the results obtained to the theoretical densities, taking the theoretical chemical compositions of the powders and their crystal structures (and proportions), as determined by XRD, into account.

Results and discussion

The results of this work are presented in the order of the characterisation approach used (see figure 1).

XRD, chemical composition and densities

The XRD and Helium pycnometry results are presented together in Table 2.

The crystal phases of powders are indicated along with their mass proportions. TiO 2 powders LSSA, MSSA and HSSA have a 100% anatase structure, TiO 2 P25 is an anatase/ rutile mixture with mass proportions 87/13. The two CaCO 3 have a 100% calcite structure. The crystal phases detected were those expected for these materials. SiO 2 and activated carbons, as MSC-30, powders are amorphous materials. By combining the crystallographic results with the chemical composition of the powders indicated by the suppliers, the theoretical densities can be selected for comparison with the skeletal densities measured by Helium pycnometry for validation. The powders studied here were considered pure to between 94.5 and 100% (Table 1). The theoretical densities for each powder therefore corresponded to the density of the corresponding raw materials. In the case of TiO 2 P25, the theoretical density combines that of anatase and rutile taking the mass ratio of each crystal phase into consideration. The theoretical densities used for the comparison were taken from the Handbook of Chemistry and Physics (96th edition).

Compared to the theoretical densities, most of the skeletal densities measured by Helium pycnometry displayed biases of less than 10%. These skeletal densities were therefore validated and used to calculate the VSSA. The bias in the skeletal densities measured was greater for two powders -TiO 2 HSSA (-13.5%) and MSC-30 (+ 17.3%) -these bias values were attributed to insufficient degassing prior to analysis, perhaps due to the fact that the powder samples were not placed under vacuum before the Helium pycnometry measurements with the Accupyc 1340 device. Thus, for these two powders, the theoretical density was used to calculate the VSSA.

SEM

Figure 2 shows representative SEM images for each of the powders at different magnifications for comparison at the 100 nm scale except for the activated carbon and CaCO 3 A. For all the powders we observed that the constituent particles were extensively agglomerated, but individual particles remained sufficiently distinguishable to allow at least 50 particles to be measured, although in many cases measurements may have been imprecise. TiO 2 P25 was made up of spherical particles corresponding to the anatase phase. The rutile particles would have been characterised by a rod-like shape on the SEM images, but they were impossible to identify. Given the mass proportions of the crystal phases of anatase (87%) and rutile (13%) for TiO 2 P25, it was assumed that only the anatase particles were counted. The CaCO 3 A and MSC-30 powders have particles in the form of platelets, the other powders are composed of spherical particles. Consequently, the value D = 1 gives a VSSA Cutoff of 20 m²/cm

Specific surface area and VSSA

Figure 3 shows the nitrogen adsorption isotherms for TiO 2 MSSA and SiO 2 . These adsorption isotherms were selected to demonstrate the most operational approach for analysis of the nitrogen adsorption isotherms for industrial powders. These adsorption isotherms were determined to be of type II for TiSO 2 MSSA and composite type I (b) +II for SiO 2 , based on the reference isotherms proposed by IUPAC 14 . The BET model was used to calculate A Ex for the TiO 2 MSSA sample. This choice is obvious as the TiO 2 MSSA isotherm is equivalent to that of the IUPAC type II isotherm. In contrast, the calculation is more difficult for SiO 2 as its isotherm combines a type I (b) and a type II form. Figure 4 shows for relative pressures P/P° between 10 -6 and 10 -3

, nitrogen adsorption for silica varies between 0 and 6 mmol/g. This represents a significant gas adsorption (almost 30% of the total) covering three orders of magnitude, as a result, we applied the t-plot model to calculate the A Ex 33, 34 . From these observations, we can conclude that the microporous surface of this silica represents 85% of the total surface area. The other nitrogen adsorption isotherms can be found in the Supplementary Information. The isotherms obtained for TiO 2 LSSA and P25, and those for CaCO 3 A and B were type II (non-porous or macroporous) whereas that for TiO 2 HSSA corresponded to a composite I (b) and II isotherm. MSC-30 presented a type I (b) adsorption isotherm. The BET model was therefore applied for TiO 2 LSSA and P25, CaCO 3 A and B powders, whereas the t-plot model was selected for TiO 2 HSSA and MSC-30. Table 3 lists the A Ex , the D factor determined by SEM, the VSSA Cutoff and the VSSA for the powders studied. Values are indicated ± 1 standard deviation. Powders for which the VSSA is greater than the VSSA Cutoff are considered nanomaterials according to this method, they are indicated by a green background. The powders not identified as nanomaterials are indicated by a red background. These results show that the VSSA could have been used in a reliable way for the studied powders without requiring EM analysis. If only the VSSA Cutoff of 60 m²/cm 3 (hypothesis D =3) is used for comparison with the experimental VSSA data, the classification of the powders as nanomaterials remains correct, except for MSC-30. TiO 2 LSSA and CaCO 3 A are not nanomaterials and the other powders are nanomaterials according to their d SEM .

These results corroborate the observations of Wohlleben et al. [START_REF] Wohlleben | Reliable nanomaterial classification of powders using the volume-specific surface area method[END_REF] who correctly classified 12 powders as nanomaterials based on their VSSA but could have avoided EM analysis to confirm this classification for the materials they tested. These new data should be considered with caution however because of the broad discrepancies observed. These latter might have been reduced with more replication of experiments or supplementary EM characterization (Transmission Electron Microscopy for instance).

The d XRD values were also compared to the d SEM , a mean bias of -25% was found. Once again, the lowest bias (0%) was obtained for TiO 2 MSSA, whereas the greatest bias (-63%) was obtained with CaCO 3 A. The other biases were between 22% and 57%. These results indicate that XRD can be used in the sole case of spherical and monocrystalline particles to calculate an equivalent particle size. These results agree with the previous study of Weibel et al

36

. Therefore, one can consider XRD as a complementary method for particle size determination. Contrary to VSSA, XRD cannot be used without EM analysis for a reliable classification of powders as nanomaterials because of the necessary shape determination (spherical particles) to apply the Sherrer equation.

Conclusion

In the context of the identification of nanomaterials, this study proposes to compare equivalent particle sizes of eight industrial powders determined by the VSSA, XRD and SEM (reference) methods through a detailed and operational characterisation approach. The results highlight the importance of sample preparation before the gas adsorption and Helium pycnometry measurements, and the careful analysis of the data to determine the VSSA. In particular, the proposed data treatment involves a precise analysis of the gas adsorption isotherms to calculate the external specific surface area for the particles making up the powders, and validation of the Helium pycnometry measurements by comparison with the theoretical density. These two parameters are used to calculate the VSSA for the powder. The comparison of results obtained by the VSSA and SEM methods shows a good correlation in terms of equivalent particle sizes, leading us to conclude the VSSA nanomaterial identification is reliable, although one microporous activated carbon was falsely classified as a nanomaterial based on its VSSA values. In contrast, comparison of the XRD method with the SEM method reveals that the XRD can only reasonably be used to calculate an equivalent particle size when the particles being studied are spherical and monocrystalline. This work provides additional details on the VSSA determination (gas adsorption and Helium Pycnometry) in complement to the recent NanoDefine European project examining the relevance of the VSSA for classification of nanomaterials. The notable results were that no false negatives were obtained with the VSSA method, and that this parameter appeared to be potentially used for the powder studied without confirmation of the nanomaterial classification with size measurement by EM. As this work was carried out on a restricted number of materials, this trend should be confirmed testing more substances with the same approach.

8 .

 8 As explained by Gao and Lowry 9

Fig. 1

 1 Fig. 1 Diagramme schematizing the general approach used in this work to determine the VSSA of powders and comparison with the XRD and SEM (reference) methods for nanomaterials identification.

Fig. 2

 2 Fig.2 (continued)

Fig. 3

 3 Fig. 3 Characteristic type II nitrogen adsorption isotherm obtained for TiO2 MSSA and mixed isotherm obtained for SiO2.

Fig. 4

 4 Fig. 4 SiO2 displaces a mixed nitrogen adsorption isotherm on a semi-log scale.

Fig. 5 :

 5 Fig. 5 : Equivalent particle diameters obtained by VSSA, XRD and SEM methods. The error bars correspond to the standard deviation.

Table 1

 1 Physico-chemical characteristics of the industrial powders studied, as indicated by suppliers.

Table 2

 2 Crystal phases of the powders, their mass proportions as measured by XRD, and skeletal densities measured by Helium pycnometry. Values are indicated with one standard deviation. SEM images of the powders studied in this work.

	Fig. 2

for CaCO 3 A and MSC-30 whereas D = 3 gives a VSSA Cutoff of 60 m²/cm

Acknowledgements

We would like to thank E. Jankowska, former member of the Central Institute for Labour Protection (CIOP -Poland) for coordinating with the Nanostruktur laboratory where the scanning electron microscopy images were produced.

Table 3 External specific surface area (AEx), shape factor (D) and VSSA obtained for the eight tested powders.

The powders studied had a large diversity of surface areas, with A Ex values between 5 m²/g and 358 m²/g, spanning almost three orders of magnitude. The VSSA values obtained were between 13 m²/cm [START_REF] Foss Hansen | Nanoproductswhat is actually available to European consumers?[END_REF] and 923 m²/cm Interestingly, when we compare all the VSSA values to the VSSA Cutoff of 60 m²/cm 3 (hypothesis D =3), which we would do if the shape of the particles was unknown, the classification remains the same.

Comparison of VSSA, XRD and SEM methods for measurement of constituent particle size

The equivalent mean diameters of the constituent particles determined for the powders, d VSSA , from their VSSA were compared to the mean particle diameters d XRD and d SEM determined by XRD and SEM, respectively (figure 5). Amorphous materials were not compared in terms of d XRD as their diffractograms were impossible to exploit. Similarly, the rutile phase of TiO 2 P25 was not used in the comparison as the VSSA could not distinguish the crystal phases of the particles and their corresponding sizes and because no rutile was visible (rod-shaped particles) on the SEM images. The sizes determined by the three methods and the bias between the results can be found in Table 4 of the Supplementary Information. The lowest bias (0%) was obtained for TiO 2 MSSA, which had a constituent particle size of 19 nm, and SiO 2 , with a constituent particle size of 10 nm. The greatest bias was obtained with MSC-30 (-100%). The other biases were between -19% and +31%. The mean bias for all experimental points combined was -12%. Generally, XRD underestimates the particle sizes whereas VSSA biases do not display trend in the discrepancies. The XRD underestimation could be attributed to the Scherrer formula application as the particle shapes are not perfectly spherical. Based on this comparison, MSC-30 is falsely identified as a nanomaterial by VSSA. Indeed, the VSSA classes this activated carbon as a nanomaterial based on its porosity and the shape of the particles (D = 1 for the platelets and a VSSA Cutoff of 20 m²/cm 3 ). However, the d SEM for carbon is 18 µm with high standard deviation attributed to the difficulty to have repeatable measures of the platelets thickness on the SEM images. This difference can be attributed to the use of the t-plot model which may not be appropriate for this type of material. In contrast, the t-plot model works well for the other microporous powders, TiO 2 HSSA and SiO 2 , for which the bias on particle size was -15% and 6%, respectively. This bias is within the tolerance range ±15 % set. For the other materials in this study, the VSSA (m²/cm

Conflicts of interest

The authors certify there are no conflicts of interest to declare.