Volume-specific surface area by gas adsorption analysis with the BET method

CHAPTER 4.1

Volume-specific surface area by gas adsorption analysis with the BET method Neil Gibsona, Petra Kuchenbeckerb, Kirsten Rasmussena, Vasile-Dan Hodoroabab, Hubert Rauschera a European Commission, Joint Research Centre (JRC), Ispra, Italy Bundesanstalt f u €r Materialforschung und -pr€ ufung (BAM), Berlin, Germany

b

Abbreviations AFM BET EC EC NM definition EM EU FWHM GHS ISO IUPAC OECD REACH SDS (S)SA STM TEM US EPA VSSA

atomic force microscopy Brunauer, Emmett, and Teller European Commission The European Commission’s recommendation on a definition of nanomaterial electron microscopy European Union full width at half maximum Globally Harmonized System of Classification and Labelling of Chemicals International Organization for Standardization International Union of Pure and Applied Chemistry Organisation for Economic Co-operation and Development (EU) Regulation concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals safety data sheet (specific) surface area scanning tunneling microscopy transmission electron microscopy United States Environmental Protection Agency volume-specific surface area

Introduction The specific surface area (SSA) is an important material parameter since particle and pore size can fundamentally alter the characteristics and performance of materials. SSA analysis of powder and/or porous materials is therefore widely used in industry as a classical material metric, and it is usually performed by applying the method of Brunauer, Emmett, and Teller (BET) [1] or modifications thereof. SSA is included in the list of basic physical and chemical properties of safety data sheets (SDS) according to the Globally Harmonized Characterization of Nanoparticles https://doi.org/10.1016/B978-0-12-814182-3.00017-1

© 2020 Elsevier Inc. All rights reserved.

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System of Classification and Labelling of Chemicals (GHS) [2]. The SSA is also considered by the Organisation for Economic Co-operation and Development (OECD) [3–6] and in the EU [7–11] and the United States [12] as a physical–chemical property relevant for the safety assessment of nanomaterials. In the context of the European Union chemicals regulation REACH [11] and specifically in its amended Annexes, it is compulsory to report the SSA of forms of substances that fulfil the criteria of the definition of nanomaterial recommended by the European Commission (EC) [13]. SSA can also be used to distinguish different nanoscale substances according to an Information Gathering Rule by the US Environmental Protection Agency (US EPA) [12]. Moreover, in the EC’s recommendation on a definition of nanomaterial (EC NM definition), the SSA by volume may be used under specific conditions to identify nanomaterials [14]. This chapter first gives an introduction to the concepts of SSA and volume-specific surface area (VSSA) and an outline of the BET method. It continues with a discussion of the relationship between particle size, shape, and the VSSA, followed by an overview of instrumentation, experimental methods, and standards. Finally, sections on the use of the VSSA as a tool to identify nanomaterials and non-nanomaterials and its role in a regulatory context provide some insight on the importance of VSSA in the current regulation of nanomaterials.

Specific surface area, volume-specific surface area, and the BET method The specific surface area (SSA, in m2/g) of a material is traditionally defined as the total surface area (SA) of a sample divided by its mass M: SSA ¼

SA M

(1)

SSA defined this way may, more precisely, be called the mass-specific surface area, or the specific surface area by mass. The total surface area includes all external and internal surface areas accessible to a probe gas. The International Union of Pure and Applied Chemistry (IUPAC) defines the SSA in the following way: ‘When the area of the interface between two phases is proportional to the mass of one of the phases (e.g. for a solid adsorbent, for an emulsion or for an aerosol), the specific surface area […] is defined as the surface area divided by the mass of the relevant phase’. [15] For a material consisting of n particles, Eq. (1) equates to X sai SSA ¼ Xi (2) m i i

Volume-specific surface area by gas adsorption analysis with the BET method

with sai being the surface area of particle i, mi being the mass of particle i, and the sums above and in the following text, running until particle n. In terms of the SSA of individual particles, SSAi, this can also be written as a mass-weighted average of the SSAi values of all individual particles: [16] X X ð m  SSA Þ sai i i i X ¼ Xi (3) SSA ¼ m m i i i i The volume-specific surface area (VSSA, in m2/cm3), or specific surface area by volume, is defined as [14,17,18] SA ¼ SSA  ρ (4) V where V is the total volume of the particles in the sample. The density value ρ (in g/cm3) used to convert SSA to VSSA is the (average) density of the ‘relevant phase’. For example, in the case of a powder, the density value used to convert the SSA to VSSA should be the density of the solid phase, not the overall (bulk) powder density that includes potential porosity. Often, the density determined by helium pycnometry [19] (commonly referred to as ‘skeletal density’, see the section ‘Instruments, experimental methods, and standards’) is used. This will normally be equal or close to the known ‘bulk material density’ available for most materials, for example, in the CRC Handbook of Physics and Chemistry [20]. Particle porosity, while increasing the surface area and decreasing overall particle density, should not affect the skeletal density unless there is a significant volume fraction of closed pores (or voids) not accessible to the test gas. As discussed in the section ‘Instruments, experimental methods, and standards’, this may be considered unlikely for some nanomaterial types. For illustration, Fig. 1 shows the volume V, the SA, and the VSSA of ideally spherical, non-porous monodisperse particles as a function of particle diameter D. While the volume and the surface are proportional to D3 and D2, respectively, the VSSA is inversely proportional to D and hence increases with decreasing particle size. The increase of the VSSA is particularly pronounced at particle sizes below 100 nm. The ‘size’ of non-porous, monodisperse particles with nonspherical shapes may be described by a characteristic external dimension, for example, the minimum Feret diameter. The VSSA of such particles decreases when that characteristic external dimension becomes larger. In analogy to the SSA, the VSSA of an ensemble of particles can also be formulated as a volume-weighted average of the VSSAi of all individual particles [see Eq. (3)]: X X ð v  VSSA Þ sai SA i i i X (5) ¼ Xi ¼ VSSA ¼ vi vi V VSSA ¼

i

where vi is the volume of particle i [16].

i

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Fig. 1 Surface area (SA), total volume (V), and volume-specific surface area (VSSA) of monodisperse spherical particles as a function of the particle size (diameter). Note the steep increase of VSSA for particles with diameters below 100 nm to values above 60 m2/cm3.

The SSA can be determined using the earlier definitions and equations. Experimental determination of the SSA of a solid (or particulate) material in air or in any other dry gaseous environment is usually based on whole-sample measurements. The method most often employed is based on the measurement of nitrogen adsorption (besides that of krypton) at low temperature according to the theory of Brunauer, Emmett, and Teller (BET method) within its range of applicability, which uses gas adsorption to measure the total (gas-accessible) inner and outer surface area of a given sample (see in the succeeding text). By convention, the BET method uses a parameter, the cross-sectional area am of adsorptive gas species (cf. section ‘Instruments, experimental methods, and standards’ ). Numbers agreed for am for N2, Kr, Ar, and other frequently used adsorptives are given in ISO 9277. Documentary standards exist for the determination of the overall specific external and internal surface area of disperse non-porous (type II isotherms) and mesoporous (type IV isotherms) solids (see also section ‘Instruments, experimental methods, and standards’) according to the BET method, including the general description in ISO 9277:2010 [21] and several application-specific standards. Certified reference materials are available for testing the performance of BET instrumentation, and several manufacturers offer instruments for SSA analysis. The overall SSA includes all gas-accessible internal and external surfaces. While SSA can be determined by other methods, BET remains by far the most commonly used method both in research laboratories and in industry. Studies by metrology institutes such as National Institute of Standards and Technology (NSIT, USA) [22,23], BAM

Volume-specific surface area by gas adsorption analysis with the BET method

(Bundesanstalt f€ ur Materialforschung und –pr€ ufung, Germany), and JRC (European Commission, Joint Research Centre, EU) have demonstrated that BET measurements are reasonably reproducible within and between laboratories, for example, generally within 5% of the certified value in the case of TiO2 powder [22]. The introductory clauses to the EC NM definition specifically mention BET as a method for measuring VSSA [14]. The calculation of VSSA from the SSA value measured with BET additionally requires the measurement or identification of an accurate average value for the skeletal density of the particulate phase as discussed earlier. VSSA is related to the size distribution of the particles in a sample and to their shape and degree of porosity. It is, however, important to note that BET analysis is not a size measurement and conversion of the VSSA to equivalent size parameters requires knowledge or assumptions regarding particle density, porosity, shape, and size distribution. The next section provides a detailed discussion on the relationship between VSSA and these characteristics. In the remainder of this section, we describe the basics of the BET method. In 1938, S. Brunauer, P. H. Emmet, and E. Teller proposed a theoretical model for gas adsorption (BET model) that allows for multilayer adsorption, as an extension of the Langmuir isotherm [1]. The BET model is based on the following assumptions: • The surface where the adsorption takes place is homogeneous. • The heat of adsorption does not depend on the degree of surface coverage. • Multilayer adsorption is governed by van der Waals interactions between the individual layers. The energy released by multilayer adsorption corresponds to the heat of condensation. • There is no interaction between adsorbed gas molecules of the same layer. • Adsorption of an infinite number of layers is possible. The BET model leads to a two-parameter adsorption isotherm (amount of gas adsorbed as a function of pressure, p, in equilibrium with the gas phase at constant temperature) of the form   p c 1 p 1 + ¼  (6) σ ½p0  p σ 0 c p0 σ0c where σ is the surface coverage (adsorbed molecules per unit area or per cm2) and σ0 is the monolayer adsorbed gas quantity (molecules per unit area or per cm2). p0 is the saturation pressure of the adsorbate gas at which an infinite number of layers can be built up on the surface. The BET constant c is given by c  eðΔHads ΔHcond Þ=RT

(7)

where ΔHads and ΔHcond are heat of adsorption of the first layer and heat of condensation of the vapour, respectively. Therefore, Δ Hads can also be determined from the BET

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isotherm if ΔHcond is known. In the BET model, the latter is assumed to be equal to the heat of adsorption above the second layer. In spite of its simplifying assumptions, the BET model is of great practical importance, provided that it is used within its range of validity. According to Eq. (6), a plot of σ ½p0pp versus pp0 yields a straight line with slope c1 σ 0 c and 1 intercept σ 0 c. Using this, the specific amount of monolayer adsorbed gas σ0 can be determined from the adsorption isotherm. This yields only the relative surface area rather than absolute values unless the area occupied per molecule of the adsorbed gas is known. An inert gas, for example, nitrogen, krypton, or argon, is normally used in applying the BET method to determine the surface of solids. In reality, the linear relationship of Eq. (6) is maintained only in the approximate range 0:05 < pp0 < 0:3. Other experimental adsorption isotherms cannot be evaluated at all using Eq. (6). A detailed discussion of different types of adsorption isotherms can be found elsewhere [24], with a brief overview also given in the section ‘Instruments, experimental methods, and standards’.

Relationship between particle size, shape, and volume-specific surface area In this section, we will examine the theoretical relationship between specific surface area and particle shapes, sizes, and size distribution type based on simulations, which can be performed using spreadsheets. Due to the fact that the SSA is directly related to the VSSA via the material skeletal density (Eq. 4), all the calculations presented will relate to the VSSA because the volume of a (non-porous) particle can be directly calculated from particle shape and size information. For particles with relatively simple geometric shapes, it is straightforward to calculate their surface area–to–volume ratio, or VSSA, see also Fig. 1. The VSSA of an ideal sphere of 100 nm in diameter is 60 m2/cm3. By convention, the VSSA is often given in m2/cm3 instead of 1/cm as the former is more intuitive and easier to visualize. As the size increases, the VSSA decreases. There are basic shapes that have a higher VSSA for the same minimum external dimension—most notably the tetrahedron—which, for a minimum external dimension (i.e. minimum Feret diameter) of 100 nm, has a VSSA of about 104 m2/cm3 [16]. It is simple to construct particle morphologies that have a higher VSSA value than the sphere with the same external dimension, for example, by introducing surface roughness or inner/coating porosity, but VSSA calculations in these cases become more complex, and the results are infinitely variable depending on the extra features included. In the rest of this section, therefore, we will focus on three more basic particle shapes, which are roughly representative of the most common shapes of fine particulate materials—spheres, platelets (or flakes), and nonhollow needles (or fibres).

Volume-specific surface area by gas adsorption analysis with the BET method

With regard to particle size distribution, in this section, calculations for three specific types of distribution are presented—normal (or Gaussian) distributions, lognormal distributions, and bimodal distributions with very narrow populations. They are calculated as distributions of the particle size (diameter), but these can easily be converted to distributions by particle volume or mass. The lognormal distribution is a normal distribution of the logarithm of the particle size, this distribution type being characterized by having no negative size values. Size distributions for real particles are anyway characterized by having only positive values, even if mathematically negative values result from a used function. When presented on a linear scale, the lognormal distribution is asymmetric with a tail that extends to larger particle sizes. Fig. 2 shows three such particle size distributions, one Gaussian and one lognormal, both with a median size of 100 nm and a standard deviation (calculated as the square root of the variance) of 35 nm, and one broader lognormal distribution with a standard deviation of 120 nm (values for the number-based distribution). It has been reported [25] that lognormal particle size distributions may often result from particle size reduction methods such as grinding or milling, while normal distributions are typical for particles grown under carefully controlled conditions to meet a specific size. While there are several ways of measuring, calculating, and visualizing particle size distributions, this often varies according to the particle size measurement procedure used [26]. The functions presented here have been chosen as they represent easily calculated and commonly used functions and also because they usefully illustrate the effects that different size distributions can have on VSSA. In the discussion, the terms ‘mass’ and ‘volume’ are used interchangeably since one is directly related to the other via the material density, which can be assumed to be uniform for powders made in a single production process. For many of the calculations presented in the succeeding text, size distributions with a median (by number) particle size of 100 nm were used. This is a deliberate choice since 100 nm is an often-used threshold between ‘nanoparticles’ and larger particles, and it also allows us to draw some useful conclusions regarding the possible use of VSSA to identify nanomaterials for regulatory purposes (see the section ‘VSSA as a tool to identify nanomaterials’).

Spherical particles The VSSA of a single particle is the ratio of the (gas-accessible) surface area to the particle volume (the volume of the condensed phase). For a sample consisting of many identical particles, the overall sample VSSA is the same as that of any single particle. Thus, in the ‘ideal case’ of a monomodal (there is only one peak in the particle size distribution), perfectly monodisperse (all particles are of the same size so that the peak shrinks to a line) particulate consisting of non-porous, spherical particles of diameter D (in nm), VSSA (in m2/cm3) is given by VSSA ¼ 6000/D, see Eq. (5) applied to a sphere.

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Characterization of nanoparticles

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Fig. 2 Visual representation of three particle number-based size distributions, all having a median particle size of 100 nm: (A) Gaussian (normal) distribution with a standard deviation of 35 nm, (B) lognormal distribution with a standard deviation of 35 nm, and (C) lognormal distribution with a standard deviation of 120 nm. The solid lines are the ‘number-based size distributions’, while the dashed lines are the corresponding ‘mass-based size distributions’.

Volume-specific surface area by gas adsorption analysis with the BET method

For more complex particle size distributions (e.g. polydisperse or multimodal), the overall VSSA can be calculated by summing up the surface areas of all particles and dividing the result by the sum of all the particle volumes (see the section ‘Specific surface area, volume-specific surface area, and the BET method’). It should be noted that this is not the same as the average of the VSSA of the individual particles. The most convenient way to do this is via a suitable spreadsheet, although one should be aware that, due to the relatively large contribution of larger particles to the total surface area and even larger contribution to the total volume, the summations need to be made over a wide enough size range to avoid truncation errors. This is especially important for size distributions that have a significant ‘tail’ at higher particle sizes, for example, lognormal distributions. For a broadened monomodal distribution of spherical particles, the VSSA is reduced compared with a perfectly or narrow monodisperse sample with the same median diameter. The broader the distribution, the more the VSSA is reduced. This is illustrated in Fig. 3 that shows the effect of both Gaussian and lognormal distribution broadening on a sample with a median particle diameter of 100 nm, as a function of standard deviation (square root of the variance). The values for Gaussian broadening are only shown for

Fig. 3 Variation of the overall sample VSSA of a polydisperse sample of spherical particles with a median particle size of 100 nm and different values of the standard deviation, calculated for both Gaussian (normal) and lognormal broadening. Also shown is the associated mass percentage of particles below 100 nm.

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a limited prange, ffiffiffiffiffiffiffiffiffi equivalent to FWHM (full width at half maximum, FWHM ¼ 2 2ln2σ  2:355σ for a Gaussian function; σ is the standard deviation) from 0 to 90 nm, because increased Gaussian broadening implies a significant tail into the negative size range. For small values of standard deviation, there are only minor differences in the results for Gaussian and lognormal distributions, although the tail of the lognormal distribution to higher particle sizes is evident in the diverging VSSA values. As the standard deviation increases, the mass percentage of particles below 100 nm strongly decreases for both distributions because the D3 dependence of mass on the particle diameter means that the large particles contribute much more to the mass than the small ones. The largest value of the standard deviation shown on the graph (σ ¼ 193.65 nm) represents a very broad lognormal distribution with a significant mass fraction of particles above 5000 nm diameter and only 0.21% of the mass in particles <100 nm in diameter (see Fig. 2C for details of a function with a standard deviation of 120 nm). Nevertheless, the number of particles having a size equal or <100 nm stays at 50%. For bimodal or multimodal samples of spherical particles where there is a significant size difference between modes, the VSSA will in general be dominated by the larger size mode/s. This can be demonstrated by imagining an ‘ideal’ bimodal sample consisting of only spherical particles with m identical small particles of diameter D1 and n identical large particles of diameter D2. The total particle surface area of such a sample is SAtot ¼ mπD21 + nπD22

(8)

Vtot ¼ mπD31 =6 + nπD32 =6

(9)

and the total volume is

A simple example has been published for the case of a perfectly bimodal sample consisting entirely of particles of the same material with 10 nm and 500 nm in diameter [16]. Even if two-thirds of the particles are of the smaller size, this equates to <0.1% of the total particle surface area of the bimodal sample and <0.002% of the volume. The overall sample VSSA is 12.01 m2/cm3—that is, essentially the same as the VSSA of the larger mode alone (i.e. without the smaller particles), which is 12.00 m2/cm3. It is instructive to create graphs that show the ratio of the overall sample VSSA to that of the larger particles alone (VSSAtot/VSSA2) against the particle size ratio D2/D1 for various relative number concentrations m:n (Fig. 4). They are independent of the particle absolute size, for example, 20 nm:150 nm has the same effect as 100 nm:750 nm. For equal numbers of particles in the two populations, the contribution of the smaller particles to the total VSSA can never cause it to rise >12% over the value of the VSSA of the larger mode alone. The VSSA peaks at about D2/D1 ¼ 1.7, and hence, the most ‘efficient’ size of the smaller particles to increase the VSSA is about 60% of the larger particle size for m ¼ n.

Volume-specific surface area by gas adsorption analysis with the BET method

Fig. 4 Graphs showing the calculated ratio of overall VSSA of a bimodal sample (VSSAtot) to the VSSA of the larger particles alone (VSSA2) against particle size ratio for perfectly bimodal samples of spherical particles with small particle size D1 and large particle size D2 and various ratios (m/n) of small to larger particles.

For higher numbers of smaller particles than larger ones, the VSSA increases by a larger factor, see Fig. 4. Additionally, the most efficient smaller particle size for increasing the VSSA shifts to a larger D2/D1 ratio, that is, to a smaller percentage of the larger particle size. It should be noted, however, that in all cases, adding significantly smaller particles (e.g. 50 times smaller) to the larger ones has much less effect than adding those with the most efficient size. It is also notable that even with 1000 times more small particles than large ones, the VSSA can only be increased (above that of the larger particles alone) by a factor of <6, no matter what the VSSA value is of the smaller particles alone. One can also calculate both the number and relative volume (or mass if the particles are of the same density) of larger particles required to reduce the VSSA of a sample below a certain target or threshold value. Clearly, the VSSA will be reduced most efficiently by adding the largest size possible, to the extreme limit of adding one large macroparticle that in effect determines volume (and mass) of the sample while minimizing the amount of additional surface area. For more realistic bimodal scenarios, where the two modes consist of fine particles and each mode is very narrow, one can calculate both the number and

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volume percentage of larger particles that needs to be added to the smaller particles to reduce the VSSA to a certain value. For example, suppose one had a sample of 50 nm diameter spherical nanoparticles and wished to reduce the VSSA from 120 m2/cm3 to 20 m2/cm3 using spherical particles with a diameter of 500 nm (these having a VSSA of 12 m2/cm3), it turns out that one would need to add just one larger particle for every 80 smaller particles. However, since each large particle has a volume 1000 times the small one, this low number percentage of larger particles equates to a volume percentage of about 92.6%.

Platelet- or flake-like particles A simple calculation serves to illustrate that VSSA determination may be an extremely useful analysis method for platelet- or flake-like particles. Such particles are employed in a number of applications, one of the most important being pigments in paints for obtaining, for example, a metallic finish. As for spherical particles, we start by considering platelets that are monodisperse with respect to their thickness. Idealizing the shape of a particle to a rectangular parallelepiped with six rectangular faces and dimensions a  b  c (in nm), the VSSA (in m2/cm3) is given by   2 2 2 VSSA ¼ 1000  + + (10) a b c If one of the three dimensions is much smaller than the other two, for example, a≪ b and a≪ c, then the VSSA is approximately given by VSSA  2000/a. The interesting point to note from this equation is that under these conditions, a measurement of the VSSA should provide a reasonably accurate estimate of the particles’ thickness. Given that even by applying electron microscopy, this parameter can be quite difficult to determine accurately; for very small values of thickness, it appears that VSSA may be a valuable method to apply. Assuming that all particles are identical and the two larger dimensions (b and c) are equal, we can plot the VSSA as a function of the ratio of the larger dimensions (length and width) to the smaller one (thickness). Such a plot is shown in Fig. 5, for a ¼ 100 nm and b (¼c) ranging from 100 to 5000 nm. One can see from this plot that as the particles become more ‘sheetlike’ the VSSA approaches asymptotically the lower limit value of 2000/a m2/cm3. It is important to note that already at an aspect ratio of 4:4:1, the VSSA has dropped to 50% of the initial value, while at a ratio of 20:20:1, the VSSA is at 22 m2/cm3, only 10% higher than the asymptotic limit value. Since many manufactured platelet- or flake-like particulates may have a more extreme dimensional ratio, it is reasonable to assume that a measurement of their VSSA will allow a reasonably reliable estimate of their thickness (assuming

Volume-specific surface area by gas adsorption analysis with the BET method

Fig. 5 Variation of VSSA with particle ‘aspect ratio’ for platelet (or flake)-like particles with a thickness of 100 nm.

of course that they are not aggregated/agglomerated in a way that prevents the test gas from accessing all surfaces). It is also important to look at the effect of thickness variation on the overall sample VSSA. As with spherical particles, one can model the effects of a Gaussian or lognormal thickness variation, or of an ideal bimodal thickness distribution, or of more complex distributions. Taking first a Gaussian thickness variation and assuming that the largest dimension does not vary, it turns out that broadening the distribution from an ideal monodisperse particle thickness distribution to a more polydisperse Gaussian thickness distribution has no effect on the overall sample VSSA (see Fig. 6). This is in fact intuitively obvious for a symmetric thickness distribution, since (assuming that the distribution width is not as large so that it mathematically results in a significant fraction of negative thickness values) for each platelet with a thickness value a-x, there is another with a thickness value a + x, and the total VSSA of these two particles combined is the same as that of a particle with a thickness of a. From a practical perspective, this is a useful result, because for some platelet production processes (e.g. via thin-film deposition), the thickness variation is typically symmetric around a mean value, and thus, a simple VSSA determination should give a good indication of the mean and median distribution values. As shown in Fig. 6, it can also be noted that, while the VSSA remains constant, as the distribution broadens, the mass percentage of particles with a thickness below 100 nm decreases.

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Fig. 6 Variation of the overall sample VSSA of a polydisperse (lognormal or Gaussian monomodal distribution of the thickness but no variation in the large dimensions) sample of platelet-/flakeshaped particles with a median thickness of 100 nm and different values of the standard deviation. A very high aspect ratio (a ≪b and a ≪c) was assumed, with all particles having the same b and c values. Also shown is the associated mass percentage of particles with a thickness below 100 nm.

Turning now to the case of an asymmetric lognormal platelet thickness variation, the calculation shows that the VSSA reduces as the distribution becomes broader. Again, this is intuitively reasonable as the lognormal distribution has a tail that runs to relatively thick particles with a much lower VSSA, and these are not symmetrically ‘balanced’ by particles with a small thickness and high VSSA. Fig. 6 also shows how the VSSA (and the mass percentage of particles with a thickness of <100 nm) changes as a function of the standard deviation of a lognormal distribution. It is interesting to compare this variation with that of spherical particles (Fig. 3). For platelets, the overall sample VSSA is considerably less sensitive to the width(s) of the distribution than in the case of spherical particles but only in the case of broadening of the thickness and not all dimensions (see in the succeeding text). The situation is somewhat different if all dimensions are allowed to vary according to the same broadening function. Such a situation may arise if the particles are synthesized by certain ‘bottom-up’ processes such as growth in a solution, in which case the aspect ratios may be more moderate. In this case, calculations show that the variation of VSSA and mass percentage of particles with a thickness below the median value follow identical curves to those shown for spheres in Fig. 3 with the only difference being that the VSSA

Volume-specific surface area by gas adsorption analysis with the BET method

values are scaled appropriately—for example, if the aspect ratio of all platelets was 4:4:1, then the corresponding maximum VSSA value would be 30 m2/cm3 and not the value for spheres shown in Fig. 3 (i.e. 60 m2/cm3). The same holds for both Gaussian and lognormal broadening functions.

Bimodal samples of platelets Simple considerations can be made for bimodal samples of platelets where the large dimensions of both modes are similar and much greater than the thickness. In that case, if the numbers of thinner and thicker platelets are equal, then as the thickness of the thinner mode tends towards zero, that is, at large a2/a1 in Fig. 7, the VSSA of the sample will tend towards double that of the thicker mode alone. This is intuitively obvious as thin platelets with the same large dimensions and almost zero thickness will effectively double the surface area of the overall sample. For samples where there are more thin platelets than thick ones, then the limit VSSA (i.e. when the thickness of the thinner platelet approaches zero) will be m/n + 1 times the VSSA of the large mode alone, where there

Fig. 7 Graphs showing the calculated ratio of overall VSSA of a bimodal sample (VSSAtot) to the VSSA of the thicker platelets alone (VSSA2) against thickness size ratio for perfectly bimodal samples of platelets, with all platelets having the same large dimensions (assumed to be much greater than the thickness), for two ratios (m/n) of thinner to thicker platelets. The thinner platelets have thickness a1, and the thicker platelets have thickness a2.

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are m thin platelets and n thick platelets. This is illustrated in Fig. 7, where the VSSA ratio is plotted as a function of the thickness ratio for m ¼ n and m ¼ 10n. We can also calculate the overall VSSA for bimodal samples of platelet-shaped particles where all dimensions scale with the thickness—that is, the thinner particles have proportionally reduced large dimensions compared with the thicker particles. In this case, the result is totally different, and in fact, the resulting graphs are identical to those for spherical particles, shown in Fig. 4. This is an important observation, since it demonstrates that these curves are independent of sample shape. In other words, if all particles in a sample have the same aspect ratio, then Fig. 4 is always valid. The same result was obtained for needle-shaped particles (see in the succeeding text).

Needle or fibrelike particles Microscopy analysis of particulates reveals that a needle-shaped morphology is not uncommon. Such particles are often crystalline and faceted and typically have two dimensions of similar size and one dimension, which is significantly larger. In analogy to platelets, and considering in this section only solid nanofibres, one can idealize the shape of a particle to a rectangular parallelepiped with six rectangular faces, and dimensions a  b  c, this time with two equal and small dimensions a ¼ b and one large dimension c, with a,b <
Volume-specific surface area by gas adsorption analysis with the BET method

Fig. 8 Variation of VSSA with particle ‘aspect ratio’ for square cross-section needle-/fibre-shaped particles with a small dimension of 100 nm.

(with all particles having a similar length) and just model a broadened distribution of the small dimension (in analogy to the thickness distribution broadening in the case of large platelets/flakes) and secondly, for relatively low aspect ratios, one can model a distribution of both small and large dimensions, using the same distribution function. This would, for example, be more appropriate for needle-shaped crystallites grown in solution. Fig. 9 shows the calculated results for both Gaussian and lognormal distributions of fibre diameter, assuming a very long and nonvarying fibre length. The curves are somewhat similar to those calculated for spherical particles (Fig. 3), apart from the fact that the VSSA decreases from a maximum of 40 m2/cm3 instead of 60 m2/cm3 and that both VSSA and mass percentage of particles with a diameter <100 nm are less sensitive to the width of the distribution than in the case of spherical particles. Turning now to the case of needle-shaped particles with relatively low aspect ratios and allowing the distribution broadening to apply to all dimensions, as with platelets, the resulting curves are identical to those for spheres (shown in Fig. 3), with the exception that the VSSA is scaled appropriately. For example, for an aspect ratio of 4:1:1, the maximum VSSA is 45 m2/cm3 (and not 60 m2/cm3 as would be the case for spherical or cubic particles of size 100 nm).

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Fig. 9 Variation of the overall sample VSSA of a polydisperse (lognormal or Gaussian monomodal distribution of the diameter, but not the fibre length) sample of needle-/fibre-shaped particles with a median diameter of 100 nm and different values of the standard deviation. A very high aspect ratio was assumed (a ≪c, b≪ c), with all particles having the same length. Also shown is the associated mass percentage of fibres with a diameter below 100 nm.

Bimodal samples of needles/fibres Finally, we can model a hypothetical sample of needle- or fibre-shaped particles in two ways—either bimodal only in the fibre diameter (and assuming the length is equal and very long) or bimodal in all dimensions. In the former case, we obtain a result similar to that of spherical particles (Fig. 4) but with modest differences in the peak value of VSSAtot/VSSA2 and also in the position (i.e. the diameter ratio) at which the modal value of the peak occurs. This is illustrated in Fig. 10 for three cases—either equal numbers of small- and large-diameter particles or 10 times or 100 times more small-diameter particles than large ones. The qualitative difference between the case of platelets and either needles or spheres (comparing Fig. 7 both with Figs 4 and 10) is easily explained by the fact that for a thickness approaching zero, the surface area of a large platelet does not tend to zero, but it does for both needles and spheres as the small dimension approaches zero. Calculations for the case of a bimodal sample of needles where the aspect ratio for both small and large particles is the same show that, as in the case of platelets where all dimensions vary, the same curves are obtained as for spheres (Fig. 4).

Volume-specific surface area by gas adsorption analysis with the BET method

Fig. 10 Calculated graphs of the ratio of overall VSSA of a bimodal sample (VSSAtot) to the VSSA of the larger-diameter fibres alone (VSSA2) against diameter ratio for perfectly bimodal samples of fibres, with all fibres having the same length (assumed to be much greater than the diameter), for various ratios (m/n) of smaller- to larger-diameter fibres. The smaller-diameter fibres have diameter a1, and the larger-diameter fibres have diameter a2.

Summary of VSSA calculation results In this section, we have calculated the overall sample VSSA for three basic sample shapes and for three model particle size distribution functions and have seen that, given some knowledge of the particle size; shape (and shape uniformity), for example from SEM, TEM, or AFM measurements; and the particle size distribution (mono- or multimodality and distribution broadening), a measurement of the VSSA can give useful additional information about the median smallest dimension of the particles in a sample. A number of salient points for practical cases (for non-porous particles) are summarized in the following table. Particle shape

Link between particle size distribution and VSSA

Spherical particles

Both normal (Gaussian) and lognormal broadening of the numberbased size distribution around a fixed median value leads to both a reduction in the overall sample VSSA and in the mass percentage of particles with a diameter below the median value. Thus, for monomodal size distributions, accurate knowledge of the form and Continued

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Particle shape

Platelet- or needleshaped particles

Platelet-/flake-shaped particles

Needle-/fibre-shaped particles

Platelet- or needleshaped particles

Strongly bimodal samples

Link between particle size distribution and VSSA

width of the size distribution means that the VSSA can be used to estimate the median particle diameter. Even if the width of the size distribution is not well known, the VSSA measurement will generally give an upper limit to the median particle diameter Where all dimensions vary according to the same function, the graphs of VSSA and mass percentage below the median value against standard deviation are identical to those for spherical particles, except that the VSSA value is scaled according to the particle shape Therefore, in analogy to the case for spherical particles, if all particles in a monomodal sample have the same known shape (aspect ratios) and the form and width of the size distribution is accurately known, the VSSA can be used to estimate the median smallest dimension or at least an upper limit to this value. Where all particles have two very large dimensions with respect to their thickness, a Gaussian variation only in the thickness, a, results in no change to the overall sample VSSA from the theoretical value of  2000/a. From a practical point of view, this means that the VSSA can be used to determine the median platelet/flake thickness in such samples if they are monomodal. This may be very useful since the thickness can be the most difficult dimension to measure accurately with electron microscopy Where all particles have one very large dimension and a circular (or square) cross-section, a, a variation only in the diameter results in a modest reduction in the VSSA from the theoretical value of  4000/a, unless a very broadened lognormal distribution function is assumed. This implies that for monomodal fibre/needle-shaped particulates with reasonably uniform particle dimensions, VSSA can be used to estimate the median value of the smallest particle dimension. If the diameter varies considerably, the VSSA can give an indication of the upper limit of the median diameter Where the aspect ratios are relatively low but fixed, knowledge of the aspect ratio is required to extract useful size information from the VSSA; where the aspect ratio varies, it may be difficult to extract useful size information For strongly bimodal samples (large size ratio of the modes) of spherical or needle-/fibre-shaped particles, the VSSA is dominated by the larger size mode. For strongly bimodal platelet-/flake-shaped particles where all dimensions vary (i.e. all particles have the same aspect ratio), the same applies. However, for platelet-/flake-shaped particles with similar larger dimensions for both modes, the overall sample VSSA depends strongly on the ratio of particle numbers in each mode and on their thicknesses. From a practical point of view, it is generally difficult or impossible to extract information about the median particle size for strongly bi- or multimodal samples from a VSSA measurement without access to detailed information about each individual mode.

Volume-specific surface area by gas adsorption analysis with the BET method

Instruments, experimental methods, and standards High-performance commercial instruments used for the determination of physisorption isotherms are now widely available. Well-known manufacturers of such equipment that include outgassing stations and high vacuum systems are Anton Paar, Micromeritics, Beckman Coulter (all USA), and Horiba (Japan). The most commonly used adsorbate is nitrogen at its boiling point of 77.3 K. This working temperature can be easily achieved by using commonly available liquid nitrogen. It is now recognized that due to its quadrupole moment, the orientation of a nitrogen molecule depends on the surface chemistry of the adsorbent. Therefore, the traditional use of a fixed molecular cross-sectional area of nitrogen (complete monolayer) of 0.162 nm2 can significantly contribute to the overall measurement uncertainties of a specific surface area result. For the same reason, N2 should not be applied to determine the pore size distribution, but it is suitable to evaluate the total surface area of the inner micropores (by definition, these are pores with diameters <2 nm) by means of for instance the t-plot method [21] explained later in this sub-section. With modern data evaluation software, an advanced user has the possibility to introduce the true value of a particular adsorbate–adsorbent combination once this value is available. For materials with a very small specific surface area (SSABET < 1 m2/g), either argon (at 87.3 K) or krypton (at 119.9 K) is recommended as adsorbate. One distinguishes between two types of measurement approaches, the so-called manometric determination and gravimetric measurement. Further details can be found in the IUPAC Technical Report from 2015 [24] and in the ISO standard 9277: ‘Determination of the specific surface area of solids by gas adsorption—BET method’ [21]. According to Chapter 9 of ISO 9277, apparatus performance should be monitored periodically using a suitable certified reference material or a quality control material.

Experimental procedure Sample preparation After taking a representative sample, it must be degassed before analysis to remove physisorbed species from the surface of the solid material by flushing with an inert gas or using vacuum at elevated temperatures. The sample is properly prepared when a constant mass or steady value of the residual gas pressure is achieved for 15–30 min. This procedure should be performed at the highest possible temperature to remove any adsorbed species, while irreversible changes to the material must be prevented. For instance, most carbonate samples can be degassed at 300°C, for example, calcium carbonate. Many hydroxides must be degassed at a lower temperature. Degassing of organics must be performed with care and often at temperatures below 100°C for several hours. Outgassing under vacuum and high temperature is particularly recommended for microporous materials. For very fine powders or materials with low density or high humidity, the temperature must be increased very carefully, to prevent

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the powder being aerosolized and escaping from the volumetric flask into the instrument. In general, predrying in a conventional drying oven is recommended. The conditions for pretreatment of the samples (outgassing time, temperature, residual pressure, and flushing gas) must be recorded. The (mass) specific surface area should be calculated using the mass of the degassed sample. Analysis At first, the dead volume of the empty sample cell must be determined under the same experimental conditions as the sorption measurement using He (see ISO 9277, § 6.3.1). The purity of the adsorptive gas used should be at least 99.999%. The gas is admitted into the evacuated sample container, which is held at a constant temperature. The temperature—possibly to be determined by measurement of the thermostat bath temperature—must be monitored during the analysis. As part of the static volumetric method, for the determination of the adsorption isotherm, it is necessary to select a set of data points of relative pressure p/p0. For the classical BET range of p/p0 ¼ 0.05 to 0.3, a minimum of four points should be selected. When micropores are present, the linear range of the BET plot shifts to lower relative pressures. Therefore, for unknown samples also in this range, the measurement curve should contain a series of measurement points. If the surface area of the micropores themselves must be determined, a series of measurement points at relative pressures p/p0 > 0.15 is necessary. For obtaining indications on the presence of mesopores (2 nm d 50 nm), the desorption curve should be also acquired. A recommendation of a set of data points is given in Table 1. The larger the expected surface area and the more micropores the sample contains, the longer the equilibrium time should be set at every measuring point.

Table 1 Recommended sets of relative pressure data points p/p0 for high grade sorption–desorption measurements Low relative pressure area

Classic BET area

Additional t-plot

Desorption

0.005 0.007 0.009 0.010 0.020 0.030 0.040

0.05 0.10 0.15 0.20 0.25 0.30

0.35 0.40 0.45 0.50 0.60 0.70 0.80 0.95

0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.80 0.95

Volume-specific surface area by gas adsorption analysis with the BET method

I(a)

I(b)

II

III

Amount adsorbed

B

IV(a)

IV(b)

V

VI

Relative pressure Fig. 11 Classification of physisorption isotherms according to Ref. [24]. (© IUPAC, De Gruyter, 2015.)

Special care must be taken when using a dynamic measurement technique to ensure that the flow rate is low enough so that the adsorptive gas and adsorbed layer are close to equilibrium at all times. Evaluation of adsorption data The evaluation of the raw data of adsorption (and desorption) measurement takes place usually by means of software supplied with the measurement instrument. First, the amount of gas adsorbed is plotted against the corresponding relative pressure to give the adsorption isotherm. The isotherm can be classified according to characteristic types, as defined in an IUPAC recommendation [27] of 1984 and as referred to by ISO [21]. In a more recent IUPAC technical report of 2015 [24], the types of isotherms have been

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expanded further into subcategories, which are all represented in Fig. 11. More details on the different types of isotherms can be found elsewhere [24]. For adsorption isotherms of Types II and IV, evaluation using the classical BET method corresponding to ISO 9277 is possible. First, from the isotherm, the so-called BET plot is generated, by plotting σ ½p0pp versus pp0 (σ ¼ amount of gas adsorbed). Here, one can find a linearity within the p/p0 range of  0.05–0.30. The correlation coefficient should be better than 0.999 for a minimum of four measurement points. Within this linear range, the BET equation holds true and allows, in the case that the molecular crosssectional area of the adsorbate is known, the determination of the sample surface area as occupied by a complete monolayer by the adsorbate molecules. When the strength of the interactions between the adsorbate and the surface is very high (e.g. graphitized carbon samples or when micropores <2 nm are present), the linear range of the BET plots shifts to lower relative pressures p/p0. The parameter c in the BET Eq. (6) as obtained from a BET plot gives a useful indication here [24]. If c is low (<2) or negative, the isotherm is of Type III or Type V, and the BET method is not applicable. If c is between 2 and about 150, then one can find linearity in the classic BET range. A value of c higher than 150 is characteristic for high adsorption energies or the filling of narrow micropores and should be found when the linear range of the BET plot has been shifted to an interval of relative pressures p/p0 lower than 0.05–0.3. In both these latter cases, an evaluation by using the BET equation is possible. If micropores are present in the sample, the solution of the equation results in a surface area value that includes the surface of the accessible micropores. In accordance with Annex C of ISO 9277, the following conditions should be fulfilled to reduce the subjectivity of the evaluation: (i) c shall be positive, and (ii) the application of the BET equation should be limited to the pressure range where the term σ(p0 p) or alternatively σ(1 p/p0) continuously increases with p/p0. In any case, guidance using the software of a particular instrument manufacturer should be followed carefully. The contribution to the surface area of the micropores can be considerable. This must be kept in mind when using the resulting value for further calculations. While VSSA (see the section ‘Specific surface area, volume-specific surface area, and the BET method’) includes the surface area of gas-accessible pores (in addition to the external surface area), when the determined surface area value is used to assess the particle size, only the surface area fraction due to the outer/external particle surfaces should be taken into account, as described in the succeeding text. Different methods have been developed to evaluate the volume of the micropores. In most cases, the t-plot and the αs-plot methods [28] are used. To account for micropores, one should measure adsorption isotherms over an extended pressure range of p/p0 (see Table 1, columns 1 and 3). The micropore analysis can then be done by comparing adsorption isotherms with that of a non-porous reference material of similar chemical surface composition. Input data on the surface chemical composition for some material classes are provided by the instrument’s software. In a comparison plot diagram, the adsorption isotherm under test is drawn as t-plot or αs-plot.

Volume-specific surface area by gas adsorption analysis with the BET method

In the former case, the change of the adsorbed gas amount is plotted against the statistical layer thickness t of a non-porous reference sample. In the latter case, αs is calculated by relating the adsorbed gas amount to that of a reference sample at a selected relative pressure p/p0. The values of the adsorbed amount are then plotted against αs values instead of p/p0. The detailed procedures for measurement and evaluation of the data are described in ISO 15901-3 [28]. The pore surface area corresponding to the determined micropore volume can be subtracted from the total surface area to obtain the surface area fraction (SAext). It should be noted that a physisorption isotherm of type IV (a) (see Fig. 11) shows that the analysed sample contains mesopores (2 nm d 50 nm). If the Type IV (a) isotherm remains nearly horizontal over the upper range of p/p0, the total pore volume VP is derived from the amount of vapour adsorbed at a relative pressure close to unity (p/p0  0.95) [24]. A precise determination of the mesopores surface area would require knowledge of their size distribution [24]. Therefore, the volume of the mesopores Vmeso calculated by subtracting the volume of the micropores Vmicro from the total pore volume VP (Vmeso ¼ VP  Vmicro) provides only a rough estimate of the mesopore contribution to the total measured surface area.

Strategy for using specific surface area in the assessment of particle size Recently, VSSA has been proposed as a screening method for identifying nanomaterials or non-nanomaterials (see also the section ‘VSSA as a tool to identify nanomaterials’) [29]. This is partly due to the fact that most powder manufacturer and service laboratories have instruments available for the analysis of specific surface area by means of gas adsorption. Furthermore, this method is fast and relatively inexpensive, and integral properties of a relative large, and hence more representative, sample volume are measured for both specific surface area and skeletal density. Surface area fractions resulting from the presence of micro- and mesopores are included in the calculation of VSSA. Consequently, porous particulate materials with median sizes above 100 nm can potentially be falsely identified as nanomaterials if their VSSA value is above 60 m2/cm3. To avoid such ‘false positive’ identifications, the following strategy is recommended: 1. Prolonged degassing, particularly when the presence of micropores is suspected. 2. Measurement of isotherm over the full range of relative pressure, in both directions, adsorption and desorption, and visual classification of the isotherm to a type according to Fig. 11. 3. Generation of the BET plot, determination of the linear range, and evaluation of the c parameter. 4a. If there are no indications of pores, calculation of the VSSA using the classical BET model and skip to point 8. 4b. Evaluation of the BET plot, if necessary at lower relative pressures, taking account of the requirements from Annex C of ISO 9277.

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Extraction of the area fraction corresponding to the micropores, by employing either t-plot or αs-plot. 6. As the circumstances require, determination of the mesopore fraction and rough estimation of the mesopores surface area. 7. Correction of the result from 4b (total surface area) by subtracting the contribution corresponding to the pores, such that outer particle surface (SAext) is the result, and calculation of the volume-specific external surface area (VSSAext ¼ SAext  (skeletal) density/mass). 8. Evaluation as to whether the material can be classified as a nanomaterial based on VSSA (for a non-porous material) or VSSAext (for a porous material). According to the EC NM definition [14], if technically feasible and requested under specific legislation, compliance with the definition may be determined on the basis of the VSSA. However, the primary criterion is that related to the median size of the particles. Thus, the earlier strategy may be used in the case of porous materials to avoid false positive classification by VSSA. It should be stressed, however, that it cannot be used to classify such materials as non-nanomaterials since that requires evaluation based on the median particle size. The use of VSSA as a criterion for identification of non-nanomaterials has been discussed in the literature [29] and is further outlined in the succeeding text. The applicability of VSSA (or VSSAext) for identification of nanomaterials and non-nanomaterials, as proxy for the number-based particle size distribution, in any case needs to be carefully checked for each material [29]. 5.

He pycnometry The density of the powder samples can be determined by helium pycnometry according to ISO 12154 [19]. This method measures the volume of a sample by placing it in a chamber of known volume, which is connected via a valve to a second chamber of known volume. Before starting the measurement, the whole system is flushed with helium gas to remove the remaining air in both chambers, which are subsequently sealed by closing the valves. The helium pressure in the sample chamber is increased by adding helium gas until a certain constant value is reached, while the second chamber stays at ambient pressure. On opening the valve between the two chambers, the pressures equilibrate, and from the pressure change in both chambers and the known chamber volumes, the sample volume can be calculated. Prior to analysis, the sample must be dried externally. The cooling should take place in a desiccator with proper desiccant, and introduction of the sample in the pycnometer must be carried out quickly, to avoid capture of humidity from the ambient air. To minimize the measurement uncertainty, the filling fraction of the sample chamber should exceed 10% by volume (cf. also the documentation of the specific instrument). As the measurement procedure relies on isothermal conditions, the temperature must be kept constant.

Volume-specific surface area by gas adsorption analysis with the BET method

The filling pressure and, thus, the flushing duration as well as the number of flushing cycles depend strongly on the fine inner morphology (or porous structure) of the sample material. Annex A of ISO 12154 contains valuable hints regarding various effects on the measurement. The measurement lasts until the measured volume value stays constant, that is, until the standard deviation corresponding to the last measured values becomes smaller than a set value. The weight of the sample is determined with a relative accuracy of 103 by means of an analytical balance. According to ISO 12154, the skeletal density is the ratio of the mass of the sample to the sample volume as determined by pycnometry. In the case that the sample does not contain closed/inaccessible pores, the result represents the true (pure) density of the measured material. If inaccessible pores or voids are present, then the skeletal density will be lower than the true density. It could be argued that for very fine nanomaterials, particularly where the powders being assessed are made up of separate nanocrystals, the presence of a significant volume fraction of micro- or mesopores may be unlikely. In any case, when reporting VSSA values, it should be specified whether tabulated true density values have been used (e.g. from the CRC Handbook of Chemistry and Physics) [20] or skeletal density values obtained by He pycnometry or another measurement method.

VSSA as a tool to identify nanomaterials As discussed in the section ‘Relationship between particle size, shape, and volumespecific surface area’, there is a relationship between the particle size distribution and the VSSA. For very simple, idealized particle systems, where the particles have a specific shape and a known size distribution, the criterion of the EC NM definition that 50% or more of the particles must have one or more external dimensions between 1 and 100 nm can be directly translated into a VSSA threshold. For example, 60 m2/cm3 is the theoretical VSSA of a non-porous, perfectly monodisperse material consisting of spherical particles with a diameter of 100 nm or cubic particles with an edge length of 100 nm. In these cases, the threshold value of 60 m2/cm3 has a direct relation to the primary (size-based) NM defining criterion and can be considered as the size-based upper VSSA cut-off for such a material: if the VSSA of such a material is larger than 60 m2/cm3, it is a nanomaterial. To expand the VSSA concept also to nonspherical particles, one can introduce a shape-dependent cut-off value (see the section ‘Relationship between particle size, shape, and volume-specific surface area’ and Refs. [29,30]): m2 δ  (11) cm3 3 where δ is the number of small dimensions (three for equiaxial particles; two for needles, fibres, and rods; and one for platelets and flakes). Accordingly, VSSAcutoff is 60 m2/cm3 for spherical particles, 40 m2/cm3 for fibre-/needle-shaped particles, and 20 m2/cm3 for platelets or sheetlike particles. Following the discussion in the section ‘Relationship VSSAcutoff ¼ 60

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between particle size, shape, and volume-specific surface area’, for samples with similar shaped particles, δ could be adjusted to other values depending on details of the particle shape. When trying to establish such a VSSA criterion with a single threshold to ‘real-world’ materials to decide whether they fulfil the EC NM definition, several material properties may prevent it from being a reliable tool for the NM identification: particle shape, porosity, roughness, aggregation, polydispersity, and multimodality, even if for some of these properties, solutions to correct for their effect are available. One can however, in a limited set of circumstances, use the following relationship to derive a value for the size of the smallest particle dimension dminVSSA from the VSSA [29], though this may not necessarily be a median value: dminVSSA ðδÞ ¼

2δ VSSA

(12)

When entering in Eq. (12) the VSSA in m2/cm3, dminVSSA is obtained in micrometres. Using VSSA instead of counting techniques such as electron microscopy (EM) to identify nanomaterials would be very attractive for several reasons. For example, VSSA determination on the basis of the BET technique has the advantage over imaging and other counting techniques that it does not involve particle dispersion protocols. The BET technique is widely used and low cost, results are already available for many commercial materials, and the same equipment allows for a deeper analysis by full isotherm evaluation. Moreover, VSSA (as determined by BET) covers a particle size range as broad as from 1 nm to 10 μm diameter and assesses the smallest dimensions (although not strictly the median value) of the particles in a sample without the need for dispersion of NMs. The EU-funded project NanoDefine [31] addressed, among others, the question of whether dminVSSA can be used to identify a material as nanomaterial (or nonnanomaterial). It evaluated the potential to use the VSSA method as a tool for both the identification of NM and of non-NM according to the EC NM definition [14] on real-world industrial materials by comparison of VSSA results with those obtained by measuring and counting constituent particles on their own, in agglomerates and in aggregates, by electron microscopy (EM). The quantitative comparison of the relationship between the median of the minimum Feret diameter as determined by EM versus the average equivalent diameter dminVSSA derived from VSSA showed indeed a good agreement, taking into account the approximate particle shape (sphere, fibre, and platelet) [29]. In most cases, the materials could be identified consistently by EM and VSSA as nanomaterials or non-nanomaterials. Based on this, a VSSA-based screening strategy was proposed [29] with shape-specific upper and lower threshold VSSA values to identify NM and non-NM with high reliability. The performance of this strategy was subsequently further tested on more industrial materials. The quantitative agreement between the VSSA-derived size dminVSSA and the median minimum Feret diameter from EM as well as the proposed screening strategy may be

Volume-specific surface area by gas adsorption analysis with the BET method

helpful for a reliable, fast, and cost-efficient identification of NM and non-NM according to the EC NM definition [14] within the region of applicability of this approach, that is, for essentially monomodal, not too polydisperse materials and no mixtures. It must be noted that one can easily find theoretical particle size distributions for which the identification as nanomaterial or non-nanomaterial by VSSA would not be consistent with a classification according to the true particle size distribution. As discussed in the section ‘Relationship between particle size, shape and volume specific surface area’, this is particularly true for extremely bimodal systems. However, the analysis of a large variety of industrial particulate materials by NanoDefine showed consistent assessment of these materials by VSSA and EM. Industrial powder materials are engineered to confer particular material properties, which require that the size distribution is not extremely polydisperse. Therefore, it is likely that for such materials, assessment by VSSA can be safely assumed to result in a correct identification as nanomaterial or non-nanomaterial. Further work is in progress to improve the VSSA method by introducing corrections via a shape descriptor (sphericity and roughness) and considering polydispersity.

References [1] S. Brunauer, P.H. Emmett, E. Teller, Adsorption of gases in multimolecular layers, J. Am. Chem. Soc. 60 (1938) 309–319. [2] Globally Harmonized System of Classification and Labelling of Chemicals (GHS), 7th revised ed., United Nations, New York and Geneva, 2017. [3] K. Rasmussen, H. Rauscher, A. Mech, J. Riego Sintes, D. Gilliland, M. Gonza´lez, P. Kearns, K. Moss, M. Visser, M. Groenewold, E.A.J. Bleeker, Physico-chemical properties of manufactured nanomaterials – characterisation and relevant methods. An outlook based on the OECD testing programme, Regul. Toxicol. Pharmacol. 92 (2018) 8–28. [4] OECD, Report of the OECD Expert Meeting on the Physical Chemical Properties of Manufactured Nanomaterials and Test Guidelines, ENV/JM/MONO(2014)15. 2014. [5] OECD, Physical-Chemical Properties of Nanomaterials: Evaluation of Methods Applied in the OECD-WPMN Testing Programme, ENV/JM/MONO(2016)7. 2016. [6] OECD, Physical-Chemical Parameters: Measurements and Methods Relevant for the Regulation of Nanomaterials. OECD Workshop Report, ENV/JM/MONO(2016)2. 2016. [7] H. Rauscher, K. Rasmussen, B. Sokull-Kl€ uttgen, Regulatory Aspects of Nanomaterials in the EU, Chem. Ing. Tech. 89 (3) (2017) 224–231. [8] European Chemicals Agency, Guidance on information requirements and chemical safety assessment, Appendix R7-1 for nanomaterials applicable to Chapter R7a - Endpoint specific guidance, European Chemicals Agency, 2017, p. 2017. https://doi.org/10.2823/412925. [9] SCENIHR (Scientific Committee on Emerging and Newly Identified Health Risks), Risk assessment of products of nanotechnologies, 19 January 2009. 2009. [10] SCCS (Scientific Committee on Consumer Safety), Guidance on the Safety Assessment of Nanomaterials in Cosmetics, SCCS/1484/12. 2012. [11] Regulation (EC), No 1907/2006 of the European Parliament and of the Council of 18 December 2006 concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH), establishing a European Chemicals Agency, Off. J. Eur. Union L396 (2006) 1–849. [12] U.S. Environmental Protection Agency (EPA), Chemical substances when manufactured or processed as nanoscale materials: TSCA reporting and recordkeeping requirements, 40 CFR Ch. I, Federal Register 82 (8) (2017). RIN: 2070-AJ54. [13] Commission Regulation (EU) 2018/1881 of 3 December 2018 amending Regulation (EC) No 1907/2006 of the European Parliament and of the Council on the Registration, Evaluation,

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[14] [15]

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

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