Benchmarking of graphene-based materials: real commercial products versus ideal graphene

The term graphene shall be used, strictly, only for a one-atom-thick sheet of hexagonally arranged, sp²-bonded carbon atoms that is not an integral part of a carbon material, but is freely suspended or adhered to a foreign substrate [8]. Stacking together two graphene sheets to form a bi-layer (with AB stacking, the most common one, or AA stacking), the electronic properties are no longer those of graphene. For thicknesses above ten layers the electronic properties are similar to those of bulk graphite [19], while mechanical properties are known to vary with the number of layers, N. For example, the bending stiffness of an elastically-isotropic plate increases as a function of its thickness cubed. It has been suggested that this will also be the case for multi-layer graphene [14]. Because of the differences in the nature of the bonding within and between the layers, multi-layer graphene is not elastically anisotropic and so the bending stiffness is not necessarily proportional to N³. Nevertheless, the bending stiffness is found to increase significantly as the number of layers increases and, although direct measurements of the stiffness are difficult to undertake, it appears that the bending stiffness increases at least as N² [20].

Even at the research level, no production technique allows 100% graphene monolayers in solution to be obtained: exfoliated graphene samples will always be composed of a mixture of mono-bi and multi-layers (conversely, graphene oxide monolayers may be obtained quantitatively in solution due to their solubility in water; they have also been studied as an 'ideal' 2D material in previous work) [13, 21].

Due to the complexity of graphene-based materials, there is no unique way to define the actual amount of graphene monolayers present in a GRM sample. The yield of graphene produced is reported as:

• 1.  
  Monolayer yield  =  number of monolayers/total number of graphitic flakes in solution.
• 2.  
  Monolayer weight yield  =  total weight of monolayers/total weight of graphitic flakes in solution.
• 3.  
  Exfoliation yield  =  weight of all graphitic material in solution/weight of starting graphite flakes.

For a more detailed discussion on exfoliation yield see the review in [22]. None of these approaches is better than the others, and their utility depends on what is important to obtain for a given application: the number of monolayers, their number plus their size, or just the total number of flakes, mono- or multi-layers, which shall be processed in solution.

Estimating the number of monolayers is a time-consuming task. The main technique used to discriminate mono- from multi-layers is Raman spectroscopy [23]; the number of graphene layers in a flake modifies the electron bands thus changing the shape, width, and position of the G peak in the Raman spectrum (up to ~5 layers). Other techniques that may be used to identify true single layers and count precisely the number of layers are atomic force microscopy (AFM) [21, 24], and transmission electron microscopy (TEM), but these techniques are typically highly localized and are not suited to analyze a statistically significant amount of data in a short time frame.

The specific surface area (SSA) is a key parameter, usually expressed in m² g⁻¹, to understand the morphology of a powder. The numerical quantification of the area of high surface powders is performed by measuring the amount of a physisorbed gas, typically nitrogen, under controlled temperature and pressure conditions. The fundamental theory used in most commercial and scientific instruments is the BET model (Brunauer–Emmett–Teller), and, for carbon based powders, the normative ASTM D6556-10 [25]. Using this technique it is possible to measure the SSA from thousands to few square meters/gram (m² g⁻¹).

The measurement of surface area has already been evaluated by the European Commission (EC) as a rapid way to discriminate nano-materials from conventional ones, combining SSA with measurement of the skeletal (i.e. absolute) density of the material [26]. Measurements of the SSA are sensitive to the measurement method used and on the chemical properties of the materials, and can be misleading in the case of, for example, microporous or sintered materials, as demonstrated by measurements performed on TiO₂, organic pigments or zeolites [27]. The test conditions of BET tests (e.g. processing in a vacuum) can also cause partial aggregation of the GRM, thus giving a SSA lower than the real one. However, results obtained by two leading FP7 projects, NANODEFINE and NANOREG, indicate that this technique could be used to allow faster and easier implementation of the EC nano-materials definition [27], an important and urgent topic also related to safety rules for new materials. Here, we use it for a more specific goal, i.e. to compare with each other GRM that share the same layered structure and the same sp² carbon-based backbone.

By measuring the SSA of GRM, it is possible to estimate the number of layers n composing each flake with the formula $n=2/\left( \rho dS \right)$, where ρ is the density of graphite (2.267 g cm⁻³), d is the spacing between stacked graphene sheets (0.34 nm) and S is the surface of the specific GRM.

This rough calculation allows to estimate the exfoliation grade of GRM: materials totally exfoliated would have SSA similar to ideal graphene (close to 2600 m² g⁻¹), while GRMs poorly exfoliated would have SSA similar to graphite powder (≈0.1 m² g⁻¹). As example, an average flake thickness of 10 monolayers would give a surface area of  ≈260 m² g⁻¹.

We should underline that SSA value does not give the actual number of monolayers or the thickness distribution, but may be used to rapidly give an estimate of how much the GRMs are exfoliated, i.e. if they are more similar to 'ideal', perfectly exfoliated graphene or to graphite powder. Measurements on SSA can be performed also in solution, measuring the adsorption of organic dyes on graphene; at research level, it is possible to correlate the macroscopic SSA with nanoscale measurements, obtained with scanning tunnelling microscopy or molecular dynamics [28]. These methods are, again, only useful at research level thus, focusing on industrial GRM, we used here standard SSA measurements based on gas adsorption. We measured the SSA of the selected GRMs by following the ASTM D6556-10 standard method. All the samples were degassed at 300 °C for 3 h. The instrument used was the ASAP 2020 (Micromeritics, USA). Two samples were prepared and measured for each powder, taking the arithmetic mean of the values measured as the main result, and the semi-dispersion as the error.

Table 1 shows, in column 2, the SSA measured. We observed a broad range of SSA values for GRM, from few m² g⁻¹ to  >1000 m² g⁻¹, close to the theoretical one of graphene. As a reference, we compared the industrial GRM also versus a highly exfoliated, thermally-reduced graphene oxide (TRGO) produced by the University of Freiburg. We selected this material as a benchmark comparison because its production is in halfway between the lab scale and the pilot plant scale [29], and because there is a large amount of data published on its characterization and applications [30].

We evaluated how much our measurements agree with those reported by the producers. In table 1, 'reported' values in column 3 are the values reported by the producers on technical datasheets or web pages, while measured values are those measured experimentally by us.

Figure 2 shows a graphical comparison of the SSA measured with that reported by the producers. The measured and reported data have the same order of magnitude for GRM with SSA  >10 m² g⁻¹, with differences  <30%. On the other hand, the area of the material showing the lowest SSA shows larger differences, but this is not unusual in measurements of materials with low SSA. Overall, our data suggest that the SSA reported by a wide range of GRM producers can be considered as reliable value to estimate the exfoliation grade of the product. The measured SSA was then correlated to other materials properties, as detailed below.

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The lateral size of 2D nanosheets is a fundamental parameter to be evaluated because it has an impact on the performance of the final materials, influencing the mechanical and electrical properties in polymer composites [31], charge transport [21], gas permeation [32] and even biological activity in cells [33].

Most published articles and technical datasheets available report only the average lateral size of GRM, quantified by two common statistical parameters: arithmetic mean ($\bar{x}$) and standard deviation ($\sigma$), often assuming that the length of the nanosheets follows a Gaussian distribution. However, all published experimental data show that for any given 2D material [12, 34] the particle size distribution (PSD) is non-Gaussian, is highly asymmetric and can show complex shapes. In particular, the standard deviation does not give direct information on the breadth of a distribution.

In general, the PSD is defined in terms of a probability density function, as follows:

$$\begin{align*} \newcommand{\e}{{\rm e}} \displaystyle &p\left( x \right)=\frac{{\rm PSD}\left( x \right)}{{{N}_{{\rm tot}}}},\nonumber \end{align*}$$

where N_tot is the total number of particles.

Thus, p (x₀) corresponds to the probability of finding particles with the given size x₀ and likewise, PSD(x₀) counts the number of particles with the corresponding size.

The PSD of exfoliated GRM can be modelled roughly using a log-normal distribution, as recently observed experimentally for graphene [35], graphene oxide [36] and boron nitride [12].

We have previously analysed the size distribution of monoatomic, perfectly 2D nanosheets of graphene oxide using statistical studies, performed by us using image recognition software on AFM, scanning electron microscopy (SEM) and fluorescent microscopy. This procedure allowed us to measure precisely not only the fraction of sheets having a given lateral size, but also their aspect ratio and form factor, i.e. how much their shape differs from a circle. Such analysis revealed that the log-normal model is just a rough approximation of a more complex size distribution, involving two different populations of large and small sheets [13].

However, this procedure requires a significant amount of data, as well as high-quality images of the material, with single sheets deposited flat on a substrate, with minimal overlap between sheets. Industrial GRM (figure 1) are instead often composed of thick, irregular or crumpled platelets, with a strong tendency to aggregate.

To encourage industrial stakeholders to adopt GRM in large scale applications, methods compatible with industrial standards are needed, capable of analysing GRMs on a large scale with high statistical significance, high speed and low cost. Fortunately, there are already several techniques commercially available to measure the size distribution of more conventional nano- or micro-powders with a classical, 3D shape. Techniques such as dynamic light scattering [12, 37, 38], analytical ultracentrifugation [36, 39] or even acoustic spectroscopy [40] have been already used at the lab scale to measure the lateral size of GRMs. This type of characterization is extensively used as a routine standard characterization in many industrial sectors (e.g. food and pharmaceuticals).

A possible problem with this approach is that most particle analysis techniques interpret data assuming that the particles have a 3D, isotropic shape. Thus, they cannot be used strictly to measure the size of 2D platelets such as graphene. In particular, the interpretation of light scattering measurements is typically based on the Stokes–Einstein equation, which assumes the particles to be hard spheres [41]; thus, it would not be suitable for anisotropic, flat 2D nanoparticles.

However, several works correlating DLS and TEM measurements suggest that standard DLS theory may be used for 2D platelets, by applying a simple scalar correction coefficient [12, 38, 42]. Furthermore, the GRM we examined cannot be approximated as 2D nanosheets, unlike perfect graphene. SEM images (figures 1(b)–(f)) show that many of the commercial materials examined are crumpled irregular aggregates of 2D nanosheets whose mesoscopic shape is 3D, more similar to that of conventional powders. Furthermore, even a perfect, ideal 2D nanosheet will not be flat in solution or in a composite matrix, but will crumple and fold assuming a 3D shape due to entropic or surface chemistry effects [43]. In practice, when measuring LS of micron-sized particles, a cumulative signal is registered coming simultaneously from an enormous number of randomly oriented particles.

We therefore selected, among the many techniques available, to use a static light scattering (LS) analysis technique as a fast throughput and reliable way to measure the size distribution of the target GRM. Should be noted that LS is already used by some industrial GRM producers to define the lateral size of their GRMs [44]. The dispersion procedure did not require the GRM to be soluble in the selected solvent, and was carefully tuned to avoid aggregation of particles on one side, but also to avoid further exfoliation or fragmentation of the particles, as example by prolonged sonication (see SI).

This technique uses a charge-coupled device (CCD) camera to register, with high resolution, the light of a laser scattered by a dispersion of nanoparticles in solution. It measures the dependence of the average scattered intensity on the scattering angle and is sensitive to spatial variations in the dielectric constant. Such a technique has several advantages over other techniques previously used [14]:

• (1)  
  it is fast, allowing a measurement to be performed in a few seconds;
• (2)  
  it works for particles in liquids, and does not require the particles to be deposited on a substrate, thus avoiding artefacts due to additional aggregation;
• (3)  
  it can measure particles with a wide size range, from 1 μm to 2.5 mm equivalent spherical diameter (in contrast, dynamic light scattering can only measure small particles with size comparable to the light wavelength, ideally a few hundred nm);
• (4)  
  it does not only provide an average size but also gives the size distribution of the particles' population. It is thus also highly suited for samples that do not follow a Gaussian size distribution, and for samples composed of mixtures of particles of different nature;
• (5)  
  it is widely used at the industrial level (e.g. in the food and pharmaceutical industries) and defined by an industrial standard (ISO13320).

We should underline that LS does not properly provide the PSD, as in the case of the microscopies previously described, due to its non-linear sampling. Moreover, while PSD is usually defined in terms of number distribution (i.e. each particle has equal weighting once the final distribution is calculated), LS measurements provide a volume distribution in which each particle volume has equal weighting. This is analytically defined as the incremental volume percent distribution (IVPD) and is derived from the cumulative volume distribution sampled in log-scale. Because of the irregularity of the shape of the particles, IVPD corresponds to the measurement or the effective diameter of an equivalent spheroid. It is very useful to describe particles with sizes spanning several orders of magnitude.

LS was thus used to give an estimate of the relative abundance in volume of particles with a given diameter (D) in a mixture; a typical size distribution measured by LS is shown in figure 3; the IVPD of all measured samples are available in the SI. They show that all GRM have very different and irregular size distributions, in many cases suggesting a combination of different populations of flakes, similarly to what we observed in more detail for GO nanosheets [13]. Such size distribution cannot be described by a scalar number, just providing the average size, but requires more refined analysis, as detailed in the following section.

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The ideal graphene is entirely composed of carbon atoms, bound together through sp² bonds to form a perfect honeycomb lattice. Graphene obtained by mechanical exfoliation can show the features of ideal graphene, but graphene obtained by industrial techniques such as exfoliation or CVD always present a wide range of defects. These can range from simple deformation of the honeycomb structure (lattice vacancies, sheet edges, Stone–Wales defects etc) to the presence of atoms other than carbon, covalently bound to or even embedded into the graphene lattice. The most common heteroatom found in GRM is oxygen, which in graphene oxide sheets represents a significant fraction of the total atoms.

Raman Spectroscopy is the main technique used to quantify defects in graphene. In particular, the D peak in the Raman spectrum of graphene is not present in perfect graphene, but increases in intensity as the number of defects increases.

The D peak is sensitive to anything disrupting the symmetry of the graphene honeycomb lattice, such as grain boundaries, vacancies, edges, C atoms with sp³ hybridization etc but does not allow the type of defect causing the disruption to be deduced.

The ratio between the intensities of the D and G peaks I(D)/I(G) is often used to estimate the levels of defects in graphene, and increases when the average distance between defects (L_a) decreases down to about 2 nm ^[10]. For highly defective materials, however, with L_a  <  2 nm this proportionality breaks down; highly-defective materials can show a value of I(D)/I(G) smaller than that of graphene a low level of defects. Furthermore, for flakes smaller in diameter than the laser spot give rise to a significant D peak from their edge sites, which may be mistaken for sp³-like defects in the basal plane. More information upon the nature of the defects in graphene can be obtained from the D' band that is often found as a high wavenumber shoulder of the G band ^[50]. In particular it is found that I(D)/I(D') is a maximum (~13) for sp³ defects, decreases for vacancy-like defects and reaches a minimum (~3.5) for boundaries.

Raman spectroscopy is (and will likely remain) the best technique to characterize high-quality graphene. However, it is important to use additional techniques capable of determining not only the number of defects, but also their chemical nature. This is important at the research level, but it is even more important for industrial products, because we do not know how they have been produced, to which chemicals they have been exposed, and thus which kind of contaminants are present. To this aim, we used x-ray photoelectron spectroscopy (XPS) to perform a systematic characterization of all the GRM studied.

In XPS the photoemission signal depends strongly on the type of emitting atoms. Different atomic species have different binding energies of their core atoms. Despite core levels not being directly involved in bonding between atoms, they are strongly affected by changes in the valence states through molecular bonding: this effect is the so-called chemical shift. The ability to measure, in a quantitative way, the presence of different atomic species, and their chemical bonds, combined with an extreme surface sensitivity, makes XPS an ideal tool for the chemical investigation of surfaces and thin films. This is why XPS is also known with the alternative acronym of ESCA (electron spectroscopy for chemical analysis).

When characterizing GRM, XPS can first be used to detect the presence of different heteroatoms (nitrogen, oxygen, metals etc). Then, a high-resolution spectrum centred on the C peak can be used to estimate the abundance of different specific bonds: aromatic sp², sp³ defects, hydroxyl C–OH, epoxy C–O–C, carbonyl (C=O) and carboxyl (O–C=O), etc ^[51]. In this way, a single technique can determine both the chemical impurities (presence of heteroatoms) and structural defects (disruption of the honeycomb lattice) in graphene nanosheets. The accuracy of determining these quantities is still challenging in XPS analysis; however, by using a new protocol to deconvolute the carbon C 1s peak we could calculate with high precision the amount of oxygen and the relative concentrations of structural defects (i.e. specific bonds such as sp², hydroxyl, epoxy, etc) ^[52].

We considered also alternative techniques for the chemical characterization of GRM such as Thermal gravimetric analysis (TGA) or infra-red spectroscopy, which are though more qualitative than XPS.

IR analysis can identify the different carbon chemical groups such as C–O and C–C, but does not provide information on the presence of other heteroatoms as contaminants in the GRM; furthermore, the oxygen content is estimated from stoichiometric considerations about the different C–O bands and not from a separate peak as the O 1s in XPS. Elemental analysis could instead give a quantitative estimation of the presence of different elements, but gives no information on the chemical state of such elements, (epoxy, sp² aromatic, etc). TGA detects the presence of different chemical moieties in the sample using their different thermal stability, but it is often difficult to deconvolute the effect of different groups on the gravimetric curve. XPS provides at the same time quantitative estimation of the presence of different elements and on their different chemical state, and is thus an ideal technique for GRM analysis.

XPS has some intrinsic limits that must be taken into account: (i) surface sensitivity: XPS is extremely sensitive to the surface oxidation and defects (sp² fraction) up to a depth of 3–10 nm, which is the optimal probing depth for highly exfoliated materials (few nm thick flakes), but less effective for the thicker, poorly exfoliated materials. (ii) adsorbed and intercalated water is always present, but can be minimized by long pre-treatment in an Ultra High Vacuum environment (24 h) ^[53].

The details on how the XPS measurements were performed are reported in the SI. In all commercial GRMs, oxygen was the most abundant species after carbon (see SI), but XPS also allowed us to detect the presence of other atoms such as nitrogen and sulphur.

Table 1 shows the amount of O atoms present in each sample. It also shows the % of sp² bonds present between C atoms, calculated from the fitting of the C 1s spectrum.

It could be expected that the amount of oxygen atoms chemically bound to the GRM should destroy the sp² lattice, and thus be directly proportional to the %sp². Figure S1 in SI (stacks.iop.org/TDM/6/025006/mmedia) shows that such a relationship is roughly present, but with strong variations from sample to sample; O and C atoms can bind together in different ways, creating epoxy, carboxy or hydroxyl groups, thus generating the complex structure typical of graphene oxide ^[54].

Another common assumption in the graphene community is that a high number of defects is needed to foster efficient exfoliation; our data indicate that this assumption is statistically correct. Figure 6 shows the correlation between the defectivity of the graphene lattice (% of sp²) and the exfoliation grade (SSA). It is possible to see that all the samples showing %sp²  >  95 are grouped in the region with SSA  <  200 m² g⁻¹ (corresponding to an average flake thickness of  ⩾13 monolayers). This means, as expected, that it is relatively easy to prepare GRMs with low percentage of defects and low degree of exfoliation. In order to obtain GRMs with low number of layers (SSA  >200 m² g⁻¹) usually it is necessary to increase the exfoliation of graphite with techniques (i.e. chemical or physical method) that often increase the damage of the aromatic network, as showed in figure 6 for GRM with SSA  >  200 m² g⁻¹. The different percentage of defects, in function of SSA of GRMs, depends from many parameters, but certainly the production techniques and the post treatment of the material, i.e. thermal annealing, strongly influence the quality and the properties of the GRM. The statistical trend we observed here only refers to commercial GRM, which should be produced in large quantity and low cost. It is of course possible to produce materials having high sp² content and high exfoliation grade on lab scale for research goals, where cost is not a limiting factor.

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The presence of sp³ defects, as compared to sp² bonds, seems thus to be the key factor hindering the re-stacking of GRM after production, allowing them to remain exfoliated even in powder form.

A property of GRM important for industrial applications (but often underestimated at research level) is their density. The 'bulk' density of a powder is the ratio of the mass of an untapped powder sample and its volume including the contribution of the inter-particulate void volume. Hence, the bulk density depends on both the density of powder particles and the spatial arrangement of particles in the powder bed.

Due to differences in morphology, the GRMs show different bulk density values and this property strongly influences the processability of GRMs in the preparation of composites.

Nano-materials such as GRM can have a very low density, looking as highly 'fluffy' powders; this gives problems for:

• (1)  
  processing (i.e. difficult to feed in a standard extruder);
• (2)  
  transport (require large containers to transport a few kg of material) and
• (3)  
  health (can easily be dispersed in air and be inhaled by nearby workers).

It is possible to overcome some of these problems working in liquid or premixing the GRM with polymer before using ^[55]. On the other hand, GRMs with low bulk density could perform better in some applications, as example as sorbent for water purification applications.

We measured the bulk density of commercial GRM powders, measured with a Scott volumeter (see SI). Figure S3 shows the values of bulk density of the different GRMs analysed. The GRMs studied present a large range of values; as expected, the most exfoliated material (TRGO) showed the lowest density of 6 mg ml⁻¹ (TRGO), but no general correlation between exfoliation and density was observed (figure S3). Some samples (e.g. Graphenit-OX and XGnP C750) also showed a relatively high density together with a good SSA, indicating that it is possible to achieve good exfoliation without increasing too much the volume occupied by the GRM.