This paper explores the capability of scanning transmission electron microscopy (STEM) techniques in determining the dispersion degree of graphene layers within the carbon matrix by using simulated high-angle annular dark-field (HAADF) images. Results ensure that unmarked graphene layers are only detectable if their orientation is parallel to the microscope beam. Additionally, gold-marked graphene layers allow evaluating the dispersion degree in structural composites. Moreover, electron tomography has been demonstrated to provide truthfully 3D distribution of the graphene sheets inside the matrix when an appropriate reconstruction algorithm and 2D projections including channelling effect are used.

1. Introduction

The usage of composite materials for industrial applications has dramatically increased since the late twentieth century. Particularly, the transport industry is continuously demanding new materials able of reducing structural weight improving performance in service [1, 2]. Aircraft manufacturers have steadily increased their relative usage of composites over the years, representing nowadays more than 50% by weight in some aircrafts [3]. One of the aimed developments for aircraft structural components is the production of nanoreinforcements that would provide antistatic properties to polymer matrix composite parts, in order to achieve electromagnetic shielding [4, 5]. To act as a shield that avoids electromagnetic interferences (EMI) such as reflection and/or adsorption of electromagnetic radiation by the devices during their useful life, an electrically conducting material with a balanced combination of conductivity, dielectric permittivity, and magnetic permeability is required. Compared with conventional metal-based EMI shielding materials, conducting polymer composites are lightweight, resistant to corrosion, and flexible and offer processing advantages [6]. Graphite, carbon black, and carbon fibre were the first to be combined with polymer to obtain EMI shields [79]. However, the EMI shielding effectiveness (SE) mainly depends on the intrinsic conductivity, the dielectric constant, and the aspect ratio of the composite material [6]. In this line, a graphene two-dimensional one-atom-thick material formed by a layer of carbon atoms in a densely packed hexagonal lattice offers a variety of intriguing attributes. Among others are a high electron mobility at room temperature (250,000 cm2/V·s) [10, 11], exceptional thermal conductivity (5000 W/m·K) [12], superior mechanical properties, Young’s modulus of 1 TPa, and fracture strength of 125 GPa [13]. Furthermore, this novel material has also an almost constant electrical permittivity over three decades of frequency, in a range from 10 to 40 GHz [14]. These characteristics, together with large aspect ratio and high electrical conductivity, would provide an extraordinary EMI shielding effectiveness in the resulting composite [1517]. This profile of material features makes graphene an ideal nanoreinforcement of polymers in aerospace applications [18, 19].

Despite their unique characteristics, to achieve high homogeneity graphene dispersion within the polymer matrix is still a challenge to overcome [2023]. The high cohesive force between graphene sheets and the weak interaction among graphene and polymer matrix limit their usage in typical industrial batch sizes. One possibility to face this problem is disrupting the bonding between graphene sheets by functionalizing the graphene surface [24]. For that reason, various chemical routes have been proposed to incorporate a huge number of suitable atoms/organic groups on graphene sheets [25]. However, to achieve the best performance of the resultant graphene-functionalized polymer, a strict interface control and an adequate dispersion degree are required. So, an important task to enable progress on this advanced nanocomposite is to control both dispersion degree and orientation of the modified graphene sheets into the polymer matrix at atomic scale. In this sense, we propose HAADF-STEM techniques to trace nanolayer distribution. When a focused beam scans a sample and the electrons scattered at high angles are collected, the resultant intensity signal in the detector is approximately proportional to the square of the average atomic number (), allowing to extract structural and compositional information at sub-angstrom level.

During the past few decades, several materials have been characterized by using HAADF-STEM techniques [2628]. It is worth mentioning that the characterization of carbonaceous materials through this technique is more challenging. The presence of carbon in both materials - graphene and polymer matrix - does not offer contrast enough in the resultant HAADF-STEM image. However, despite the low atomic number of carbon, this imaging technique has been used, for example, to count the number of graphene layers of stacked graphene sheets [29]. As this technique is a very useful one for locating high atomic-number materials surrounded by a light matrix, we suggest the marking of functionalized graphene sheets with a heavy metal such as gold to improve contrast in the formed HAADF-STEM image. Experimentally, because of the low chemical activity of pristine graphene, the presence of oxygen functionalities at the graphene surface provides reactive sites for the nucleation and growth of different metallic particles [30]. An example of individual gold atoms detected in a few graphene layers with this technique can be found in [31]. Furthermore, HAADF-STEM also allows electron tomography to 3D reconstruction of atomic structures, when a proper microscope holder is used. This -contrast technique has been previously used to reconstruct gold nanoparticles deposited on amorphous carbon [32] or platinum nanoparticles on a carbon nanofiber [33]. Other chemical analyses through TEM-techniques at nanometre scale, such as electron energy-loss spectroscopy (EELS) or energy-dispersive X-ray spectroscopy (EDX), are not considered in this work because they require longer exposition time to the electron beam, causing large radiation damage in the studied sample.

The aim of this work is to explore the capability of the HAADF-STEM technique in determining the state of dispersion of graphene sheets within polymer matrices. In order to contribute to the optimization of possible manufacturing techniques, with the support of atomic structure models and their corresponding simulated HAADF-STEM images, we propose methods to obtain information about the 3D dispersion degree of graphene sheets within amorphous carbon.

2. Simulation Details

2.1. Modelling

In this work, several atomic structures were generated by using MATLAB software. These models consist of portions of amorphous carbon matrices encircling unmarked or gold-marked graphene sheets at different orientations.

Graphene sheets were modelled as monolayers of sp2-hybridized carbon atoms () arranged in a two-dimensional hexagonal lattice, taking into account the atomic bond conditions shown in Table 1 [34]. For the case of gold-marked functionalized graphene sheets, the most stable adsorption site without breaking the graphene structure corresponds to an adsorption site located over the carbon atoms that form the hexagonal ring, known as the -site position. In this configuration, the bond energy Au-C is 0.8 eV and the migration energy of Au over the graphene sheet is only 0.03 eV, which allows keeping gold atoms attached to carbon atoms with a bond distance of 0.241 nm [35, 36].

Amorphous carbon is a noncrystalline carbon containing a mixture of diamond (sp3-hybridized carbon atoms) and graphite (sp2-hybridized carbon atoms) crystal structures, whose characteristics are summarized in Table 1. The amorphous carbon materials’ properties usually lie between diamond and graphite ones [37]. With a relatively large proportion (65%) of diamond-like sp3 bonds between pairs of carbon atoms and a relatively small proportion (35%) of graphite-like sp2 bonds, the resultant material can be considered amorphous rather than crystalline [38]. In this line, an amorphous carbon matrix formed by 65% of diamond and 35% of graphite has been modelled considering the number of neighbouring atoms, bond angles, and bond distances given by the hybridization type and the pondered average density, which confers certain short-range order upon this amorphous material.

Different models described in each section have been used to explore the capability of HAADF-STEM techniques in determining graphene sheet location, dispersion, and orientation within an amorphous carbon matrix. Although, these models might not result in a chemically realistic structure, they offer sufficient accuracy for image simulation and analysis purposes.

2.2. Image Simulation

Simulated HAADF-STEM images of these models have been obtained by using SICSTEM simulation software [39]. This algorithm uses a parallel implementation of the multislice method [40]. SICSTEM runs on the CAI cluster composed of 80 nodes, each biprocessor node having a double core and 640 Gb of main memory, achieving a peak performance of 3.8 TFlops (billions of floating point operations per second) [41]. SICSTEM takes into account thermal diffuse scattering (TDS) in the calculation of the intensity in the object exit plane. The simulation settings are summarized in Table 2. Though it is well known that graphene is very sensible to the beam-sample interactions and experiments should be carried out at lower voltages [42], we have used 100 kV in order to obtain good-quality images.

2.3. Tomography Simulation

To compute a volume through electron tomography, four main steps are required: acquisition of a series of 2D projections at different tilt angles (tilt-series data), image alignment, reconstruction, and visualization. It is worth mentioning that the tomogram’s resolution is degraded by missing information as a consequence of the specimen tilt range and finite tilt increments. As each 2D projection corresponds to a plane of information in reciprocal space, specimens with needled shape geometry permit the full 180° tilt range. However, practical limitations, such as the sample in itself and the specimen holder’s geometry, normally restrict the tilt range to less than ±70°.

In our particular cases, each 2D projection corresponds to one simulated HAADF-STEM image of the atomic model shown in Figure 1 at a specific view angle. Concretely, a tilt-series of 73 2D projections was acquired by rotating the model at equal-slope increment of 2.5° along the -axis. The tilt-series data was viewed with ImageJ processing free software [43]. The alignment and reconstruction processes of the tomographic series were performed by using TomoJ, an ImageJ plug-in. The tomographic reconstruction of the simulated tilt-series data were performed using two algorithms: the simultaneous iterative reconstruction technique (SIRT) [44] and the compressed sensing-based algorithm (CS) for the total variation minimization (TVM) technique [45]. The SIRT algorithm is an iterative method based on the algebraic reconstruction technique. 100 iterations and a relaxation coefficient of 1 were selected [46]. The CS allows reducing considerably the amount of data necessary for the reconstruction of the final volume. In the field of CS, an underestimated system of equations can lead to an exact solution if the signal (or an expression of the signal in another basis) is sparse enough. In the case of electron tomography, this effect can be present in the gradient of the signal. Thus, when this prior knowledge is exploited, the algorithms based on TVM can be used. To carry out TVM reconstruction, the TVAL3 solver was used [47]. A regularization parameter () equal to 27 was considered. The reconstructions were implemented in MATLAB using ASTRA Toolbox [48]. The tomograms were then rendered and analysed using AVIZO 3D-viewing software.

3. Results and Discussion

To analyse the possibility of displaying graphene sheets inside polymeric nanocomposites, atomic models representing a piece of amorphous carbon about 150 nm3 in volume were generated. In each model, the graphene sheets vary in orientation in relation to the incident electron probe. Subsequently, the HAADF-STEM images of the models were simulated. Figure 2(a) shows the atomic model that represents a matrix of amorphous carbon (green colour) that surrounds three graphene sheets perpendicularly oriented to the electron beam (blue colour). The corresponding simulated HAADF-STEM image is shown in Figure 2(b). As it was expected, given by the similar chemical nature of the amorphous carbon and graphene sheets, it is hard to determine the graphene sheet location. Nevertheless, in the case where the graphene sheet is oriented along the electron beam of the microscope (as it is shown in the model of Figure 2(c)), its position inside the amorphous matrix is clearly detected in the resultant HAADF-STEM image (Figure 2(d)), registering a much stronger contrast than the amorphous carbon alone. In order to compare the differences of the intensity values, a comparison between intensity profiles taken from both images is shown in Figure 2(e). The selected integration areas have been marked in the simulated HAADF-STEM images with blue and red rectangles, respectively. As it can be appreciated, due to the random orientation of the carbon atoms inside the amorphous matrix, the intensity value depends on the number of carbon atoms that cross the beam. Therefore, the area of the image where the three sheets of the model are located in Figure 2(b) slightly increases the intensity value (~10%) with respect to the area free of graphene. However, when the graphene sheet is oriented parallel to the electron beam, the given HAADF-STEM intensity is about 70% higher than any other orientation, allowing its right visualization. This happened as a clear consequence of the so called channelling effect. This phenomenon typically occurs when the electron beam interacts with crystalline solid at certain angles, in which the path of charged particles is constrained and individual acts of dispersion are turned into a cooperative effect. Channelling is enhanced in this 2D material when the surface of the graphene sheet is oriented along the electron beam, because this configuration allows a larger fraction of electrons being dispersed at higher angles, so image intensity is increased.

Once the difficulty of locating graphene sheets by Z-contrast imaging is exposed, new models with gold atoms added to the graphene surface are considered in order to increase the intensity in the resultant HAADF-STEM images. In this sense, Figure 3(a) shows an atomic model representing a piece of amorphous carbon of about 200 nm3 in volume encircling two gold-marked graphene layers. Its corresponding simulated HAADF-STEM image is in Figure 3(b). As it can be observed, gold atoms are clearly identified as peaks of intensity in the HAADF-STEM image (). In addition, the gold atoms of the same graphene sheet, i.e., located at equal height () inside the amorphous carbon, give the same intensity value. Furthermore, a constant intensity variation has been measured when gold-marked graphene layers are leaning. To better illustrate that effect, an atomic model representing a graphene sheet 60° oriented with respect to the -plane within the amorphous carbon matrix and its corresponding simulated HAADF-STEM image are shown in Figures 3(c) and 3(d), respectively. As it can be seen, the maximum intensity value associated to a gold atom changes slightly from the one nearby. However, a gradual intensity variation related to the -gold atom position is clearly appreciated when comparing intensity values among them ( units). These results point out a linear correlation between HAADF-STEM intensity and graphene layer sloping. On the one hand, when graphene sheets are oriented parallel to the -plane, all gold atoms over the surface have the same HAADF-STEM intensity value (i.e., when these values are compared one to each other: ). On the other hand, when the sheet is sloping to the -plane, the HAADF-STEM intensity peaks increase or decrease progressively depending on its 3D location (i.e., when the intensity of different gold atoms is compared among them: ΔIz = constant). As gold peak intensity values depend not only on sheet height but also on their relative inclination with respect to the -plane, dissimilar graphene dispersion configurations may agree with the same intensity image contrast. Therefore, when the orientation of graphene sheets is not known beforehand, it is not possible to accurately guess it only by observing peaks of intensity values in HAADF-STEM images.

In case of structural materials in which graphene sheets need to maintain a similar alignment within the matrix [49], the sensibility of HAADF-STEM intensity values to the position of gold atoms may be used as a way to know the dispersion degree of the graphene sheets. For that, we investigated whether the changes in graphene dispersions are somehow noticeable by image histograms, the statistical graph of the frequency distribution of the HAADF-STEM image intensity values. We consider histograms because they are easily obtained.

Figure 4 shows the atomic models used in this study together with their corresponding simulated HAADF-STEM images. Specifically, they consist of a piece of amorphous matrix of about 3000 nm3 containing 1% of graphene filler. The graphene sheets have been distributed in a way that represents different dispersion states: (a) a homogeneous gold-marked dispersion model; (b) a random dispersion one, which represents gold-marked graphene sheets distributed without any predictable pattern; (c) a grouped one, representing a model in which gold-marked sheets are accumulated in specific zones and there are areas without filling. In addition, a model representing a homogeneous dispersion containing marked and unmarked graphene sheets is shown in (d). Finally, a uniform unmarked graphene model is included as reference in (e). Although nowadays in real composites the sheets may not be as perfectly positioned as those in the model are, there are manufacturing techniques being currently developed to achieve this [50, 51].

To be able to compare the resulting histograms from images in Figure 4, firstly we have changed all histograms into the same bin size and the number of pixels in every image was normalized. Then, to achieve a more accurate measurement of the intensity distribution in the HAADF-STEM images, the histograms were fitted to probability graphs, concretely to a simple Gaussian distribution. Figure 4(f) shows the probability distribution graphs of the intensity data corresponding to the HAADF-STEM images shown in Figure 4. Under the established imaging conditions in Table 2, results disclose a bell-shaped and symmetric data distribution for the unmarked model (black dashed line), meaning that intensity variation in the simulated image is built up of many independent small causes of variation, the carbon atom distribution in the atomic model. Moreover, in this case the mean intensity value (0.045 a.u.) and the standard deviation (0.006) are the lowest ones, meaning that most of the intensity values are close to the mean one. This happens because most of pixels in the HAADF-STEM image are formed after the interaction of the beam probe with barely the same number of carbon atoms, giving as a result similar intensity values. However, in gold-marked models (a-d) the typical Gauss bell changes towards a right-tailed intensity distribution. In the case of gold-marked graphene layers, because of the presence of heavy atoms, the population of pixels brighter than the mode increases, tending the histogram to be skewed to the right. Results also disclose a reduction in the curve height together with an increment in the full width at half maximum (FWHM) as graphene sheets get more stacked, decreasing their correlation with the unmarked model (shown as inset in Figure 4(f)). So, observing the fitted graphs, it is relatively easy to distinguish among a homogeneous graphene layers distribution (blue and green curves) from an intercalated distribution (red curve) and a stacked one (yellow curve). These results suggest that HAADF intensity image histograms are somehow sensible to sheet dispersion. For example, the HAADF-STEM simulated image of an unmarked but homogeneously dispersed model (e) depicts a very similar contrast to the one presented by the marked graphene but heavily stacked (c). Nevertheless, the shape of their resultant Gauss curves is dissimilar enough to distinguish both graphene sheet distribution inside the amorphous carbon.

Though histograms may provide some qualitative information about graphene distributions, these curves and their related HAADF-STEM images (due to their 2D nature) offer enough information to establish the volumetric dispersion of graphene layers inside the matrix, as needed in case of nanocomposites for electrical applications. In the graphene-based nanocomposites, to improve electrical properties in the resultant composites, a random distribution of graphene layers is essential to achieve a better interconnection among graphene layers [52].

To solve this matter, a HAADF-STEM tomography study was carried out using the atomic model described in Figure 1. Additionally, to gain more insight concerning the feasibility of electron tomography for the visualization of the graphene layers inside the matrix, three different scenarios were considered. In particular, we have investigated the effect of (i) the number of projections over a maximum tilt range, (ii) the limit tilt range, and (iii) the influence of the angular sampling and 5°. For the limited tilt range, we simulated a tilt series from −90° to +50°, containing projections with graphene sheets well oriented, and tilt series from −70° to +70°. Note that in this case, the graphene sheets are disoriented. Additionally, all these scenarios were reconstructed using SIRT and TVM algorithms. The HAADF-STEM tilt series movie-file, from a maximum tilt range every 2.5°, is shown in Supporting Information (Movie 1). From this aligned file, the rest of the schemes are extracted to be reconstructed.

Figure 1 shows the atomic model used for the tomographic study, consisting of 119,467 atoms, representing a compound of 700 nm3, consisting of an amorphous carbon matrix encircling two graphene sheets. The graphene sheets are marked with gold atoms. The upper layer is tilted 30° and the lower one 50° with respect to the -axis. The model includes five randomly dispersed gold atoms. Simulated HAADF-STEM images of the model at different tilt angles are displayed at the right. Although graphene sheets are present in all 2D projections of the tilt series, they are only slightly visualized inside the amorphous matrix (white squares in Figure 1(g)) when the model is rotated with respect to the beam direction at high angles (values over ±82°) and clearly detected at ±90° as it can be observed in Figure 1(b), because of the channelling effect described previously (see Supporting Information Movie 1).

Figure 5 shows slices extracted from the SIRT (first row) and the TVM (second row) reconstructions, respectively. The slices were perfectly oriented at the same plane of the upper graphene layer surrounded by the amorphous carbon matrix. For the best of the proposed acquisition scheme, 180° with 73 projections, both reconstruction algorithms enable the visualization of the graphene layer. However, in the SIRT reconstruction, streaking artefacts arising from the gold markers are present, reducing the quality for graphene/matrix contrast imaging. In the TVM reconstruction, these artefacts are less pronounced. For a better visualization of these artefacts caused by the gold markers, Figure 6 shows volume rendering of eight reconstructions. In the case of the SIRT algorithm (Figure 6(a)), the streaking artefacts are visibly along the -axis with gold markers distorted from the original spherical morphology. But if the number of projections is reduced to 37, increasing the tilt increment from 2.5° to 5° (scheme 2), the streaking effects are more pronounced for SIRT reconstruction (Figures 5(b) and 6(b)). In contrast, TVM is less affected by the largest tilt increment and the contrast between the graphene and the matrix still remains acceptable (Figures 5(f) and 6(f)).

As the channelling effect influences the quality of the reconstructions, its influence is also evaluated for the schemes labelled as 3 and 4. For these acquisition schemes, the tilt range is limited to 140°. In scheme 3 with a tilt range from -90° to +50°, we are considering a tilt series with projections where the channelling effect is present and hence with a much stronger contrast than the amorphous carbon. For this case, in the SIRT reconstruction, in addition to streaking artefacts, an elongation in the direction of the missing wedge is present (Figures 5(c) and 6(c)). In the TVM reconstruction, these artefacts are less pronounced and practically did not show differences from the previous better acquisition condition schemes (Figures 5(g) and 6(g)). Nevertheless, in the case where any of the projections used to reconstruct the volume did not suffer from channelling effects, this is assumed in this work considering the tilt range between ±70° (scheme 4); the visualization of the graphene sheets dramatically decreases for both SIRT (Figures 5(d) and 6(d)) and TVM (Figures 5(h) and 6(h)). Results show that the appropriate tomographic 3D reconstruction of the model provides truthfully 3D distribution of the graphene sheets inside the matrix (see Figure 6 and Supporting Information Movie 2), being possible to check the method used to produce the nanocomposite, in order to manufacture homogeneous or inhomogeneous dispersion.

4. Conclusions

In summary, based on the results obtained from the simulations of the studied atomic models, we show that graphene sheets in organic composites are clearly identifiable by HAADF-STEM techniques when graphene layers are oriented in the direction of the electron beam, due to the channelling effect. In order to improve the contrast, we propose marking graphene sheets with heavy atoms, e.g., gold. To explore the chance of determining the dispersion degree in structural composites by using 2D-projected HAADF-STEM images, a statistical study is carried out in models representing three different dispersion states. Although in the image intensity probability graphs some differences are found among homogenous, intercalated, and stacked dispersions, the 2D nature of this technique does not allow an accurate correlation of the resultant intensity curve shape with the position and orientation of graphene sheets in case of interconnected graphene layers’ distributions.

To overcome these limitations, an electron tomography study is proposed. Results from simulated HAADF-STEM electron tomography reveals that this technique is a successful one to identify and locate reinforced areas in nanocomposites and therefore a way of controlling graphene sheet dispersion. Moreover, we find that SIRT reconstruction is more affected by variations in the acquisition parameters like maximum tilt range and tilt increment. In contrast, TVM reconstruction significantly reduces noise and sharpens transitions between graphene sheets and the carbon matrix which will enable a simpler and easier segmentation of the reconstruction. Additionally, the TVM algorithm suffers less from the incomplete sampling in Fourier space due to the missing wedge and is not strongly affected from the lower number of projections. These advantages can be extremely useful for very sensible materials, like graphene, when quick tilt series needs to be acquired to reduce beam-sample interactions even when low voltages are used. Expectedly, the fidelity of both reconstruction methods decreases when the channelling effect is dismissed. To avoid this in practice, the operator should select only those areas from which, tilting as much as possible according with their instrumental limitations, channelling effects on the HAADF-STEM images are detected.

Data Availability

The simulation detail data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


This work was supported by the Spanish MINECO (projects TEC2014-53727-C2-2-R and TEC2017-86102-C2-2-R) and the Junta de Andalucía (PAI research groups TEP-946 INNANOMAT, TIC-145, and FQM334). Cofinancing from UE-FEDER is also acknowledged. J.C.H-G. acknowledges support from the Ramón y Cajal Fellowships Program of MINECO (RYC-2012-10004). M.L-H acknowledges support from the Juan de la Cierva Fellowships Program of MINECO (IJCI-2014-19367).

Supplementary Materials

The uploaded supplementary material as a .zip file includes two movies showing 3D visualization of the 2D projections at different angles related to the model used by tomography study (Movie 1) and the reconstruction of the same model using two algorithms TVM and SIRT (Movie 2). Similar images shown in the article have been taken from these movies. (Supplementary Materials)