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Surface electrostatic potentials in carbon nanotubes and graphene membranes investigated with electron holography
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available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/carbon
Surface electrostatic potentials in carbon nanotubes and graphene membranes investigated with electron holography Luca Ortolani a,*, Florent Houdellier b, Marc Monthioux b, Etienne Snoeck b, Vittorio Morandi a a b
CNR IMM-Bologna, Via Gobetti, 101, 40129 Bologna, Italy CNRS CEMES, 29, Rue Jeanne Marvig, 31055 Toulouse, France
A R T I C L E I N F O
A B S T R A C T
Article history:
We used low-voltage transmission electron holography to probe surface electrostatic poten-
Received 21 October 2010
tials in graphene membranes and carbon nanotubes, as the number of graphenes varies.
Accepted 3 December 2010
Further, we measured the phase shift induced by an individual graphene, and mapped
Available online 7 December 2010
the phase shift variation throughout a whole few-graphene-crystal as a function of the local number of layers. We found a size/surface effect as the ratio between the surface and the total number of atoms increases for an individual nanotube or graphene membrane. This surface phase term can be related to a fine electrostatic potentials redistributions occurring at the outer layers in carbon nanotubes and graphene membranes. Ó 2010 Elsevier Ltd. All rights reserved.
1.
Introduction
Single-walled carbon nanotubes (SWCNTs) [1] and recently isolated graphene membranes [2,3] represent prototype low dimensional systems, composed only of surface atoms. In these materials carbon atoms are arranged in a two-dimensional honeycomb lattice, rolled into a cylinder in the case of carbon nanotubes. In multi-walled carbon nanotubes (MWCNTs) and few-graphene-crystal (FGC) membranes, where layers are stacked, respectively, concentrically and vertically and where graphenes are bound just by weak van der Waals forces. While the in-plane bonding between carbon atoms is not significantly affected upon FGC and MWCNT formation, nevertheless the chemical and physical properties of those materials depend strongly on the number of walls and/ or sheets. In particular, the chemical and thermal stability of CNTs increase both with the number of walls [4–6], while their Young’s modulus increases as the thickness is reduced [7] up to the maximum value of 3.5 TPa for an individual SWCNT [8]. Further, individual graphene membranes show a peculiar electronic structure, where the energy of the charge
carriers is linear in the momentum. This linearity is at the origin of all the extraordinary properties of this material, which however change dramatically, and eventually disappear, when even just two layers are stacked to form few-graphenes crystals [9–11]. Hence, a better understanding of the structural and electronic modifications occurring when the number of walls (in CNTs) and the thickness (in FGCs) reduces to one monoatomic layer is mandatory in order to understand the properties of these materials. In this article we use transmission electron holography to measure the surface electrostatic charge distributions in CNTs and FGCs as a function of the number of layers/walls. While structural characterization techniques such as electron diffraction [12,13], and high-resolution transmission electron microscopy (HRTEM) [14,15], are extremely sensitive to the position of core electrostatic charges, therefore providing accurate data on the position of atoms in a lattice, on the other hand they are little affected by the actual distribution of valence electrons, which is the key to understand the electronic properties of such material. Combining HRTEM imaging and electron holography [16], we investigated the
* Corresponding author: Fax: +39 051 639 9216. E-mail address: [email protected] (L. Ortolani). 0008-6223/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2010.12.010
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redistribution of crystal charges, in both their core and valence part [17], in CNTs, as the number of walls decreased from 20 down to an individual SWCNT, and in a FGC, as the number of layers varied from an individual graphene up to four. We were able to obtain unprecedented sensitivity in the electron phase reconstructions, mapping phase shift induced by individual monoatomic graphene layers, and measuring surface phase variations in CNTs and FGCs, possibly originating from fine electronic charge redistribution at the surface atoms.
2.
Experimental results
2.1.
Holographic mapping of crystal charges
Electron holography is an experimental technique capable of retrieving the full electronic wavefront of the electronic radiation that has interacted with the sample [18]. Basically, a hologram is the interference pattern between the beam that has passed through the sample, and a reference one from the vacuum nearby. The electronic wave, passing through the specimen, interacts with the distribution of charges in the crystal, and a detailed map of the distribution of the electric and magnetic fields is stored in the phase term of the retrieved wavefront [19], which is reconstructed by analyzing the deformations of the interference fringes of the hologram [18]. In the absence of either magnetic contributions or free charges in the material, as in the case of FGC membranes and CNTs, the measured electronic phase map / is simply related to the electrostatic potential V in the sample, as follows [16]: Z ð1Þ /ðx; yÞ ¼ CB Vðx; y; zÞdz where CB is an interaction constant depending on the energy of the beam electrons. The result of the integration in Eq. (1) is the projection along the z-axis of the electrostatic potential generated by the charge distribution in the crystal [20]. The spatial resolution obtained in the phase reconstruction is not sufficient to map the potential distribution of individual atomic charges [16,17], hence the measured phase shift is the result of the average electrostatic potential over an area of several crystal unit cells. Under those conditions, Eq. (1) can be expressed in terms of the second moment of the electrostatic charge distribution hr2 i, as [17,21]: / ¼ CB k0
2pNz 2 hr i 3Acell
ð2Þ
where Acell is the area of the unit cell of the crystal, k0 = 1.447 V nm/e is the Coulomb’s force constant, and Nz is the number of unit cells in the direction perpendicular to the electronic beam, i.e. the number of layers in a FGC or the number of walls in a CNT.
2.2.
Holographic investigation of CNTs
Commercially available arc-discharge MWCNTs were prepared for TEM observations by dispersing the nanotubes powder in isopropanol with the aid of a ultrasonicator. TEM samples were obtained by putting a drop of the solutions onto
standard holey carbon grids, and letting the solvent to evaporate. To reduce the amount of residual water and to remove most of volatile contaminants, TEM grid were heated on a hotplate at 200 °C for 15 min before inserting them in the microscope. The TEM used for the experiments was a Tecnai F20 equipped with a CEOS aberrations corrector, operated at a lowered accelerating voltage of 100 kV, instead of the conventional 200 kV, to reduce the radiation damage to the sample. Fig. 1a shows the TEM micrograph of an 8-walls nanotube. The number of walls composing the tube is easily determined by the image, observing the (0 0 0 2) fringes at the nanotube borders. Even if particular attention was given to reduce contamination from the samples, few amorphous carbonaceous contaminants are grafted over the tube. Nevertheless, sufficiently large portions of the tube are atomically clean and therefore suitable for holographic investigation. In the phase map of Fig. 1b, the vacuum surrounding the tube appears darker than the bright area of the tube where the carbon atoms of the lattice modify the phase of the beam electrons. To measure the shift induced by the walls of the tube, a line profile of the phase was acquired along the horizontal direction over the region marked by the rectangle, and averaged over its vertical height. Fig. 1c shows the plot of the phase profile and a cartoon showing the modeled structure for the eight-walls nanotube, where the arrow indicates the direction of the beam electrons. The profile clearly shows two peaks, corresponding to the portion of the walls that are almost parallel to the electron beam. In this region the spatial density of atoms is higher due to the projection effect, resulting in a larger phase shift. The measure of the total phase shift produced by the stacked graphene layers was performed in the central part of the profile, between the two peaks, where the eight upper and eight lower walls of the tube were almost perpendicular to the electron beam. The electrons traversed a total of 16 graphene walls, and their phase was shifted by (0.72 ± 0.02 rad), as indicated by the red horizontal line in the graph, therefore each graphene layer shift the beam by (0.038 ± 0.01 rad). The same holographic analysis has been done on SWCNTs, grown by CVD and commercially available. Fig. 2 shows the result of the analysis for one of those tubes, with a diameter of 1.6 nm. Fig. 2a shows the reconstructed phase map of a freestanding SWCNT. The brighter walls of the tube are clearly visible, along with a small cluster of carbon contamination sufficiently small not to prevent the analysis of the phase shift over the clean region of the tube. Even in this case a phase line profile has been acquired over the area indicated by the yellow rectangle, averaged over the vertical dimension. Fig. 2b shows the obtained phase profile and a structural model of the SWCNT. Again, the measurement of the phase shift induced by the two almost parallel walls has been done in the region between the two maxima corresponding to the walls portion parallel to the electron beam. The total phase shift has been estimated in (0.10 ± 0.01 rad). The estimate of the phase error was done analyzing the oscillations of the phase in the vacuum region. The electrons in the microscope passed through two walls and we can calculate that each graphene lattice induced a phase shift of (0.050 ± 0.005 rad).
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Fig. 1 – Holographic analysis of an eight-walls CNT. (a) HRTEM image of the tube. (b) Phase map as reconstructed from the hologram. Bright contrast corresponds to the induced phase shift. (c) Phase profile acquired over the rectangle in (b) along the horizontal direction and averaged over its vertical width. The horizontal line indicates the value of the phase shift produced by the 16 walls perpendicular to the beam direction, as shown in the drawings.
Fig. 2 – Holographic analysis of a SWCNT. (a) Reconstructed phase map of a freestanding SWCNT. (b) Plot of the phase profile acquired over the rectangle in (a). Horizontal line indicates the value of 0.10 rad corresponding to the phase shift induced by the two graphenes perpendicular to the electron beam. The cartoon in the inset shows a model structure for the SWCNT, at the same scale of the profile plot.
Using the same holographic technique and the same analysis approach, we investigated variations in the average phase shift per graphene in the case of CNTs composed of 20, 18, 2 and single-wall, as shown in Fig. 3. Even in the presence of a relatively large error in the phase measurement for thinner tubes, it is evident that there is systematic increase of the average phase shift as the number of walls composing the nanotube reduces from 20-walls nanotubes down to doublewalled and ultimately single-walled tubes.
2.3.
Holographic investigation of graphene membranes
We applied the same analysis to graphene stacks, produced by a liquid assisted mechanical exfoliation, as described by Coleman and coworkers [22]. TEM samples were prepared by putting a drop of the solution onto standard holey carbon grid for TEM observations and heat-treated just before the observations, similarly to nanotubes samples, to reduce the amount of contaminants.
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Fig. 3 – Phase shift per individual graphene layer as function of number of walls. The horizontal line indicates 0.04 rad, which is the expected theoretical value for bulk graphene stacks.
Fig. 4a shows the HRTEM image of a turbostratic FGC membrane, in a region around a suspended edge. Even if the electrons of the beam are not accelerated enough to induce a significant displacement of the carbon atoms in the crystal, nonetheless the energy transferred from the beam to the lattice is sufficient to trigger the chemical decomposition of the graphene [23,24]. Decomposition starts from defective sites in the lattice, drilling holes in the honeycomb network, and peeling successive layers from the FGC. As evident in Fig. 4a), the surface of the flake presents several areas
few nanometers large, where locally missing graphenes expose the underlying structure. Analyzing those areas, like the ones labeled as (1)–(3) in Fig. 4a, it is possible to determine the complete stacking structure of the individual flake. Fig. 4b shows the Fast-Fourier-Transform (FFT) of region (1), where only one individual graphene is left. The FFT shows the hexagonal pattern of an individual honeycomb network, with each spot corresponding to the distance of 0.213 nm. Fig. 4c shows the FFT of the region (2) in the HRTEM micrograph. In addition to the previous set of spots, indicated by yellow circles, there is an additional pattern, indicated by the blue circles. Hence, in that region the flake is composed of two graphenes. The two sets of spots in the FFT are rotated by h = 13°, indicating that the two layers are in a turbostratic arrangement and are rotated accordingly. In region (3), the flake is composed of four graphenes. Interestingly, the related FFT, displayed in Fig. 4d, reveals that the two additional graphenes are stacked each one with the same rotation angle h, resulting in the four graphenes of the stack all having the same relative orientation of 13°. The presence of holes in the surface of the flake due to beam damage, as visible in Fig. 4a, gives us the opportunity to individually measure, with electron holography, the phase displacement due to each graphene, up to four. Fig. 5a shows the reconstructed phase map in false colors. The red regions, which have the same value as in vacuum level, reveal the presence of holes over the surface of the flake. Fig. 5b shows the phase profile acquired from the region indicated by (1) in Fig. 5a, while Fig. 5c shows the phase profile from region (2). In the proximity of the holes the flake is thinner, as more graphene layers are peeled off from the crystal. Despite the noisy signal, the graphs clearly display step-like phase profiles, with values ranging from approximately zero in correspondence to vacuum, up to 0.24 rad, where four graphenes are stacked. In particular, in Fig. 5b a phase level of 0.06 rad is clearly visible, while all the other phase values correspond to multiple integers of this amount. Thus, as the number of graphenes in the FGC changes, within the precision of the phase measurement, we do not observe any change in the average phase displacement per individual graphene, which is constantly (0.06 ± 0.01 rad). The contribution on the phase shift by the weak van der Waals potentials, responsible for the interaction between graphenes, is expected to be too small to be measured with an accuracy of 0.01 rad.
3. Fig. 4 – HRTEM image of the border of a FGC flake where graphenes were stacked turbostratically. (b) FFT spectrum from region (1), where only one layer is present. Yellow circles highlight the hexagonal pattern from honeycomb lattice. (c) FFT from region (2) where two graphenes are stacked. FFT shows the patterns from two honeycomb lattices (yellow and blue), rotated by 13°. (d) FFT spectrum from region (3). Spectrum shows four patterns from honeycomb networks (yellow, blue, green and red), revealing that each graphene is rotated by 13° with respect to its neighbors. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Discussion of the results
The most striking feature in the data presented in the graph of Fig. 3 is the relatively large variation in the phase shift induced by each graphene between an individual SWCNT and thicker tubes of tens of walls. From 0.038 rad of a 20-walls CNT, the phase increases constantly up to 0.055 rad for a SWCNT. The measured values of 0.055 rad and 0.05 rad for the phase shift of individual SWCNTs are in agreement with previously reported data [25]. Interestingly, the value of the phase shift for a thick MWCNT is significantly different from that of a SWCNT, but it is perfectly matching the theoretically calculated value of 0.04 rad for bulk graphite (Bernal stacking). This value was obtained modeling the distribution of crystal
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Fig. 5 – Reconstructed phase map of the turbostratic FGC. (a) Phase map in false colors. Red corresponds to vacuum values, showing the presence of holes over the surface of the flake. Vacuum phase level has been renormalized to zero. (b) and (c) show the phase profile along the line indicated by (1) and (2) in the phase map. In both profiles, each level indicated by the lines corresponds to an integer multiple of 0.06 rad. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
charges in graphene lattice, and taking into account the valence charge redistributions induced by bonding, both inplane and between the layers [26,27]. The average phase shift per graphene in the case of MWCNTs matches that of bulk ABAB stacked graphite. Notwithstanding the types of van der Walls potentials in these two different stacks are certainly different and, with the actual precision, electron holography is not capable of distinguishing between them, nevertheless, variations in the average phase per graphene in stacks of different thickness clearly show a surface/size effect on the phase shift of the electron wave, with a surface contribution of the order of 0.02 rad from the single graphene sheet to the bulk value. A similar increase of the phase shift as the dimension of nanostructure decreases has been observed experimentally in the case of gold nanoparticles [28–30]. In that case, it has been proposed that this phase rise originates from the redistribution of charges induced by the under-coordinated atoms of the surface [31]. As the dimension of the nanostructure is reduced, the portion of surface skin atoms increases with respect to those in the inner volume. Due to the reduced coordination, the charge in the surface redistributes, and the bond length locally contracts. A similar effect on the distribution of valence charges has also been predicted for carbon nanotubes [32], even if the bonding between graphene layers is provided by weak van der Waals attraction and therefore there is no change in the coordination of the surface atoms. Nevertheless, according to the model proposed by the authors, subtle charge redistributions should occur in surface atoms of carbon nanotubes and in SWCNTs, compared to bulk MWCNTs, the average electrostatic potential, hence the phase shift through Eq. (1) should increase of about 70% [32]. This prediction is indeed in good agreement with our val-
ues, since we measured an increase of about 50% of the value of the phase shift per graphene from thick MWCNTs to SWCNTs. Holographic investigation of the FGC (Fig. 5) shows a different behavior of the average phase shift per graphene as the thickness of the stack increases. The phase shift in the case of an individual graphene is 0.06 rad, which is comparable to that of a SWCNT (Fig. 3), within the experimental error. Interestingly, the phase shift per graphene in the FGC is not changing as the number of layers stacked changes from one to four. As the two systems are very similar, we would expect a reduction in the phase shift between one and four as it is observed in the CNTs. If we consider again the above theory, the origin of the surface phase shift addition in SWCNTs is due to the presence of unbound graphene layers and therefore it could also explain why we do not observe any change in the average phase shift per graphene in the FGC. Indeed, graphene membranes have a peculiar stacking geometry, with all the layers rotated by 13° with respect to its neighbors. This particular configuration is also called turbostratic commensurable, as adjacent graphene lattices become commensurable and superlattice geometry can be defined [33], a condition that is not possible in CNTs due to the curvature of the walls. According to the theoretical modeling of the valence charge distribution [10,33,34], in this configuration each graphene in the stack is completely electronically decoupled from each other. Therefore each layer in that FGC behaves as a free unbound graphene surface, inducing the additional phase shift on the electron wave we observe, independently of the number of graphenes in the stack. In the case of gold nanoparticles, the surface phase term extracted from the holographic experiments on gold nanoparticles is about 0.4 rad [30], while we measured a surface
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contribution of 0.02 rad in carbon nanotubes and graphene membranes, i.e. an order of magnitude lower. This could be explained by the different nature of bonding in the systems (i.e. covalent in nanoparticles, and of van der Waals type in graphene based structures) as the valence charge redistributions occurring at unbound surfaces is expected to be much stronger in covalently bound surface gold atoms. Nevertheless, the above mentioned model for the origin of the surface phase shift observed in graphene based materials lacks the experimental evidence for the expected contraction of the bond length and wall thickness. Indeed, associated with the electronic charge redistribution at the under-coordinated surfaces, the carbon–carbon distance in the graphene lattice is expected to contract to 0.125 nm, compared to the bulk 0.143 nm, and the thickness of the graphene wall should reduce to 0.12 nm, compared to an inter-wall distance of 0.35 nm in MWCNTs. Size/surface phase effect similar to what we observed in graphene membranes, carbon nanotubes and gold nanoparticles has been recently reported for amorphous carbon films of different thicknesses [35]. In this case the thickness independent surface contribution to the phase shift was estimated to be about 0.497 rad, possibly due to the presence of adsorbates over the surface of the films, as it could be reduced to 0.36 rad by heating the samples before the observation. In the Supplementary informations available online, we detail a model of the phase shift induced by a layer of surface dipoles adsorbed on SWCNTs. According to our calculations (see Section S1), the presence of surface contaminants, like water molecules, is capable of significant phase shifts in the internal volume
of the tube, but they are not able to completely explain the experimental profiles like the one shown in Fig. 2b. The phase investigation also represents an elegant and powerful method to determine the thickness of a FGC sample. Fig. 6 shows the contour plot of the phase map of flake in Fig. 5a, where each contour is plotted every 0.06 rad; hence the phase map can be immediately converted into a map of number of graphene layers in the flake. In Fig. 6, black refers to the vacuum, while colors range from pink to azure, corresponding to crescent graphene layers, from one to four as shown in the legend. Regions with a phase value higher than corresponding to four layers are represented in orange, and they correspond to thicker areas where the amorphous carbon support or some contaminants, are present. We point out that, unlike scanning probe techniques, the local thickness can be measured for freestanding FGCs. This can be an important asset of electron holography, since it is well documented that, in scanning probe techniques, the interactions between the graphene or flake and the substrate, and/or the presence of residual solvents between them generate a substrate-dependent bias, which is certainly disturbing and it is far from being fully understood [36].
4.
Conclusions
We used low-voltage transmission electron holography to probe surface electrostatic potentials in FGCs and CNTs, as the number of layers/walls varies. The phase investigation of the stacking of graphenes in concentric MWCNTs revealed a size/surface effect as the proportion of surface atoms over the total number for an individual nanotube increases. This surface phase term can be related to subtle valence charge redistributions occurring at the outer layers in CNTs and graphene membranes. The question about the origin of such surface phase effects in carbon based nanostructures and nanoparticles is still open, and further experiments are advised to elucidate the role of different graphene stacking geometries or surface functionalization. Moreover, for the first time to our knowledge, we measured the phase shift induced by an individual single-atom-thin graphene, and mapped the phase shift variation throughout a whole FGC in relation with the local number of graphenes, showing that low-voltage electron holography is a valuable experimental technique to investigate electrostatic surface potentials in low-dimensional materials, and particularly in carbon nanotubes and graphene membranes.
Acknowledgments
Fig. 6 – Phase contour map. Contours are traced each 0.06 rad, starting from vacuum level (black). Each color corresponds to a different number of graphene layers in the flake. Orange areas correspond to phase values larger than 0.24 rad. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
This work was supported by the EU projects ‘‘European Integrated Activity of Excellence and Networking for Nano and Micro-Electronics Analysis’’ ANNA, Contract No. RII3:026134, and by ESTEEM ‘‘Enabling Science and Technology for European Electron Microscopy’’, Contract No. IP3:0260019.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2010.12.010.
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4 9 ( 2 0 1 1 ) 1 4 2 3 –1 4 2 9
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/carbon
Surface electrostatic potentials in carbon nanotubes and graphene membranes investigated with electron holography Luca Ortolani a,*, Florent Houdellier b, Marc Monthioux b, Etienne Snoeck b, Vittorio Morandi a a b
CNR IMM-Bologna, Via Gobetti, 101, 40129 Bologna, Italy CNRS CEMES, 29, Rue Jeanne Marvig, 31055 Toulouse, France
A R T I C L E I N F O
A B S T R A C T
Article history:
We used low-voltage transmission electron holography to probe surface electrostatic poten-
Received 21 October 2010
tials in graphene membranes and carbon nanotubes, as the number of graphenes varies.
Accepted 3 December 2010
Further, we measured the phase shift induced by an individual graphene, and mapped
Available online 7 December 2010
the phase shift variation throughout a whole few-graphene-crystal as a function of the local number of layers. We found a size/surface effect as the ratio between the surface and the total number of atoms increases for an individual nanotube or graphene membrane. This surface phase term can be related to a fine electrostatic potentials redistributions occurring at the outer layers in carbon nanotubes and graphene membranes. Ó 2010 Elsevier Ltd. All rights reserved.
1.
Introduction
Single-walled carbon nanotubes (SWCNTs) [1] and recently isolated graphene membranes [2,3] represent prototype low dimensional systems, composed only of surface atoms. In these materials carbon atoms are arranged in a two-dimensional honeycomb lattice, rolled into a cylinder in the case of carbon nanotubes. In multi-walled carbon nanotubes (MWCNTs) and few-graphene-crystal (FGC) membranes, where layers are stacked, respectively, concentrically and vertically and where graphenes are bound just by weak van der Waals forces. While the in-plane bonding between carbon atoms is not significantly affected upon FGC and MWCNT formation, nevertheless the chemical and physical properties of those materials depend strongly on the number of walls and/ or sheets. In particular, the chemical and thermal stability of CNTs increase both with the number of walls [4–6], while their Young’s modulus increases as the thickness is reduced [7] up to the maximum value of 3.5 TPa for an individual SWCNT [8]. Further, individual graphene membranes show a peculiar electronic structure, where the energy of the charge
carriers is linear in the momentum. This linearity is at the origin of all the extraordinary properties of this material, which however change dramatically, and eventually disappear, when even just two layers are stacked to form few-graphenes crystals [9–11]. Hence, a better understanding of the structural and electronic modifications occurring when the number of walls (in CNTs) and the thickness (in FGCs) reduces to one monoatomic layer is mandatory in order to understand the properties of these materials. In this article we use transmission electron holography to measure the surface electrostatic charge distributions in CNTs and FGCs as a function of the number of layers/walls. While structural characterization techniques such as electron diffraction [12,13], and high-resolution transmission electron microscopy (HRTEM) [14,15], are extremely sensitive to the position of core electrostatic charges, therefore providing accurate data on the position of atoms in a lattice, on the other hand they are little affected by the actual distribution of valence electrons, which is the key to understand the electronic properties of such material. Combining HRTEM imaging and electron holography [16], we investigated the
* Corresponding author: Fax: +39 051 639 9216. E-mail address: [email protected] (L. Ortolani). 0008-6223/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2010.12.010
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redistribution of crystal charges, in both their core and valence part [17], in CNTs, as the number of walls decreased from 20 down to an individual SWCNT, and in a FGC, as the number of layers varied from an individual graphene up to four. We were able to obtain unprecedented sensitivity in the electron phase reconstructions, mapping phase shift induced by individual monoatomic graphene layers, and measuring surface phase variations in CNTs and FGCs, possibly originating from fine electronic charge redistribution at the surface atoms.
2.
Experimental results
2.1.
Holographic mapping of crystal charges
Electron holography is an experimental technique capable of retrieving the full electronic wavefront of the electronic radiation that has interacted with the sample [18]. Basically, a hologram is the interference pattern between the beam that has passed through the sample, and a reference one from the vacuum nearby. The electronic wave, passing through the specimen, interacts with the distribution of charges in the crystal, and a detailed map of the distribution of the electric and magnetic fields is stored in the phase term of the retrieved wavefront [19], which is reconstructed by analyzing the deformations of the interference fringes of the hologram [18]. In the absence of either magnetic contributions or free charges in the material, as in the case of FGC membranes and CNTs, the measured electronic phase map / is simply related to the electrostatic potential V in the sample, as follows [16]: Z ð1Þ /ðx; yÞ ¼ CB Vðx; y; zÞdz where CB is an interaction constant depending on the energy of the beam electrons. The result of the integration in Eq. (1) is the projection along the z-axis of the electrostatic potential generated by the charge distribution in the crystal [20]. The spatial resolution obtained in the phase reconstruction is not sufficient to map the potential distribution of individual atomic charges [16,17], hence the measured phase shift is the result of the average electrostatic potential over an area of several crystal unit cells. Under those conditions, Eq. (1) can be expressed in terms of the second moment of the electrostatic charge distribution hr2 i, as [17,21]: / ¼ CB k0
2pNz 2 hr i 3Acell
ð2Þ
where Acell is the area of the unit cell of the crystal, k0 = 1.447 V nm/e is the Coulomb’s force constant, and Nz is the number of unit cells in the direction perpendicular to the electronic beam, i.e. the number of layers in a FGC or the number of walls in a CNT.
2.2.
Holographic investigation of CNTs
Commercially available arc-discharge MWCNTs were prepared for TEM observations by dispersing the nanotubes powder in isopropanol with the aid of a ultrasonicator. TEM samples were obtained by putting a drop of the solutions onto
standard holey carbon grids, and letting the solvent to evaporate. To reduce the amount of residual water and to remove most of volatile contaminants, TEM grid were heated on a hotplate at 200 °C for 15 min before inserting them in the microscope. The TEM used for the experiments was a Tecnai F20 equipped with a CEOS aberrations corrector, operated at a lowered accelerating voltage of 100 kV, instead of the conventional 200 kV, to reduce the radiation damage to the sample. Fig. 1a shows the TEM micrograph of an 8-walls nanotube. The number of walls composing the tube is easily determined by the image, observing the (0 0 0 2) fringes at the nanotube borders. Even if particular attention was given to reduce contamination from the samples, few amorphous carbonaceous contaminants are grafted over the tube. Nevertheless, sufficiently large portions of the tube are atomically clean and therefore suitable for holographic investigation. In the phase map of Fig. 1b, the vacuum surrounding the tube appears darker than the bright area of the tube where the carbon atoms of the lattice modify the phase of the beam electrons. To measure the shift induced by the walls of the tube, a line profile of the phase was acquired along the horizontal direction over the region marked by the rectangle, and averaged over its vertical height. Fig. 1c shows the plot of the phase profile and a cartoon showing the modeled structure for the eight-walls nanotube, where the arrow indicates the direction of the beam electrons. The profile clearly shows two peaks, corresponding to the portion of the walls that are almost parallel to the electron beam. In this region the spatial density of atoms is higher due to the projection effect, resulting in a larger phase shift. The measure of the total phase shift produced by the stacked graphene layers was performed in the central part of the profile, between the two peaks, where the eight upper and eight lower walls of the tube were almost perpendicular to the electron beam. The electrons traversed a total of 16 graphene walls, and their phase was shifted by (0.72 ± 0.02 rad), as indicated by the red horizontal line in the graph, therefore each graphene layer shift the beam by (0.038 ± 0.01 rad). The same holographic analysis has been done on SWCNTs, grown by CVD and commercially available. Fig. 2 shows the result of the analysis for one of those tubes, with a diameter of 1.6 nm. Fig. 2a shows the reconstructed phase map of a freestanding SWCNT. The brighter walls of the tube are clearly visible, along with a small cluster of carbon contamination sufficiently small not to prevent the analysis of the phase shift over the clean region of the tube. Even in this case a phase line profile has been acquired over the area indicated by the yellow rectangle, averaged over the vertical dimension. Fig. 2b shows the obtained phase profile and a structural model of the SWCNT. Again, the measurement of the phase shift induced by the two almost parallel walls has been done in the region between the two maxima corresponding to the walls portion parallel to the electron beam. The total phase shift has been estimated in (0.10 ± 0.01 rad). The estimate of the phase error was done analyzing the oscillations of the phase in the vacuum region. The electrons in the microscope passed through two walls and we can calculate that each graphene lattice induced a phase shift of (0.050 ± 0.005 rad).
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Fig. 1 – Holographic analysis of an eight-walls CNT. (a) HRTEM image of the tube. (b) Phase map as reconstructed from the hologram. Bright contrast corresponds to the induced phase shift. (c) Phase profile acquired over the rectangle in (b) along the horizontal direction and averaged over its vertical width. The horizontal line indicates the value of the phase shift produced by the 16 walls perpendicular to the beam direction, as shown in the drawings.
Fig. 2 – Holographic analysis of a SWCNT. (a) Reconstructed phase map of a freestanding SWCNT. (b) Plot of the phase profile acquired over the rectangle in (a). Horizontal line indicates the value of 0.10 rad corresponding to the phase shift induced by the two graphenes perpendicular to the electron beam. The cartoon in the inset shows a model structure for the SWCNT, at the same scale of the profile plot.
Using the same holographic technique and the same analysis approach, we investigated variations in the average phase shift per graphene in the case of CNTs composed of 20, 18, 2 and single-wall, as shown in Fig. 3. Even in the presence of a relatively large error in the phase measurement for thinner tubes, it is evident that there is systematic increase of the average phase shift as the number of walls composing the nanotube reduces from 20-walls nanotubes down to doublewalled and ultimately single-walled tubes.
2.3.
Holographic investigation of graphene membranes
We applied the same analysis to graphene stacks, produced by a liquid assisted mechanical exfoliation, as described by Coleman and coworkers [22]. TEM samples were prepared by putting a drop of the solution onto standard holey carbon grid for TEM observations and heat-treated just before the observations, similarly to nanotubes samples, to reduce the amount of contaminants.
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Fig. 3 – Phase shift per individual graphene layer as function of number of walls. The horizontal line indicates 0.04 rad, which is the expected theoretical value for bulk graphene stacks.
Fig. 4a shows the HRTEM image of a turbostratic FGC membrane, in a region around a suspended edge. Even if the electrons of the beam are not accelerated enough to induce a significant displacement of the carbon atoms in the crystal, nonetheless the energy transferred from the beam to the lattice is sufficient to trigger the chemical decomposition of the graphene [23,24]. Decomposition starts from defective sites in the lattice, drilling holes in the honeycomb network, and peeling successive layers from the FGC. As evident in Fig. 4a), the surface of the flake presents several areas
few nanometers large, where locally missing graphenes expose the underlying structure. Analyzing those areas, like the ones labeled as (1)–(3) in Fig. 4a, it is possible to determine the complete stacking structure of the individual flake. Fig. 4b shows the Fast-Fourier-Transform (FFT) of region (1), where only one individual graphene is left. The FFT shows the hexagonal pattern of an individual honeycomb network, with each spot corresponding to the distance of 0.213 nm. Fig. 4c shows the FFT of the region (2) in the HRTEM micrograph. In addition to the previous set of spots, indicated by yellow circles, there is an additional pattern, indicated by the blue circles. Hence, in that region the flake is composed of two graphenes. The two sets of spots in the FFT are rotated by h = 13°, indicating that the two layers are in a turbostratic arrangement and are rotated accordingly. In region (3), the flake is composed of four graphenes. Interestingly, the related FFT, displayed in Fig. 4d, reveals that the two additional graphenes are stacked each one with the same rotation angle h, resulting in the four graphenes of the stack all having the same relative orientation of 13°. The presence of holes in the surface of the flake due to beam damage, as visible in Fig. 4a, gives us the opportunity to individually measure, with electron holography, the phase displacement due to each graphene, up to four. Fig. 5a shows the reconstructed phase map in false colors. The red regions, which have the same value as in vacuum level, reveal the presence of holes over the surface of the flake. Fig. 5b shows the phase profile acquired from the region indicated by (1) in Fig. 5a, while Fig. 5c shows the phase profile from region (2). In the proximity of the holes the flake is thinner, as more graphene layers are peeled off from the crystal. Despite the noisy signal, the graphs clearly display step-like phase profiles, with values ranging from approximately zero in correspondence to vacuum, up to 0.24 rad, where four graphenes are stacked. In particular, in Fig. 5b a phase level of 0.06 rad is clearly visible, while all the other phase values correspond to multiple integers of this amount. Thus, as the number of graphenes in the FGC changes, within the precision of the phase measurement, we do not observe any change in the average phase displacement per individual graphene, which is constantly (0.06 ± 0.01 rad). The contribution on the phase shift by the weak van der Waals potentials, responsible for the interaction between graphenes, is expected to be too small to be measured with an accuracy of 0.01 rad.
3. Fig. 4 – HRTEM image of the border of a FGC flake where graphenes were stacked turbostratically. (b) FFT spectrum from region (1), where only one layer is present. Yellow circles highlight the hexagonal pattern from honeycomb lattice. (c) FFT from region (2) where two graphenes are stacked. FFT shows the patterns from two honeycomb lattices (yellow and blue), rotated by 13°. (d) FFT spectrum from region (3). Spectrum shows four patterns from honeycomb networks (yellow, blue, green and red), revealing that each graphene is rotated by 13° with respect to its neighbors. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Discussion of the results
The most striking feature in the data presented in the graph of Fig. 3 is the relatively large variation in the phase shift induced by each graphene between an individual SWCNT and thicker tubes of tens of walls. From 0.038 rad of a 20-walls CNT, the phase increases constantly up to 0.055 rad for a SWCNT. The measured values of 0.055 rad and 0.05 rad for the phase shift of individual SWCNTs are in agreement with previously reported data [25]. Interestingly, the value of the phase shift for a thick MWCNT is significantly different from that of a SWCNT, but it is perfectly matching the theoretically calculated value of 0.04 rad for bulk graphite (Bernal stacking). This value was obtained modeling the distribution of crystal
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Fig. 5 – Reconstructed phase map of the turbostratic FGC. (a) Phase map in false colors. Red corresponds to vacuum values, showing the presence of holes over the surface of the flake. Vacuum phase level has been renormalized to zero. (b) and (c) show the phase profile along the line indicated by (1) and (2) in the phase map. In both profiles, each level indicated by the lines corresponds to an integer multiple of 0.06 rad. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
charges in graphene lattice, and taking into account the valence charge redistributions induced by bonding, both inplane and between the layers [26,27]. The average phase shift per graphene in the case of MWCNTs matches that of bulk ABAB stacked graphite. Notwithstanding the types of van der Walls potentials in these two different stacks are certainly different and, with the actual precision, electron holography is not capable of distinguishing between them, nevertheless, variations in the average phase per graphene in stacks of different thickness clearly show a surface/size effect on the phase shift of the electron wave, with a surface contribution of the order of 0.02 rad from the single graphene sheet to the bulk value. A similar increase of the phase shift as the dimension of nanostructure decreases has been observed experimentally in the case of gold nanoparticles [28–30]. In that case, it has been proposed that this phase rise originates from the redistribution of charges induced by the under-coordinated atoms of the surface [31]. As the dimension of the nanostructure is reduced, the portion of surface skin atoms increases with respect to those in the inner volume. Due to the reduced coordination, the charge in the surface redistributes, and the bond length locally contracts. A similar effect on the distribution of valence charges has also been predicted for carbon nanotubes [32], even if the bonding between graphene layers is provided by weak van der Waals attraction and therefore there is no change in the coordination of the surface atoms. Nevertheless, according to the model proposed by the authors, subtle charge redistributions should occur in surface atoms of carbon nanotubes and in SWCNTs, compared to bulk MWCNTs, the average electrostatic potential, hence the phase shift through Eq. (1) should increase of about 70% [32]. This prediction is indeed in good agreement with our val-
ues, since we measured an increase of about 50% of the value of the phase shift per graphene from thick MWCNTs to SWCNTs. Holographic investigation of the FGC (Fig. 5) shows a different behavior of the average phase shift per graphene as the thickness of the stack increases. The phase shift in the case of an individual graphene is 0.06 rad, which is comparable to that of a SWCNT (Fig. 3), within the experimental error. Interestingly, the phase shift per graphene in the FGC is not changing as the number of layers stacked changes from one to four. As the two systems are very similar, we would expect a reduction in the phase shift between one and four as it is observed in the CNTs. If we consider again the above theory, the origin of the surface phase shift addition in SWCNTs is due to the presence of unbound graphene layers and therefore it could also explain why we do not observe any change in the average phase shift per graphene in the FGC. Indeed, graphene membranes have a peculiar stacking geometry, with all the layers rotated by 13° with respect to its neighbors. This particular configuration is also called turbostratic commensurable, as adjacent graphene lattices become commensurable and superlattice geometry can be defined [33], a condition that is not possible in CNTs due to the curvature of the walls. According to the theoretical modeling of the valence charge distribution [10,33,34], in this configuration each graphene in the stack is completely electronically decoupled from each other. Therefore each layer in that FGC behaves as a free unbound graphene surface, inducing the additional phase shift on the electron wave we observe, independently of the number of graphenes in the stack. In the case of gold nanoparticles, the surface phase term extracted from the holographic experiments on gold nanoparticles is about 0.4 rad [30], while we measured a surface
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contribution of 0.02 rad in carbon nanotubes and graphene membranes, i.e. an order of magnitude lower. This could be explained by the different nature of bonding in the systems (i.e. covalent in nanoparticles, and of van der Waals type in graphene based structures) as the valence charge redistributions occurring at unbound surfaces is expected to be much stronger in covalently bound surface gold atoms. Nevertheless, the above mentioned model for the origin of the surface phase shift observed in graphene based materials lacks the experimental evidence for the expected contraction of the bond length and wall thickness. Indeed, associated with the electronic charge redistribution at the under-coordinated surfaces, the carbon–carbon distance in the graphene lattice is expected to contract to 0.125 nm, compared to the bulk 0.143 nm, and the thickness of the graphene wall should reduce to 0.12 nm, compared to an inter-wall distance of 0.35 nm in MWCNTs. Size/surface phase effect similar to what we observed in graphene membranes, carbon nanotubes and gold nanoparticles has been recently reported for amorphous carbon films of different thicknesses [35]. In this case the thickness independent surface contribution to the phase shift was estimated to be about 0.497 rad, possibly due to the presence of adsorbates over the surface of the films, as it could be reduced to 0.36 rad by heating the samples before the observation. In the Supplementary informations available online, we detail a model of the phase shift induced by a layer of surface dipoles adsorbed on SWCNTs. According to our calculations (see Section S1), the presence of surface contaminants, like water molecules, is capable of significant phase shifts in the internal volume
of the tube, but they are not able to completely explain the experimental profiles like the one shown in Fig. 2b. The phase investigation also represents an elegant and powerful method to determine the thickness of a FGC sample. Fig. 6 shows the contour plot of the phase map of flake in Fig. 5a, where each contour is plotted every 0.06 rad; hence the phase map can be immediately converted into a map of number of graphene layers in the flake. In Fig. 6, black refers to the vacuum, while colors range from pink to azure, corresponding to crescent graphene layers, from one to four as shown in the legend. Regions with a phase value higher than corresponding to four layers are represented in orange, and they correspond to thicker areas where the amorphous carbon support or some contaminants, are present. We point out that, unlike scanning probe techniques, the local thickness can be measured for freestanding FGCs. This can be an important asset of electron holography, since it is well documented that, in scanning probe techniques, the interactions between the graphene or flake and the substrate, and/or the presence of residual solvents between them generate a substrate-dependent bias, which is certainly disturbing and it is far from being fully understood [36].
4.
Conclusions
We used low-voltage transmission electron holography to probe surface electrostatic potentials in FGCs and CNTs, as the number of layers/walls varies. The phase investigation of the stacking of graphenes in concentric MWCNTs revealed a size/surface effect as the proportion of surface atoms over the total number for an individual nanotube increases. This surface phase term can be related to subtle valence charge redistributions occurring at the outer layers in CNTs and graphene membranes. The question about the origin of such surface phase effects in carbon based nanostructures and nanoparticles is still open, and further experiments are advised to elucidate the role of different graphene stacking geometries or surface functionalization. Moreover, for the first time to our knowledge, we measured the phase shift induced by an individual single-atom-thin graphene, and mapped the phase shift variation throughout a whole FGC in relation with the local number of graphenes, showing that low-voltage electron holography is a valuable experimental technique to investigate electrostatic surface potentials in low-dimensional materials, and particularly in carbon nanotubes and graphene membranes.
Acknowledgments
Fig. 6 – Phase contour map. Contours are traced each 0.06 rad, starting from vacuum level (black). Each color corresponds to a different number of graphene layers in the flake. Orange areas correspond to phase values larger than 0.24 rad. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
This work was supported by the EU projects ‘‘European Integrated Activity of Excellence and Networking for Nano and Micro-Electronics Analysis’’ ANNA, Contract No. RII3:026134, and by ESTEEM ‘‘Enabling Science and Technology for European Electron Microscopy’’, Contract No. IP3:0260019.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2010.12.010.
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