J. Phys. Chem. C 2010, 114, 21083–21087
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Modeling Direct Exfoliation of Nanoscale Graphene Platelets Olga V. Pupysheva,† Amir A. Farajian,*,† Cory R. Knick,† Aruna Zhamu,‡ and Bor Z. Jang†,‡ Department of Mechanical and Materials Engineering, Wright State UniVersity, 3640 Colonel Glenn Highway, Dayton, Ohio 45435, United States, and Angstron Materials LLC, 1240 McCook AVenue, Dayton, Ohio 45404, United States ReceiVed: July 30, 2010; ReVised Manuscript ReceiVed: October 1, 2010
Direct ultrasonication of graphite particles dispersed in water, in the presence of a surfactant, is a promising way to produce pristine nanoscale graphene platelets (NGPs) without graphite intercalation or oxidation. We investigate possible exfoliation mechanisms, specifically those involving sodium dodecylbenzenesulfonate (SDBS) surfactant, and compare their corresponding energies. The model includes interlayer van der Waals interactions and a force-field approach capable of treating charged surfactant and solvent. Our calculations reveal the significant role of SDBS in liquid-phase NGP production, through a locking mechanism that prevents restacking. I. Introduction Graphene is an emerging class of nanomaterials expected to have a revolutionary impact on nanotechnology.1,2 It is necessary to find inexpensive ways for producing large volumes of graphene.3 The large-scale production methods of graphene are described, for example, in the reviews 2 and 4-7 and references therein. Generally, these methods can be divided into two groups: epitaxial growth of graphene and graphene exfoliation from graphite. The latter, less expensive methods can involve chemically modified graphite, such as graphite oxide (GO), but pristine graphite is preferred. Liquid-phase methods of graphene production, which involve the ultrasonic agitation of graphite particles dissolved in a judiciously selected solvent, allow producing pristine single-layer graphene.7 This requires graphene stabilization in solution, which can be achieved by using organic solvents whose surface energies match that of graphene, such as N-methylpyrrolidone (NMP).8 However, the most promising method of producing pristine graphene directly from graphite without going through chemical intercalation, oxidation, or solvent dissolution is the direct ultrasonication method developed by Zhamu et al. in 20079 and studied later by Lotya et al.10 This method entails dispersing graphite particles in water containing sodium dodecylbenzenesulfonate (SDBS) surfactant to form a suspension and consequent ultrasonic cleavage of graphite.9 No undesirable chemical, such as sulfuric acid or organic solvent, is used. The resulting graphene is truly pristine, as opposed to the chemically reduced version of graphene oxide. In the present work, we reveal the details of graphene exfoliation during direct ultrasonication of graphite particles dispersed in water in the presence of SDBS surfactant. II. Method In order to assess the energetics of graphene exfoliation, as a first step, the energy required for separation of one or more graphene layer(s) from a graphite particle in the absence of solvent or surfactant is determined. The separation occurs * To whom correspondence should be addressed. E-mail: amir.farajian@ wright.edu. † Wright State University. ‡ Angstron Materials LLC.
Figure 1. Top view of a sample nanoscale graphene platelet (side length is approximately 10 nm). The directions 1 and 2 correspond to two main slide directions: 1 is perpendicular and 2 is parallel to the surface of layers.
through a shift of graphene layer(s) with respect to the neighboring layers of the graphite particle. This shift can in principle occur along two main directions: either parallel or perpendicular to the surface of neighboring layers, as depicted in Figure 1. The separation energy is defined as the difference between the interlayer interaction energy of an unperturbed graphite particle, which consists of AB-stacked graphene layers, and that of a graphite particle with shifted graphene layer(s). The separation energy ∆E is therefore a function of the shift distance d: ∆E(d) ) E(d) - E(0), where E is the interlayer energy. The forces that keep together the layers in graphite are π-π and van der Waals interactions.11 The graphite nanoparticles include up to hundreds of thousand of atoms. In order to include van der Waals forces in such large systems, E is calculated using a reliable Lennard-Jones potential12 that has been successfully used to model solid C60,13 nanotube bundles,14,15 large multiple-shell fullerenes,16 and nanopeapods.12 Subsequently, the adsorption of SDBS surfactant on relatively small graphene patches with hydrogen-terminated edges is investigated using the Gaussian 09 package.17 In order to include van der Waals interactions between SDBS and graphene, and to be able to model the systems consisting of a few hundreds
10.1021/jp1071378 2010 American Chemical Society Published on Web 11/11/2010
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of atoms, we use the universal force-field (UFF) method.18 The electrostatic interactions are computed using partial atomic (point) charges, determined by the QEq formalism.19 Taking into account the SDBS dissociation in water solutions and presuming that the adsorption of the well-hydrated Na+ cation on graphene is negligible, we consider only the adsorption of the dodecylbenzenesulfonate anion (DBS-). The UFF structural optimizations are carried out in aqueous solution because the optimizations in vacuum cannot account for the charge screening, which is especially important for our systems with nonzero total charge. To consider a system in the presence of solvent, the solute is modeled as placed in a cavity within the solvent reaction field. The polarizable continuum model (PCM) using the integral equation formalism variant (IEF-PCM) is utilized, as implemented in Gaussian 09. This method creates the solute cavity via a set of overlapping spheres corresponding to the solute atoms (see review 20 and references therein). The continuity and smoothness of the reaction field and continuity of its derivatives are ensured by a smoothing algorithm,21 which is based on the Karplus-York formalism.22 The solvent is water, with dielectric constant εd ) 78.3553.
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Figure 2. Interlayer van der Waals energy results for a platelet consisting of two monolayers of various side lengths, for different shifts perpendicular to the platelet surface. The energy values are divided by the number of surface atoms.
III. Results and Discussion Two possible mechanisms of graphene exfoliation from graphite nanoparticles under sonication are considered. One possible mechanism, which can be called resonant exfoliation, is caused by the ultrasound alone, while the other also involves the adsorption of the SDBS surfactant on the partially exfoliated graphene. The former process takes advantage of resonant oscillations of graphene nanoplatelets and would be possible if the resonant oscillation frequencies are close to that of ultrasound. The latter mechanism, however, does not need the resonance condition, but is possible due to the presence of surfactant in the solution. Below we discuss the feasibility of these two processes, resonant and nonresonant exfoliation mechanisms, based on their estimated energies. III.A. Effect of Graphene Layer Shift on Interlayer Energy. First, we present the energetics of graphene exfoliation from graphite particles. Square-shaped nanoscale graphene platelets of various side lengths are considered. These graphene layers are assumed to be stacked according to the AB-stacking pattern to generate the graphite particles. The exfoliation process starts with a small shift of one (or more) layer(s) with respect to the neighboring ones under ultrasonic agitation. The effect of such a shift, whose main direction can be perpendicular or parallel to the graphene surface, on the interlayer energy, is discussed below. One sample nanoscale graphene platelet and two main shift directions are shown in Figure 1. III.A.1. Perpendicular Shift. We first consider only two graphene layers. For the shifts perpendicular to the surface of graphene platelets, several interlayer separations are considered, and the corresponding van der Waals energies are calculated in each case. The resulting energy vs separation curves are depicted in Figure 2. From Figure 2 one can observe that increasing the side length results in convergence of the calculated energies. For side lengths larger than 10 nm, the results remain essentially unchanged. The lower energies of larger platelets can be explained by the boundary effects. When the nanoplatelets are small, their (open) boundary has a significant effect on the interlayer energy. This effect vanishes for large platelets in which the surface area approaches that of an infinite graphene plane and prevails over the boundary effects. III.A.2. Parallel Shift. Based on the experimentally known properties of graphite, one can expect that the parallel (in-plane)
Figure 3. Interlayer van der Waals energy results for a platelet consisting of two monolayers for different shifts parallel to the platelet surface, along different shift directions. The energy values are divided by the number of surface atoms. The platelet side length is 10 nm.
shifts of a graphene layer would require less energy than the perpendicular shifts considered above. In other words, such parallel shifts resemble the “soft modes” of vibration as compared to the “hard modes” corresponding to the perpendicular shift. For two graphene layers and for the shifts parallel to the graphene surface, different shift directions are considered, namely, along the zigzag edge, armchair edge, and diagonal of the square platelet. The resulting van der Waals energies are depicted in Figure 3 for a nanoplatelet with a side length of 10 nm. Note that none of these curves is symmetrical regarding zero shift, as the two-layer particle considered here does not have a symmetry plane (see Figure 1 for the view of its top layer). It can be seen from Figure 3 that for the shifts along the armchair edge and diagonal direction, the energy minima occur at nonzero values of the shift. As the zero shift in Figure 3 corresponds to the AB stacking, the curves in Figure 3 show that the stable stacking configuration is slightly different from the AB pattern. This is in agreement with previous results,23 where the minimum energy was located at ∼0.2 Å shift along the armchair direction. Comparison of the energies of perpendicular shifts (Figure 2) with those of parallel shifts (Figure 3) indeed confirms our prediction that they resemble the “hard” and “soft” oscillations, respectively.
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TABLE 1: Force Constants k for Different Numbers of Layers and Different Shift Directionsa force constants (eV/Å2) for specific shift directions no. of layers in a
no. of layers in b
reduced mass (in units of m)
perpendicular
parallel, along zigzag edge
parallel, along armchair edge
parallel, along diagonal
1 1 1 2 2 3 5
1 2 3 2 3 3 5
1/2 2/3 3/4 1 6/5 9/6 25/10
647.06 639.34 638.66 630.96 630.16 629.32 628.90
4.1056 4.1474 4.1528 4.1946 4.2012 4.2084 4.2134
4.5436 4.5862 4.5914 4.6338 4.6404 4.6472 4.6524
4.2622 4.3042 4.3096 4.3518 4.3584 4.3654 4.3704
a Notations a and b refer to the two parts of the graphite particle that are separated through exfoliation. Each graphene layer is square-shaped with a side length of 10 nm and contains N ) 3680 atoms. The mass of such monolayer is m ) (N/NA) × 12.0 g, with NA being Avogardo’s number. When each of a and b contain a graphene monolayer (see the first row of the table), the resonance frequencies for perpendicular, zigzag edge, armchair edge, and diagonal shifts are obtained as 2674, 213, 224, and 217 GHz, respectively.
III.A.3. Oscillation Frequencies of Resonant Exfoliation. Here we consider the oscillations that can result in exfoliation. Based on the energy calculations described above, we estimate the resonance frequencies by fitting a parabola at the minimum of each energy curve. The resonance frequency is given by the equation
f)
1 2π
µk
(1)
where k is the effective force constant (in units of eV/Å2), i.e., twice the coefficient of the second-order term in the parabolic fit of energy, and µ is the reduced mass corresponding to the two parts of the graphite nanoparticle, a and b, that are separated through exfoliation. The estimated force constants for perpendicular and parallel shifts are presented in Table 1. For the case when each of a and b contain a graphene monolayer (the first row of Table 1), the resonance frequencies for the perpendicular shifts and parallel (in-plane) shifts along the zigzag edge, armchair edge, and diagonal direction are 2674, 213, 224, and 217 GHz, respectively. Several important features can be inferred from Table 1. The perpendicular exfoliation mode turns out to be hard, while that of parallel exfoliation is relatively soft. Among the parallel exfoliation modes, the one along the zigzag edge is the softest, i.e., most feasible. One can also observe from Table 1 that for the perpendicular shifts, it is slightly more difficult to separate a single layer than a multilayer graphene. For the in-plane shifts, the pattern is opposite. This can be explained as follows. For a small shift h of the subsystem a regarding subsystem b, the force constant k, by definition, equals
∂ 2E k) 2 ) ∂h
∑
i∈a,j∈b
∂2Vij
(2)
∂h2
where Vij denotes the interatomic pair-potential used to model van der Waals interactions. Addition of one extra layer ∆a to the subsystem a changes the force constant by ∆k:
∆k )
∑
i∈∆a,j∈b
∂2Vij 2
∂h
)
∑
i∈∆a,j∈b
[
( )]
∂2Vij ∂rij ∂Vij ∂2rij + ∂rij ∂h2 ∂rij2 ∂h
2
(3)
When the added layer ∆a is relatively far from the shifting part b, that is, the interatomic distances rij are large, the first derivatives of the Lennard-Jones pair potential Vij with respect to rij are positive, while the second derivatives are negative. As a result, the sign of ∆k is determined by the dependence of rij on the value of the shift h, as well as its direction. Furthermore, due to the short-range character of the Lennard-Jones forces, the main contribution to ∆k originates from the pairs of atoms with the shortest distances rij, i.e., those with the rij vectors orthogonal, or almost orthogonal, to the surface of the graphene layers. Consequently, for such pairs of atoms which contribute most to ∆k, the shifts perpendicular to the surface of the layers make the derivatives ∂2rij/∂h2 in the first terms of eq 3 close to zero, and the negative second terms dominate. On the contrary, the derivatives ∂rij/∂h vanish and the positive first terms dominate when the shifts are parallel to the layers. Indeed, Table 1 demonstrates that the force constants decrease with the number of layers in the subsystems a and b for the perpendicular shifts, but increase for the parallel shifts. Another consequence of the short-range character of the interatomic forces is the significant dependence of the force constants k on the number of the closest “contacts” between the two subsystems a and b, i.e., on the number of atoms in one graphene layer. In comparison, the number of layers in the subsystems is less essential. In fact, the resonance frequencies f are basically independent of the size of graphene layers if the number of layers in a and b is kept constant, as both the force constant and the reduced mass in eq 1 are increased by approximately the same factor. When, for a fixed graphene layer size, the number of layers in a and/or b is increased n times, the change of the resonance frequencies is mainly determined by the reduced mass µ, not the force constant k. As µ is proportional to n, the resonance frequency is reduced by a factor of n. Therefore, a reduction of frequency by 1 order of magnitude requires a 100 times increase of the number of layers. It is clear from our force constant results that the resonance frequencies are of the order of 0.1-1 THz. These frequencies are significantly larger than the ultrasonic frequency (20 kHz) used in experiments. Our order-of-magnitude argument demonstrates that simple resonance phenomena cannot explain graphene exfoliation by ultrasound, even when the formed subsystems contain thousands of layers. It is thus necessary to consider nonresonant mechanisms, including the effects of surfactants. III.B. SDBS Adsorption on Graphene. Let us now consider the role of the surfactant in the process of graphene exfoliation. It was shown earlier10 that SDBS adsorption on the graphene
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platelets in aqueous solution helps prevent their reaggregation. The present study further shows that it can also facilitate the exfoliation itself. Our proposed scenario for the nonresonant exfoliation, to which the presence of surfactants is essential, is as follows. In order for the surfactant molecules to facilitate exfoliation, some part of the graphene platelet should be exposed, i.e., not covered by another graphene layer. As soon as some part of the graphene surface is exposed, surfactant molecules can adsorb on it and prevent it from returning to its previous position in the graphite nanoparticle, where it would be covered again by the other layer. The initial exposure could happen as a result of parallel slide of the graphene sheets, similar to the soft mode of vibration discussed above. The important point is to compare the adsorption energy of the surfactant with the energy required to expose a part of the surface, so as to validate this mechanism. III.B.1. Adsorption Energy. First we find the binding energy of SDBSsor, to be exact, of the dodecylbenzenesulfonate anion (DBS-)son graphene. It is defined as Eb(DBS-@NGP) ) -[E(DBS-@NGP) - E(DBS-) - E(NGP)]
(4) where E(X) is the energy of the molecule X with the geometry obtained by the structural optimizations carried out as described in section II. To increase the reliability of our calculations, the solvent is taken into account, which, in turn, necessitates a noticeable decrease of the size of the graphene patch used for the optimizations. Based on the rough preliminary modeling using a square-shaped NGP with 10 nm side length, we determine the minimum area of graphene that is covered by an adsorbed DBS- anion and, thus, must be taken into account when calculating the adsorption energy. This area is a rectangle 2.4 × 1.2 nm2, containing 132 carbon atoms (6 aromatic six-member rings along the armchair edge and 5 rings along the zigzag edge of the nanoplatelet). Subsequent calculations are performed using this small graphene patch of 132 C atoms, whose edges are saturated by hydrogen atoms. The straightforward structural optimization of the small graphene patch with adsorbed DBS- anion results in graphene wrapped around the surfactant, with a reasonable adsorption energy value of 109 meV. However, our aim is to model an NGP of a much larger size, which may be still partially covered by other graphene layers and may have more than one DBSadsorbed on it. It is clear that for such a large NGP this wrapping cannot take place. To avoid the wrapping, we perform a two-step optimization, namely, a partial optimization with the frozen graphene patch, followed by a full optimization of the DBS-graphene system. The resulting binding energy equals 36 meV, and the geometry is shown in Figure 4. III.B.2. Resonance Frequency Change upon Surfactant Adsorption. As DBS- adsorption changes the mass of a graphene platelet, here we consider the resultant change of the resonance frequencies presented in section III.A.3. Let us estimate the frequency change for a nanoparticle that contains two graphene monolayers and is fully covered by the surfactant on both sides. For example, a square platelet with 10 nm side length can accommodate up to 35 tightly packed DBSadsorbates on one side. This leads to 25.8% increase of the mass of each monolayer and, correspondingly, of the reduced mass µ in eq 1. The resulting frequency values for all oscillations become ∼89% of the corresponding values in the absence of
Figure 4. SDBS molecule adsorbed on a graphene nanoplatelet: (a) top view and (b, c) side views.
the surfactants. This estimation is independent of the size of the nanoplatet. It is therefore clear that DBS- adsorption does not result in significant change of the resonance frequencies. As we explain in the next section, the adsorbate surfactants affect the exfoliation procedure through another mechanism. III.B.3. Energy Required for Graphene Exfoliation. Our van der Waals calculations discussed in section III.A allow us to estimate the energy required to cause the smallest exposure capable of accommodating surfactant adsorption. For the parallel slides along the armchair and zigzag edges, this exposure energy is found to be approximately 2.229 and 2.176 eV per area under the DBS- surfactant, respectively. If we include the effect of the permittivity of solvent (water), this energy is reduced to ∼28 meV for both slide directions. For the case of parallel slide along the diagonal direction, the exposure energy is estimated to be approximately 2.071 eV per area under DBS-. Upon inclusion of solvent, this value is reduced to ∼26 meV. These estimates are obtained by shifting one monolayer of graphene on top of another monolayer, each of them being square-shaped with a side length of 10 nm. The slide distances are 1.2 nm for the shift along the armchair and zigzag edges and 1.7 nm for the shift along the diagonal direction, which are the minimum shifts required to make the DBS- adsorption possible. Note that a single slide will expose parts of two surfaces, the lower surface of the upper graphene layer and the upper
Exfoliation of Nanoscale Graphene Platelets surface of the lower layer. This double exposure is accounted for in our estimates. We therefore observe that the adsorption energy of DBSon graphene, 36 meV, is larger than the exposure energy for the most feasible routes to exfoliation, i.e., the parallel shifts of one graphene monolayer with respect to another one. We find the same to be true for the parallel shifts of graphene multilayers as well, despite the fact that their exposure energy is slightly larger than that of a monolayer (Table 1). This means that the partially exposed nanoscale graphene platelets with adsorbed surfactants are stable and would not go back to their unexposed stacked arrangement. Thus surfactant adsorption serves as a lock and prevents the restacking of the partially exposed graphene layers. The partial exposure can thus continue until full exfoliation is achieved. IV. Conclusions In conclusion, graphene exfoliation from graphite particles is investigated by a computational modeling that includes the van der Waals interactions and the effects of charged surfactant and solvent. The energetics of exfoliation and surfactant adsorption, as well as the relevant resonance frequencies, are calculated. Our results demonstrate that direct exfoliation of pristine nanoscale graphene platelets by ultrasound cannot happen as a result of resonant oscillations. Instead, a nonresonant locking mechanism involving surfactant molecules is shown to be a feasible exfoliation mechanism through direct ultrasonication. Acknowledgment. The authors thank Vladimir I. Pupyshev and Iskander S. Akhatov for fruitful discussions. This work is supported by the National Science Foundation through NSF STTR Phase I grant no. 0930342. References and Notes (1) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183–191. (2) Rao, C. N. R.; Sood, A. K.; Subrahmanyam, K. S.; Govindaraj, A. Graphene: The New Two-Dimensional Nanomaterial. Angew. Chem., Int. Ed. 2009, 48, 7752–7777. (3) Segal, M. Selling Graphene by the Ton. Nat. Nanotechnol. 2009, 4, 612–614. (4) Jang, B. Z.; Zhamu, A. Processing of Nanographene Platelets (NGPs) and NGP Nanocomposites: A Review. J. Mater. Sci. 2008, 43, 5092–5101. (5) Park, S.; Ruoff, R. S. Chemical Methods for the Production of Graphenes. Nat. Nanotechnol. 2009, 4, 217–224. (6) Choi, W.; Lahiri, I.; Seelaboyina, R.; Kang, Y. S. Synthesis of Graphene and Its Applications: A Review. Crit. ReV. Solid State Mater. Sci. 2010, 35, 52–71. (7) Coleman, J. N. Liquid-Phase Exfoliation of Nanotubes and Graphene. AdV. Funct. Mater. 2009, 19, 3680–3695.
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