Tunable Energy Barrier for Intercalation of a Carbon Nanotube into

Article Cite This: J. Phys. Chem. C 2019, 123, 1974−1986

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Tunable Energy Barrier for Intercalation of a Carbon Nanotube into Graphene Nanosheets: A Molecular Dynamics Study of a Hybrid Self-Assembly Prasad Rama,† Arup R. Bhattacharyya,‡ Rajdip Bandyopadhyaya,§ and Ajay S. Panwar*,‡ †

Centre for Research in Nanotechnology and Science, ‡Department of Metallurgical Engineering and Materials Science, and Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

§

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S Supporting Information *

ABSTRACT: Molecular dynamics (MD) simulations were utilized to explore the energetics of formation of a graphene−carbon nanotube (CNT) hybrid in an aqueous environment, resulting from the intercalation of a single-walled CNT into a gallery defined by two parallel graphene sheets. It was found that the formation of a graphene− CNT hybrid can be divided into three processes involving (a) exfoliation of graphene sheets by repulsive interactions, (b) intercalation of a CNT into the graphene gallery associated with an activation energy barrier, and (c) spontaneous self-assembly/association of constituent CNT and graphene sheets driven by hydrophobic interactions or electrostatic attraction, leading to the formation of a three-dimensional hybrid. In contrast with pristine graphene sheets, ionic functionalization makes graphene sheets more hydrophilic and enhances their exfoliation in water, resulting in a significant lowering of the CNT intercalation barrier by nearly 150 kcal/mol. The simulations predict that the lowest intercalation barriers would arise for cases where both the energetic cost for graphene exfoliation and steric repulsions between the incoming CNT and graphene sheets are the lowest. Once the CNT moves past the barrier, its further incorporation into the graphene gallery is spontaneous and is assisted by strong hydrophobic interactions between the CNT and graphene surfaces. The most stable hybrid complex was observed when the CNT and graphenes are functionalized with oppositely charged ionic groups.

1. INTRODUCTION Three-dimensional (3D) hybrid carbon nanomaterials are of considerable interest because of their potential of combining merits1−8 of both one-dimensional (1D) and two-dimensional (2D) nanostructures. The integration of carbon nanotubes (CNTs) and graphene into a 3D hierarchical structure prevents the restacking of graphene sheets, thus providing a large accessible surface area,9,10 which can enable high energy storage,11 better catalytic activity,12 excellent electrical and thermal conduction,13,14 and improved surface wettability.15 These 3D graphene−CNT hybrid nanomaterials find promising applications in the fields of batteries,16 supercapacitors,17 sensors,18 and membranes.19 For instance, supercapacitors fabricated using graphene and CNT exhibited an outstanding electrochemical performance with a maximum energy density of 117.2 Wh L−1 having a power density of 424 kW L−1.17 Electrodes prepared with carbon nanocables sandwiched between reduced graphene oxide (rGO) sheets displayed exceptionally good lithium storage performance with high reversible specific capacity of 1600 mAh g−1 at 2.1 A g−1, with 80% capacity retention after 100 cycles.20 Graphene with its large surface area provides a 2D path for phonon transport and incorporation of 1D CNT in between the two graphene sheets provides an interconnected structure, making 3D pathways for © 2019 American Chemical Society

phonon transport, thereby minimizing the thermal contact resistance leading to higher thermal conductivity. Hence, graphene−CNT hybrid materials/nanostructures are also being exploited as a thermal management material in Li-ion batteries21 and nano-electromechanical applications22 for efficient heat dissipation. The introduction of CNTs as spacers between graphene sheets also helps in bridging defects,23 increases the basal plane spacing between the graphene sheets,24 and enhances storage capacities of layered nanomaterials (for example, accommodating lithium ions16 or hydrogen gas25,26). Covalent (or noncovalent) surface modification of constituent CNTs/graphenes can be used to modify interactions between graphene sheets and CNTs and, thereby, to control ease of CNT intercalation between graphene sheets, CNT− graphene affinity, interlayer spacing, and distribution of CNTs between the graphene galleries. The formation of graphene− CNT hybrids can be understood as resulting from three processes: (i) exfoliation of graphene sheets, (ii) CNT intercalation into a graphene gallery, and (iii) finally selfReceived: November 12, 2018 Revised: December 27, 2018 Published: January 2, 2019 1974

DOI: 10.1021/acs.jpcc.8b10958 J. Phys. Chem. C 2019, 123, 1974−1986

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The Journal of Physical Chemistry C

Figure 1. Simulation snapshots illustrating the stages of intercalation of a CNT into a graphene gallery: (a) G−C; (b) GF⊖−C; (c) G−CF⊖; (d) GF⊖−CF⊖; (e) GF⊖−CF⊕; and (f) G−C_L. Water molecules are not shown here for clarity.

exploiting both short-range interactions, such as hydrophobic affinity between graphene and CNTs,11,26−28 and long-range electrostatic interactions between graphene and CNTs functionalized by oppositely charged moieties.29 In another report, Núñez and co-workers30 have shown that the selfassembly is aided by cooperatively strengthened OH···OC hydrogen bonds between the carboxylic groups of the oxidized CNTs and oxygen functional groups of graphene oxide in a graphene oxide−CNT hybrid. Despite the importance of hybrid materials, there exist very few fundamental investigations into the factors influencing the

assembly of constituent CNT and graphene sheets into a 3D hybrid nanostructure. The energetics of each process is influenced by a complex interplay of various short- and longrange interactions between graphene and CNTs. These include (a) electrostatic repulsions, steric interactions and solvation forces that lead to graphene exfoliation, (b) electrostatic attractions, hydrophobic interactions, and hydrogen bond formation that influence CNT intercalation, and (c) hydrophobic effects and electrostatic attractions that lead to the spontaneous assembly of the hybrid. There are several recent reports of self-assembly of graphene−CNT hybrids by 1975


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The Journal of Physical Chemistry C Table 1. Different Intercalation Systems Considered in the Study simulation case

symbolic notation

graphene (G)

CNT (C)

a b c d e f g

G−C GF⊖−C G−CF⊖ GF⊖−CF⊖ GF⊖−CF⊕ G−C_L G−C(rep.)

bare graphenes carboxylate edge-functionalized graphenes bare graphenes carboxylate edge-functionalized graphenes carboxylate edge-functionalized graphenes bare graphenes bare graphenes with repulsive LJ interactions

bare CNT (head-on) bare CNT (head-on) carboxylate edge-functionalized CNT (head-on) carboxylate edge-functionalized CNT (head-on) amine edge-functionalized CNT (head-on) bare CNT (sideways) bare CNT with repulsive LJ interactions (head-on)

2. SIMULATION METHOD The intercalation process is simulated using MD as the entry of a single-walled CNT into a gallery is defined by the interlayer space between two graphene sheets. The different simulation systems considered in this study are as shown in Figure 1a−e. The differences between the simulation systems arise from the way the CNTs or graphene sheets are functionalized, the details of which are presented in Table 1. In our simulations, graphene sheets corresponding to an area of 30 × 30 Å2 and CNTs (with a (7,7) chirality) of length 30 Å and diameter 9.5 Å were used. Visual molecular dynamics (VMD)35 and Avogadro36 were used to generate initial coordinates for graphene sheets and the CNT. When considering functionalized graphene (or CNTs) in a simulation, each graphene sheet was covalently edge-functionalized with 16 carboxylate (-COO−) functional groups (4 groups along each edge) and the CNT was edge-functionalized with 14 (-COO−) functional groups (7 groups each on either ends of the CNT). In this study, two different kinds of edge-functionalized CNTs were used, one with negatively charged carboxylate (-COO−) groups and the other with positively charged aminated ((CH2)2CONH-NH3+) groups37,38 (the -OH group of (-COOH) is exchanged with NH2(CH2)2NH2). Sodium or chloride ions were added to the simulation box to make the whole system electrically neutral depending on the net charge due to the functional groups. A simulation box of volume 140 × 70 × 70 Å3 was considered with periodic boundary conditions applied along all three directions. Two graphene sheets of the same size were placed parallel to each other in such a way that they were in the X−Z plane (normal to the Y-axis) and separated by a distance of 12 Å. The center of mass of the two graphene sheets (considered together) coincided with the center of the simulation box (also the origin for our reference here). A CNT with its cylindrical axis aligned along the X-axis was placed with its center of mass located at a distance of 40 Å from the origin. This initial configuration of the CNT at a distance of 40 Å from the two graphene sheets was then solvated with water molecules corresponding to a water density of 1 g/cm3. There were a total of 74 332 atoms in the simulation box including the graphene sheets, CNT, and water molecules. All MD simulations were performed using the package large-scale atomic/molecular massively parallel simulator (LAMMPS).39 The CHARMM40 force field was used to model all interatomic interactions, and the TIP3P model was used to describe water molecules. The detailed description of the simulation setup and the method adopted are provided in the Supporting Information of Section S1, and the same information discussed extensively can be found in publications from our group.41−43 Figure 1 shows the six of the seven cases that were considered in the simulations. Figure 1a−f shows two different

intercalation process through exfoliation of graphene and the interactions between the constituent components in hybrid materials. Lee and Carignano31 used molecular dynamics (MD) simulations to show that size differences between two intercalants, propylene carbonate (PC) and ethylene carbonate (EC), could induce different exfoliation behavior of graphene even without chemical decomposition of intercalated electrolyte. Their observations revealed that the energy barrier of exfoliation observed for the PC intercalated system was about 11 times higher than that for the EC intercalated system. Using density functional theory, Jha et al.32 elucidated that the strength of interactions between graphene oxide (GO) and CNT in a graphene−CNT complex is decided by a competition between hydrogen bonding and dispersion interactions. Dyer et al.33 concluded that the optimal curvature of a folded graphene sheet upon incorporation of a CNT was a result of both elastic energy and van der Waals interactions. Strong π−π stacking interactions between CNT and GO nanosheets have also been implicated in the formation of CNT/GO core−shell nanostructures.34 Nearly all instances of hybrid formation also involve functionalization of either graphene sheets, CNTs, or both, as a crucial processing step, so that CNT/graphene interactions can be controlled. In aqueous medium, this is usually accomplished by incorporating ionic functional groups to take advantage of long-range electrostatic interactions to influence the energetics of the intercalation process. There are several fundamental aspects of CNT intercalation, in between graphene sheets, that have not been adequately addressed. An important question is related to how the energy barrier of intercalation changes with respect to the types of ionic functional groups and the extent to which the energy barrier can be tuned by altering the nature and positioning of functional groups. Another aspect is related to the interplay between long-range electrostatic interactions and various shortrange interactions, including van der Waals and hydrophobic interactions, in determining the energy landscape of the intercalation process. In addition, the orientation of the intercalating CNT can also change the energetics of the intercalation process. In the current work, we utilize fully atomistic MD simulations and free energy calculations to understand the effect of ionic functionalization on the intercalation of a single-walled CNT into a graphene gallery formed by two parallel graphene sheets. Specifically, the energy of intercalation of the graphene−carbon nanotube system has been extensively investigated in this work to understand the importance of electrostatic and short-range interactions in tuning the energy barrier of intercalation between graphene sheets. To the best of our knowledge, the current investigation is one of the early attempts to gain insight into the factors influencing the intercalation process and formation of hybrid graphene/CNT materials. 1976


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the CNT approaches the graphene sheets, the PMF rises from zero to a finite value and reaches a maximum value, which defines the barrier to the entry of the CNT into the graphene gallery. Once the barrier is crossed, the PMF decreases rapidly and turns attractive, corresponding to the formation of a graphene−CNT hybrid complex. The attraction is mainly due to the hydrophobic interactions between the CNT and graphene sheets. The only exception to the general trend is the hypothetical case G−C(rep.), where CNT/graphene interactions are assumed to be purely repulsive. For this case, the PMF shows a continuously increasing trend. Interestingly, both the barrier height and the barrier location seem to be dependent on the interactions between the graphene and the CNT. The interactions between the graphene and the CNT, in turn, depend on the nature of the functionalization of the CNT and graphene. As the nature of interactions change from one case to another, the PMF plots also change from displaying a mostly attractive interaction (G−C) with a very small barrier to significantly larger barriers (GF⊖−CF⊖) and then a completely repulsive trend for G− C(rep.). Thus, the plots show that the CNT/graphene interactions can be tuned continuously by varying the functionalization of graphene and CNT. However, calculation of the PMFs in Figure 2 is subject to the graphene interlayer spacing being constrained to be 12 Å. The equilibrium interlayer spacing between two graphene sheets in water would depend on the nature of graphene functionalization and differ from one case to the other. For instance, the interlayer spacing is expected to be close to 3.4 Å for two bare graphene sheets. The energy barrier for intercalation of an approximately 10 Å diameter CNT is expected to be very high for bare graphene sheets, and it may require an extremely tedious simulation to evaluate the PMF for the intercalation process. For functionalized graphene sheets, the interlayer spacing is expected to be larger (close to 10 Å for GO44,45). Constraining the graphene interlayer spacing to be 12 Å in our simulation has two important consequences. First, it implies an implicit assumption that the two graphene sheets are partially exfoliated to an extent by some prior process (such as ultrasonication in a typical solution-based dispersion process). Second, the interlayer spacing remains constant for the PMF calculations for the seven cases considered here. The role of exfoliation energy is discussed later in Section 3.2. 3.1.1. Intercalation Energy: Effect of Functionalization. PMF plots for the different cases presented in Figure 2 were examined in greater detail by comparing every case to the case of a bare CNT intercalating into bare graphene sheets (G−C) in Figure 3. Figure 3a compares the PMF curves corresponding to the cases of G−C and GF⊖−C. For the case of G−C intercalation, the PMF rises gradually to a small barrier of height 1 kcal/mol at r = 35.5 Å. As the CNT moves closer to the entrance of the graphene gallery, the PMF curve shows an attractive minimum at r = 34 Å, which corresponds to the CNT situated at the entrance of the graphene gallery in contact with the graphene edge. The PMF is negative because of the attractive hydrophobic interaction between the CNT and graphene. However, the PMF rises again to a value close to 0 (though it is still negative) as it enters the graphene gallery. This increase in PMF takes place because the distance between the graphene sheets is constrained at 12 Å and the CNT has to push the graphene sheets apart to be intercalated between the sheets. At this stage also, the CNT barely enters the gallery but

states of the graphene−CNT interaction for each of the six cases: front view of a CNT completely intercalated in a graphene gallery (left) and side view of the CNT attempting to enter the graphene gallery (right). The following nomenclature was used to represent CNTs and graphene sheets in various states of functionalization: bare graphene (G), bare CNT (C), carboxylate edge-functionalized graphene sheets (GF⊖), carboxylate edge-functionalized CNT (CF⊖), amine edgefunctionalized CNT (CF⊕), and bare CNT oriented along the Z-axis (C_L). Table 1 describes the seven intercalation cases considered in the simulations. Furthermore, case (g) corresponds to a hypothetical scenario where the interactions between the CNT and graphene atoms have been modified to include only the repulsive part of the LJ interaction. The coordinates (0,0,0), (33,0,0), and (23,0,0) shown in Figure 1 represent the locations of CNT during the intercalation stages. For cases (a)−(e), the CNT intercalates “head-on” into the graphene gallery because its axis remains oriented along the direction of movement of the CNT (X-axis). However, for case (f), the CNT intercalates “sideways” because its axis is oriented along the Z-axis, which is perpendicular to the direction of movement of the CNT (X-axis).

3. RESULTS AND DISCUSSION 3.1. Intercalation Energy. Figure 2 shows PMF curves representing the energy of intercalation for all seven cases

Figure 2. PMF curves representing the energy of intercalation for different cases of both functionalized and nonfunctionalized graphene and CNTs. Schematics representing the intercalation process of CNT at the entry and at the center of the graphene gallery are superimposed on the plot.

(listed in Table 1) as a function of the distance between the center of mass of the CNT and the graphene sheets, r. The initial state for the intercalation process corresponds to the graphene sheets being located at the origin (0,0,0) and the CNT center of mass being located at (40,0,0). Thus, the initial separation between the graphene sheets and the CNT is 40 Å, and it is assumed that interactions between the CNT and graphene sheets are relatively weak at this separation. Hence, this state (r = 40 Å) is also chosen as the reference state for the PMF plots, where the PMF values for all cases are assumed to be zero. The final state, when r = 0 Å, corresponds to a state where the CNT is completely intercalated between the two graphene sheets. For all of the cases considered here, an energy barrier is observed as the CNT enters the graphene gallery. In general, as 1977


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Figure 3. Comparison of PMF curves for different systems of both functionalized and nonfunctionalized graphene and carbon nanotubes: (a) CNT intercalating bare graphene sheets and functionalized graphene oxide sheets (head-on); (b) bare CNT intercalating graphene sheets assuming a hypothetical repulsive interaction; (c) negatively and positively charged functionalized CNT intercalating bare and functionalized graphene sheets; and (d) bare CNT intercalating bare graphene sheets along its diameter and length (sideways).

any further decrease in r results in a rapid decrease in PMF values. This happens because of an increase in the graphene− CNT interfacial contact, which is energetically favorable because both are hydrophobic in nature. A significant change in the PMF is observed when only graphene is edgefunctionalized with carboxylate groups in the GF⊖−C case. A wider barrier spanning approximately 7 Å from 33 < r < 37 Å, with a height of 4 kcal/mol, is observed with the maximum located at r = 34 Å. The barrier is wider and higher because of the increased steric repulsion between the CNT and the graphene edges due to the presence of carboxylate functional groups. An increased steric repulsion between the CNT and graphene would make it more difficult for the CNT to be intercalated into the graphene gallery. However, once the CNT enters the graphene gallery (r = 30 Å), the PMF turns negative and drops continuously and rapidly for r < 30 Å. In fact, the PMF curves for the cases GF⊖−C and G−C are nearly parallel to each other for r < 30 Å. The energy observed for the completely intercalated states for both G−C and GF⊖−C systems is nearly −150 kcal/mol (at r = 0 Å) with respect to the reference state at r = 40 Å. Using MD and nudged elastic band calculations, Mirzayev et al.46 estimated diffusion barriers for a C60 diffusing between the edges of two fullerene crystallites. The two crystallites were simultaneously sandwiched between two graphene layers, and they estimated a diffusion barrier of 371 meV (8.5 kcal/mol) for C60 diffusion across the gap between the two crystallite edges. These simulations were used to understand the dynamics observed through direct STEM measurements reported in the same work. Although our simulations are in an aqueous medium, the energy barriers (Ea) observed for unmodified CNT intercalation in our simulations are of the same order of magnitude.

Figure 3b compares the PMF profiles corresponding to the cases of G−C and G−C(rep.). For G−C(rep.), interactions between the carbon atoms of graphene and CNT have been modified to include only the repulsive part of the LJ interactions. The case of CNT intercalation for G−C(rep.) is a hypothetical scenario, where we would like to see the kind of PMF profile that would develop in the presence of only shortranged repulsive interactions between the CNT and graphene sheets. The PMF profile of G−C(rep.) shows a completely repulsive behavior as the CNT enters into the graphene gallery, which is in contrast with the original curve of the G−C system. The PMF values observed for the completely intercalated states (at r = 0 Å) for the G−C and G−C(rep.) systems are nearly opposite to each other, corresponding to values of −150 and 150 kcal/mol, respectively, clearly underscoring the significant role played by the nature of interactions between the graphene and CNT in a graphene−CNT hybrid complex. In Figure 3c, we compare the PMF profiles of the three cases with charge functionalization, GF⊖−CF⊖, G−CF⊖, and GF⊖− CF⊕, with those of the G−C system. The energy profile for the GF⊖−CF⊖ system shows a huge energy barrier at r = 27 Å, shifted to the left, with a barrier height of 60 kcal/mol. This barrier arises because of the long-range repulsive electrostatic interactions between negatively charged carboxylate groups on both the functionalized CNT and graphene sheets. The observed shift of the energy barrier to smaller values of r can be attributed to the opening of the graphene gallery because of the repulsive interactions between the carboxylate groups on the graphene edges and the carboxylate groups on the approaching CNT. Like-charge repulsion between the groups forces edges of the graphene sheets apart and increases their separation at the edges. For the completely intercalated state corresponding to low values of r (0 ≤ r ≤ 5 Å), the well depth 1978


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gradient for G−C_L (in comparison to G−C) when the system transitions from the state when the CNT is at the entrance of the graphene gallery to the fully intercalated state (0 ≤ r ≤ 16 Å). The rapid decrease in the PMF profile of G− C_L as compared to that of G−C can be attributed to the large surface area of CNT that is in contact with the graphene sheet edges when the CNT is placed at the entrance of the graphene gallery. A larger contact area leads to a higher magnitude of attractive CNT−graphene interactions and a more rapid decrease in PMF as the CNT moves further into the graphene gallery. Table 2 summarizes the locations and the heights of energy barriers observed for the intercalation of different systems

of the PMF minima has a higher value compared to that of most of the other systems studied (−70 kcal/mol as opposed to −150 kcal/mol for the rest). This can be attributed to the repulsive interactions between negatively charged carboxylate groups of graphene sheets and CNT because the negatively charged functional groups are forced into close contact in the completely intercalated state. The PMF profile for G−CF⊖ also shows a large energy barrier of 58 kcal/mol at r = 30 Å corresponding to the state where the CNT is at the entrance of the graphene gallery. As the CNT protrudes further into the graphene gallery, the PMF values decrease from the maximum at r = 30 Å and turn negative because of the attractive van der Waals interactions between the carbon atoms of CNT and graphene sheets. The fully intercalated state for the G−CF⊖ system corresponds to PMF minimum of −82 kcal/mol at r = 1 Å, which is lower compared to that for GF⊖−CF⊖ but still much higher compared to that of −150 kcal/mol observed for the other cases. The reason is the large repulsion between the closely placed carboxylate groups on the edges of the CNT. The energy profile of GF⊖−CF⊕ shows a dip at r = 35 Å, with a barrier height of 22 kcal/mol, shifted to larger values of r (compared with GF⊖−CF⊖ and G−CF⊖). The shift in the location of the energy barrier can be attributed to the electrostatic attraction between the positively charged amine groups of edge-functionalized CNT and the negatively charged carboxylate groups of the graphene sheets, thereby allowing the CNT to easily intercalate into the graphene gallery, with less energy expended, in comparison to all of the other cases considered in this study. As the CNT protrudes into graphene gallery, the PMF curve rises again to show another maximum at r = 31 Å, with a barrier height of 20 kcal/mol. The occurrence of the second maximum can be attributed to the steric repulsion between the long-chain amine groups of CNT and graphene atoms. Among the different combinations of functionalized systems considered in our study, the GF⊖−CF⊕ intercalated system seemed to be the most stable because it showed the deepest PMF well depth of −153.6 kcal/mol corresponding to the fully intercalated state. This is primarily due to the attractive interaction between oppositely charged functional groups on the CNT and the graphene sheets. This observation suggests that the CNT remains strongly attached to the negatively charged GO nanosheets, resulting in the assembly of a stable hybrid complex. 3.1.2. Intercalation Energy: Effect of Orientation. To understand the influence of CNT orientation on intercalation into graphene sheets, we have considered two cases: one in which CNT intercalates “head-on” into the graphene gallery (G−C) and the other in which the CNT intercalates “sideways” into the graphene gallery (G−C_L). Figure 3d represents the comparison of PMF profiles for the energy of intercalation of G−C and G−C_L systems with respect to CNT orientation. The PMF for the case of G−C_L intercalation rises gradually to a small barrier of height 2 kcal/mol at r = 27 Å. As the CNT moves closer to the entrance of the graphene gallery, the PMF curves show an attractive minimum at r = 25 Å, which corresponds to the CNT situated at the entrance of the graphene gallery in contact with the graphene edge. The PMF is negative because of the attractive hydrophobic interaction between the CNT and graphene. The PMF again rises as the CNT protrudes into the graphene sheets, showing an energy barrier at r = 23 Å with a barrier height of 3.8 kcal/mol, and decreases thereafter. An interesting observation is that the PMF profile shows a much larger

Table 2. Location and Height of Energy Barrier in the PMF Curves for the Different Intercalation Systems simulation system

location of energy barrier (Å)

height of energy barrier, Ea (kcal/mol)

G−C G−C_L GF⊖−C G−CF⊖ GF⊖−CF⊖ GF⊖−CF⊕

35 23 34 30 28 31

1.1 3.8 4.8 58.8 60.7 20.1

considered here. Thus, Figures 2 and 3 show that both the energy barrier for the intercalation process and the nature of the PMF curve can be continuously tuned by altering the interactions between the CNT and graphene sheets. Of the cases considered here, Figure 3c presents the most significant comparison of intercalation scenarios resulting from changing long-range electrostatic interactions between the (functionalized) CNT and (functionalized) graphene sheets. Surface modification of either CNT or graphene by way of ionic functional groups is the most important means of altering interactions and controlling their states of dispersion in an aqueous environment. The following sections examine in detail the role of electrostatic interactions in altering CNT/graphene interactions and determining the energy barriers for the intercalation process. 3.2. Energy of Exfoliation and Energy of Intercalation. The equilibrium interlayer spacing in graphite is 3.4 Å, and graphene layers in graphite are held by strong van der Waals interactions. In an aqueous medium, hydrophobic bare graphene sheets tend to agglomerate in stacks with an interlayer spacing close to that of graphite, resulting in an unstable dispersion. Usually, surface modification or chemical functionalization of graphene leads to increased interlayer repulsion and enhances exfoliation of graphene sheets from the graphitic assembly. Chemical functionalization with ionic functional groups, such as in the case of carboxylatefunctionalized graphene sheets, is very effective in an aqueous medium because of long-range electrostatic interactions leading to stable graphene dispersions. Thus, an increase in the interlayer spacing also enhances the ease of intercalation of CNTs between the graphene galleries, as it leads to a reduction in the energy barriers involved in the intercalation process. However, the energy of exfoliation of the two graphene sheets is not taken into account when we harmonically constrain the separation between the two graphene sheets at 12 Å. Therefore, we need to evaluate the energy required to separate (exfoliate) two graphene sheets from their equilibrium 1979


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Figure 4. Simulation snapshots of graphene sheets separated by a distance of 12 Å for (a) bare graphene sheets and (b) edge-functionalized graphene sheets with carboxylate groups. Water molecules are not shown here for clarity. (c) Comparison of PMF profiles for the two bare and carboxylate edge-functionalized graphene sheets. (d) Activation energy barriers for intercalation before (blue curve) and after (red curve) considering the energy of exfoliation of graphene sheets.

location of the PMF minimum can be interpreted as the equilibrium spacing between the two sheets, the well depth can be used as an estimate of the exfoliation energy required to increase the interlayer spacing from the equilibrium spacing to a value of 12 Å (where the PMF values are close to 0). In contrast to the G−G case, where the exfoliation energy is 358 kcal/mol, it is only 264 kcal/mol for the GF⊖−GF⊖ case, implying that 94 kcal/mol of less energy would be expended to exfoliate the GF⊖−GF⊖ sheets in comparison to the G−G sheets. Thus, this difference in exfoliation energies for the two cases, ΔEexf = 94 kcal/mol, can be added to the Ea values in Table 2, for all intercalation cases involving G−G galleries, to obtain revised estimates for intercalation energies. The intercalation energy barrier estimates, before and after this revision, are shown in Figure 4d. When these energies are added to the corresponding intercalation energies of G−C and GF⊖−C systems, the total energy required to intercalate CNT into the bare graphene system is found to be larger than the energy of intercalation of CNT into the functionalized graphene sheets, as shown in Figure 4d. A general observation from the revised energy barrier estimates is that it is easier to intercalate CNTs into carboxylate-functionalized graphene galleries as opposed to the bare graphene galleries. This is mainly due to the large amount of energy required to exfoliate the bare graphene sheets, which becomes easier when the graphene sheets are functionalized. As a result, the energy barrier is highest for the G−CF⊖ case and lowest for the GF⊖−C case. Thus, functionalized graphene oxide sheets (GF⊖) can act as dispersing agents to process insoluble CNTs,49,50 as compared to the bare graphene sheets, because of their better dispersion in water and adhesion of CNTs onto the flat GO sheets through strong π−π stacking

separation in water to a distance of 12 Å. Exfoliation energies were estimated for two cases, G−G and GF⊖−GF⊖, because all seven intercalation instances in Figure 2 consider graphene galleries corresponding to one of these two cases. Figure 4a,b shows simulation snapshots of two systems of bare graphene sheets (G−G) and two carboxylate edge-functionalized graphene sheets (GF⊖−GF⊖ ), respectively, where the intersheet separation is 12 Å in both cases. The thermodynamic perturbation method was used to estimate the energy of exfoliation for two graphene sheets by calculating the PMF between two parallel graphene sheets as a function of their intersheet distance. While only the separation distance between the two graphene sheets was varied, all other degrees of freedom of the graphene sheets (including translations and rotations) were frozen for the thermodynamic perturbation calculations. More details of our implementation of thermodynamic perturbation for the evaluation of PMF between graphene sheets can be found in our previous publications.42,43,47 The calculated free energy profiles of these systems are shown in Figure 4c. The PMF curve for the G−G case shows a strong attraction between the two graphene sheets, with a minimum located at 3.5 Å, corresponding to a well depth of −358 kcal/mol. This value translates to −0.40 kcal/(mol Å2) and agrees quite well with a value of approximately −225 kJ/mol (−0.41 kcal/(mol Å2)) predicted by Choudhury and Pettitt48 for two graphene sheets of area 11 × 12 Å2 in water. However, for the GF⊖− GF⊖ case, the well depth of the attractive minimum reduces to −264 kcal/mol and the location of the minimum shifts to a larger value of 4.1 Å. This occurs because of the electrostatic repulsion between the negatively charged carboxylate groups attached to the edges of the graphene sheets. Because the 1980


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Figure 5. Electrostatic potential plots sampled at the center of the XY-plane for the cases of (a) intercalated CNT at the center of the graphene gallery and (b) CNT at the entrance of graphene gallery. The dotted lines at x = +15 and x = −15 represent the edge locations of the graphene sheet in the XY-plane.

graphene gallery. These two states are schematically shown in Figure 5a,b, respectively. For these calculations, two different simulation systems corresponding to the above-mentioned intercalation states were generated for five of the seven cases [G−C_L and G−C(rep.) were not considered]. The separation between the two graphene sheets was constrained at 12 Å, their orientations (plane normals) were constrained along the Y-axis, and translations in all three directions were constrained to maintain the center of mass of the graphenes at the origin. The CNT orientation and translations were also constrained in such a manner that the CNT remained in the same state, either fully intercalated between the graphene sheets or at the entrance of the graphene gallery, over the course of the simulation. However, atoms corresponding to water and all ions were allowed to move freely during simulations. Simulations of 5 ns duration each were then carried out for the different cases of CNT intercalation into the graphene sheets. Electric potential values corresponding to each system were generated by time-averaging values at regular intervals, over the final 1 ns of the simulation run. The evaluation of the electric potential considered all of the charges that were present in the simulation box, including carboxylate ions, counterions, amine groups, and all partial charges of the water molecules. The variation of the electrostatic potential along the X-direction (direction of CNT and graphene separation) is shown in Figure 5 corresponding to the Y = 0 plane, which defines the mid-plane parallel to the two graphene sheets. The dotted lines shown in Figure 5 at −15 and +15 Å are the locations of the edges of the graphene sheets. Figure 5a shows the electrostatic potential distribution for the five cases of the graphene−CNT hybrid complexes in fully intercalated states. The electrostatic potential calculated for the G−C system shows a positive value in contrast to neutral, which can be attributed to water dipole orientations at the hydrophobic interfacial regions of graphene or CNT.51 The GF⊖−C, G−CF⊖, and GF⊖−CF⊖ complexes show negative electrostatic potentials at the graphene sheet’s edges because of the presence of carboxylate functional groups. In contrast, the GF⊖−CF⊕ hybrid shows a large positive potential. These potentials can be interpreted as surface potentials for the CNTintercalated graphene hybrids, where the net value is determined by the surface charge densities on the CNT and

interactions. Interestingly, the energy barrier is lower for the GF⊖−CF⊖ case (when compared to the bare graphene cases), where large electrostatic repulsion exists between the likecharged CNT and graphene sheets. As expected, the energy barrier is lower for the GF⊖−CF⊕ case, where CNT intercalation is also assisted by electrostatic attraction between oppositely charged groups on the CNT ((CH2)2CONHNH3+) and graphene sheets (-COO−). There are two important implications of the revised estimates of the intercalation energy barriers. The first is that functionalization of the graphene sheets by ionic functional groups lowers the energy barrier for CNT intercalation by rendering the graphene sheets less hydrophobic and increasing their exfoliation in water. Thus, intercalation energies are, in general, found to be higher for all cases involving unmodified, bare graphene sheets. The second important result is that for all cases involving carboxylate-functionalized graphene sheets the energy barrier is then decided by the state of functionalization of the intercalating CNT. The obtained results could depend on several length scales, including the graphene sheet size and CNT length and diameter. For certain quantities, their scaling with characteristic length scales is more obvious and straight forward. For example, the exfoliation energy calculated in Section 3.2 (Figure 4c) is expected to scale with the area of the graphene sheets. In contrast, the scaling is not so obvious for the intercalation energy barrier, Ea. However, one would expect Ea to increase with the diameter of the CNT for the case of “headon” entry of the CNT into the graphene gallery, at constant values of CNT length and graphene interlayer spacing. For the “head-on” entry scenario, the entry of a critical length of the CNT into the gallery may correspond to the activation energy barrier, implying that the total CNT length may not influence the value of Ea. In an analogous way, the activation energy barrier for the lateral entry of the CNT may depend on a minimum contact area between the CNT and the graphene sheets, rather than the overall CNT diameter. 3.3. Electrostatic Potential. In Figure 5, we discuss the spatial variation of electrostatic potential for two important states of intercalation, namely, the fully intercalated state, where the CNT is at the center of the graphene gallery, and the other state where the CNT is positioned at the entrance of the 1981


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Figure 6. Two-dimensional (2D) water density contour maps representing distribution of water in the XY-plane of CNT intercalating into graphene sheets: CNT at the center of the graphene gallery (left) and CNT positioned at the entrance of the graphene gallery (right); (a) G−C, (b) GF⊖−C, (c) G−CF⊖, (d) GF⊖−CF⊖, and (e) GF⊖−CF⊕.

of ±0.089 e/Å2, whereas the charge density on a functionalized graphene edge is much smaller at approximately ±0.022 e/Å2. As a result, the largest negative potential (−0.35 V) is observed

the graphene sheets. A crude estimate of the surface charge density (see the Supporting Information, Section S3) shows that functionalized CNT edges correspond to a charge density 1982


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Figure 7. Counterion density distribution around carboxylate and amine functional groups of a graphene−CNT hybrid complex when CNT is at the center of the graphene gallery: (a) GF⊖−C; (b) G−CF⊖; (c) GF⊖−CF⊖; and (d) GF⊖−CF⊕. The dotted lines at x = +15 and x = −15 represent the edge locations of the graphene sheet in the YZ-plane. Simulation snapshots illustrating the counterion condensation around carboxylate and amine functional groups in a graphene−CNT hybrid complex are placed alongside their respective plots. Water molecules are not shown here for clarity.

at the graphene edges for the GF⊖−CF⊖ system, which contributes to a strong repulsion between graphene sheets, when compared with all other systems. Extending this argument also shows why the G−CF⊖ system shows a more negative surface potential when compared to that of the GF⊖− C system. Although the fully intercalated states for the two cases are similar, the higher charge density on the functionalized CNT in the G−CF⊖ hybrid leads to a more negative value of the electrostatic potential. For a similar reason, the GF⊖−CF⊕ system shows a positive potential at both ends of the graphene sheets because the functionalized CNT edge has a positive charge density, which is higher than the negative charge density on the functionalized graphene edge. From all of these observations, we conclude that the negative potential in the GF⊖−CF⊖ system leads to a stronger repulsive interaction between the graphene sheets. This keeps the graphene sheets separated and prevents their restacking. The GF⊖−CF⊕ system displays a large positive potential at both edges of the hybrid complex, which leads to a strong electrostatic binding with the oppositely charged carboxylate groups on the graphene sheets, resulting in the formation of a stable GF⊖−CF⊕ hybrid complex. This is also evident from a comparison of PMF plots for a charged system in Figure 3c, where the GF⊖−CF⊕ system shows the lowest PMF value at r = 0 Å. Figure 5b displays the relatively more important scenario of the CNT just before its entry into the graphene gallery and shows the electric potential distribution for the five systems. On the left-side edges of the graphene sheets (x = −15 Å), electrostatic potentials are found to be negative only for GF⊖−

C, GF⊖−CF⊖, and GF⊖−CF⊕ cases, where graphene sheets are functionalized with carboxylate groups. Coincidentally, these also correspond to intercalation scenarios with relatively lower energy barriers [Figure 4d], which were attributed to the ease of exfoliation of GF⊖ sheets. The variation of the electrostatic potential at the graphene edges clearly shows that the repulsion between GF⊖ sheets is electrostatic. However, there exists a greater diversity in the electrostatic potentials near the right-side edges of the graphene sheets (x = 15 Å). The GF⊖−CF⊖ system shows a negative electric potential of −0.16 V at the entrance of the graphene gallery, which leads to an electrostatic barrier for the entry of the negatively charged CNT in between the GF⊖ sheets. This supports our result from Figure 3c, where the PMF curve for the GF⊖−CF⊖ system shows a huge barrier at the entrance of graphene gallery. In contrast, a very large potential drop of nearly 0.65 V over the region, 0 < x < 10 Å, is observed for GF⊖−CF⊕, which assists intercalation of the positively charged CNT in between the GF⊖ sheets. The electrostatic attraction between CNT and graphene sheets results in a much lower energy barrier when compared to that for the GF⊖−CF⊖ case. An attractive dip is also observed at r = 35 Å in the PMF curve for the GF⊖−CF⊖ system. Detailed two-dimensional contour plots of the electrostatic potential in the XY-plane are shown in Figure S4a−e for a plane that passes through the middle of the graphene sheets (Z = 0) reiterating all of the important results of Figure 5. 3.4. Wettability of Graphene. Figure 6a−e shows the two-dimensional contour plots of the water density distribution for the systems at two states, which are schematically 1983


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because the CNT and the graphene sheets are functionalized with oppositely charged groups. Plots of counterion densities along the X-axis, for all of the four cases, are shown next to the respective snapshots in Figure 7a−d. Ion densities are calculated by averaging ion densities over the last 1 ns of a 5 ns simulation described for Figures 5 and 6. The calculation of ion densities involves binning counterion counts in volume slices that span the simulation box dimensions along the Y- and Z-directions and have a thickness of 0.5 Å in the X-direction. The dashed lines represent the edges of the graphene sheets for the fully intercalated states shown in Figure 7. Counterion (Na+) condensation is observed around the edges of the graphene sheet for the GF⊖−C case [Figure 7a]. In contrast, counterion condensation appears to be localized near the edges of the intercalated CNT for the G−CF⊖ case [Figure 7b] because only the CNT contains ionic functional groups. Moreover, the counterion density is much higher compared to that observed in Figure 7a because functionalized CNT edges have a higher charge density compared to that of a functionalized graphene edge. The counterions are found to be condensed near all of the edges of the hybrid complex for the GF⊖−CF⊖ case in Figure 7c, with significant condensation on the graphene edges parallel to the intercalated CNT (compared with densities in Figure 7a). However, the counterion densities are much higher on the graphene edges, which also contain the carboxylated CNT edges. It is to be noted that the negative charge density is very high in this case because both components are negatively charged. Hence, the electrostatic potential energy of the system is lowered by condensation of a large number of Na+ counterions at those surfaces. In contrast to the other three cases, the GF⊖−CF⊕ case [Figure 7d] shows the lowest counterion densities because the electrostatic potential energy is lowered as a result of complexation of oppositely charged components in the hybrid complex. Condensation of a chloride ion (Cl−) is observed around the positively charged aminefunctionalized CNT.

shown in Figure 5a,b. The plots represent the two scenarios of completely intercalated CNT (left-side images) and the CNT at the entrance of the graphene gallery (right-side images), respectively. The most important observation from the water density plots is that they clearly show that the presence of ionic functional groups renders a hydrophobic colloid (graphene or CNT) into a relatively more hydrophilic colloid. The effect is most clearly seen when the cases with bare graphene sheets [Figure 6a,c] are compared with the cases involving functionalized GF⊖ sheets [Figure 6b,d,e]. In the fully intercalated states, water densities are increased around the surface of the hybrid complex in the presence of charged functional groups. Even in the case of the G−CF⊖ system, water density increases near the surface of the hybrid because of the presence of the carboxylate groups on the CNT. Hydrophobic/hydrophilic effects are more prominently observed when we compare the pre-intercalation states for the five cases. For the G−C system, the graphene sheets clearly behave as hydrophobic colloids and the interlayer water density is lowered as compared with the bulk density, clearly indicating that water is excluded from the region between the sheets. For the cases with GF⊖ sheets [Figure 6b,d,e], there is an increase in water density in the region between the GF⊖ sheets. In fact, water density in the interlayer region is higher than the bulk density for all three cases, clearly showing that the presence of the carboxylate groups on graphene sheets has rendered the graphene surfaces hydrophilic. The enhanced wettability of the GF⊖ sheets leads to intercalation of water between the graphene sheets, which directly results into an increase in the interlayer spacing between graphene sheets. Ultimately, an increased interlayer spacing would make intercalation of the larger CNT much easier into the graphene gallery. Of course, in our simulation, a harmonic constraint is applied on the two graphene sheets, which constrains the separation distance between their centers of mass along the Y-axis of 12 Å. However, this may still lead to an increased separation at the graphene edges because of an increase in water density in the case of the GF⊖ sheets and also because of the electrostatic repulsion between like-charged carboxylate groups. The separation at the graphene edges can be clearly seen for the cases with GF⊖ sheets in Figure 6b,d,e. 3.5. Counterion Density Distribution for Graphene− CNT Hybrid Complexes. Electrostatic potentials in Figure 5 clearly show that intercalation of CNT into the graphene gallery leads to the formation of highly charged hybrid complexes for cases where either CNT or graphene is ionically functionalized. The magnitude of electrostatic potential in the fully intercalated state was dependent on the respective charge densities of graphene sheets and CNT. Next to a charged surface, the electrostatic potential energy is lowered by condensation of a certain fraction of counterions, the extent of which is determined by the surface potential and the surface charge density. In the context of graphene−CNT hybrids, condensation of counterions provides useful insight into the localization of counterions as a result of counterion condensation. Simulation snapshots, shown in Figure 7, of equilibrated graphene−CNT hybrid complexes in the fully intercalated states correspond to the four possible cases involving ionically functionalized CNT/graphene. It is clear from the snapshots in Figure 7 that the extent of counterion condensation varies for each case and appears to be higher in hybrids with a higher surface density of carboxylate functional groups, GF⊖−CF⊖. There is very little counterion condensation (either Na+ or Cl−) for the GF⊖−CF⊕ case [Figure 7d]

4. CONCLUSIONS In summary, we have used MD simulations and free energy calculations to investigate the energetics of a 3D hybrid formation resulting from the intercalation of a CNT into a graphene sheet gallery. It was found that the formation of a graphene−CNT hybrid can be divided into three processes involving (a) exfoliation of graphene sheets by repulsive interactions, (b) intercalation of a CNT into the graphene gallery associated with an activation energy barrier, and (c) spontaneous self-assembly/association of constituent CNT and graphene sheets driven by hydrophobic interactions or electrostatic attraction, leading to the formation of a 3D hybrid. It was also shown that the intercalation energy barrier for the entry of a CNT into a graphene gallery can be tuned over 2 orders of magnitude by altering the type of ionic functional groups on the CNT and graphene. The main conclusions drawn from the observations of simulation results are as follows. The energy required for exfoliation of functionalized graphene sheets is much lower compared to the case of pristine graphene sheets (≈0.1 kcal/(mol Å2), Figure 4c) because of the electrostatic repulsion induced by ionic functional groups on edge-functionalized graphene sheets. In addition to inducing electrostatic repulsion between the graphene sheets, ionic functionalization renders the graphene 1984


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The Journal of Physical Chemistry C Notes

sheets hydrophilic and entrains water in the graphene gallery; both effects enable easier exfoliation of functionalized graphene sheets in water. Easier exfoliation of graphene sheets also leads to lower intercalation barriers for entry of the CNT into the graphene gallery. Thus, significantly lower intercalation energy barriers are observed for all cases where functionalized graphene sheets are considered (Figure 4d). The intercalation barrier is larger by nearly 150 kcal/mol for G−CF⊖ when compared to that for GF⊖−C, which shows the lowest barrier of all cases considered here. However, the ease of CNT entry into the graphene gallery is hindered by steric interactions. Consequently, even in the case of functionalized graphene sheets, energy barriers increase when functionalized CNTs are considered. As expected, the barrier decreases when both CNT and graphene sheets are functionalized with oppositely charged groups. Once the intercalating CNT moves past the activation energy barrier, the amphiphilic nature of functionalized CNT and graphene sheets leads to their spontaneous association into a 3D hybrid complex. Short-range hydrophobic and van der Waals interactions between the CNT and graphene sheets lead to a steep decrease in PMF profiles, resulting in the formation of stable hybrid complexes. The most stable hybrid complex was observed in the case of GF⊖−CF⊕ because of the strengthened electrostatic interaction between the negatively charged graphene oxide sheets and positively charged CNT. The present calculations help us understand the complex interplay between various interactions in tuning the energy barrier for the intercalation of CNT into graphene nanosheets. Graphene−CNT hybrid nanostructures have numerous applications in the fields of nanofiltration, sensors, lithiumion batteries, and energy storage devices (supercapacitors). For instance, the long-range Coulombic repulsion exerted between negatively charged carboxylate groups located at the edges of the graphene sheet and CNT in GF⊖−CF⊖ lead to increased separation of graphene sheets in the hybrid. These expanded interlayer spacings could be accessed by water molecules, ions, and hydrogen gas, thereby contributing to the wetting of graphene sheets, huge potential for hydrogen storage, and lithium ion transport. To the best of our knowledge, this is the first systematic attempt to understand the energetics of graphene−CNT hybrid formation in terms of exfoliation, intercalation, and spontaneous self-assembly processes.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge grant SR/S3/ME/ 0016/2011 from the Department of Science and Technology, Ministry of Science and Technology, India, for funding support, and National PARAM Supercomputing Facility at Centre for Development of Advanced Computing (CDAC), Pune, India, for giving us access to use PARAM Yuva II.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b10958.

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REFERENCES

Details of the simulation method, surface charge density on CNT and graphene sheets, equilibrium separation between the edge-located atoms of the graphene sheet, and contour plots of the electrostatic potential (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-22-2576-7644. ORCID

Prasad Rama: 0000-0003-1578-3100 Arup R. Bhattacharyya: 0000-0002-2099-2655 Rajdip Bandyopadhyaya: 0000-0001-5902-5171 Ajay S. Panwar: 0000-0001-6245-6896 1985


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Tunable Energy Barrier for Intercalation of a Carbon Nanotube into

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