Design Rules for Graphene and Carbon-Nanotube Solvents and

a number of design rules that will aid the identification of the best solvent or ... defect-free graphene, essentially resulting in a material that is...
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Design Rules for Graphene and Carbon Nanotube Solvents and Dispersants Adam Hardy,† James Dix,‡ Christopher D. Williams,‡ Flor R. Siperstein,‡ Paola Carbone,‡ and Henry Bock*,† †

Institute of Chemical Sciences, Heriot Watt University, Edinburgh EH14 4AS, United Kingdom School of Chemical Engineering and Analytical Science, University of Manchester, Manchester M13 9PL, United Kingdom

‡

S Supporting Information *

ABSTRACT: The constantly widening industrial applications of carbon-based nanomaterials puts into sharp perspective the lack of true solvents in which the materials spontaneously exfoliate to individual molecules. This work shows that the different geometry of graphene compared to that of carbon nanotubes can change the potency of a molecule to act as a solvent or dispersant. Through analysis of the structure/function relationships, we derive a number of design rules that will aid the identification of the best solvent or dispersant candidates. KEYWORDS: graphene solvents, solvent design, corresponding distances method, computer simulation, potential of mean force raphene, first isolated by mechanical exfoliation from graphite in 2004,1 has attracted an impressive interest of the scientific community due to its mechanical, electronic, and thermal properties. Many of its potential applications require bulk quantities of defect-free monolayer graphene sheets in a well-dispersed form. Applications include printable electronics,2 electrodes for energy storage and sensors,3 laminated membrane for water purification,4,5 or the production of composite polymeric materials with enhanced properties.6,7 However, the development of production techniques for monolayer graphene suitable for industrial scale-up provides an ongoing challenge.8,9 Liquid-phase exfoliation is believed to be the most promising option for producing graphene at low cost because of its scalabily and compatibility with existing manufacturing processes.10,11 One of the earliest approaches is oxidative exfoliation, using strong oxidizing agents, such as sulfuric acid or potassium permanganate.12 However, this method introduces a large number of oxygen-containing functionalities that cannot be reduced back to defect-free graphene, essentially resulting in a material that is not graphene and therefore unsuitable for many of graphene’s applications. Alternatively, graphene sheets can be exfoliated by mechanical means using sonication or high-shear mixing.8,12 Once the strongly attractive van der Waals forces between individual sheets have been overcome, the separated graphene sheets must be stabilized against reaggregation. This can be achieved in two ways. If the processing liquid creates a high enough free-energy barrier between the dispersed and the aggregated states, the dispersed state gets kinetically trapped,

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© 2018 American Chemical Society

and one obtains a dispersion. The alternative is that the liquid destabilizes the aggregated state, then the exfoliated state becomes thermodynamically stable. While both processes are very useful, dispersants have the disadvantage that their reaggregation barrier also hinders exfoliation. The graphene exfoliation efficacy of many liquids, liquid mixtures, and solutions has been investigated experimentally, including organic solvents,11 block copolymers,13 and aqueous solutions containing surfactants.14 For example, Coleman measured the amount of graphene that could be brought into and held in solution/suspension for a wide range of liquids. To aid the development of better solvents/dispersants, they correlated their results with the liquids’ surface tension and solubility parameters.15 While these parameters appear to be predictive in the sense that they identify poor solvents/ dispersants quite well, they are less effective in identifying good ones. Thus, the key problem remains that even the best achieved graphene loadings are rather low, which represents a serious issue for industrial implementation. This is compounded by the observation that much of the graphene is not exfoliated to monolayers. This lack of efficient dispersant or solvent molecules is a shared problem with another class of low-dimensional carbonbased materials, for example, carbon nanotubes (CNTs). As manufactured, carbon nanotubes are in an aggregated Received: July 21, 2017 Accepted: January 23, 2018 Published: January 23, 2018 1043

DOI: 10.1021/acsnano.7b05159 ACS Nano 2018, 12, 1043−1049

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Figure 1. Solvent-mediated PMF (blue), direct graphene/graphene interaction potential (red), and sum of the two, i.e., the full PMF (green) for (a) CBrCl3 and (b) H2O. The PMF is shown per unit area of graphene; therefore, the values reported are independent of the simulated graphene flake size. Data for water shown in this figure were obtained using the GROMOS force field. Data obtained using the Steele potential are qualitatively very similar and are shown in the Supporting Information.

screening, provided a sufficiently accurate and efficient methodology exists. The standard simulation approach to assess solvent and dispersant efficacy is to calculate a potential of mean force (PMF)32 between two graphene sheets or CNTs in a liquid using, for example, molecular dynamics (MD) simulation. The PMF profile describes the thermodynamic stability of the aggregated state relative to the well-dispersed state, as well as the free-energy landscape linking these two states. The PMF can be separated into sheet/sheet and solvent-mediated contributions, allowing a molecular-level analysis of the solvent’s role. Free-energy calculations have been applied previously to study graphene exfoliation in a variety of polar solvents33,34 and for ionic liquids,35 and similar calculations have been performed on CNTs.25,26 Here, our aim is to compare the quality of different solvents for graphene and CNTs and investigate the important impact of solute geometry on their performance. This work will aid the development of design rules for graphene and CNT solvents and dispersant and will impact the many applications that rely on the success of liquid-phase exfoliation processes.

(bundled) state. The bundling tendency originates from strong tube/tube cohesion, for example, approximately −40kT nm−1 for a pair of (10,10) tubes (⌀ = 1.36 nm).16 Considering that the tubes can be centimeters long, this results in very high energies, which make the bundles very stable. The most common dispersion systems for CNTs are based on aqueous surfactant solutions with the surfactant molecules acting as a physical spacer between the CNTs and, in this way, preventing them from bundling.17−20 However, while surfactant solutions can efficiently maintain individual tubes or sheets dispersed, they are generally found to be ineffective in aiding the exfoliation process.21,22 Thus, solvents (in the thermodynamic sense) are the key to liquidphase processing for these materials. There has been a large effort to identify the best solvents for CNTs, and several time-consuming and systematic studies are reported in the literature.23−30 Bergin et al.24 experimentally tested dozens, repeatedly measuring the amount of dispersed tubes for each. One of the key results of this work was finding one particular molecule, CHP (cyclohexylpyrrolidinone), outperforming all other solvents by a factor of 5, dispersing 3.5 mg of CNTs in 1 mL of solvent. Interestingly the experimental data indicate that solvents which disperse CNTs reasonably well do not show the same efficacy for graphene exfoliation, for which N-methylpyrrolidone and dimethylformamide are normally used.15 This fact has been also observed for the oxidized materials (graphene oxide and oxidized CNT), for which, in polar aprotic solvents, they show similar dispersion behavior, but in polar protic solvents, such as ethanol and isopropyl alcohol, the graphene derivatives did not show dispersion stability, whereas the oxidized CNTs did.31 While in the latter case one can argue that the oxidized materials might not show similar chemistry due to different surface distribution of the functional groups, in the case of the pristine materials, it becomes intriguing to understand why different solvents are needed to achieve similar dispersion. While experimental testing is conclusive for determining the suitability of individual liquids for the exfoliation process, it is time-consuming and may not provide sufficient understanding of the molecular-level processes that govern exfoliation, solubilization, and dispersion to create a knowledge base on which further development can be founded. Computer simulations, in principle, provide full access to the structure function relationships and lend themselves to systematic

RESULTS The potential of mean force w(d) (PMF) is a convenient tool to assess the efficacy of a liquid as a solvent or dispersant for graphene. It is equal to the system’s free energy (except for an additive constant) and, therefore, provides the correct dependence of the system’s free energy on the sheet/sheet distance d. It is obtained from the mean force F(d) between two (parallel) graphene sheets via integration w(d) = −

∫d

∞

F(d)dd

(1)

The mean force F(d) is readily available from a series of parallel-sheet computer simulations at various distances d or from a single simulation using the corresponding distances method (CDM) and can be decomposed into the solid and solvent-mediated contributions. This solvent-mediated contribution, smPMF, is additive (at least in all common model systems) to the direct sheet/sheet interaction and responsible for the solvent’s effectiveness. The PMF curves for trichlorobromomethane (CBrCl3) and H2O provide insight into the different performance of these solvents, as shown in Figure 1. The most prominent feature of the smPMF for CBrCl3 is a large region at d ≲ 0.9 nm, where the smPMF is large and 1044

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Figure 2. Atom density profiles of (a) CBrCl3 and (b) H2O on a single graphene sheet. The surface layer for CBrCl3 is quite thick, terminating 0.7 nm away from the sheet, whereas the surface layer for H2O terminates at 0.5 nm.

positive (Figure 1a). This repulsive region in the smPMF is created by the large force that is required to squeeze out the last layer of CBrCl3 molecules from the space between the sheets. It is also present in the full PMF for distances larger than approximately 0.5 nm. Although a similar barrier is observed in the smPMF for H2O, it is significantly smaller and the attraction between graphene sheets dominate the full PMF curve (Figure 1b). Therefore, the barrier for reaggregation in the full PMF curve is negligible in water. This suggests that CBrCl3 is a good dispersant for graphene, whereas water is neither a solvent nor a dispersant. To understand the difference in performance of these two solvents, it is convenient to analyze the structure of the adsorbed layer using the solvent atom density profiles for an individual graphene sheet (Figure 2). The orientational order of the CBrCl3 molecules in the surface layer is very strong, whereas other layers show very little or no order. Nevertheless, clear formation of multiple layers is observed, which results in small oscillations of the PMF at long distances. Water also forms a clear monolayer and a less-defined second layer, but most of the structure is lost after 1 nm. The thickness of the monolayers is also different: CBrCl3’s monolayer terminates at approximately 0.7 nm, and the monolayer for water terminates at approximately 0.5 nm. This suggests that the monolayer of CBrCl3 is stabilized in pores of approximately 0.95 nm (taking into account the thickness of the fluid layer and the carbon in the solid surface), whereas the monolayer of water is stabilized in pores of approximately 0.75 nm. As a result, the repulsion provided by the water monolayer is not sufficient to compensate for the strong graphene/graphene attraction, whereas CBrCl3 shows a significant barrier to aggregation due to its relatively strong and long-range repulsion. The large energy barrier observed in the smPMF of CBrCl3 suggests a stable monolayer and reflects a strong tendency of the molecules to move between the sheets and push them apart. However, this tendency is not sufficient to compensate the even stronger graphene/graphene attraction. Although the free energy of the aggregated state is reduced from −80 to −40kT nm−2, it is still strongly negative, and the aggregated state remains thermodynamically stable. Thus, CBrCl3 is not a solvent for graphene in the thermodynamic sense. The analysis of the van der Waals potentials between a carbon atom and the atoms in the fluid molecules considered provides additional insight. From Figure 3, one can easily conclude that the adhesion between water molecules and graphene is much weaker compared to that between CBrCl3

Figure 3. Van der Waals interaction potentials (solid lines) and the associated force curves (dashed lines) for oxygen/carbon (blue), chlorine/carbon (green), and bromine/carbon (red) pairs, to highlight that, to the left of the potential minimum, the force is already repulsive, whereas the potential is still negative. Note that the bromine/carbon potential is 50% deeper compared to the chlorine/carbon potential.

and graphene; not only are the van der Waals interactions for each atom much lower, but CBrCl3 adheres with three atoms, whereas in water only the oxygen atom interacts with the graphene sheets. This is in sharp contrast to the intermolecular interactions which are very strong between water molecules due to the formation of intermolecular hydrogen bonds. However, these stronger water/water interactions seem to be partially compensated by entropic effects. Water and CBrCl3 have very similar critical temperatures, 647 and 610 K, respectively, suggesting that in the bulk they have a very similar entropy/ enthalpy balance. Thus, the key difference between the solvents is the interaction with graphene. Based on this simplified argument, we expect that it is much easier to squeeze out water molecules from between graphene sheets than it is to squeeze out CBrCl3, which is consistent with our observations (Figure 1). The range of the strongly positive region of the smPMF for any solvent is always larger than that of the strongly negative region of the direct graphene/graphene van der Waals interaction; therefore, a barrier forms between the exfoliated and the aggregated state. In the case of CBrCl3, the barrier is very high +40kT nm−2. Thus, assuming that a barrier 40 times the thermal energy is sufficient to prevent reaggregation, CBrCl3 would prevent reaggregation of flakes as small as 1 nm2, whereas the barrier for graphene reaggregation in water is only 1045

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Figure 4. Comparison of the (a) smPMF and the (b) PMF for graphene (solid) and (10,10) carbon nanotubes (dashed) immersed in CBrCl3 to demonstrate that the geometry of the immersed nanomaterial has a large effect on solvent performance.

Figure 5. Comparison of the (a) smPMF and the (b) PMF for graphene (solid) and (10,10) carbon nanotubes (dashed) immersed in water to demonstrate that the geometry of the immersed nanomaterial has a large effect on solvent performance.

a few kT nm−2. This argument would also apply for parallel sheets with a relative horizontal offset as long as the overlap area is at least 1 nm2. Similar considerations for nonparallel sheets are more challenging and require more information about the contribution from edges. However, although the potential for CBrCl3 to be a good graphene dispersant cannot be estimated conclusively, the very high PMF barrier of +40kT nm−2 suggests that it prevents reaggregation for most sheet/sheet alignments. It is interesting to compare the smPMF and the PMF observed for the graphene sheets to the case of carbon nanotubes (Figure 4). The smPMF for graphene and carbon nanotubes in CBrCl3 is significantly different. The strong repulsive barrier observed in the smPMF of graphene is not present in that calculated for carbon nanotubes, where a gradual increase in the smPMF is observed. As a result, a small reaggregation barrier of around +10kT nm−1 is observed in the full PMF of the CNTs (Figure 4b), in agreement with the experimental data that indicate that CBrCl3 is indeed a poor dispersant.24 This is in contrast to the significant barrier of +40kT nm−2 observed in the full graphene PMF suggesting that CBrCl3 is potentially a good dispersant for graphene. Our calculations indicate that this difference arises from the cylindrical geometry of carbon nanotubes, which allows the monolayer of liquid molecules between them to be squeezed out gradually, leading to a slowly increasing smPMF at small d, whereas the process is very rapid for graphene, resulting in the very steep rise of the smPMF at d = 0.85 nm. In the case of water, most of the differences between the smPMF calculated between the nanotubes and that between the graphene sheets are masked by the graphene−graphene attractive contribution due to the small thickness of the adsorbed layer (see Figure 5),

resulting in the water not being a good solvent nor dispersant for both geometries. It is interesting to note that the smPMF for water on CNTs shows a barrier slightly larger than that in graphene, which may relate to the ability of water to form a three-dimensional hydrogen bond network around the nanotube, which is not observed in the case of graphene.36

CONCLUSIONS We have used MD simulations combined with the corresponding distances method (CDM) to identify design rules for efficient dispersants (or solvents) for two carbon-based solutes: graphene and carbon nanotubes. By studying the thermodynamics of aggregation of two graphene sheets and the solvent structure close to their surfaces in two different solvents, CBrCl3 and water, we show that the ability of a liquid to act as good dispersant is determined mainly by the stability of the monolayer formed between the surfaces of the approaching solute molecules. We show, therefore, that the different geometry of graphene compared to that of carbon nanotubes can change the potency of a molecule as nanoparticle solvent or dispersant. As water is a relatively small molecule with very strong intermolecular interactions and comparatively weak adhesion to graphene, it is neither a solvent nor a dispersant for graphene, consistent with our expectations. However, our results suggest that CBrCl3 should be a good dispersant for graphene but not for CNTs, for which the reaggregation barrier is only +10kT nm−1 compared with +40kT nm−2 calculated for the graphene sheets. Investigation of the structure/function relationship leads us to conclude that good dispersant quality is a less demanding requirement on a liquid in the case of graphene compared to CNTs. In other words, it should be much easier to find good dispersants for graphene than for CNTs. 1046

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carbon nanotubes.57,58 In this case, the cross-species parameters were obtained using the Lorentz−Berthelot combining rules. Finally, for a consistent comparison between the PMF profiles obtained for graphene and CNTs, we also performed free-energy calculations for two CNT(10,10) in water using the GROMOS 53a6 force field to model the CNT. The computational details for these simulations can be found in ref 26. The details of the simulations as well as the validation of the CDM method against the standard parallel molecular dynamics simulations are reported in the Supporting Information.

Our analysis of the causal chain between structure and function allows us to draw some general conclusions for solvent design. It is plausible that the adsorption free energy, via the stability of the confined monolayer, controls the strength of the repulsive region in the smPMF, whereas the size of the molecules controls its range. Thus, good dispersants are relatively large molecules that adhere well and therefore generate a high reaggregation barrier at distances larger than the range of interaction between two graphene sheets. Good solvents must adhere very strongly to compensate the very strong sheet/sheet cohesion but should be as small as possible to not create a too high exfoliation barrier. These simple “design rules” facilitate a more rational solvent design for graphene.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b05159. Methodology used, simulation parameters and the validation of the CDM for graphene (PDF)

METHODS In this work, we perform free-energy calculations for graphene sheets in two solvents: water and trichlorobromomethane. These solvents were selected as extreme cases. Water is not expected to be a good solvent for either material based on its solubility parameters, whereas CBrCl3 could be expected to be a good solvent based on its solubility parameters, even when it is known not to be a good solvent for CNTs.23,24 The resulting PMF profiles are then compared with those obtained for CNTs in the same solvents.25 All the free-energy calculations were performed using the CDM.25,37 The concept is based on sampling all possible distances between the graphene sheets, d, in the same simulation, by creating a fixed configuration in which the two nanomaterials intersect at some predefined acute angle. The relevant distances, d, are then scanned by traversing along one of the nanomaterials away from the point of intersection to the end of the material. The full PMF is calculated in the conventional manner by evaluating the ensemble average of the force for narrow sections of the sheet. For more information on the method, we refer the reader to the original papers,25,37 where the method was developed for one-dimensional molecules (e.g., CNTs). Here, we show that the methodology can also be successfully extended to 2D solute molecules, allowing the free-energy profiles to be obtained in a computationally efficient way. The molecular dynamics simulations were performed using the GROMACS 5.1 simulation package38−44 in double precision for all aspects of this study. CBrCl3 was modeled using the GROMOS 53a645 force field and parametrized with the aid of the automated topology builder.46−48 The GROMOS 53a6 force field is parametrized to match solvation free energies of amino acids (in water and cyclohexane) and to reproduce the properties (density and heat of vaporization) of a range of solvent molecules. These two criteria are related to the problem being studied in this paper, and thus we consider it is a suitable choice. All cross-species Lennard-Jones length and strength parameters were obtained using the geometric mean of the respective purecomponent parameters in the GROMOS 53a6 force field. The water model was SPC/E constrained using SHAKE/SETTLE.49 Graphene sheets were approximated as rigid and are “frozen” in the simulations; that is, the graphene carbon atoms do not interact with each other; all other forces and energies were calculated as normal, but the positions of the graphene atoms were not updated. This allowed us to obtain the solvent-mediated part of the mean force directly from the simulations. The graphene/graphene potential was calculated separately in a singlestep vacuum MD simulation. We also employed the Lennard-Jones parameters from the Steele potential50−52 to represent the carbon atoms of graphene. The carbon parameters of the Steele potential σC = 0.34 nm and ϵC = 0.2328 kJ mol−1 were originally obtained by fitting the interaction energy between the graphene sheets in graphite to its compressibility perpendicular to the graphene plane.50,53,54 The combination of Steele carbon and SPC/E water has been extensively used to study, for example, the wettability of graphene,55 adsorption isotherms,52,56 and the properties of water confined in narrow graphene channels and

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Adam Hardy: 0000-0003-4362-9143 Christopher D. Williams: 0000-0002-5073-5924 Flor R. Siperstein: 0000-0003-3464-2100 Paola Carbone: 0000-0001-9927-8376 Henry Bock: 0000-0002-6778-7464 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk). This work was supported by the North-West Nanoscience Doctoral Training Centre, EPSRC Grants EP/G03737X/1 and EP/K016946/1 (graphene-based membranes). REFERENCES (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666−669. (2) Torrisi, F.; Hasan, T.; Wu, W.; Sun, Z.; Lombardo, A.; Kulmala, T. S.; Hsieh, G.-W.; Jung, S.; Bonaccorso, F.; Paul, P. J.; Chu, D.; Ferrari, A. C. Inkjet-Printed Graphene Electronics. ACS Nano 2012, 6, 2992−3006. (3) Pumera, M. Electrochemistry of Graphene: New Horizons for Sensing and Energy Storage. Chem. Rec. 2009, 9, 211−223. (4) Williams, C. D.; Dix, J.; Troisi, A.; Carbone, P. Effective Polarization in Pairwise Potentials at the Graphene-Electrolyte Interface. J. Phys. Chem. Lett. 2017, 8, 703−708. (5) Abraham, J.; Vasu, K. S.; Williams, C. D.; Gopinadhan, K.; Su, Y.; Cherian, C. T.; Dix, J.; Prestat, E.; Haigh, S. J.; Grigorieva, I. V.; Carbone, P.; Geim, A. K.; Nair, R. R. Tunable Sieving of Ions Using Graphene Oxide Membranes. Nat. Nanotechnol. 2017, 12, 546−550. (6) Gonciaruk, A.; Althumayri, K.; Harrison, W. J.; Budd, P. M.; Siperstein, F. R. PIM-1/Graphene Composite: A Combined Experimental and Molecular Simulation Study. Microporous Mesoporous Mater. 2015, 209, 126−134. (7) Shin, Y.; Prestat, E.; Zhou, K.-G.; Gorgojo, P.; Althumayri, K.; Harrison, W.; Budd, P. M.; Haigh, S. J.; Casiraghi, C. Synthesis and Characterization of Composite Membranes Made of Graphene and Polymers of Intrinsic Microporosity. Carbon 2016, 102, 357−366. (8) Paton, K. R.; Varrla, E.; Backes, C.; Smith, R. J.; Khan, U.; O’Neill, A.; Boland, C.; Lotya, M.; Istrate, O. M.; King, P.; Higgins, T.; 1047

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