Design Rules for Graphene and Carbon Nanotube Solvents and

Subscriber access provided by READING UNIV

Article

Design Rules for Graphene and Carbon-Nanotube Solvents and Dispersants Adam Hardy, James Dix, Christopher David Williams, Flor R. Siperstein, Paola Carbone, and Henry Bock ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b05159 • Publication Date (Web): 23 Jan 2018 Downloaded from http://pubs.acs.org on January 29, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Nano is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

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, UK ‡School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, M13 9PL, UK E-mail: [email protected] 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 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 Graphene, 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 1

ACS Paragon Plus Environment

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 sulphuric acid or potassium permanganate. 12 However, this method introduces a large number of oxygen-containing functionalities that can not 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 (VDW) forces between individual sheets have been overcome, the separated graphene sheets must be stabilized against re-aggregation. 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 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’

2


Page 2 of 22

Page 3 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

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 dimension carbon-based materials e.g. carbon nanotubes (CNT). As manufactured, carbon nanotubes are in an aggregated (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 physical spacer between the CNTs and preventing in this way them to bundle. 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 liquid phase processing for this materials. As for graphene, there has been a large effort to identify the best solvents for CNT and several, time-consuming, 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 (cyclohexyl-pyrrolidinone), 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 that can disperse reasonably well CNTs, do not show the same efficacy for graphene exfoliation, for which N-methyl-

3


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

pyrrolidone (NMP) and dimethylformamide (DMF) 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 isopropanol, 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, solubilisation 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 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 solvents 33,34 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 CNT and investigate if and how the solely solute geometry affects their performance. This work will aid the development of design rules for graphene and CNT solvents and dispersant and will

4


Page 4 of 22

Page 5 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

impact the many applications that rely on the success of liquid-phase exfoliation processes.

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

Z w(d) = −

∞

F (d)dd

(1)

d

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 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 CBrCl3 and H2 O 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 . 0.9nm where the smPMF is large and positive (Figure 1(a)). The 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. This repulsive region is also present in the full PMF for distances larger than approximately 0.5nm. Although a similar barrier is observed in the smPMF for H2 O, it is significantly smaller and the attraction between graphene sheets dominate the full PMF curve (Figure 1(b)). 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 or a dispersant. 5


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: The solvent mediated PMF (blue), the direct graphene/graphene interaction potential (red) and the sum of the two, i.e. the full PMF (green) for (a) CBrCl3 and (b) H2 O. 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 was obtained using the GROMOS force field. Data obtained using the Steele potential is qualitatively very similar and is shown in the Supporting information. 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 result 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 1nm. The thickness of the mono-layers is also different: CBrCl3 ’s monolayer terminates at approximately 0.7nm and the monolayer for water terminates at approximately 0.5nm. This suggests that the monolayer of CBrCl3 is stabilized in pores of approximately 0.95nm (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 0.75nm. As a result, the repulsion that provides the water monolayer is not sufficient to compensate for the strong graphene-graphene attraction, whereas CBrCl3 shows a significant barrier to aggregation. The large energy barrier observed in the smPMF of CBrCl3 suggests a stable mono-

6


Page 6 of 22

Page 7 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Figure 2: Atom density profiles of (a) CBrCl3 and (b) H2 O on a single graphene sheet. The surface layer for CBrCl3 is quite thick, terminating 0.7nm away from the sheet, whereas the surface layer for H2 O terminates at 0.5nm. layer and reflects a strong tendency of the molecules to move in 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 −80kT nm−2 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 CBrCl3 and graphene, not only are the van der Waals interactions for each atom much lower, CBrCl3 adheres with three atoms, whereas in the 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, 647K and 610K, 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

7


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3: The 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. 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 , although the barrier for graphene reaggregation in water is only 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 1nm2 . Similar considerations for non-parallel 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 can not 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 8


Page 8 of 22

Page 9 of 22

of graphene is not present in that calculated between 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 CNT (Figure 4b) in agreement with the experimental data that indicate that CBrCl3 is indeed a poor dispersant. 24 The significant barrier of +40kT nm2 observed in the full graphene PMF suggests that CBrCl3 is potentially a good dispersant for graphene. 50

CNT Graphene

40 30

w(d)CNT / kT nm-1 (300K) w(d)graphene / kT nm-2 (300K)

smw(d)CNT / kT nm-1 (300K) smw(d)graphene / kT nm-2 (300K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

20 10 0 -10 -20 -30 -40

0

0.2

0.4

0.6

0.8

1

1.2

50 30 20 10 0 -10 -20 -30 -40

1.4

CNT Graphene

40

0

0.2

0.4

d / nm

0.6

0.8

1

1.2

1.4

d / nm

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. 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 = 0.85nm. In the case of water, most of the differences between the 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 CNT shows a slightly larger barrier than in graphene, which may relate to the ability of water to form a 3-dimensional hydrogen bond network around the nanotube, which is not observed in the case of graphene. 36

9


10

w(d)CNT / kT nm-1 (300K) w(d)graphene / kT nm-2 (300K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

smw(d)CNT / kT nm-1 (300K) smw(d)graphene / kT nm-2 (300K)

ACS Nano

0 -10 -20 -30 -40 -50 -60

CNT Graphene

-70 -80

0

0.2

0.4

0.6

0.8

1

1.2

Page 10 of 22

10 0 -10 -20 -30 -40 -50 -60 -80

1.4

CNT Graphene

-70 0

0.2

d / nm

0.4

0.6

0.8

1

1.2

1.4

d / nm

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.

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 (CNT). By studying the thermodynamics of aggregation of two graphene sheets and the solvent structure close to their surfaces in two different solvents, trichlorobromomethane (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 that therefore the different geometry of graphene compared to 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 of +10kT nm−1 compared with +40kT nm−1 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.

10


Page 11 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

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.

Methods In this work we perform free energy calculations for graphene sheets in two solvents: water and trichlorobromomethane (CBrCl3 ). These solvents were selected as extreme cases. Water is not expected to be a good solvent for either material based on its solubility parameters, while 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 Corresponding Distances Method (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 pre-defined 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 manuscripts 25,37 where the method was developed for 1 dimensional molecules (e.g. CNT). Here we show that the methodology can also be

11


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

successfully extended to 2D solute molecules allowing to obtain in a computationally efficient way the free energy profiles. The molecular dynamics simulations were performed using the GROMACS 5.1 simulation package 38–44 in double precision for all aspects of this study. CBrCl3 was modeled using the GROMOS 53a6 45 forcefield and parameterized with the aid of the Automated Topology Builder. 46–48 The GROMOS 53a6 forcefield is parameterized 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 pure-component parameters in the GROMOS 53a6 forcefield. The water model was SPC/E constrained using SHAKE/SETTLE. 49 Graphene sheets were approximated as rigid and are ’frozen’ in the simulations, i.e. 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 single-step vacuum MD simulation. We also employed the Lennard-Jones parameters from the Steele potential 50–52 to represent the carbon atoms of graphene. The carbon parameters of the Steele potential σC = 0.34nm and C = 0.2328kJ 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 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

12


Page 12 of 22

Page 13 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

CNTs, we also performed free energy calculations for two CNT(10,10) in water using the GROMOS 53a6 forcefield to model the CNT. The computational details for these simulations can be found in. 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.

Acknowledgement 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 grant EP/G03737X/1 and EP/K016946/1 (Graphene-based membranes).

Supporting Information Available Supporting Information contains details of the methodology used, simulation parameters and the validation of the CDM for graphene. This material is available free of charge via the Internet at http://pubs.acs.org/.

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.

13


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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, PMID: 28121448. 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. PIM1/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.; Barwich, S.; May, P.; Puczkarski, P.; Ahmed, I.; Moebius, M.; Pettersson, H.; Long, E.; Coelho, J.; O’Brien, S. E. et al. Scalable Production of Large Quantities of Defect-Free Few-Layer Graphene by Shear Exfoliation in Liquids. Nat. Mater. 2014, 13, 624–630. 9. Novoselov, K. S.; Fal0 ko, V. I.; Colombo, L.; Gellert, P. R.; Schwab, M. G.; Kim, K. A Roadmap for Graphene. Nature 2012, 490, 192–200. 10. Stankovich, S.; Piner, R. D.; Nguyen, S. T.; Ruoff, R. S. Synthesis and Exfoliation of Isocyanate-Treated Graphene Oxide Nanoplatelets. Carbon 2006, 44, 3342–3347. 14


Page 14 of 22

Page 15 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

11. Hernandez, Y.; Nicolosi, V.; Lotya, M.; Blighe, F. M.; Sun, Z.; De, S.; Mcgovern, I. T.; Holland, B.; Byrne, M.; Gun’ko, Y. K.; Boland, J. J.; Niraj, P.; Duesberg, G.; Krishnamurthy, S.; Goodhue, R.; Hutchison, J.; Scardaci, V.; Ferrari, A. C.; Coleman, J. N. High-Yield Production of Graphene by Liquid-Phase Exfoliation of Graphite. Nat. Nanotechnol. 2008, 3, 563–8. 12. Nicolosi, V.; Chhowalla, M.; Kanatzidis, M. G.; Strano, M. S.; Coleman, J. N. Liquid Exfoliation of Layered Materials. Science 2013, 340, 1226419–1226419. 13. Seo, J.-W. T.; Green, A. A.; Antaris, A. L.; Hersam, M. C. High-Concentration Aqueous Dispersions of Graphene Using Nonionic, Biocompatible Block Copolymers. J. Phys. Chem. Lett. 2011, 2, 1004–1008. 14. Schlierf, A.; Yang, H.; Gebremedhn, E.; Treossi, E.; Ortolani, L.; Chen, L.; Minoia, A.; Morandi, V.; Samorì, P.; Casiraghi, C.; Beljonne, D.; Palermo, V. Nanoscale Insight into the Exfoliation Mechanism of Graphene with Organic Dyes: Effect of Charge, Dipole and Molecular Structure. Nanoscale 2013, 5, 4205. 15. Coleman, J. N. Liquid Exfoliation of Defect-Free Graphene. Acc. Chem. Res. 2013, 46, 14–22. 16. Girifalco, L. A.; Hodak, M.; Lee, R. S. Carbon Nanotubes, Buckyballs, Ropes, and a Universal Graphitic Potential. Phys. Rev. B 2000, 62, 13104–13110. 17. Moore, V. C.; Strano, M. S.; Haroz, E. H.; Hauge, R. H.; Smalley, R. E.; Schmidt, J.; Talmon, Y. Individually Suspended Single-Walled Carbon Nanotubes in Various Surfactants. Nano Lett. 2003, 3, 1379–1382. 18. Clark, M. D.; Subramanian, S.; Krishnamoorti, R. Understanding Surfactant Aided Aqueous Dispersion of Multi-Walled Carbon Nanotubes. J. Colloid Interface Sci. 2011, 354, 144–151.

15


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

19. Islam, M. F.; Rojas, E.; Bergey, D. M.; Johnson, A. T.; Yodh, A. G. High Weight Fraction Surfactant Solubilization of Single-Wall Carbon Nanotubes in Water. Nano Lett. 2003, 3, 269–273. 20. Chen, Q.; Saltiel, C.; Manickavasagam, S.; Schadler, L. S.; Siegel, R. W.; Yang, H. Aggregation Behavior of Single-Walled Carbon Nanotubes in Dilute Aqueous Suspension. J. Colloid Interface Sci. 2004, 280, 91–97. 21. Angelikopoulos, P.; Bock, H. The Science of Dispersing Carbon Nanotubes with Surfactants. Phys. Chem. Chem. Phys. 2012, 14, 9546. 22. Xu, Z.; Yang, X.; Yang, Z. A Molecular Simulation Probing of Structure and Interaction for Supramolecular Sodium Dodecyl Sulfate/Single-Wall Carbon Nanotube Assemblies. Nano Lett. 2010, 10, 985–991. 23. Detriche, S.; Zorzini, G.; Colomer, J. F.; Fonseca, A.; Nagy, J. B. Application of the Hansen Solubility Parameters Theory to Carbon Nanotubes. J. Nanosci. Nanotechnol. 2008, 8, 6082–6092. 24. Bergin, S. D.; Sun, Z.; Rickard, D.; Streich, P. V.; Hamilton, J. P.; Coleman, J. N. Multicomponent Solubility Parameters for Single-Walled Carbon Nanotube-Solvent Mixtures. ACS Nano 2009, 3, 2340–2350. 25. Hardy, A.; Bock, H. Assessing the Quality of Solvents and Dispersants for LowDimensional Materials Using the Corresponding Distances Method. J. Phys. Chem. B 2016, 120, 11607–11617. 26. Hardy, A.; Bock, H. Toward High-Throughput Computational Screening of Carbon Nanotube Solvents. Langmuir 2017, 33, 12267–12275. 27. Cheng, Q.; Debnath, S.; O’Neill, L.; Hedderman, T. G.; Gregan, E.; Byrne, H. J. Sys-

16


Page 16 of 22

Page 17 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

tematic Study of the Dispersion of SWNTs in Organic Solvents. J. Phys. Chem. C 2010, 114, 4857–4863. 28. Bergin, S. D.; Nicolosi, V.; Streich, P. V.; Giordani, S.; Sun, Z.; Windle, A. H.; Ryan, P.; Niraj, N. P. P.; Wang, Z.-T. T.; Carpenter, L.; Blau, W. J.; Boland, J. J.; Hamilton, J. P.; Coleman, J. N. Towards Solutions of Single-Walled Carbon Nanotubes in Common Solvents. Adv. Mater. 2008, 20, 1876–1881. 29. Ausman, K. D.; Piner, R.; Lourie, O.; Ruoff, R. S.; Korobov, M. Organic Solvent Dispersions of Single-Walled Carbon Nanotubes: Toward Solutions of Pristine Nanotubes. J. Phys. Chem. B 2000, 104, 8911–8915. 30. Furtado, C. A.; Kim, U. J.; Gutierrez, H. R.; Pan, L.; Dickey, E. C.; Eklund, P. C. Debundling and Dissolution of Single-Walled Carbon Nanotubes in Amide Solvents. J. Am. Chem. Soc. 2004, 126, 6095–6105. 31. Kim, D. H.; Yun, Y. S.; Jin, H.-J. Difference of Dispersion Behavior Between Graphene Oxide and Oxidized Carbon Nanotubes in Polar Organic Solvents. Curr. Appl. Phys. 2012, 12, 637 – 642. 32. Roux, B. The Calculation of the Potential of Mean Force Using Computer Simulations. Comput. Phys. Commun. 1995, 91, 275–282. 33. Shih, C.-J.; Lin, S.; Strano, M. S.; Blankschtein, D. Understanding the Stabilization of Liquid-Phase-Exfoliated Graphene in Polar Solvents: Molecular Dynamics Simulations and Kinetic Theory of Colloid Aggregation. J. Am. Chem. Soc. 2010, 132, 14638–14648. 34. Raghav, N.; Chakraborty, S.; Maiti, P. K. Molecular Mechanism of Water Permeation in a Helium Impermeable Graphene and Graphene Oxide Membrane. Phys. Chem. Chem. Phys. 2015, 17, 20557–20562.

17


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

35. Chaban, V. V.; Fileti, E. E. Graphene Exfoliation in Ionic Liquids: Unified Methodology. RSC Adv. 2015, 5, 81229–81234. 36. Li, L.; Bedrov, D.; Smith, G. D. Water-Induced Interactions between Carbon Nanoparticles. J. Phys. Chem. B 2006, 110, 10509–10513, PMID: 16722760. 37. Müter, D.; Bock, H. Interactions between Nanofibers in Fiber-Surfactant Suspensions: Theory of Corresponding Distances. Phys. Rev. Lett. 2014, 112, 128301. 38. Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, and Free. J. Comput. Chem. 2005, 26, 1701–1718. 39. Pronk, S.; Páll, S.; Schulz, R.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; van der Spoel, D.; Hess, B.; Lindahl, E. GROMACS 4.5: A High-Throughput and Highly Parallel Open Source Molecular Simulation Toolkit. Bioinformatics 2013, 29, 845–854. 40. Abraham, M.; van der Spoel, D.; Lindahl, E.; Hess, B.; The GROMACS Development Team, GROMACS User Manual Version 5.1.1 ; www.gromacs.org, 2015. 41. Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447. 42. Páll, S.; Abraham, M. J.; Kutzner, C.; Hess, B.; Lindahl, E. In Solving Software Challenges for Exascale; Markidis, S., Laure, E., Eds.; Lecture Notes in Computer Science 8759; Springer International Publishing, 2014; pp 3–27. 43. Erik Lindahl,; Berk Hess,; van der Spoel, D. GROMACS 3.0: A Package for Molecular Simulation and Trajectory Analysis. J Mol Model 2001, 306–317. 44. Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. GROMACS: A Message-Passing

18


Page 18 of 22

Page 19 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Parallel Molecular Dynamics Implementation. Comput. Phys. Commun. 1995, 91, 43– 56. 45. Oostenbrink, C.; Villa, A.; Mark, A. E.; Van Gunsteren, W. F. A Biomolecular Force Field Based on the Free Enthalpy of Hydration and Solvation: The GROMOS ForceField Parameter Sets 53A5 and 53A6. J. Comput. Chem. 2004, 25, 1656–1676. 46. Malde, A. K.; Zuo, L.; Breeze, M.; Stroet, M.; Poger, D.; Nair, P. C.; Oostenbrink, C.; Mark, A. E. An Automated Force Field Topology Builder (ATB) and Repository: Version 1.0. J. Chem. Theory Comput. 2011, 7, 4026–4037. 47. Canzar, S.; El-Kebir, M.; Pool, R.; Elbassioni, K.; Malde, A. K.; Mark, A. E.; Geerke, D. P.; Stougie, L.; Klau, G. W. Charge Group Partitioning in Biomolecular Simulation. J. Comput. Biol. 2013, 20, 188–198. 48. Koziara, K. B.; Stroet, M.; Malde, A. K.; Mark, A. E. Testing and Validation of the Automated Topology Builder (ATB) Version 2.0: Prediction of Hydration Free Enthalpies. J. Comput. Aided Mol. Des. 2014, 28, 221–233. 49. Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269–6271. 50. Steele, W. A. The Interaction of Gases With Solid Surfaces, 1st ed.; The International Encyclopedia of Physical Chemistry and Chemical Physics. Topic 14: Properties of Interfaces v. 3; Pergamon Press: Oxford, New York, 1974. 51. Cheng, A.; Steele, W. A. Computer Simulation of Ammonia on Graphite. I. Low Temperature Structure of Monolayer and Bilayer Films. J. Chem. Phys. 1990, 92, 3858–3866. 52. Striolo, A.; Chialvo, A. A.; Cummings, P. T.; Gubbins, K. E. Water Adsorption in Carbon-Slit Nanopores. Langmuir 2003, 19, 8583–8591.

19


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

53. Crowell, A. D. Potential Energy Functions for Graphite. Journal of Chem. Phys. 1958, 29, 446–447. 54. Steele, W. A. The Interaction of Gases with Solid Surfaces, repr. [der ausg.] oxford 1974 ed.; Franklin Book Company: Elkins Park, PA, 1992; OCLC: 830954533. 55. Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. On the WaterCarbon Interaction for Use in Molecular Dynamics Simulations of Graphite and Carbon Nanotubes. J. Phys. Chem. B 2003, 112, 14090–14090. 56. Ulberg, D. E.; Gubbins, K. E. Water Adsorption in Microporous Graphitic Carbons. Mol. Phys. 1995, 84, 1139–1153. 57. Liu, J.-C.; Monson, P. A. Does Water Condense in Carbon Pores? Langmuir 2005, 21, 10219–10225. 58. Gordillo, M.; Martı´, J. Hydrogen Bonding in Supercritical Water Confined in Carbon Nanotubes. Chem. Phys. Lett. 2001, 341, 250–254.

20


Page 20 of 22

Page 21 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Graphical TOC Entry

21


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40x17mm (300 x 300 DPI)


Page 22 of 22

Design Rules for Graphene and Carbon Nanotube Solvents and

Recommend Documents