Thermodynamics of Adsorption on Graphenic Surfaces from Aqueous

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Condensed Matter, Interfaces, and Materials

Thermodynamics of Adsorption on Graphenic Surfaces from Aqueous Solution Ettayapuram Ramaprasad Azhagiya Singam, Yuntao Zhang, Géraldine Magnin, Ingrid Miranda-Carvajal, Logan Coates, Ravindra Thakkar, Horacio Poblete, and Jeffrey Comer J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00830 • Publication Date (Web): 28 Dec 2018 Downloaded from http://pubs.acs.org on January 2, 2019

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Journal of Chemical Theory and Computation

Thermodynamics of Adsorption on Graphenic Surfaces from Aqueous Solution E. R. Azhagiya Singam,† Yuntao Zhang,† Geraldine Magnin,† Ingrid Miranda-Carvajal,‡ Logan Coates,† Ravindra Thakkar,† Horacio Poblete,¶ and Jeffrey Comer∗,† †Institute of Computational Comparative Medicine, Nanotechnology Innovation Center of Kansas State, Department of Anatomy and Physiology, Kansas State University, Manhattan, Kansas, 66506-5802 ‡Universidad Nacional de Colombia, sede Bogotá, Facultad de Ciencias, Departamento de Qu´ımica, Carrera 30 No. 45-03, Bogotá, 111321, Colombia ¶Center for Bioinformatics and Molecular Simulation, Facultad de Ingenier´ıa, Nucleo Cient´ıfico Multidiciplinario-DI, Millennium Nucleus of Ion Channel-Associated Diseases (MiNICAD), Universidad de Talca, 3460000 Talca, Chile E-mail: [email protected] Abstract Adsorption of organic molecules from aqueous solution to the surface of carbon nanotubes or graphene is an important process in many applications of these materials. Here we use molecular dynamics simulation, supplemented by analytical chemistry, to explore in detail the adsorption thermodynamics of a diverse set of aromatic compounds on graphenic materials, elucidating the effects of the solvent, surface coverage, surface curvature, defects, and functionalization by hydroxy groups. We decompose the adsorption free energies into entropic and enthalpic components and find that different

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classes of compounds—such as phenols, benzoates, and alkylbenzenes—can easily be distinguished by the relative contributions of entropy and enthalpy to their adsorption free energies. Overall, entropy dominates for the more hydrophobic compounds, while enthalpy plays the greatest role for more hydrophilic compounds. Experiments and independent simulations using two different force field frameworks (CHARMM and Amber) support the robustness of these conclusions. We determine that concave curvature is generally associated with greater adsorption affinity, more favorable enthalpy, and greater contact area, while convex curvature reduces both adsorption enthalpy and contact area. Defects on the graphene surfaces can create concave curvature, resulting in localized binding sites. As the graphene surface becomes covered with aromatic solutes, the affinity for adsorbing an additional solute increases until a complete monolayer is formed, driven by more favorable enthalpy and partially canceled by less favorable entropy. Similarly, hydroxylation of the surface leads to preferential adsorption of the aromatic solutes to remaining regions of bare graphene, resulting in less favorable adsorption entropy, but compensated by an increase in favorable enthalpic interactions.

KEYWORDS: graphene, carbon nanotubes, molecular dynamics simulation, thermodynamic decomposition, graphitic materials, free-energy calculations, benzene derivatives, adsorption entropy, graphene defects, hydroxygraphene

Introduction Carbon nanotubes, graphene, and their derivatives, find growing use in research, industry, medicine, and commercial products. 1–8 Hence, there is an increasing need to study the behavior of these nanomaterials in living systems and the environment. On contact with biological fluids, a corona of organic molecules adsorbs to the surface of many types of nanomaterials, strongly influencing their biological activity 9–12 and affecting their toxicity and immunogenicity. 13–19 Graphenic nanomaterials, especially, exhibit high affinity for organic 2


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solutes; therefore, the thermodynamics of adsorption from aqueous solution to graphenic nanomaterial surfaces is crucial for understanding their biological impact. Despite the chemical and structural simplicity of the graphenic materials relative to many other materials, adsorption at the graphene–water interface is quite complex. 20,21 At first sight, it might be assumed that hydrophobic collapse would be the dominant effect driving adsorption; however, while the hydrophobic effect is indeed important, graphene’s reputation as a hydrophobic material may be exaggerated due to its tendency for hydrocarbon contamination. 22 The somewhat amphiphilic nature of graphene might be surmised from the fact that the octanol–water partition coefficient of benzene (log POW = 2.13) is considerable lower than that for its saturated analog, cyclohexane (log POW = 3.44). 23 Consistent with this characterization, the correlation between the octanol–water partition coefficient and the adsorption affinity of a set of small molecules at the graphene–water interface is poor (r = 0.53). 24 This lack of correlation can in many instances be attributed to the fact that graphenic surfaces interact strongly with certain polar moieties, including nucleobases 25 and nitro, 24,26 amide, 27–29 and ionized guanidinium groups. 30 Indeed, molecular simulations suggest that the most hydrophobic amino acids 31 (leucine, isoleucine, and valine) have some of the weakest affinities for graphene, 30 while the charged amino acid arginine, along with mildly hydrophobic aromatic amino acids (tyrosine, tryptophan) exhibit the strongest graphene binding. Experimental determination of adsorption affinities are essential in understanding how different interactions give rise to adsorption on graphenic surfaces from aqueous solution. 26,27,32–40 However, molecular simulation can give insight into atomic scale interactions between surfaces and solutes that are difficult to access experimentally and can serve as an efficient tool for the design of functional nanomaterials. Explicit-solvent molecular dynamics simulations have been used to investigate the interaction of graphene, graphite, and carbon nanotubes with peptides and proteins, 29,30,41–49 nucleic acids, 25,50–53 lipids, 54–56 polysaccharides, 57,58 and other organic molecules. 24,59–63 Molecular dynamics has also been applied to studying adsorp-

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tion on chemically modified graphenic materials, including graphene oxide, 64,65 hydroxylated carbon nanotubes, 24,29 and graphene surfaces conjugated with organic polymers. 24 We have previously shown that molecular dynamics simulation, coupled with a commonly used force field and a simple model of graphene, can predict the affinities of adsorption of small aromatic molecules on with high correlation (r ≥ 0.90) to experiment. 24 The exquisite detail provided by molecular dynamics allows binding thermodynamics to be broken down into an array of different entropic and enthalpic contributions, yielding insight into the competition among different physicochemical effects that underlies binding. 66 The goal of the present article is to examine in detail the thermodynamics of adsorption to graphenic surfaces. We decompose the adsorption free energy into its entropic and enthalpic components and observe how these components are related to the physicochemistry of the 31 small aromatic molecules considered in this work, listed Table S1 of the SI. For two representative solutes, we break down the enthalpy and entropy into contributions from different subsystems to pinpoint which interactions are most important for adsorption to graphenic materials from aqueous solution. To better understand what phenomena may be artifacts of the parameters used to describe the interatomic interactions, we compare simulations using the General Amber Force Field (GAFF) 67 to those using the CHARMM General Force Field (CGenFF). 68 We then explore how the properties of the solution and graphenic material influence adsorption thermodynamics, including effects of solvation, surface coverage, surface curvature, defects, and hydroxylation. The balance among solute–graphene, solute–solvent, and graphene–solvent interactions determines adsorption thermodynamics; therefore, we consider the effect changing the solution composition by the addition of different concentrations of salt. Solute–solute interactions can also be important for many applications, because the affinity of aromatic solutes for graphene is sufficiently high that coverage of the surface can become considerable, even when the concentration of the solute in bulk solution is relatively low. For this reason, we determine how the adsorption thermodynamics of toluene changes as its coverage of the

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surface increases. While graphene and carbon nanotubes have similar physicochemical properties, the curvature of nanotube surfaces can influence adsorption thermodynamics. 61 Moreover, real graphene and nanotube structures exhibit defects, 69 resulting in altered physicochemical properties and undulations that also may affect adsorption of solutes. We therefore calculate adsorption free energies and entropies for two solutes on surfaces of varying curvature and on a surface including defects. Finally, oxygen-containing derivatives of graphene and carbon nanotubes are more watersoluble and more easily wet 70 than their parent materials and, therefore, have found use in biological and environmental applications where a hydrophilic surface is desirable. 3,39,71–74 Graphene oxide and its partially reduced derivatives (reduced graphene oxide) have been intensely studied and are non-stoichiometric materials consisting of a defect-rich graphene substrate 75,76 decorated by a variety of oxygen functionalities—most commonly hydroxy, epoxide, and carbonyl groups. 77–79 Furthermore, hydroxylated carbon nanotubes 80 and graphene, where hydroxy groups are the dominant functionality, have been commercially available for some time and nearly stoichiometric materials (“hydroxygraphene” or “graphol”) can be synthesized. 81,82 Hence, owing to the importance of hydroxylated derivatives, we also investigate the thermodynamics of solute adsorption on a graphene surface decorated with hydroxy groups.

Methods Adsorption Experiments. The equilibrium constants for adsorption of eight compounds (toluene, benzyl alcohol, propylbenzene, phenyl acetate, 4-ethylphenol, methyl benzoate, 4nitrotoluene, and biphenyl) were determined using solid phase microextraction (SPME) and gas chromatography with mass spectrometry (GC/MS) as previously described. 34 Briefly, the compounds were purchased from Fisher Scientific (Waltham, Massachusetts, USA), and

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Z

Figure 1: Rendering of a typical simulation system, consisting of two layers of graphene (gray) and an aromatic solute (green). Although represented explicitly in the simulation, water is shown here as a translucent surface. The definition of the transition coordinate used in the free-energy calculations (Z), the distance between the center of mass of the solute and the central plane through the upper sheet of graphene, is shown. The graphene sheets have effectively infinite lateral extent, owing to the periodic boundary conditions.

multiwall carbon nanotubes were obtained from Cheap Tubes (Cambridgeport, Vermont, USA). The morphology of the nanotubes was verified by transmission electron microscopy, which showed long multiwall nanotubes with diameters 8–20 nm (see Fig. S1 of the SI). To allow calculation of the enthalpy, we performed the experiments at two different temperatures: in a cold room at 4 ◦ C and in an incubator set to 45 ◦ C. Each measurement was performed in tripicate. Experimental uncertainties in Fig. 4 propagated were from the standard deviation of the replicated results. A quantity of nanotubes (2.00 mg) was added to 200 µL of deionized water in a 2 mL vial and the mixture was sonicated at room temperature for 5 minutes. We then added 1.00 mL of a working solution containing deionized water and concentrations of the probe compounds given by Chen et al. 37 These concentrations were sufficiently small that the equilibrium constant was similar to its dilute limit. 24 The vials were agitated in a rotary shaker for 5 hours at the appropriate temperature and then quickly transferred to the sample holder for SPME-GC/MS analysis.

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Solute Parameterization. Table S1 lists the solutes in order of their experimentally determined octanol-water partition coefficients. In the simulations using the CHARMM framework to describe interatomic interactions, the solutes were parameterized in accordance with CGenFF 68 version 3.0.1. Many of the compounds have standard parameterizations within this force field. The remaining compounds were parameterized consistently with the same force field using the ParamChem web interface. 83,84 For the Amber force field simulations, the solutes were parameterized in accordance with GAFF 67 by the Antechamber module 85 of Amber14.

Molecular Dynamics. Molecular dynamics simulations and associated free-energy calculations were performed using the program NAMD, 86 a 4 fs timestep, 87 rigid covalent bonds involving hydrogen, 88,89 particle-mesh Ewald electrostatics, 90 a Langevin thermostat, and a Langevin piston barostat. 91 Complete details are given in the SI.

Free-Energy Calculations. The potentials of mean force were calculated by the adaptive biasing force method (ABF), 92,93 using the implementation provided in the Colvars module of NAMD. 94 Force samples were collected in bins of size 0.05 ˚ A along Z, beginning at Z = 3.0 ˚ A for CGenFF. We began at Z = 2.8 ˚ A for GAFF, due to the fact that the minimum of potential of mean force was located at smaller values of Z for GAFF. The end of the interval was chosen as 12 ˚ A for the minimal pristine graphene system, 15 ˚ A for the larger system, and 18 ˚ A for surfaces with co-absorbed molecules. The calculations were not stratified; i.e. they were performed in a single window over the complete domain of Z. We adhered to the convention that the free energy is zero for large separations between the solute and surface; thus, all potentials of mean force were shifted so that the average value in the last 0.5 ˚ A of the interval was zero. All free-energy calculations comprised >150 ns of simulation, with longer times of 200–500 ns being used for the more complex structures such as toluene-loaded surfaces, as specified in the SI. When enthalpy and entropy were calculated using potentials of mean force at three different temperatures, (280, 300, or 320 K), simulations at each 7



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temperature lasted >1500 ns to obtain sufficiently low uncertainty. Error bars representing the uncertainty in potentials of mean force were estimated as described in the Supporting Information of Poblete et al. 29 As detailed in the SI, the free-energy perturbation method was used to validate the use of Equations 4 and 5 with ∆T = 40 K.

Estimation of Orientational Entropy. To estimate the orientational entropy of the aromatics, we first calculated the vector normal the phenyl ring from the simulation frames of the adsorbed and unbound trajectories described in the Enthalpy decomposition section. For water, we calculated the normal to the plane of each molecule’s atoms for water molecules within 0.05 ˚ A of Zmin (adsorbed) and within 0.05 ˚ A of Z = 15.0 ˚ A (unbound). These normal vectors for each interval were then partitioned into equal area bins on the surface of a sphere using the HEALPix scheme. 95 The orientational entropy was computed by

S = −kB

X

Pi ln Pi ,

(1)

i

where Pi is the estimated probability of the orientation being in bin i. Far from the graphene unbound /kB = 9.40 ± 0.02 for all molecules, which is surface, the unitless entropies are Sorient

consistent with an isotropic distribution of phenyl group/water orientations, Sisotropic /kB = ln(12288) ≈ 9.41, where 12288 is the number of HEALPix bins. The full orientational entropy change included a considerably smaller component related to rotation around the normal vector, which was also calculated using Equation 1 with a histogram bin width of 1 degree.

Estimation of Conformational Entropy. The change in conformational entropy of propylbenzene and 4-nitrotoluene upon binding to graphene was calculated using quasiharmonic method implemented in the GROMACS package, 96 using adsorbed and unbound simulation trajectories described in the Enthalpy decomposition section. First, we fit the structure of the solute in each frame to a reference structure by an optimal rigid trans-

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formation. We then constructed the mass-weighted covariance matrix from the Cartesian coordinates. Subsequently, we calculated the eigenvalues and eigenvectors of the covariance matrix. Conformational entropy was then computed using the g anaeig program of the GROMACS package. To estimate the statistical uncertainty, we partitioned the original trajectories into three subtrajectories and reran the calculations on these subtrajectories. Differences between the entropies in the adsorbed and unbound states were used to calculate −T ∆Sconform . Pristine Graphene Models. The minimal systems, exemplified in Fig. 1, consisted of two rectangular patches of graphene (totaling 320 carbon atoms) with x and y dimensions of 19.6 and 21.1 ˚ A, stacked to form a bilayer. These two layers were solvated with 292 water molecules, giving an average size of 28.8 ˚ A along the z axis. Periodic boundary conditions were active in along all three axes, producing effectively infinite graphene surfaces in the xy plane. The use of this minimal system was validated (see Fig. S3) by simulations using larger sheets of graphene and a thicker water layer. For convenience, the atoms of the lower graphene layer were restrained to z = −8.674 ˚ A by weak harmonic restraints (energy ˚−2 ) acting along only the z-axis. In the free-energy calculations, constants 1 kcal mol−1 A the solute made contact with only the upper layer, which was completely free to move and bend. Both layers diffused freely in the xy plane. For CGenFF simulations, graphene carbon atoms were represented by the generic aromatic carbon type (CG2R61), while, for GAFF simulations, these atoms used the parameters of Hummer et al. 97

Nanotube and Curved Graphene Models. A (5,5) armchair nanotube was created by linking zigzag edges of the minimal pristine graphene model, giving a diameter of ≈ 7 ˚ A. The atoms of the nanotube were unrestrained except that restraint was applied to keep the center of mass of the nanotube at (0, 0, −9) ˚ A. Nanotubes with larger radii of curvature were difficult to fit in a small simulation box; hence, for computational efficiency, curved surfaces were made by cutting the periodic minimal graphene model along a zigzag edge (y9



axis), terminating the raw edges with hydrogen atoms, and applying restraints to maintain cylindrical cross sections of different radii of curvature in the yz-plane. The nanotube and curved sheets remained periodic along the x-axis. During the free-energy calculations, a center of mass restraint was applied (force constant 10 kcal mol−1 ˚ A−2 ) to keep the solute near the apex of the curved graphene surfaces and away from the hydrogenated edges. To ensure that no large artifacts were introduced by the restraints used for the curved surfaces, a free energy calculation was performed with a flat surface with similar restraints and hydrogenated edges and compared with the fully periodic model (see Fig. S2 of the SI).

Defect-Rich Graphene Model. Defects were produced by heating a graphene sheet in a reactive molecular dynamics simulation based on the ReaxFF 98 framework. We made use of the the ReaxFF implementation 99 in the program LAMMPS. 100 Carbon atoms were represented using the ReaxFFC-2013 parameters of developed by Srinivasan et al. 101 for a similar purpose. A 19.6×21.1 ˚ A2 periodic graphene sheet was equilibrated at 3000 K in vacuum and then subjected to rapid heating from 3000 to 5400 K over 80 ps using a Langevin thermostat. The structure was then cooled from 5400 to 300 K over 100 ps. The resulting atomic configuration was manually assigned a Kekulé structure and parameterized into CGenFF using ParamChem. 83,84 For consistency with the other simulations, two identical layers of this defective sheet were stacked atop one another. The transition coordinate for the free energy calculations was defined as the z-axis distance from the center of the four lowest graphene carbon atoms and center of mass of the solute. Restraints (energy constants 1 kcal mol−1 ˚ A−2 ) were added to all atoms of the patch to keep the topological features of the patch from flipping inside-out, which happened a few times in preliminary free-energy calculations. The free energy map shown in Fig. 9 was derived from a simulation in which ABF was applied along all three coordinate axes, yielding a three-dimensional potential of mean force. The coordinate Z was perpendicular to the average plane of the graphene sheet, as in the one-dimensional calculations, while the X and Y coordinates specified the position within

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the plane of the graphene sheet. The transition coordinates X, Y and Z were sampled on the domains [−9.6, 9.6], [−10.4, 10.4], and [3.5, 11.9] ˚ A with bin sizes of 0.2, 0.2, and 0.15 ˚ A, respectively. Similar to the one-dimensional calculations, the free energy function ∆G3D (X, Y, Z) was shifted so that it average value for Z > 11.5 ˚ A was zero. The map in Fig. 9 was created by selecting the minimum free energy for each set of grid points with a fixed X and Y .

Hydroxylated Graphene Model. The hydroxylated graphene model was created by adding 12 hydroxy groups to the pristine graphene model using the TopoTools plugin 102 of VMD. 103 To facilitate sampling of different x, y-positions during the free energy calculations, the OH groups were arranged to form four identical patches, i.e. the surface used in the simulations was a 2×2 supercell of a hydroxylated graphene unit cell containing three OH groups. As in previous work, 24 the charges and Lennard-Jones parameters were assigned based on the CGenFF representation of tert-butanol. Bonded parameters were obtained from a CGenFF model of hydroxylated circumcoronene. Although these parameters could probably be improved, they are likely sufficient for obtaining qualitative insight into adsorption on graphenic surfaces derivativized with hydrophilic groups.

Results and Discussion Calculation of Entropy and Enthalpy. The adsorption free energy for small molecules can be obtained using molecular dynamics coupled with efficient free-energy calculation techniques, such as the ABF method 92,93 employed here. Our calculations are made along the transition coordinate Z, illustrated in Fig. 1, where Z was defined as the distance between the center of mass of the solute and center of mass of the atoms of the first layer of graphene, projected onto the z axis (normal to the graphene sheets). We refer to the system shown in Fig. 1 as the minimal system because its size has been chosen to maximize efficiency, while still being large enough that errors due to finite size effects are small (see Fig. S3 11



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of the SI). The result of our free-energy calculations are the potentials of mean force as a function of the distance between the surface and the solute, ∆G(Z). A convenient method to extract entropy (and therefore enthalpy) from simulations is to perform similar free-energy calculations at multiple temperatures, from which the entropy and enthalpy of the system can be obtained by the relations 104–107

∂∆G ∂T

, ∆S = − N,p ∂(β∆G) , ∆H = ∂β N,p

(2) (3)

where β = (kB T )−1 is the inverse thermal energy and the derivatives of the Gibbs energy are taken with fixed particle number N and pressure p. In practice, we compute the finite differences

∆S(Z, T ) ≈ −

∆G(Z, T + ∆T /2) − ∆G(Z, T − ∆T /2) , ∆T

∆H(Z, T ) ≈ ∆G(Z, T ) + T ∆S(Z, T ),

(4) (5)

which are good approximations when the heat capacity is nearly constant over the temperature interval ∆T . 104 To allow direct comparison between entropic and enthalpic effects, we will mostly refer to the entropic contribution to the free energy (or entropic free energy) defined by −T ∆S(Z), rather than the entropy itself. We first consider results from simulations using CGenFF, a popular set of potential energy functions for representing interactions between organic molecules. As examples of free energy decomposition, consider two aromatic compounds with different properties: propylbenzene, which is one of the most hydrophobic compounds considered (log POW = 3.69), and 4-nitrotoluene, which is considerably more hydrophilic (log POW = 2.30). 23 The free energies, scaled by the thermal energy kB T , for these two solutes at three different temperatures (280, 300, 320 K) are shown in Fig. 2A. This scaled free energy, β∆G(Z, T ), is monotonically

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A

4

propylbenzene

Energy [kcal/mol]

0 -2 -4 -6 -8 -10 -12 -14

ΔG(Z)/(kBT)

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


280 K 300 K 320 K

2

B

0

280 K 300 K 320 K

4

6

8

Distance from graph. (Z) [Å]

2 -2

-4

-4

-6 ΔG(Z) -8 2 4

-6 6

8

10

4-nitrotoluene ΔH(Z)

C

0

–TΔS(Z)

-2

4-nitrotoluene

4

propylbenzene ΔH(Z)

-8 12 2

Distance from graphene [Å]

–TΔS(Z) ΔG(Z) 4

6

8

10

12


Figure 2: Calculation of entropic and enthalpic components of the adsorption free energy in molecular dynamics simulations using the CHARMM General Force Field (CGenFF). 68 (A) Potentials of mean force (Gibbs energy) divided by the thermal energy kB T as a function of solute distance from the graphene surface for two different solutes at three different temperatures. According to Equation 3, a lack of change in the plotted quantity (∆G(Z)/(kB T )) with temperature, as seen here for propylbenzene, implies that entropy dominates adsorption. (B,C) Entropic (−T ∆S) and enthalpic (∆H) contributions to the free energy at 300 K, calculated from the change in the potentials of mean force with temperature. The symbols represent entropies (black squares) and enthalpies (orange diamonds) obtained by free-energy perturbation at a single temperature, corroborating the results calculated from simulations at different temperatures. Similar results for the General Amber force field (GAFF) are shown in Fig. S4 of the SI. related to the probability of finding the center of mass of the solute at a distance Z from the graphenic surface. First, it is clear that, in accord with experiment, 24 propylbenzene adsorbs to graphene much more weakly than 4-nitrotoluene, despite the former’s greater hydrophobicity. However, the adsorption probability of 4-nitrotoluene diminishes with temperature, while that of propylenzene is nearly independent of temperature. As clearly seen from Equation 3, near temperature independence of β∆G implies that ∆H ≈ 0 and that the interaction is purely entropic. Calculations of entropic free energy and enthalpy by Equations 4 and 5 are shown in Fig. 2B,C for the two exemplary molecules. Consistent with the near-independence of β∆G(Z) for propylbenzene on temperature, Fig. 2B shows that the enthalpy ∆H(Z) has a small magnitude ( 4.5 µs of simulation (> 1.5 µs at each temperature).

For all compounds and force fields, the most favorable entropy occurs farther from the surface than the minimum free energy, similar to that shown in Fig. 2 and Fig. S4 for the two exemplary compounds. The minimum free energy is likewise slightly farther from the surface than the minimum enthalpy (an exception is benzene, which has no prominent enthalpy well near the surface). The minimum free energy occurs at positions in the range 3.45 ≤ Zmin ≤ 3.80 ˚ A for CGenFF and 3.10 ≤ Zmin ≤ 3.55 ˚ A for GAFF, which is partially

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due to the Lennard-Jones size parameter (Rmin ) of graphenic carbon atoms being about 0.2 ˚ A smaller for GAFF than for CGenFF. As might be expected, molecules with one very thin dimension have the smallest Zmin values (phenol, fluorophenol, naphthalene, nitrobenzene, benzonitrile), while the center of mass of the bulkiest solutes remains farthest from the surface (the phenylalkanols, propylbenzene, ethylbenzene, phenyl acetate). The enthalpy reaches its minimum over a range of slightly shorter distances (3.35 ≤ Z ≤ 3.60 ˚ A for CGenFF and 3.00 ≤ Z ≤ 3.35 ˚ A for GAFF), which like the free energy seems to be determined by the thinness of the solute. On the other hand, the maximum entropy occurs in the range 3.80 ≤ Z ≤ 4.35 ˚ A for CGenFF and 3.55 ≤ Z ≤ 4.00 ˚ A for GAFF, with no clear correlation with solute geometry or chemistry. Biphenyl and ethyl benzoate reach their maximum entropies at the shortest and longest distances, respectively. Considering the above, we see that the entropic force opposes adsorption for Z < 3.8 ˚ A, while the enthalpic force begins to favor adsorption near this range. Hence, the minimum free energy occurs as a compromise between an outwardly directed entropic force and an inwardly directed enthalpic force.

Comparison to Experiment. To verify the results of our simulations, we performed experiments to determine the adsorption thermodynamics of eight probe compounds on large-diameter multiwall carbon nanotubes. Similar to the simulations, the measurements were made at two different temperatures to allow estimation of the enthalpy. The adsorption equilibrium constants are determined from the experiments by

K(T ) =

V c0 − ce (T ) , m ce (T )

(6)

where V is the volume of solution in the vial, m is the mass of nanotubes, c0 is the concentration of the probe compound prior to adsorption to the nanotubes, and ce (T ) is the concentration of the probe compound remaining in solution after equilibrium with the nanotubes is attained at a temperature T . This equilibrium constant can be estimated from the

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simulations by 24 Z K(T ) = σ

dZ exp [−β∆G(Z, T )] ,

(7)

where σ is the specific surface area of the nanotubes. Differentiating ln [K(T )] and applying Equation 2 provides a link to the simulation enthalpy as a function of the transition coordinate: ∂ ln K(T ) = ∂T

R

dZ ∆H(Z, T ) exp [−β∆G(Z, T )] h∆H(Z, T )i R = . 2 kB T 2 kB T dZ exp [−β∆G(Z, T )]

(8)

This formula is essentially the van ’t Hoff equation, although it is important to note the peculiar definition of ∆H ◦ = h∆H(Z, T )i as a weighted average over the transition coordinate. Accordingly, h∆H(Z, T )i is approximately equal to the enthalpy at the point of minimum free energy, ∆H(Zmin ), which is the quantity plotted in Fig. 3. σ is conveniently absent from Equation 8 because, in an idealized model, increasing the specific surface area while keeping all other properties constant only changes the number of binding sites available to a solute, increasing its adsorption entropy, but not affecting the adsorption enthalpy. The standard entropy can be expressed as

−T ∆S ◦ = −∆H ◦ − kB T ln(KC0 ),

(9)

where C0 = 1 g/mL is the standard concentration. It should be noted that ∆S ◦ depends explicitly on the choice of C0 and the specific surface area (σ), making it distinct from ∆S(Zmin ). Although our previous work 24 showed high correlation between the K values of the probe compounds derived from experiment and those derived from simulations, the latter were systematically lower than the former. Here we compare the enthalpic and entropic contributions to the K values, which help us better understand the origin of this discrepancy.

18


Page 19 of 50

Fig. 4 compares the predictions of ∆H ◦ and ∆S ◦ by our simulations to those determined by experiment. While both the experimental and calculated values have relatively large uncertainties, there appears to be correlation between over the set of eight probe compounds considered. As expected, the simulations give ∆H ◦ and ∆S ◦ values systematically less favorable for adsorption than the experiments. However, the discrepancy in the enthalpies is quite small. Therefore, it appears that most of the error in the affinities predicted by

0

A tol

-1

PhPr

biphenyl

BnOH

-2

PhOAc

-3

EtPl

-4

BzOMe

-5 -5

nitro-tol

-4

-3

-2

-1

ΔΗ° (expt.) [kcal/mol]

0

–TΔS° (sim.) [kcal/mol]

simulation is a consequence of underestimation of the adsorption entropy.

ΔΗ° (sim.) [kcal/mol]

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


0

B

-1 -2

EtPl nitro-tol tol

BnOH BzOMe

PhOAc PhPr

-3 biphenyl -4 -8 -7 -6 -5 -4 -3 -2 -1 0

–TΔS° (expt.) [kcal/mol]

Figure 4: Comparison between experiments and simulations for the enthalpic and entropic contributions to the standard Gibbs free energy. Standard enthalpy (A) or standard entropic free energy (B) for adsorption of eight compounds onto graphenic surfaces. The standard concentration is 1 g/mL. Simulations are based on the CGenFF parameters. The gray line indicates points of exact agreement between experiment and simulation.

The experimental and computational results presented here appear to be in qualitative agreement with results published by other groups. Shen et al. 33 report quite favorable enthalpies for adsorption of nitroaromatics on multiwall carbon nanotubes, including values of −8.77 and −5.99 kcal/mol for 3-nitrotoluene (a different isomer than that considered here) and nitrobenzene. Although these values are more negative than those from our experiments and simulations, perhaps due to differences in the carbon materials, their ranking is consistent with our calculated values for 4-nitrotoluene and nitrobenzene. Furthermore, the addition of polar groups to nitrobenzene, making 1,3-dinitrobenzene and 4-nitrophenol, was found to give more a favorable enthalpy, which was partially canceled by less favorable entropy, 33 a 19



phenomenon that can also be observed in Fig. 3. For more hydrophobic solutes, previous experiments indicate adsorption driven more by entropy than enthalpy, in accord with our predictions. For instance, Peng et al. 111 report endothermic adsorption with ∆H ◦ = +1.4 and +3.9 kcal/mol for 1,3-dichlorobenzene on two different types of carbon nanotubes. While no comparably positive adsorption enthalpy is found in our data, the GAFF prediction for propylbenzene is statistically consistent with a possible weakly endothermic transition. The dye methylene blue has also been reported to adsorb endothermically. 112

A

B 1.2

280 K 300 K 320 K

3

Energy [kcal/mol]

Water density [g/mL]

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

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2 1 0 2

ΔG(Z) –TΔS(Z) ΔH(Z)

0.8 0.4 0

-0.4

CGenFF 4

6

-0.8 2

8 10 12 14


CGenFF 4

6

8 10 12 14


Figure 5: Aqueous solvation of graphene. (A) Mass density of water as a function of distance from the graphene surface for simulations parameterized by CGenFF at the different temperatures. (B) Entropic (−T ∆S) and enthalpic (∆H) contributions to the free energy (∆G) of water on a graphene surface parameterized by CGenFF at 300 K. Similar results for GAFF are shown in Fig. S5 of the SI.

Solvation of Graphene. Adsorption on graphenic surfaces in an aqueous environment requires expulsion of water molecules from the surface, which, due to the slightly hydrophilic nature of graphenic surfaces, 22 incurs a considerable free-energy penalty. This hydrophilicity is manifested in a layer of water near the graphene surface with a density about triple that of bulk water. Fig. 5A shows the mass density of water as function of distance from the surface at temperatures of 280, 300, and 320 K, calculated in equilibrium simulations using CGenFF. Results using GAFF are shown in Fig. S5 of the SI and are qualitatively similar. Fig. S6 of the SI provides more detail on these calculations. Far from the graphene surface, the water 20


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densities reach values consistent with bulk TIP3P water at room temperature: ≈1 g/mL. At the graphene surface, a distinct primary layer is apparent, with peaks in density located at Z = 3.33 ˚ A for CGenFF and 3.13 ˚ A for GAFF. This first water layer is well-separated from the second by an unfavorable low density region centered around Z ≈ 5 ˚ A, where the density drops below 0.5 g/mL. A second density peak occurs at Z ≈ 6 ˚ A, followed by several smaller density oscillations. The maximum density, coinciding with the primary layer of water, decreases considerably with increasing temperature, having values of 3.36, 3.13, and 2.92 g/mL for CGenFF and 3.13, 2.92 and 2.73 g/mL for GAFF at temperatures of 280, 300, and 320 K. GAFF predicts slightly lower affinity between graphene and water than CGenFF. The decrease in the maximum density with temperature outpaces the corresponding change in the bulk, implying a significant enthalpic component to the graphene–water interaction, which can be confirmed in Fig. 5B. While mostly enthalpic, water adsorption to the primary layer is also driven by a weak favorable entropic component. Interestingly, entropy–enthalpy cancelation is a consistent feature of the thermodynamic potentials for distances beyond the first water layer. The free energy maximum between the first and second water layers (Z = 4.90 ˚ A) lies near a local maximum of ∆H(Z) that is partially canceled by the global minimum of −T ∆S(Z). While ∆G(Z) is relatively flat for Z > 9 ˚ A, appreciable oscillations persist in ∆H(Z) and −T ∆S(Z), which are opposite and nearly equal in magnitude at least out to Z = 14 ˚ A. The favorable entropy in the primary layer might be surprising given the presumably restricted orientation and arrangement of water molecules in this layer. However, because the van der Waals profile of water molecules, both real and modeled, is nearly spherical, 113 the distribution of water orientations is only slightly anisotropic in the primary layer, as demonstrated by a small change in the orientational part of the entropic free energy between the primary water layer and bulk: −T ∆Sorient (Zmin ) ≈ 0.2 kcal/mol. As shown in Fig. S7 of the SI, the addition of ions, namely Na+ and Cl− , to the solution slightly increases the adsorption affinity of the aromatic solutes on graphene. However, the

21



magnitude of the free energy change is modest (< 0.5 kcal/mol), even at a relatively high ion concentration (500 mmol/L). These results are consistent with previous experiments, which show no appreciable dependence on ionic strength for adsorption of neutral aromatics on carbon nanotubes. 114 Table 1: Decomposition of adsorption enthalpy (in kcal/mol) on graphene for two solutes. ∆Uij is the change in the interaction potential energy from simulation frames in which the solute was free to those in which it was adsorbed. ∆H ∗ is the enthalpy obtained by summing the previous rows. ∆H(Zmin ) is the enthalpy at the position of minimum free energy derived from ABF calculations at three different temperatures.

∆Usolute−solute ∆Ugraph−graph ∆Uwater−water ∆Usolute−graph ∆Usolute−water ∆Ugraph−water p∆V ∆H ∗ ∆H(Zmin )

CGenFF CGenFF GAFF GAFF propylbenzene 4-nitrotoluene propylbenzene 4-nitrotoluene 0.24 ± 0.01 −0.37 ± 0.01 0.23 ± 0.01 −0.37 ± 0.01 0.01 ± 0.06 0.08 ± 0.06 0.08 ± 0.06 −0.05 ± 0.06 −5.42 ± 0.12 −6.12 ± 0.11 −4.69 ± 0.10 −5.98 ± 0.10 −13.98 ± 0.09 −15.68 ± 0.08 −13.52 ± 0.09 −16.77 ± 0.09 6.77 ± 0.17 6.28 ± 0.15 6.58 ± 0.14 6.46 ± 0.14 11.38 ± 0.19 10.57 ± 0.18 10.43 ± 0.17 9.72 ± 0.17 −4 −4 −4 1.6 × 10 1.2 × 10 2.6 × 10 1.6 × 10−4 −1.00 ± 0.30 −5.24 ± 0.28 −0.89 ± 0.26 −6.99 ± 0.26 −1.11 ± 0.32 −4.95 ± 0.35 −0.17 ± 0.42 −5.53 ± 0.41

Decomposition of Adsorption Enthalpy. As described in the SI, we decompose the change in enthalpy from the unbound state to the adsorbed state into pressure–volume work and internal energy components, which are given in Table 1. The internal energy changes within and between three subsystems are considered— namely, the solute molecule (propylbenzene or 4-nitrotoluene), the graphene layers, and all water molecules. First, we find that the change in the intramolecular energy of the solute (∆Usolute−solute ) upon adsorption is quite small and unfavorable for propylbenzene but favorable for 4-nitrotoluene. While the mechanical strain of propylbenzene increases upon adsorption, as reflected by an increase in bonded energy terms, the relatively flat 4-nitrotoluene experiences reduced strain when adsorbed to the flat graphene surface. The graphene layers, being quite rigid, undergo little deformation when the solute is adsorbed, leading to negligible ∆Ugraph−graph . The intra-water change in 22


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energy ∆Uwater−water can be thought of as similar to moving an air bubble from bulk water to a water–air interface. The water molecules around the solute are perturbed from their arrangement in bulk in a way that is unfavorable in the absence of the solute, so banishing this arrangement to a region where the water–water interaction is already nonoptimal, the graphene–water interface, is favorable and ∆Uwater−water < 0 in all cases. The ∆Uwater−water of 4-nitrotoluene, is more favorable than of propylbenzene, particularly in its electrostatic component, which is likely because the polar nitro group of 4-nitrotoluene perturbs the structure of water more than the nonpolar groups of propylbenzene. The largest magnitude contribution to the adsorption enthalpy is the direct interaction between the solute and graphene surface, ∆Usolute−graph .

GAFF predicts stronger

∆Usolute−graph for 4-nitrotoluene than CGenFF. The other two interactions counteract the favorable ∆Usolute−graph and ∆Uwater−water energies. ∆Usolute−water represents the energy penalty for partially desolvating the solutes at the graphene–water interface. As demonstrated in Fig. 5B, water molecules have a favorable enthalpic interaction with graphene; therefore, there is also an energy cost (∆Ugraph−water ) to expel water molecules from the first water layer to accommodate the adsorbing solute. In general, CGenFF and GAFF predict qualitatively similar changes in enthalpy components between propylbenzene and 4-nitrotoluene. Because GAFF predicts a lower affinity between graphene and water than CGenFF (see Fig. 5), ∆Ugraph−water represents lower penalties for solute adsorption under GAFF than under CGenFF. However, it is notable that ∆Usolute−graph exhibits a larger magnitude difference between the two solutes under GAFF than under CGenFF. As has been noted previously, 107,115 pressure–volume work for nanoscale binding processes in water is typically very small. The simulation systems are kept at atmospheric pressure by a barostat algorithm, which allows for changes in volume. Their average volume increases perceptibly as the solutes adsorb to the surface: ∆V = 11.30 ± 0.70 and 7.90 ± 0.60 ˚ A3 for propylbenzene and 4-nitrotoluene with CGenFF. With GAFF, these values are ∆V =

23



Page 24 of 50

˚3 . However, in all cases, the associated pressure–volume work 18.0 ± 0.60 and 7.50 ± 0.60 A is negligible, being several orders of magnitude smaller than the contributions from internal energy. Hence, enthalpy and internal energy are numerically equivalent for the adsorption processes considered here. The enthalpy components in Table 1 were calculated by monitoring the potential energies of simulations at 300 K, an approach distinct from our earlier calculation of ∆H(Z) using ABF at three distinct temperatures. However, these two approaches are consistent: the sums of the internal energy terms, represented by ∆H ∗ in Table 1, agree with the value of ∆H(Z) at the position of minimum free energy. The only exception is 4-nitrotoluene under GAFF, where the discrepancy might be related to the exceptional steepness of ∆H(Z) in Fig. S4C. Table 2: Decomposition of the adsorption entropy on graphene for two solutes. The solvation entropy (Swater ) was computed from ABF simulations in which the orientation and conformation of the solute was restrained. The orientational entropy (Sorient ) was determined from a geometric analysis between simulation frames in the bound and unbound states. The conformational entropy (Sconform ) was determined from applying the quasi-harmonic method to these sets of frames. 116 −T ∆S ∗ is the entropic contribution to the adsorption free energy obtained by summing the previous rows. −T ∆S(Zmin ) is entropic contribution to the adsorption free energy at the position of minimum free energy determined computed from ABF calculations at three different temperatures. All energies are in kcal/mol. CGenFF CGenFF GAFF GAFF propylbenzene 4-nitrotoluene propylbenzene 4-nitrotoluene −T ∆Swater −7.67 ± 0.38 −6.09 ± 0.39 −8.73 ± 0.46 −6.80 ± 0.54 −T ∆Sorient 1.55 ± 0.01 2.41 ± 0.01 1.57 ± 0.01 2.53 ± 0.01 −T ∆Sconform 2.73 ± 0.03 0.72 ± 0.02 1.21 ± 0.01 0.81 ± 0.08 ∗ −T ∆S −3.54 ± 0.43 −3.07 ± 0.43 −5.95 ± 0.48 −3.46 ± 0.63 −T ∆S(Zmin ) −4.57 ± 0.32 −3.25 ± 0.35 −5.60 ± 0.42 −3.81 ± 0.41

Decomposition of Adsorption Entropy. We consider three major contributors to the adsorption entropy: the solvent entropy (∆Swater ), the orientational entropy of solute (∆Sorient ), and the conformational entropy of the solute (∆Sconform ). Unlike the enthalpy, which can be rigorously separated into the components in Table 1, entropy cannot, in principle, be rig24


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orously decomposed. For example, entropy associated with correlations between the solute conformation and the water arrangement are not captured by decomposition into ∆Swater , ∆Sorient , and ∆Sorient . However, these three quantities appear to capture the most dominant components. The calculated entropies are given in Table 2 for both the force fields. The favorable entropy of adsorption for all compounds considered here is driven by liberation of water molecules adsorbed to the surface and surrounding the solute. ? However, favorable ∆Swater is opposed by a considerable loss of orientational and conformational freedom as the molecule approaches the surface, owing to steric effects. 117 The change is lower for propylbenzene because the orientation of the phenyl ring is less constrained owing to the presence of the bulky propyl group, which prevents its phenyl ring from approaching the graphene surface as closely as the phenyl ring of 4-nitrotoluene (see Fig. 6A,B). The entropy associated with the normal to the phenyl ring accounts for a majority of orientational entropy change, while the contribution from rotation around this normal is weak (< 0.2 kcal/mol in all cases). The conformational entropy change also differs between the two solutes. While the propyl group of propylbenzene is quite flexible, 4-nitrotoluene is relatively rigid. Correspondingly, the changes in the conformational entropy are considerably more unfavorable for propylbenzene and than for 4-nitrotoluene. Loss of conformational entropy for 4-nitrotoluene is similar between CGenFF and GAFF, while this quantity for the propylbenzene is considerably higher with CGenFF than GAFF. As we have established the similarity between the predictions of CGenFF and GAFF, in the remainder of this article, we will consider results using only CGenFF.

Surface Coverage. Owing to the high affinity of aromatic solutes for graphenic surfaces, high loading of the surface can be expected even at small ambient solute concentrations. For example, given the experimentally determined adsorption affinities for graphenic nanomaterials and the maximum monolayer density determined from molecular dynamics, ambient concentrations of a few µmol/L should be sufficient to cover a majority of a graphene sur-

25



A

B

Figure 6: Conformational freedom of the adsorbed solutes. (A) The ensemble of adsorbed structures of propylbenzene includes significant contributions from conformations in which the propyl group is situated above, in the same plane as, or below the phenyl group. (B) The absorbed ensemble of 4-nitrotoluene exhibits much less conformational variation, showing only rotation of the methyl group and some tilting of the nitro group.

face with high affinity solutes, such as 4-nitrotoluene. 24 Therefore, we performed simulations to determine the dependence of the adsorption thermodynamics on the number of solutes present in the system. We chose toluene for these simulations since it has one of the weakest affinities for graphene of the solutes considered here and, therefore, its dissociation can be observed on the simulation timescale (see Methods). Based on its experimentally derived affinity, toluene is expected to half-cover graphene at a solution concentration ∼1 mmol/L. Fig. 7 shows the results of simulations of a small patch of graphene surface with different numbers of toluene. For numbers of toluene molecules N < 9, all molecules spend a vast majority of their time in direct contact with the surface, and the number of toluene molecules in this first monolayer grows almost in lock-step with the total number in the system (Fig. 7B). The surface becomes fully saturated with 9 toluene molecules in the system, which corresponds to a surface density of 2.2 molecules/nm2 . An example of the packing of the toluene

26


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A

B Number in layer

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


16 C in first layer 14 in second layer 12 10 8 6 4 2 00 2 4 6 8 10 12 14 16

Energy [kcal/mol]

Page 27 of 50

Total number

0

–TΔS

-2 -4 -6 ΔG

ΔH

-8 0 2 4 6 8 10 12 14 16 Number of toluene

Figure 7: Effect of the number of adsorbed molecules on adsorption thermodynamics of an additional molecule. (A) Toluene molecules on a graphene surface at a density of 2.2 molecules/nm2 . (B) Number of toluene molecules in the first and second adsorbed layers as a function of the number of toluene molecules in the system. The first layer becomes full with 9 toluene molecules, corresponding to a density of 2.2 molecules/nm2 . (C) Contributions to the minimum free energy as a function of the number of toluene molecules in the system.

molecules into a complete monolayer is rendered in Fig. 7A. Due to steric constraints, it is difficult to pack more than 9 molecules on the surface and additional molecules begin to occupy a second layer having a density maximum near Z = 7 ˚ A. Fig. 7C displays the free energy change for adding toluene molecules to the system, determined by performing ABF calculations for a single toluene molecule on surfaces loaded with different numbers of toluene molecules. The minimum ∆G(Z) for a single toluene molecule on a bare surface is −5.02 ± 0.03 kcal/mol. Adding a second toluene molecule to the surface, at a density of 0.24 molecules/nm2 , slightly strengthens the interaction of the first molecule with the interface, with the minimum ∆G(Z) decreasing to −5.42 ± 0.17 kcal/mol. Thus, initially, loading the surface with toluene favors further adsorption of toluene. The enthalpic and entropic components shown in Fig. 7C demonstrate that the increase in the favorability of adsorption as the surface is loaded is driven by decreasing enthalpy. Beyond N = 5 toluene molecules, entropic contributions begin to partially cancel the more favorable enthalpy, owing to the reduced freedom of the additional toluene molecule on an already crowded surface. The trend of increasing adsorption affinity with N continues until N = 8. 27



Adding an eighth molecule to a graphene surface loaded with 7 toluene molecules (a density of 1.7 molecules/nm2 ), results in a free energy change of −7.9 ± 0.2 kcal/mol, the largest magnitude observed. At N = 9, the monolayer is complete, and adding a tenth molecule results in a dramatic reduction of the favorability of adsorption to a level similar to that of a bare graphene surface (−5.7 ± 0.2 kcal/mol). ∆G remains fairly near its value for a bare surface as the second layer is filled, accompanied by changes in entropy and enthalpy that almost exactly cancel each other.

Surface Curvature. So far, we have considered computational models of graphene sheets that are flat, on average. However, curvature likely plays an important role in adsorption to small diameter nanotubes and to defective graphene structures. Furthermore, the experiments to which we have compare were performed with carbon nanotubes. 24 While we argued that the diameters of these nanotubes were sufficiently large that they can be accurately approximated by flat surfaces, it is important to determine the limits of this approximation. As shown in Fig. 8, we calculated the potential of mean force of 4-nitrotoluene as a function of distance from graphene surfaces of varying curvature, corresponding to the exterior surface of nanotubes having diameters of 0.7, 2.0, 4.0, and 8.0 nm. A concave surface is also considered, representing the interior of a 4.0 nm diameter nanotube or, perhaps, a region of a nonideal nanotube or graphene surface. As shown in Fig. 8C, weakest adsorption is seen at the surface of the (5,5) nanotube. The affinity increases substantially as the effective diameter increases from 0.7 to 2.0 nm. From 2.0 and 8.0 nm the affinity continues to increase, although more modestly. A convex surface curves away from the solute and, in the case of roughly flat rigid solutes like the aromatics considered here, this reduces the contact area between the surface and the adsorbed solute. On the other hand, a concave surface curves toward the solute, leading to increased contact area. To quantify the link between contact area and surface curvature, we calculated the solvent-accessible surface area (probe radius 1.7 ˚ A) of 4-nitrotoluene in

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solution and in its adsorbed state using VMD. 103 The contact area with the graphenic surface was calculated by subtracting the solvent-accessible surface area of the molecule ˚2 , the mean solvent-accessible area of 4-nitrotoluene in when adsorbed from 324.6 ± 0.8 A free solution. Fig. 8D reveals the close association between contact area and adsorption free energy. As the curvature becomes more concave, both the contact area and strength of adsorption increase. Fig. 8E demonstrates that the increased adsorption affinity for the concave surface is due to substantially more favorable enthalpy, likely owing to a stronger direct van Waals interaction between 4-nitrotoluene and the graphene surface. A similar trend of more favorable enthalpy for more concave curvature is seen for propylbenzene (see Fig. S8 of the SI), along with also more favorable entropy. The multiwall carbon nanotubes used in the experiments to which we compare were verified by electron microscopy to have diameters ranging from 8–20 nm (see Fig. S1) and lengths of about 2 µm. The smallest nanotubes in the experiment would correspond to the “8 nm” curve in Fig. 8C. Although statistically distinguishable from a flat surface, the difference is small. Hence, a flat graphene surface is a good approximation of nanotubes with diameters of ≥ 8 nm for solutes similar to the size of 4-nitrotoluene. It should be noted that this approximation is only valid when the radius of curvature of the nanotube is much larger than the longest dimension of solute. The curvature of an 8 nm-diameter nanotube would be more relevant for a larger solute, such as a protein. Unlike the relatively independent nanotubes shown in Fig. S1, smaller nanotubes tend to form bundles, with adsorption occuring at different types of sites, including nanotube–nanotube interfaces. 21,118 Previous simulations have shown that adsorption to ordered nanotube aggregates may favor nanotube–nanotube interfaces. 63

Defects and Topography. Real carbon nanotubes and graphene invariably contain some defects and irregularities. To model such defects, we produced a defective graphene surface by rapidly heating and cooling the pristine model in a ReaxFF simulation (see Methods).

29



0.7 nm

C 2

B

diameter

Free Energy [kcal/mol]

A

–4 nm

8 nm

4 nm

2 nm

-4 -5

E

0.7 nm

-6 -7 -8

2 nm 4 nm

-10 100

8 nm flat

-9

–4 nm

120

0 -2

0.7 nm 2 nm 4 nm 8 nm flat –4 nm

-4 -6 -8 -102

4

6

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140

Energy [kcal/mol]

D

Minimum ΔG(Z) [kcal/mol]

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

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2 0 -2 -4 -6 -8 2

160

ΔH(Z) 2 nm flat –4 nm

4

6

8

–TΔS(Z) 2 nm flat –4 nm

10

12


2

Contact area [Å ]

Figure 8: Effect of surface curvature on adsorption thermodynamics. (A) Rendering of atomistic model for calculation of the adsorption free energy of 4-nitrotoluene on a (5,5) carbon nanotube with an approximate diameter of 0.7 nm. (B) Rendering of the surface models used to represent different degrees of curvature. Adsorption of the solute to the upper surface is considered, and negative curvature implies a concave surface. (C) Free energy as a function of distance between a 4-nitrotoluene molecule and the middle of the curved structures shown in panels A and B. ∆G(Z) is labeled by the diameter of curvature. (D) Minimum free energy as a function of the contact area between 4-nitrotoluene and the graphenic surface for different surface curvatures. (E) −T ∆S(Z) and ∆H(Z) for 4nitrotoluene on convex, flat, and concave graphene surfaces.

Rather than being composed of only six-member carbon rings, the defective graphene patch, shown in Fig. 9A, has 10 five-member rings, 8 seven-member rings, and 1 eight-member ring. Similar structures have been experimentally observed in graphene by electron microscopy. 69 Fig. 9B demonstrates that these defects result in a sheet with undulating topography. Our results for curved surfaces (Fig. 8) suggest that regions of concave curvature, such as near (X, Y ) = (0, 0) in Fig. 9B, might have higher affinity for adsorbates than regions of convex curvature. We performed a three-dimensional free-energy calculation of 4-nitrotoluene in the vicinity of the defect-rich graphene sheet to determine the adsorption free energy at different positions on the sheet (Fig. 9C). As expected, the adsorption free energy is generally lowest

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in concave pockets and highest on surface protrusions.

A

B

C

Figure 9: Effect of graphene defects on adsorption thermodynamics of 4-nitrotoluene. (A) Topology and topography of the defective graphene structure. Surface height is indicated by the darkness of the bonds, with depressions shown in black. (B) Surface height as a function of lateral position over the surface. The height was measured along the z axis from the center of mass of the graphene atoms using a probe atom of radius 3 ˚ A. (C) Minimum free energy for 4-nitrotoluene adsorption over this surface determined from a three-dimensional free-energy calculation.

Hydroxylated Surfaces. Oxygen-containing derivatives of graphene typically have greater aqueous wettability than pristine graphene. To understand how derivatization with such hydrophilic groups might alter adsorption thermodynamics, we performed free-energy calculations using a graphene model on which OH groups were covalently attached to the basal plane. The effect of different densities and arrangements of OH groups on the adsorption affinity was explored in previous work; 24,29 so, here, we consider only a single arrangement of OH groups, illustrated in Fig. 10A, having a density of 2.9 groups/nm2 . The potentials of mean force for the interaction of propylbenzene and 4-nitrotoluene with hydroxylated graphene and graphene are shown in Fig. 10E. ∆G(Z) for the two compounds is similar between hydroxylated and pristine graphene; however, there is a major shift in the balance between entropy and enthalpy (see Fig. 10F,G). For all solutes, the position of lowest free energy is associated with direct contact with regions of bare graphene (sp2 carbon atoms), 31



which agrees with previous findings for these aromatics 24 and for molecules including peptide linkages. 29 Representative adsorbed configurations of propylbenzene and 4-nitrotoluene are shown in Fig. 10A,C. Because the most probable adsorbed configurations are associated with direct contact between bare graphene and the solute, the accessible surface area for adsorption to hydroxylated graphene is effectively reduced from that of unmodified graphene, as can be observed in Fig. 10B,D. This nonuniform distribution of x, y positions in the bound state contributes ≈ +1 kcal/mol to the entropic free energy, as calculated by the Gibbs entropy formula (Equation 1). This entropic cost, compounded by reductions in orientational and conformational freedom on the hydroxylated surface relative to the unmodified surface, is apparent in the less favorable −T ∆S(Z) shown in Fig. 10F,G. However, this less favorable entropy is offset by stronger enthalpic contributions to the adsorption free energy, partially due to favorable electrostatic interactions between the solute and surface-bound OH groups.

Conclusion In this study, we used molecular dynamics simulation to better understand the adsorption thermodynamics of graphenic nanomaterials. We extracted the contributions of enthalpy and entropy to the adsorption free energies and found that adsorption of hydrophobic compounds was driven more by entropy than enthalpy, while for hydrophilic compounds, enthalpy was a greater contributor. Microsecond-length ABF simulations performed at temperatures separated by 40 K were sufficient to accurately determine entropies and enthalpies along a coordinate tracking the adsorption of a small molecule. This approach was validated by free-energy perturbation calculations performed at a single temperature, as well as direct averaging of the internal energy in the end-point states. Furthermore, the predicted adsorption entropies and enthalpies of the set benzene derivatives exhibited clear correlations with the results of our experiments. We also investigated how the force field parameters determined the predicted adsorption thermodynamics. Although we point out some modest quantitative

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B

0 E

C

Propylbenzene Graphene Graphene OH

-2 -4 -6

4-nitrotoluene Graphene Graphene OH

-8 2

4

6

8

10

2 F

Energy [kcal/mol]

A

ΔG(Z) [kcal/mol]

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


12


D

ΔH Graphene Graphene OH

0

–TΔS

-2

Graphene Graphene OH

-4 -6 -8 2

2G

ΔH Graphene Graphene OH

0

–TΔS

-2

Graphene Graphene OH

-4 -6

4

6

8

10

12


-8 2

4

6

8

10

12


Figure 10: Favorable conformations of solutes adsorbed on a hydroxylated graphene model and plots of the associated thermodynamics. (A) A representative conformation of propylbenzene adsorbed to the graphene-OH model. (B) Ensemble of adsorbed conformations of propylbenzene consistent with the position (Zmin ) of minimum free energy. (C) A representative conformation of 4-nitrotoluene adsorbed to the graphene-OH model. (D) Ensemble of adsorbed conformations of 4-nitrotoluene consistent with the position (Zmin ) of minimum free energy. For clarity, in panels B and D, only the phenyl rings (green) are shown. Hydroxy groups are shown in red and white. The graphene surface is shown in gray. (E) Comparison of ∆G(Z) between unmodified and hydroxylated graphene for the two solutes. (F,G) Entropic (−T ∆S) and enthalpic (∆H) contributions to the free energy, comparing unmodified and hydroxylated graphene.

differences, CGenFF and GAFF predict similar trends for the relation between the chemical nature of the solute and its adsorption thermodynamics on graphene. The simulations predicted that the concentration of water at the graphenic surface is enhanced relative to that in bulk, resulting in significant solvation effects on adsorption. Our study of toluene loading showed that co-adsorbed molecules can increase or decrease the adsorption affinity of a given adsorbate, with the adsorption entropy becoming less favorable as the surface becomes more crowded. Furthermore, we found that hydroxylation of the surface considerably increases the favorability of the adsorption enthalpy, at the expense 33



of increasing the entropic cost, due to a reduction in the area of the surface available for binding. We used reactive molecular dynamics simulations to create plausible defect-rich graphene structures, which were then investigated using conventional simulations. We determined the effect on adsorption of surface curvature and defects, demonstrating that a convex graphenic surface, such as the outer portion of a carbon nanotube, diminished the contact area for a relatively rigid adsorbate compared to a flat surface, reducing adsorption enthalpy. On the other hand, surfaces that are concave on at the length scale of the adsorbate were able to increase the affinity. Although we consider only benzene derivatives in this work, the results are likely applicable to other solutes. For example, the behavior of polar benzenoids on hydroxylated graphene was similar to that seen previously for alanine dipeptide. 29 However, the importance of certain free-energy components might shift for larger solutes. Adsorption of large flexible molecules likely requires overcoming larger penalties associated with conformational entropy than adsorption of relatively rigid benzene derivatives. The effects of curvature on the adsorption thermodynamics is likely determined by the ratio between the radius of curvature of graphenic surface and the relevant dimension of the solute. That is, a surface that appears flat for a small solute may appear curved for a larger solute. On the other hand, surface undulations caused by defects can create localized binding sites for small molecules as seen in Fig. 9. Particular arrangements of defects might result in specific adsorption for solutes of a particular shape and size. The influence of solute flexibility is likely to be considerable, since flexible molecules can more easily adapt their conformation to curved or uneven surfaces than rigid molecules. Further work needs to be done to understand thermodynamics of corona formation on graphenic materials, particularly in complex solutions like biological fluids and natural waters. In these fluids, small molecules, owing to their high mobilities, are likely to arrive at the graphene–water interface before larger molecules such as lipids, proteins, and polysac-

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charides. Hence, these larger components adsorb not to pristine graphenic surfaces, but to surfaces already loaded with a layer of small molecules, similar to that shown in Fig. 7A. The composition and structure of this layer is likely to depend sensitively on the bulk concentrations of molecules in the solution, their affinities for the graphene–water interface, and the interactions between them in the adsorbed phase. Furthermore, contaminants unavoidably present on graphenic materials 22 used in experiments may be important to consider when comparing experiments with simulations.

Supporting Information Available Additional methological details and figures as described in the text. This material is available free of charge via the Internet at http://pubs.acs.org This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement JC thanks Adri C. T. van Duin for advice on the choice of ReaxFF parameters. This work was partially supported by the Kansas Bioscience Authority funds to the Institute of Computational Comparative Medicine (ICCM) and to the Nanotechnology Innovation Center of Kansas State University (NICKS). A majority of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CHE-1726332, CNS-1006860, EPS-1006860, and EPS-0919443. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. HP is grateful for Fondecyt grant No. 1171155 as well as the Millennium Nucleus of Ion Channel-Associated Diseases (MiNICAD), which is a Millennium Nucleus supported by the Iniciativa Cient´ıfica Milenio of the Ministry of Economy, Development and Tourism (Chile).

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References 1. Segal, M. Selling Graphene by the Ton. Nature Nanotech. 2009, 4, 612–614. 2. Loh, K. P.; Bao, Q.; Eda, G.; Chhowalla, M. Graphene Oxide as a Chemically Tunable Platform for Optical Applications. Nature Chem. 2010, 2, 1015–1024. 3. Chung, C.; Kim, Y.-K.; Shin, D.; Ryoo, S.-R.; Hong, B. H.; Min, D.-H. Biomedical Applications of Graphene and Graphene Oxide. Acc. Chem. Res. 2013, 46, 2211–2224. 4. De Volder, M. F.; Tawfick, S. H.; Baughman, R. H.; Hart, A. J. Carbon Nanotubes: Present and Future Commercial Applications. Science 2013, 339, 535–539. 5. Ali-Boucetta, H.; Kostarelos, K. Carbon Nanotubes in Medicine & Biology—Therapy and Diagnostics. Adv. Drug Deliver. Rev. 2013, 65, 1897–1898. 6. Zurutuza, A.; Marinelli, C. Challenges and Opportunities in Graphene Commercialization. Nature Nanotech. 2014, 9, 730–734. 7. Saito, N.; Haniu, H.; Usui, Y.; Aoki, K.; Hara, K.; Takanashi, S.; Shimizu, M.; Narita, N.; Okamoto, M.; Kobayashi, S. et al. Safe Clinical Use of Carbon Nanotubes as Innovative Biomaterials. Chem. Rev. 2014, 114, 6040–6079. 8. Lee, J.; Kim, J.; Kim, S.; Min, D.-H. Biosensors Based on Graphene Oxide and Its Biomedical Application. Adv. Drug Deliver. Rev. 2016, 105, 275–287. 9. Dutta, D.; Sundaram, S. K.; Teeguarden, J. G.; Riley, B. J.; Fifield, L. S.; Jacobs, J. M.; Addleman, S. R.; Kaysen, G. A.; Moudgil, B. M.; Weber, T. J. Adsorbed Proteins Influence the Biological Activity and Molecular Targeting of Nanomaterials. Toxicol. Sci. 2007, 100, 303–315. 10. Walczyk, D.; Bombelli, F. B.; Monopoli, M. P.; Lynch, I.; Dawson, K. A. What the Cell “Sees” in Bionanoscience. J. Am. Chem. Soc. 2010, 132, 5761–5768. 36


Page 36 of 50

Page 37 of 50 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


11. Lee, W. C.; Lim, C. H. Y.; Shi, H.; Tang, L. A.; Wang, Y.; Lim, C. T.; Loh, K. P. Origin of Enhanced Stem Cell Growth and Differentiation on Graphene and Graphene Oxide. ACS Nano 2011, 5, 7334–7341. 12. Saptarshi, S. R.; Duschl, A.; Lopata, A. L. Interaction of Nanoparticles with Proteins: Relation to Bio-reactivity of the Nanoparticle. J. Nanobiotechnol. 2013, 11, 26. 13. Salvador-Morales, C.; Flahaut, E.; Sim, E.; Sloan, J.; Green, M. L.; Sim, R. B. Complement Activation and Protein Adsorption by Carbon Nanotubes. Mol. Immunol. 2006, 43, 193–201. 14. Kennedy, A. J.; Hull, M. S.; Steevens, J. A.; Dontsova, K. M.; Chappell, M. A.; Gunter, J. C.; Weiss, C. A. Factors Influencing the Partitioning and Toxicity of Nanotubes in the Aquatic Environment. Environ. Toxicol. Chem. 2008, 27, 1932–1941. 15. Hu, W.; Peng, C.; Lv, M.; Li, X.; Zhang, Y.; Chen, N.; Fan, C.; Huang, Q. Protein Corona-mediated Mitigation of Cytotoxicity of Graphene Oxide. ACS Nano 2011, 5, 3693–3700. 16. Ge, C.; Du, J.; Zhao, L.; Wang, L.; Liu, Y.; Li, D.; Yang, Y.; Zhou, R.; Zhao, Y.; Chai, Z. et al. Binding of Blood Proteins to Carbon Nanotubes Reduces Cytotoxicity. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 16968–16973. 17. Syed, S.; Zubair, A.; Frieri, M. Immune Response to Nanomaterials: Implications for Medicine and Literature Review. Curr. Allergy Asthma Rep. 2013, 13, 50–57. 18. Mbeh, D. A.; Akhavan, O.; Javanbakht, T.; Mahmoudi, M.; Yahia, L. Cytotoxicity of Protein Corona-graphene Oxide Nanoribbons on Human Epithelial Cells. Appl. Surf. Sci. 2014, 320, 596–601. 19. De Paoli, S. H.; Diduch, L. L.; Tegegn, T. Z.; Orecna, M.; Strader, M. B.; Karnaukhova, E.; Bonevich, J. E.; Holada, K.; Simak, J. The Effect of Protein Corona 37



Composition on the Interaction of Carbon Nanotubes with Human Blood Platelets. Biomaterials 2014, 35, 6182–6194. 20. Pan, B.; Xing, B. Adsorption Mechanisms of Organic Chemicals on Carbon Nanotubes. Environ. Sci. Technol. 2008, 42, 9005–9013. 21. Apul, O. G.; Karanfil, T. Adsorption of Synthetic Organic Contaminants by Carbon Nanotubes: a Critical Review. Water Res. 2015, 68, 34–55. 22. Kozbial, A.; Zhou, F.; Li, Z.; Liu, H.; Li, L. Are Graphitic Surfaces Hydrophobic? Acc. Chem. Res. 2016, 49, 2765–2773. 23. Sangster, J. Octanol-water Partition Coefficients of Simple Organic Compounds. J. Phys. Chem. Ref. Data 1989, 18, 1111–1229. 24. Comer, J.; Chen, R.; Poblete, H.; Vergara-Jaque, A.; Riviere, J. E. Predicting Adsorption Affinities of Small Molecules on Carbon Nanotubes Using Molecular Dynamics Simulation. ACS Nano 2015, 9, 11761–11774. 25. Johnson, R. R.; Johnson, A.; Klein, M. L. The Nature of DNA-Base–Carbon-Nanotube Interactions. Small 2010, 6, 31–34. 26. Chen, W.; Duan, L.; Zhu, D. Adsorption of Polar and Nonpolar Organic Chemicals to Carbon Nanotubes. Environ. Sci. Technol. 2007, 41, 8295–8300. 27. Chen, W.; Duan, L.; Wang, L.; Zhu, D. Adsorption of Hydroxyl-and Amino-substituted Aromatics to Carbon Nanotubes. Environ. Sci. Technol. 2008, 42, 6862–6868. 28. Imai, Y. N.; Inoue, Y.; Nakanishi, I.; Kitaura, K. Amide–π Interactions between Formamide and Benzene. J. Comput. Chem. 2009, 30, 2267–2276. 29. Poblete, H.; Miranda-Carvajal, I.; Comer, J. Determinants of Alanine Dipeptide Conformational Equilibria on Graphene and Hydroxylated Derivatives. J. Phys. Chem. B 2017, 121, 3895–3907. 38


Page 38 of 50

Page 39 of 50 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


30. Hughes, Z. E.; Walsh, T. R. What Makes a Good Graphene-binding Peptide? Adsorption of Amino Acids and Peptides at Aqueous Graphene Interfaces. J. Mater. Chem. B 2015, 3, 3211–3221. 31. Wolfenden, R.; Andersson, L.; Cullis, P.; Southgate, C. Affinities of Amino Acid Side Chains for Solvent Water. Biochemistry 1981, 20, 849–855. 32. Yan, X.; Shi, B.; Lu, J.; Feng, C.; Wang, D.; Tang, H. Adsorption and Desorption of Atrazine on Carbon Nanotubes. J. Coll. Interf. Sci. 2008, 321, 30–38. 33. Shen, X.-E.; Shan, X.-Q.; Dong, D.-M.; Hua, X.-Y.; Owens, G. Kinetics and Thermodynamics of Sorption of Nitroaromatic Compounds to as-grown and Oxidized Multiwalled Carbon Nanotubes. J. Coll. Interf. Sci. 2009, 330, 1–8. 34. Xia, X. R.; Monteiro-Riviere, N. A.; Mathur, S.; Song, X.; Xiao, L.; Oldenberg, S. J.; Fadeel, B.; Riviere, J. E. Mapping the Surface Adsorption Forces of Nanomaterials in Biological Systems. ACS Nano 2011, 5, 9074–9081. 35. Wu, T.; Cai, X.; Tan, S.; Li, H.; Liu, J.; Yang, W. Adsorption Characteristics of Acrylonitrile, p-toluenesulfonic Acid, 1-naphthalenesulfonic Acid and Methyl Blue on Graphene in Aqueous Solutions. Chem. Eng. J. 2011, 173, 144–149. 36. Zaib, Q.; Khan, I. A.; Saleh, N. B.; Flora, J. R.; Park, Y.-G.; Yoon, Y. Removal of Bisphenol A and 17β-estradiol by Single-walled Carbon Nanotubes in Aqueous Solution: Adsorption and Molecular Modeling. Water, Air, & Soil Pollution 2012, 223, 3281– 3293. 37. Chen, R.; Zhang, Y.; Darabi Sahneh, F.; Scoglio, C. M.; Wohlleben, W.; Haase, A.; Monteiro-Riviere, N. A.; Riviere, J. E. Nanoparticle Surface Characterization and Clustering through Concentration-Dependent Surface Adsorption Modeling. ACS Nano 2014, 8, 9446–9456.

39



38. DeFever, R. S.; Geitner, N. K.; Bhattacharya, P.; Ding, F.; Ke, P. C.; Sarupria, S. PAMAM Dendrimers and Graphene: Materials for Removing Aromatic Contaminants from Water. Environ. Sci. Technol. 2015, 49, 4490–4497. 39. Chen, X.; Chen, B. Macroscopic and Spectroscopic Investigations of the Adsorption of Nitroaromatic Compounds on Graphene Oxide, Reduced Graphene Oxide, and Graphene Nanosheets. Environ. Sci. Technol. 2015, 49, 6181–6189. 40. Chen, R.; Zhang, Y.; Monteiro-Riviere, N. A.; Riviere, J. E. Quantification of Nanoparticle Pesticide Adsorption: Computational Approaches Based on Experimental Data. Nanotoxicology 2016, 1–11. 41. Balamurugan, K.; Singam, E. A.; Subramanian, V. Effect of Curvature on the α-helix Breaking Tendency of Carbon Based Nanomaterials. J. Phys. Chem. C 2011, 115, 8886–8892. 42. Gopalakrishnan, R.; Balamurugan, K.; Singam, E. R. A.; Sundaraman, S.; Subramanian, V. Adsorption of Collagen onto Single Walled Carbon Nanotubes: a Molecular Dynamics Investigation. Phys. Chem. Chem. Phys. 2011, 13, 13046–13057. 43. Mijajlovic, M.; Penna, M. J.; Biggs, M. J. Free Energy of Adsorption for a Peptide at a Liquid/solid Interface via Nonequilibrium Molecular Dynamics. Langmuir 2013, 29, 2919–2926. 44. Camden, A. N.; Barr, S. A.; Berry, R. J. Simulations of Peptide-graphene Interactions in Explicit Water. J. Phys. Chem. B 2013, 117, 10691–10697. 45. Hughes, Z. E.; Tomásio, S. M.; Walsh, T. R. Efficient Simulations of the Aqueous Biointerface of Graphitic Nanostructures with a Polarisable Model. Nanoscale 2014, 6, 5438–5448.

40


Page 40 of 50

Page 41 of 50 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


46. Penna, M. J.; Mijajlovic, M.; Tamerler, C.; Biggs, M. J. Molecular-level Understanding of the Adsorption Mechanism of a Graphite-binding Peptide at the Water/graphite Interface. Soft Matter 2015, 11, 5192–5203. 47. Zhang, B.; Xu, J.; Mo, S.-F.; Yao, J.-X.; Dai, S.-Y. Molecular Dynamics Simulations of the Orientation Properties of Cytochrome c on the Surface of Single-walled Carbon Nanotubes. J. Mol. Mod. 2016, 22, 300. 48. Roccatano, D.; Sarukhanyan, E.; Zangi, R. Adsorption Mechanism of an Antimicrobial Peptide on Carbonaceous Surfaces: A Molecular Dynamics Study. J. Chem. Phys. 2017, 146, 074703. 49. Zou, X.; Wei, S.; Jasensky, J.; Xiao, M.; Wang, Q.; Brooks III, C. L.; Chen, Z. Molecular Interactions between Graphene and Biological Molecules. J. Am. Chem. Soc. 2017, 139, 1928–1936. 50. Johnson, R. R.; Kohlmeyer, A.; Johnson, A. C.; Klein, M. L. Free Energy Landscape of a DNA–carbon Nanotube Hybrid Using Replica Exchange Molecular Dynamics. Nano Lett. 2009, 9, 537–541. 51. Wells, D.; Belkin, M.; Comer, J.; Aksimentiev, A. Assessing Graphene Nanopores for Sequencing DNA. Nano Lett. 2012, 12, 4117–4123. 52. Banerjee, S.; Wilson, J.; Shim, J.; Shankla, M.; Corbin, E. A.; Aksimentiev, A.; Bashir, R. Slowing DNA Transport Using Graphene–DNA Interactions. Adv. Funct. Mater. 2015, 25, 936–946. 53. Landry, M. P.; Vukovic, L.; Kruss, S.; Bisker, G.; Landry, A. M.; Islam, S.; Jain, R. M.; Schulten, K.; Strano, M. S. Comparative Dynamics and Sequence Dependence of DNA and RNA Binding to Single Walled Carbon Nanotubes. J. Phys. Chem. C 2015, 119, 10048–10058.

41



54. Qiao, R.; Ke, P. C. Lipid-carbon Nanotube Self-assembly in Aqueous Solution. J. Am. Chem. Soc. 2006, 128, 13656–13657. 55. Monticelli, L.; Salonen, E.; Ke, P. C.; Vattulainen, I. Effects of Carbon Nanoparticles on Lipid Membranes: a Molecular Simulation Perspective. Soft Matter 2009, 5, 4433– 4445. 56. Li, Y.; Yuan, H.; von dem Bussche, A.; Creighton, M.; Hurt, R. H.; Kane, A. B.; Gao, H. Graphene Microsheets Enter Cells through Spontaneous Membrane Penetration at Edge Asperities and Corner Sites. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 12295–12300. 57. Liu, Y.; Chipot, C.; Shao, X.; Cai, W. Free-energy Landscape of the Helical Wrapping of a Carbon Nanotube by a Polysaccharide. J. Phys. Chem. C 2011, 115, 1851–1856. 58. Fu, H.; Chipot, C.; Shao, X.; Cai, W. Why Do the Structural Properties of Complexes Formed by Glucans and Carbon Nanotubes Differ So Much? RSC Adv. 2015, 5, 95682– 95689. 59. Lin, S.; Hilmer, A. J.; Mendenhall, J. D.; Strano, M. S.; Blankschtein, D. Molecular Perspective on Diazonium Adsorption for Controllable Functionalization of Single-walled Carbon Nanotubes in Aqueous Surfactant Solutions. J. Am. Chem. Soc. 2012, 134, 8194–8204. 60. Xu, L.; Yang, X. Molecular Dynamics Simulation of Adsorption of Pyrene–polyethylene Glycol onto Graphene. J. Coll. Interf. Sci. 2014, 418, 66–73. 61. Ulissi, Z. W.; Zhang, J.; Sresht, V.; Blankschtein, D.; Strano, M. S. 2D Equation-ofState Model for Corona Phase Molecular Recognition on Single-Walled Carbon Nanotube and Graphene Surfaces. Langmuir 2015, 31, 628–636. 62. Ding, H.; Shen, X.; Chen, C.; Zhang, X. Molecular Dynamics Simulations of Simple

42


Page 42 of 50

Page 43 of 50 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


Aromatic Compounds Adsorption on Single-walled Carbon Nanotubes. RSC Adv. 2016, 6, 80972–80980. 63. Calbo, J.; López-Moreno, A.; de Juan, A.; Comer, J.; Ort´ı, E.; Pérez, E. M. Understanding Noncovalent Interactions of Pyrene Derivatives with Carbon Nanotubes. Chem. Eur. J. 2017, 23, 12909–12916. 64. Sun, X.; Feng, Z.; Hou, T.; Li, Y. Mechanism of Graphene Oxide as an Enzyme Inhibitor from Molecular Dynamics Simulations. ACS Appl. Mater. Interfaces 2014, 6, 7153– 7163. 65. Golkaram, M.; van Duin, A. C. Revealing Graphene Oxide Toxicity Mechanisms: A Reactive Molecular Dynamics Study. Materials Discovery 2015, 1, 54–62. 66. Chen, J.; Brooks, C. L.; Scheraga, H. A. Revisiting the Carboxylic Acid Dimers in Aqueous Solution: Interplay of Hydrogen Bonding, Hydrophobic Interactions, and Entropy. J. Phys. Chem. B 2008, 112, 242–249. 67. Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25, 1157–1174. 68. Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I. et al. CHARMM General Force Field: A Force Field for Drug-like Molecules Compatible with the CHARMM All-atom Additive Biological Force Fields. J. Comput. Chem. 2010, 31, 671–690. 69. Robertson, A. W.; Warner, J. H. Atomic Resolution Imaging of Graphene by Transmission Electron Microscopy. Nanoscale 2013, 5, 4079–4093. 70. Wei, N.; Lv, C.; Xu, Z. Wetting of Graphene Oxide: A Molecular Dynamics Study. Langmuir 2014, 30, 3572–3578.

43



71. Song, Y.; Qu, K.; Zhao, C.; Ren, J.; Qu, X. Graphene Oxide: Intrinsic Peroxidase Catalytic Activity and Its Application to Glucose Detection. Adv. Mater. 2010, 22, 2206–2210. 72. Zhao, G.; Li, J.; Ren, X.; Chen, C.; Wang, X. Few-layered Graphene Oxide Nanosheets as Superior Sorbents for Heavy Metal Ion Pollution Management. Environ. Sci. Technol. 2011, 45, 10454–10462. 73. Sreeprasad, T.; Maliyekkal, S. M.; Lisha, K.; Pradeep, T. Reduced Graphene Oxide– metal/metal Oxide Composites: Facile Synthesis and Application in Water Purification. J. Hazard. Mater. 2011, 186, 921–931. 74. Liu, J.; Cui, L.; Losic, D. Graphene and Graphene Oxide as New Nanocarriers for Drug Delivery Applications. Acta Biomater. 2013, 9, 9243–9257. 75. Dave, S. H.; Gong, C.; Robertson, A. W.; Warner, J. H.; Grossman, J. C. Chemistry and Structure of Graphene Oxide via Direct Imaging. Chem. Mater. 1999, 11, 771–778. 76. Bagri, A.; Grantab, R.; Medhekar, N.; Shenoy, V. Stability and Formation Mechanisms of Carbonyl-and Hydroxyl-decorated Holes in Graphene Oxide. J. Phys. Chem. C 2010, 114, 12053–12061. 77. Cai, W.; Piner, R. D.; Stadermann, F. J.; Park, S.; Shaibat, M. A.; Ishii, Y.; Yang, D.; Velamakanni, A.; An, S. J.; Stoller, M. et al. Synthesis and Solid-state NMR Structural Characterization of 13C-labeled Graphite Oxide. Science 2008, 321, 1815–1817. 78. Bagri, A.; Mattevi, C.; Acik, M.; Chabal, Y. J.; Chhowalla, M.; Shenoy, V. B. Structural Evolution during the Reduction of Chemically Derived Graphene Oxide. Nature Chem. 2010, 2, 581–587. 79. Hunt, A.; Dikin, D. A.; Kurmaev, E. Z.; Boyko, T. D.; Bazylewski, P.; Chang, G. S.;

44


Page 44 of 50

Page 45 of 50 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


Moewes, A. Epoxide Speciation and Functional Group Distribution in Graphene Oxide Paper-Like Materials. Adv. Funct. Mater. 2012, 22, 3950–3957. 80. Bradley, R. H.; Cassity, K.; Andrews, R.; Meier, M.; Osbeck, S.; Andreu, A.; Johnston, C.; Crossley, A. Surface Studies of Hydroxylated Multi-wall Carbon Nanotubes. Appl. Surf. Sci. 2012, 258, 4835–4843. 81. Sun, J.; Deng, Y.; Li, J.; Wang, G.; He, P.; Tian, S.; Bu, X.; Di, Z.; Yang, S.; Ding, G. et al. A New Graphene Derivative: Hydroxylated Graphene with Excellent Biocompatibility. ACS Appl. Mater. Interfaces 2016, 8, 10226–10233. 82. Pumera, M.; Sofer, Z. Towards Stoichiometric Analogues of Graphene: Graphane, Fluorographene, Graphol, Graphene Acid and Others. Chem. Soc. Rev. 2017, 46, 4450– 4463. 83. Vanommeslaeghe, K.; MacKerell Jr, A. D. Automation of the CHARMM General Force Field (CGenFF) I: Bond Perception and Atom Typing. J. Chem. Inf. Model. 2012, 52, 3144–3154. 84. Vanommeslaeghe, K.; Raman, E. P.; MacKerell Jr, A. D. Automation of the CHARMM General Force Field (CGenFF) II: Assignment of Bonded Parameters and Partial Atomic Charges. J. Chem. Inf. Model. 2012, 52, 3155–3168. 85. Wang, J.; Wang, W.; Kollman, P. A.; Case, D. A. Automatic Atom Type and Bond Type Perception in Molecular Mechanical Calculations. J. Mol. Graph. Model. 2006, 25, 247–260. 86. Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781–1802.

45



87. Hopkins, C. W.; Le Grand, S.; Walker, R. C.; Roitberg, A. E. Long-time-step Molecular Dynamics through Hydrogen Mass Repartitioning. J. Chem. Theory Comput. 2015, 11, 1864–1874. 88. Miyamoto, S.; Kollman, P. A. SETTLE: an Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Models. J. Comput. Chem. 1992, 13, 952–962. 89. Andersen, H. C. RATTLE: A “Velocity” Version of the SHAKE Algorithm for Molecular Dynamics Calculations. J. Chem. Phys. 1983, 52, 24–34. 90. Darden, T. A.; York, D. M.; Pedersen, L. G. Particle Mesh Ewald: An N log N Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089–10092. 91. Feller, S. E.; Zhang, Y. H.; Pastor, R. W.; Brooks, B. R. Constant Pressure Molecular Dynamics Simulations — The Langevin Piston Method. J. Chem. Phys. 1995, 103, 4613–4621. 92. Darve, E.; Pohorille, A. Calculating Free Energies Using Average Force. J. Chem. Phys. 2001, 115, 9169–9183. 93. Comer, J.; Gumbart, J. C.; Hénin, J.; Lelièvre, T.; Pohorille, A.; Chipot, C. The Adaptive Biasing Force Method: Everything You Always Wanted to Know But Were Afraid to Ask. J. Phys. Chem. B 2015, 119, 1129–1151. 94. Fiorin, G.; Klein, M. L.; Hénin, J. Using Collective Variables to Drive Molecular Dynamics Simulations. Math. Probl. Eng. 2013, 111, 3345–3362. 95. Gorski, K. M.; Hivon, E.; Banday, A.; Wandelt, B. D.; Hansen, F. K.; Reinecke, M.; Bartelmann, M. HEALPix: a Framework for High-resolution Discretization and Fast Analysis of Data Distributed on the Sphere. Astrophys. J. 2005, 622, 759. 96. Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E.

46


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GROMACS: High Performance Molecular Simulations through Multi-level Parallelism from Laptops to Supercomputers. SoftwareX 2015, 1, 19–25. 97. Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Water Conduction through the Hydrophobic Channel of a Carbon Nanotube. Nature 2001, 414, 188–190. 98. Senftle, T. P.; Hong, S.; Islam, M. M.; Kylasa, S. B.; Zheng, Y.; Shin, Y. K.; Junkermeier, C.; Engel-Herbert, R.; Janik, M. J.; Aktulga, H. M. et al. The ReaxFF Reactive Force-field: Development, Applications and Future Directions. npj Computational Materials 2016, 2, 15011. 99. Aktulga, H. M.; Fogarty, J. C.; Pandit, S. A.; Grama, A. Y. Parallel Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques. Parall. Comp. 2012, 38, 245–259. 100. Plimpton, S. Fast Parallel Algorithms for Short-range Molecular Dynamics. J. Chem. Phys. 1995, 117, 1–19. 101. Srinivasan, S. G.; van Duin, A. C.; Ganesh, P. Development of a ReaxFF Potential for Carbon Condensed Phases and Its Application to the Thermal Fragmentation of a Large Fullerene. J. Phys. Chem. A 2015, 119, 571–580. 102. Kohlmeyer, A. TopoTools: Release 1.7. 2016, DOI: 10.5281/zenodo.50249. 103. Humphrey, W.; Dalke, A.; Schulten, K. VMD – Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33–38. 104. Smith, D. E.; Haymet, A. Free Energy, Entropy, and Internal Energy of Hydrophobic Interactions: Computer Simulations. J. Chem. Phys. 1993, 98, 6445–6454. 105. Wan, S.; Stote, R. H.; Karplus, M. Calculation of the Aqueous Solvation Energy and Entropy, as Well as Free Energy, of Simple Polar Solutes. J. Chem. Phys. 2004, 121, 9539–9548. 47



106. Liu, P.; Dehez, F.; Cai, W.; Chipot, C. A Toolkit for the Analysis of Free-energy Perturbation Calculations. J. Chem. Theory Comput. 2012, 8, 2606–2616. 107. Jo, S.; Chipot, C.; Roux, B. Efficient Determination of Relative Entropy Using Combined Temperature and Hamiltonian Replica-exchange Molecular Dynamics. J. Chem. Theory Comput. 2015, 11, 2234–2244. 108. Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Kollmann, P. A. Application of RESP Charges to Calculate Conformational Energies, Hydrogen Bond Energies, and Free Energies of Solvation. J. Am. Chem. Soc. 1993, 115, 9620–9631. 109. Pratt, L. R. Theory of Hydrophobic Effects. Annu. Rev. Phys. Chem. 1985, 36, 433– 449. 110. Lum, K.; Chandler, D.; Weeks, J. D. Hydrophobicity at Small and Large Length Scales. J. Phys. Chem. B 1999, 103, 4570–4577. 111. Peng, X.; Li, Y.; Luan, Z.; Di, Z.; Wang, H.; Tian, B.; Jia, Z. Adsorption of 1,2dichlorobenzene from Water to Carbon Nanotubes. Chem. Phys. Lett. 2003, 376, 154– 158. 112. Yao, Y.; Xu, F.; Chen, M.; Xu, Z.; Zhu, Z. Adsorption Behavior of Methylene Blue on Carbon Nanotubes. Bioresour. Technol. 2010, 101, 3040–3046. 113. Finney, J. L. The Water Molecule and Its Interactions: the Interaction between Theory, Modelling, and Experiment. J. Mol. Liq. 2001, 90, 303–312. 114. Chen, J.; Chen, W.; Zhu, D. Adsorption of Nonionic Aromatic Compounds to Singlewalled Carbon Nanotubes: Effects of Aqueous Solution Chemistry. Environ. Sci. Technol. 2008, 42, 7225–7230. 115. Hansen, N.; Van Gunsteren, W. F. Practical Aspects of Free-energy Calculations: a Review. J. Chem. Theory Comput. 2014, 10, 2632–2647. 48


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116. Karplus, M.; Kushick, J. N. Method for Estimating the Configurational Entropy of Macromolecules. Macromolecules 1981, 14, 325–332. 117. Ashbaugh, H. S.; Paulaitis, M. E. Entropy of Hydrophobic Hydration: Extension to Hydrophobic Chains. J. Phys. Chem. 1996, 100, 1900–1913. 118. Agnihotri, S.; Mota, J. P.; Rostam-Abadi, M.; Rood, M. J. Adsorption Site Analysis of Impurity Embedded Single-walled Carbon Nanotube Bundles. Carbon 2006, 44, 2376–2383.

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ENTHALPIC

Graphical TOC Entry –TΔS [kcal/mol]

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

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50

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ENTROPIC -1 0

–ΔH [kcal/mol]


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Thermodynamics of Adsorption on Graphenic Surfaces from Aqueous

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