Universal Repulsive Contribution to the Solvent-Induced Interaction

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Letter

Universal Repulsive Contribution to the Solvent-Induced Interaction Between Sizable, Curved Hydrophobes B. Shadrack Jabes, Dusan Bratko, and Alenka Luzar J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b01442 • Publication Date (Web): 27 Jul 2016 Downloaded from http://pubs.acs.org on August 1, 2016

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The Journal of Physical Chemistry Letters

Universal Repulsive Contribution to the Solvent-Induced Interaction Between Sizable, Curved Hydrophobes B. Shadrack Jabes, Dusan Bratko, and Alenka Luzar∗ Department of Chemistry, Virginia Commonwealth University, Richmond, USA E-mail: [email protected]

Abstract In addition to the direct attraction, sizable hydrophobes in water experience an attractive force mediated by interfacial water. Using simple geometric arguments, we identify the conditions at which the water-induced interaction between curved hydrocarbon surfaces becomes repulsive. The repulsive contribution arises from the thermodynamic penalty due to the emergence of the liquid/vapor boundary created as water gets expelled between curved hydrophobes. By augmenting the mean field approach with atomistic simulations of pristine and alkyl-coated graphitic nanoparticles in three distinct geometries, spherical, cylindrical and planar, immersed in water, we show the macroscopic thermodynamics remarkably works down to the molecular scale. The new insights improve the prediction and control of wetting and dispersion properties for a broad class of nonpolar nanoparticles.

Water molecules adjacent to the suspended hydrophobic nanoparticles are deprived of some of their hydrogen bonds, hence destabilizing the liquid state. 1 Because of unfavorable surface thermodynamics, for a sufficient solute size, water tends to withdraw from the region between ∗ To

whom correspondence should be addressed

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approaching particles. Spontaneous expulsion supports the formation of contact (as opposed to solvent-separated 2 ) pairs with a stronger bond than the same solutes would form in the absence of the solvent. 3,4 The mechanism underlies association of bigger particles (typically exceeding one nm size 5 ), where the interaction is predominantly enthalpic and has been shown to scale in proportion to the dehydrated area of the solutes brought into contact. 6–8 The particle geometry has, however, been known to play a role. 8–10 In this Letter, we discuss examples of even qualitatively different features of the solventinduced interaction between particles of identical compositions and diameters, but different shapes. We consider sizable solutes (diameter ≥ 1 nm) with realistic molecular potentials and focus on the effect of a single property, i.e. geometry, without changing any other characteristic of the waterexposed particle surface. To this end, we use pristine graphitic nanoparticles and their propylfunctionalized counterparts at constant areal density of exposed methyl groups at the solute/water contact plane. This contrasts the reported transitions 11–13 within small-solute series, varying not only in size but also in hydrophilicity as both the density per volume, 11,14 and the density per solvent-accessible area 14 of the solute increase simultaneously with the solute size. Using a simple mean field (MF) model allows us to predict the sign of solvation interactions between adjacent hydrophobes and classify them into repulsive or attractive regimes based on the competition between the favorable particle dewetting and simultaneous formation of a liquid/gas interface between the particles. We validate the MF predictions in molecular dynamics (MD)/umbrella sampling simulations of the interaction profiles between particles of different shapes. We consider bare graphitic nanoparticles with three principal geometries, fullerene C60 , carbon nanotubes (CNT-s) and graphane (hydrogenated graphene) 15 platelets, as well as propyl-functionalized particles with identical carbon backbones. Due to the alkyl coating, the functionalized particles are much bigger and more hydrophobic, with the platelet contact angle of ∼ 110◦ , as opposed to near 80◦ for the bare graphene 16–18 and 75◦ for its hydrogenated form. 15,19 Simulations of pristine fullerenes 10,11,20–22 and carbon nanotubes (CNT-s) 10,23 in water demon-


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strated a repulsive solvent-induced interaction for near-contact separations. The proposed rationales included insufficient size 21 or hydrophobicity, 24 and structural changes in confined water. 11,20,25 In what follows, we show that simple geometric arguments, applied to curved particles, predict a seemingly hydrophilic solvation interaction even for significantly enlarged and strongly hydrophobic solutes like alkyl-coated nanoparticles we use in direct simulations. The repulsion does not need to rely on the solute hydrophilicity implied in refs., 21,24 or on the distinct properties of intervening water. 20 It can be explained in terms of the thermodynamic penalty 26–28 associated with the emergence of a liquid/vacuum interface connecting adjacent curved hydrophobes; for finite curvatures, the penalty does not vanish even in the contact state. As illustrated in Figure 1, drying of an area between curved solutes, e.g. spheres or cylinders, inevitably involves a creation of liquid/vapor interface Slv and the concomitant loss of water-water coordination. The associated free energy cost can offset the favorable effect of dewetting the hydrophobe surfaces. As a consequence, water does not evacuate spontaneously. Instead, work is required for expulsion as particles are brought into contact. In these cases, the radius of the dry area, a, Fig. (1) is determined by the size of the region that is sterically inaccessible to solvent molecules separated by the surface-to-surface distance D. When the solvent expulsion is spontaneous, on the other hand, the free energy minimization can result in a bigger radius of the dried surface, a. To the 1st st approximation, the energetics of the expulsion can be estimated at the continuum level. Following the previous works, 26–29 we approximate the grand potential change, ∆Ω, upon water expulsion as ∆Ω = Ssv γ cosθc + Slv γ − (Pv − P)∆V

(1)

where θc is the contact angle of water on given material, Ssv and Slv are the areas of solid (s), liquid (l) and vacuum (v) interfaces. γ is the liquid surface tension and −γ cosθc = γsl − γsv the wetting free energy of the dissolved particles. The wetting free energy is therefore positive for obtuse, and negative for acute contact angles. The third term, representing the PV work, is negligible in comparison with the surface terms for nano-sized particles at ambient pressure. The condition for



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To favor the contact pair formation, the particles have to satisfy the inequality of Eq. 2 at D = 0. In this case, Eq. 2 for spherical solutes simplifies to 2R +1 1 p σR ≥0 + (4 σ + 1) cosθc

(6)

and a similar analysis for a pair of parallel, infinitely long cylindrical solutes yields the condition R (2 + 1)cos−1 σ

2 σR 2 σR

+1

!

+

1 ≥0 cosθc

(7)

A generalization to cylinders of finite L is given in the Supporting Information. In the planar geometry, Slv vanishes in contact, reducing the condition for the spontaneous evacuation and the solvation-driven formation of a contact pair to cosθc < 0. Solving Equations 2, 5 and 6 for σ = 3.166 (molecular diameter of water), we construct a state diagram with two variables: the curvature radius of the nanoparticles and the contact angle of the material and compare three distinctly different geometries. For every contact angle, the solute radii R below or to the left of the respective curve in Fig. 2 correspond to situations where the repulsive free-energy term γ Slv overwhelms the favorable term associated with drying of the hydrophobic area, Ssv γ cosθc . Small curvatures and big contact angles of a material favor water expulsion and thus contribute to attractive solvent-induced interaction and the formation of contact pairs. For big curvatures and small contact angles, on the other hand, expulsion of water requires work. In the latter case, the solvent-induced contribution to the short range interaction is repulsive. For planar particles, the transition between the repulsive and attractive solvent-induced contributions takes place at contact angle 90◦ irrespective of the size. The curvature, however, reduces the propensity for the expulsion, which means that for small particles like C60 , the threshold contact angle increases well above 90◦ . In comparison to spheres, the cylindrical geometry gives a more favorable ratio between Ssv and Slv , hence the solvation interaction can be attractive at comparatively smaller radii, R, or at lower contact angles θc . This advantage is less pronounced for cylinders of a finite length. Figure 2 shows the dependence of the threshold radius R for the 5 ACS Paragon Plus Environment


cylindrical particles of length 34.6Å we used in the MD simulation. 40 30 R/m

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Figure 2: The variation of the minimal reduced size σR supporting spontaneous solvent expulsion between spherical (blue curve), cylindrical (green curve), or planar solutes (red vertical line) at contact, plotted as a function of the solute material’s contact angle. R and σ /2 are the excluded volume radii of the nanoparticles and the solvent molecules, respectively. Solvent-induced attraction is promoted by increased R and θc . The attractive regime is expected in blue regions shown in separate plots for the planar, cylindrical, and spherical particles in the top row. The dotted lines in the bottom plot correspond to the size of functionalized solutes and the contact angle of propylated graphane, θc ≃ 110◦ . Contact angles of the bare particles are close to 18 or below 15 the estimated contact angle of neat graphene θc ≈ 79◦ 17 suggesting repulsive solvent-induced interactions between the bare particles in the geometries. Using aqueous C60 and CNT-s of equal radius in our examples, Figure 2 suggests their solutesolvent contact distance, R ≃ 5.1Å , R/σ ≃ 1.6 would support an attractive solvent-induced contact interaction only at unrealistically high contact angles. The contact angle for the prevalent force fields of graphene is close to or below 90◦ 15,30 and similar area densities of carbon atoms in fullerenes, CNT-s and graphene suggest comparable hydrophobicities for all three principal structures. According to Fig. 2, a slight excess of θc above 90◦ could still secure a solvent-induced attraction in the platelet geometry, but not for C60 or CNT-s. Both the solvent-induced repulsion 10 and attraction 8 among graphene platelets have been reported, while a repulsive solventinduced interaction was consistently observed in realistic-model simulations of CNT-s 23,31 and 6 ACS Paragon Plus Environment

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fullerenes. 10,11,20–22,32 To broaden the range of the conditions necessary to test the predictions from Eqs. 2-6 for the bigger and strongly hydrophobic particles, below we present MD results for potentials of mean force (W ) between alkyl-functionalized graphitic particles in all three geometries. In Fig. 3, we present the results for the propylated graphane 15 platelets, CNT-s and C60 , as well as those obtained by applying the same simulation methodology to respective pristine species with identical carbon backbones. We first take a look at the bare particles. We plot the water-induced contribution to the potential of mean force, W (D) = Ω(D) − Ω(∞), as a function of the distance between the closest atoms on a pair of bare solutes, D = r − σs . σs ≡ 2R is the excluded volume diameter of the solute. r, is the center to center distance between the two nanoparticles. This definition of pair separation allows us to compare the W (D) profiles for nanoparticles of different geometries and sizes. The solvent induced interaction, W ∗ (D) is computed from the difference between W (D) in solvent and vacuum, further normalized by the number of atoms comprised in the two opposing solute surfaces. (See Figs. 1 and 2 in the Supporting Information for total W (D) and a separate result for direct solute-solute contribution). The oscillatory W ∗ (D) reflects the solvent layering, an effect most pronounced in the planar geometry. Because the contact angle of pristine particles is acute, local dewetting of approaching particles gives rise to a positive contribution to the potential of mean force. Unlike the repulsive term associated with the creation of the liquid/vacuum interface between the curved particles, this repulsive contribution to W ∗ (D) at θc < 90◦ is present in all geometries and increases in proportion to the size of the area inaccessible to water during interparticle contact. The solvent-induced potential (per atom) increases from C60 to CNT-s to the platelets. If the results for the different geometries are compared according to their relative importance for the total W (D) 10 , however, the solvent-induced contribution increases in the reverse order, with the smallest relative contribution in the plate geometry and the biggest for the fullerenes as further described and illustrated in Fig. 3 of the Supporting Information. In Figure 3 bottom, we present MD results for W ∗ (D) between significantly bigger and strongly



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Figure 3: Left: bare and propyl-coated graphitic nanoparticles in three geometries. Middle: the solvent induced contribution to the solute-solute interaction, W ∗ (D) as a function of the interparticle separation D. W ∗ (D)between the bare particles is normalized by the number of atoms present at the opposing surfaces of pristine solutes (30 for C60 , 183 for CNT, 255 for graphane). For propylated particles, W ∗ (D) is normalized by the number of propyl chains on the opposing surfaces of the particles (19 for graphane, 30 for CNT and 12 for fullerene). Right: The distribution of water molecules around bare (top) or propylated (bottom) graphane platelets, CNT-s, or fullerenes, as a function of separation Dαβ = rαβ − σαβ where σαβ = 21 (σα + σβ ) is the contact distance between species α and β . σα is the diameter of species α : 2.5 Å for bare graphane and 10.1 Å for CNT and C60 . These values increase to 10.5 Å and 17.34 Å for propyl-coated particles. The molecular diameter of model water is 3.166 Å . rαβ is the center to center distance between the two particles. Error bars are estimated from block averages. hydrophobic particles in the three different geometries but all with the identical propyl coating. The water contact angle of ∼ 110◦ 15 and γsl − γsv ∼22 mN m−1 unequivocally support hydrophobic hydration in all three geometries. Separation D is defined the same way as with bare particles. W ∗ (D) is normalized by the number of chains on the inside half of each solute (See Fig. 3). The oscillations of W ∗ (D) with the platelet separation D correspond to the removal of consecutive layers of hydration water between graphanes. Comparison between the functionalized and pristine nanoparticles shows the peaks in W ∗ (D) between propylated platelets, and CNT-s, are shifted to a bigger separation D ∼ 4 − 5 Å . A much smaller shift is observed with C60 . For propylated plates and CNT-s, the shift indicates spontaneous evacuation to take place before water could be squeezed


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out for sterical reasons, as is the case when forming the contact pairs of the propylated fullerenes, and between pristine particles in the three geometries. 33 The ratios of the nanoparticle radius and the solvent-molecule diameter,

R σ,

for the propyl-

coated graphane, CNT and C60 are 1.65, 2.73 and 2.73 respectively. For these sizes and material contact angle of ∼ 110◦ the MF model predicts a strongly attractive solvent-induced interaction for functionalized graphane and CNT while solvation interaction is repulsive for propyl-functionalized C60 (Fig. 2). The MF predictions are in complete agreement with the simulation. Looking at related examples in the literature, the MF approach also captures the water-induced attraction among artificially repulsive (highly hydrophobic) fullerenes C240 22 and CNT-s, 34 as well as the repulsion between C240 22 and CNT-s 23,31,34 with realistic solute-water potentials. These comparisons affirm the model captures a universal repulsive contribution to the solvent-induced interaction between curved nanoparticles. It also clarifies the difference in the sign of the big-solute limits of W ∗ (0) observed in studies of the small-to-large solute transitions by Zangi 8 and Makowski et al. 11 In these studies, the solvent-induced interaction itself, 11 or per contact area, 8 weakens initially with size because of the increasing density (per molecular volume) of the solutes, however, it remains attractive for planar hydrophobes 8 while it becomes repulsive for the curved ones. 11 The increased expulsion propensity of water confined between hydrophobic particles is consistent with the slight withdrawal of the 1st solvation layer away from an isolated propylated particle. As shown in Fig. 3, the shift of the 1st hydration peak is bigger for the planar than curved 35 hydrophobized solutes, while it is not observed 10 with the bare particles. The W ∗ (D) profiles presented in Fig. 3 indicate water is spontaneously expelled at about twice the distance of the first hydration peak for CNT-s and graphane plates, but persists between the fullerenes until much smaller separation. These observations are reinforced by calculations of the water structure between the particles. Figure 4a shows the average density of water as a function of the separation D between the functionalized nanoparticles. The data pertain to the hydration shell between the solutes, no farther than ∼5Å from the hydrophobe/water contact plane. The volume of the test region around C60 is 9 ACS Paragon Plus Environment


∼ 0.55 nm3 . In order to keep the test volume and the lateral distance around the CNT and graphane comparable to the spherical scenario, we choose the dimensions of the cylindrical confinement to be 6.8Å . Similarly, the length and width of the planar confinement are 10.9Å x 10Å respectively. Because of the inclusion of the depleted interfacial layer, the average density remains below the bulk value at all separations D. The separation dependence of the density of the hydration shell water between propylated plates and CNT-s resembles a step function, indicative of a spontaneous expulsion. In the case of the fullerenes, water is removed solely due to the steric exclusion. 1

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Figure 4: The variation of (a) the density of water molecules confined between two solutes within a radius of ∼5 Å from the surface of the solute and (b) the reduction of the average number of hydrogen bonds per water molecule as a function of pair separation D measured relative to the solute-solute contact distance σs . The simulation snapshots for the C60 , CNT and graphane correspond to the pair separations, D= 2.12Å , 4.01Å , and 4.5Å , respectively. The critical separation Dc at which water evacuates the confinement between the plates and CNT-s is close to 4.5 Å and 4.3 Å respectively. The Dc for propylated graphane is in good agreement with the predictions from the modified Kelvin equation for finite-size plates (3.9Å ). 26,27 Studies of bare carbon nanoparticles have shown that the average number of hydrogen bonds 10 ACS Paragon Plus Environment

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per water molecule between a pair of solutes, < nHB >, decreases from the bulk value of ∼ 3.56 to ∼ 2.7 for the last layer between graphenes, 10 ∼ 2.9 for CNT-s 10 and ∼ 3.2 for C60 -s. 10,20 Figure 4b illustrates the reduction of < nHB > between propylated carbon nanoparticles assessed in the same test region we used in Figure 4a. Unlike water around bare nanoparticles, 10,20 a severe reduction in the extent of the hydrogen bonding is observed near the functionalized surfaces of graphane and CNT at small separations. The reduction is consistent with the spontaneous expulsion of water between approaching plates and cylinders, but not between functionalized fullerenes. In the latter case, the much milder loss of hydrogen bonds reflects the reduced coordination of water molecules situated at the liquid boundaries, similar to water between pristine carbon particles in all three geometries. 10 The milder disruption of water structure near a curved solute is consistent with the reduced volatility of the hydration water around the isolated nanoparticles. We quantify this dependence in terms of the local compressibility we calculate following Evans and Stewart. 36 Maximal interfacial compressibilities of 9, 7 and 4. 10−9 bar−1 we observe near a propylated platelet, CNT, and C60 , respectively, reveal a curvature effect that impacts both the hydrophobic hydration and interaction. COMPUTATIONAL DETAILS Models. We compare equally patterned particles in three principal geometries; planar, cylindrical and spherical. We consider bare and propylated forms of graphane, 15 carbon nanotube and fullerene C60 . The surface densities of water-exposed -CH3 groups on functionalized particles was ∼ 4.0 groups per nm2 of solute-water contact surface, mimicking self-assembled monolayers. 15,37,38 At ∼ 110◦ , the contact angle of the propylated graphane is just slightly below the saturation (114◦ ) with respect to the length of the alkyl groups and propyl groups are the longest ones that can sterically accommodate the desired surface density at the high surface curvature of C60 . 24 propyl chains are necessary to achieve the desired surface density on C60 . We use nanotubes of diameter identical to that of fullerene and tube length 34.6Å , which corresponds to 366 carbon atoms. We plant 60 propyl chains on the functionalized solute. The graphane platelet has dimensions of 16.53Å x 35.8Å matching the length and width of the CNT. This requires 255 C atoms



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on the backbone. 19 propyl chains, all planted on the same side, produce the desired area density of methyl groups. We use the OPLS-AA force field 39 for the solutes and the extended simple point charge model (SPC/E 40 )for water. We define hydrogen bonds using the geometric criterion outlined in ref. 41 Additional details and the force field parameters are given in the Supporting Information. Molecular Dynamics/umbrella sampling simulation: Constant pressure and temperature (NPT) MD simulations of the bare and molecular-coated graphitic nanoparticles surrounded by up to 5.6. 103 water molecules, with periodic boundary conditions implemented by the Particleparticle-particle mesh (PPPM) method, were performed using the LAMMPS package with Verlet algorithm and 1 fs timestep. The cutoff of short-range interactions was 12 Å . During umbrella sampling calculations of W (D) between the hydrophobes, a pair of solutes ∼ 30 Å apart were initially equilibrated for 9-10 ns and then gradually pulled to smaller separations with the rate of 0.1Å per 100-150 ps to generate initial configurations for use in 2-3 ns equilibration and 3-6 ns production runs at selected separations. This brings the runtime for a typical W (D) curve to ∼300 ns. A detailed account of the simulation methods is provided in the SI. Acknowledgement: SJB and AL acknowledge the support for this work from the US National Science Foundation (CHE-1213814) and DB thanks for partial support from DOE/BES (DE-SC 0004406). We also acknowledge supercomputing time allocations from the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF Grant No. OCI-1053575, and the National Energy Research Scientific Computing Center (NERSC), supported by the Office of Science of the U.S. Department of Energy (DEAC02-05CH11231). Supporting Information Available: Further information about the methodology and additional computational results are available in the Supporting Information. This material is available free of charge at http://pubs.acs.org.


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(11) Makowski, M.; Czaplewski, C.; Liwo, A.; Scheraga, H. A. Potential of Mean Force of Association of Large Hydrophobic Particles: Toward the Nanoscale Limit. J. Phys. Chem. B 2010, 114, 993–1003. (12) Ben-Amotz, D. Hydrophobic Ambivalence: Teetering on the Edge of Randomness. J. Phys. Chem. Lett. 2015, 6, 1696–1701. (13) Ben-Amotz, D. Water-mediated Hydrophobic Interactions. Ann. Rev. Phys. Chem. 2016, 67, 617–638. (14) Harris, R. C.; Pettitt, B. M. Effects of Geometry and Chemistry on Hydrophobic Solvation. Proc. Natl. Acad. Sci. 2014, 111, 14681–14686. (15) Vanzo, D.; Bratko, D.; Luzar, A. Wettability of Pristine and Alkyl-functionalized Graphane. J. Chem. Phys. 2012, 137, 034707. (16) Ondarcuhu, T.; Thomas, V.; Nunez, M.; Dujardin, E.; Rahman, A.; Black, C. T.; Checco, A. Wetting of Partially Suspended Graphene. Sci. Rep. 2016, 6, 24237. (17) Li, T.; Wang, Y. J.; Kozbial, A.; Shenoy, G.; Zhou, F.; McGinley, R.; Ireland, P.; Morganstein, B.; Kunkel, A.; Surwade, S. P.; Li, L.; Liu, H. T. Effect of airborne contaminants on the wettability of supported graphene and graphite. Nature Mater. 2013, 12, 925–931. (18) Driskill, J.; Vanzo, D.; Bratko, D.; Luzar, A. Wetting transparency of graphene in water. J. Chem. Phys. 2014, 141, 18C517. (19) Further, when thin material like graphene is wetted from both sides, ≃ 10◦ reduction of the contact angle has been predicted 18 and confirmed in the experiment. 16 (20) Zangi, R. Are Buckyballs Hydrophobic? J. Phys. Chem. B 2014, 118, 12263–12270. (21) Graziano, G. On the Pairwise Hydrophobic Interaction of Fullerene. Chem. Phys. Lett. 2010, 499, 79–82. 14 ACS Paragon Plus Environment

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(22) Morrone, J. A.; Li, J. J.; Berne, B. J. Interplay between Hydrodynamics and the Free Energy Surface in the Assembly of Nanoscale Hydrophobes. J. Phys. Chem. B 2012, 116, 11537– 11544. (23) Ou, S.; Patel, S.; Bauer, B. A. Free Energetics of Carbon Nanotube Association in Pure and Aqueous Ionic Solutions. J. Phys. Chem. B 2012, 116, 8154–8168. (24) Remsing, R. C.; Weeks, J. D. Dissecting Hydrophobic Hydration and Association. J. Phys. Chem. B 2013, 117, 15479–15491. (25) Djikaev, Y. S.; Ruckenstein, E. Effect of Water Hydrogen Bonding on the Solvent-mediated Oscillatory Repulsion of C60 Fullerenes in Water. J. Phys. Chem. Lett. 2015, 6, 1761–1766. (26) Lum, K.; Luzar, A. Pathway to Surface-induced Phase Transition of a Confined Fluid. Phys. Rev. E 1997, 56, R6283–R6286. (27) Luzar, A. Activation Barrier Scaling of the Spontaneous Evaporation of Confined Water. J. Phys. Chem. B. 2004, 108, 19859–19866. (28) Cerdeirina, C. A.; Debenedetti, P. G.; Rossky, P. J.; Giovambattista, N. Evaporation Length Scales of Confined Water and Some Common Organic Liquids. J. Phys. Chem. Lett. 2011, 2, 1000–1003. (29) Berne, B. J.; Weeks, J. D.; Zhou, R. Dewetting and Hydrophobic Interaction in Physical and Biological systems. Annu. Rev. Phys. Chem 2009, 60, 85–103. (30) Leroy, F.; Liu, S. J.; Zhang, J. G. Parametrizing Nonbonded Interactions from Wetting Experiments via the Work of Adhesion: Example of Water on Graphene Surfaces. J. Phys. Chem. C 2015, 119, 28470–28481. (31) Uddin, N. M.; Capaldi, F. M.; Farouk, B. Molecular Dynamics Simulations of Carbon Nanotube Dispersions in Water: Effects of Nanotube Length, Diameter, Chirality and Surfactant Structures. Comp. Mat. Sci. 2012, 53, 133–144. 15 ACS Paragon Plus Environment


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(32) Li, L.; Bedrov, D.; Smith, G. D. A Molecular-dynamics Simulation Study of Solvent-induced Repulsion Between c60 Fullerenes in Water. J. Chem. Phys. 2005, 123, 204504. (33) The reduction of W ∗ (D) for the propylated fullerenes near contact is attributed to the partial interpenetration of propyl brushes, an effect absent with CNT-s and the platelets where contact areas are significantly bigger. (34) Walther, J. H.; Jaffe, R. L.; Kotsalis, E. M.; Werder, T.; Halicioglu, T.; Koumoutsakos, P. Hydrophobic Hydration of C60 and Carbon Nanotubes in Water. Carbon 2004, 42, 1185– 1194. (35) Mamatkulov, S. I.; Khabibullaev, P. K.; Netz, R. R. Water at Hydrophobic Substrates: Curvature, Pressure, and Temperature Effects. Langmuir 2004, 20, 4756–4763. (36) Evans, R.; Stewart, M. C. The Local Compressibility of Liquids Near Non-adsorbing Substrates: a Useful Measure of Solvophobicity and Hydrophobicity? J. Phys. Cond. Matt. 2015, 27, 194111. (37) Bain, C. D.; Whitesides, M. W. Molecular-level Controlo over Surface Order in SelfAssembled Monolayer Films of Thiols on Gold. Science 1988, 62-63, 6374–6379. (38) Wang, J. H.; Bratko, D.; Luzar, A. Probing Surface Tension Additivity on Chemically Heterogeneous Surfaces By a Molecular Approach. Proc. Natl. Acad. Sci. 2011, 108, 6374–6379. (39) Jorgensen, W. L.; Maxwell, D. S.; Rives, T. J. Development and Testing of the OPLS AllAtom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225–11236. (40) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269–6271. (41) Luzar, A.; Chandler, D. Structure and Hydrogen Bond Dynamics of Water-dimethyl Sulfoxide Mixtures by Computer Simulations. J. Chem. Phys. 1993, 98, 8160–8173. 16 ACS Paragon Plus Environment

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80

e/o 100

90

110

120

30

R/m

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Ssva cose < Slva

20

Ssva cose > Slva

10

W(D)/kBT

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*

0

2

*

0 ï2

R/m = 2.7; e = 110o

’imaginary_line_toc_b’ ’imaginary_line_toc_b’

0

4

8

12

D/Å

1

ACS Paragon Plus Environment

Universal Repulsive Contribution to the Solvent-Induced Interaction

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