Universal Repulsive Contribution to the. Solvent-Induced Interaction Between Sizable, Curved Hydrophobes: Supporting Information

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1 Universal Repulsive Contribution to the Solvent-Induced Interaction Between Sizable, Curved Hydrophobes: Supporting Information B. Shadrack Jabes, Dusan Bratko, and Alenka Luzar Department of Chemistry, Virginia Commonwealth University, Richmond, VA, USA Additional computational details Models: In this section we describe the details of the model used for simulating bare and hydrophobized graphitic nanoparticles immersed in SPC/E water. 1 The molecular parametrization obtained from the all-atom optimized potentials for liquid simulation force field (OPLS-AA), 2 is used to model the alkyl chains on the solute surface. Alkyl chains: Surface hydrophobicity can be controlled by functionalization with flexible n- alkyl groups of general formula C n H (2n+1). In an earlier work, we have shown that the equilibrium contact angle of water on a sheet of n-alkyl functionalized graphane increases with chain length until it saturates around 114 for all chain lengths with n 4. 3 The number of chains required to yield a number density per surface area (4.01 nm 2 ) on the surface of a highly curved solute such as functionalized fullerene is 24. To fix the areal density of methyl endgroups in contact with water requires additional chains if the length is increased beyond n = 3, leading to steric issues. Therefore we use propyl chains to functionalize the graphitic nanoparticles. The contact

2 angle of the water drop on propylated graphane is The OPLS-AA potential parameters and charges used for modelling n-alkyl functionalized graphane system are shown in Tables Functionalized Graphane: Graphane is a saturated form of graphene with sp 3 hybridization. Therefore, it is easy to functionalize graphane without changing the planarity. We choose the chair conformation where the hydrogen atoms covalently bonded to the carbon atoms alternate on both sides of the carbon backbone. The equilibrium graphane geometry was obtained from ab-inito calculations 4,5 and was subsequently confirmed in the experiment. 6 The number of carbon atoms in the backbone of the planar graphane sheet is 255. The graphane sheet is modeled as all-atom model. The symmetry of the sheets is preserved by treating them as rigid molecules during the simulation. Propyl-functionalized graphane sheet dimension of Å x 35.8 Å is used in the simulation. The C-C, C-H bond lengths are Å, 1.11 Å and C-C-C, C-C-H bond angles are and , respectively. There are 19 chains on the surface of graphane, which results in number density per surface area of 4.01 nm 2. The functionalized nanoparticles were placed initially at the center-to-center distance of Å along x-axis using VMD. 7 This dimer is finally placed at the center of an orthogonal box of size 67 Å x 35 Å x 50 Å. These box dimensions suffice to avoid any significant solute/replica-solute interaction. Functionalized carbon nanotube (CNT): In order to compare the solutes of different geometry, we chose the solute sizes and dimensions based on the effective diameter of the propylated fullerene σ s. In order for the carbon nanotube to have an equal diameter, we choose the nanotube chiral index to be n=2 x m=8. R total, is the effective radius of the functionalized solutes measured from the center of mass of fullerene to the extended propyl chain length. The length of the CNT-s and graphane plates was 34.6Å, which corresponds to 366 carbon atoms. The all-atom CNT model was built using VMD nanotube builder. 7 The symmetry of the CNT-s was preserved by treating them as rigid molecules during the simulation. To achieve the desired density of 4.01 terminal groups per nm 2 of solute/water contact plane, 60 propyl chains were planted on the surface of a CNT molecule. 2

3 Functionalized Fullerenes: The fullerene C 60 model used in this study has an icosahedron geometry. Atomic coordinates were obtained from the program Fullerene. 8,9 The symmetry of the fullerenes were preserved by treating them as rigid molecules during the simulation. The functionalized fullerene carried 24 chains resulting in the density of terminal methyl groups per surface area of the contact plane with water of 4.01 nm 2. Bond lengths and bond angles used to model the functionalized solutes are described by E bond = K r (r r eq ) 2 (1) bonds E angle = K θ (θ θ eq ) 2 (2) angle K r (kcal Å 2 ), K θ (kcal rad 2 ) are the force constants and r eq, θ eq are the equilibrium bond length and bond angle respectively. The OPLS triple cosine potential is used for torsional interactions given by E(φ) = V 1 2 [1 + cos(φ + f 1)] + V 2 [1 + cos(φ + f 2)]+ 2 V 3 [1 + cos(φ + f 3)] 2 V 1, V 2, V 3 are constants, f 1, f 2, f 3 are phase angles. Non bonded interactions are modeled using the following functional form (3) E ab = a b i j [q i q j e 2 /r i j + 4ε i j (σ 12 i j /r 12 i j σ 6 i j/r 6 i j)] f i j (4) where, f i j = 0.5 if i,j are 1,4; otherwise, f i j = 1.0 Methods Molecular dynamics simulations: MD of the bare and molecular-coated graphitic nanoparticle system were performed using the LAMMPS package. 10 The box dimension, the number of water molecules used to solvate the functionalized solutes and the number of alkyl chains used on the 3

4 Table 1: OPLS-AA Lennard-Jones parameters and charges used for propyl functionalized solutes: graphane, carbon nanotube and fullerene. ID is the identification label for each atom. Atom σ (Å) ε (kcal mol 1 ) q(e 0 ) ID C, RCH C1 C, R 2 CH C2 C, R 3 CH C3 C, R 4 C C4 H, RH H Table 2: OPLS-AA/CHARMM22 equilibrium bond lengths and bond force constants used for propyl functionalized graphane, carbon nanotube and fullerene. 2 Atom r 0 (Å) k r (kcal mol 1 Å 2 ) C2-C C1-H C2-CX C1-C C2-H C2-C Table 3: OPLS-AA/CHARMM22 equilibrium angle and force constants used for propyl functionalized graphane, carbon nanotube and fullerene. 2 Atom θ 0 (deg) k θ (kcal mol 1 rad 2 ) C1-C2-C C4-C2-H C2-C2-C H-C1-H C2-C1-H H-C2-H C1-C2-H C2-C2-H Table 4: OPLS-AA Fourier coefficients for dihedral angles for propyl functionalized graphane, carbon nanotube and fullerene. 2 Atom V 1 (kcal/mol) V 2 (kcal/mol) V 3 (kcal/mol) V 4 (kcal/mol) C4-C2-C2-C C4-C2-C2-H C1-C2-C2-H C2-C2-C1-H H-C2-C2-H H-C2-C1-H

5 Table 5: Box dimensions, number of water molecules and number of propyl chains on functionalized solutes with different geometries. Functionalization System box (Å 3 ) N water N propyl C 60 67x35x Bare CNT 70x40x Graphane 67x35x C 60 67x35x Propyl CNT 70x40x Graphane 67x35x solutes are given in Table 5. The SHAKE algorithm was used to constrain the bonds in water molecules. The non-bonded cut-off distance was set to 12Å. The simulation timestep was 1fs. The velocity Verlet algorithm was used to integrate the equations of motion. Equilibration runs were performed in the NPT ensemble at 1 atm pressure and 300 K. During equilibration, the two solutes were treated as rigid molecules at a large separation (Table 6), allowed to rotate around their centers of mass under the influence of the solvent forces. Particle-particle-particle mesh solver (PPPM) with a real space cut off of 12.0Å and a relative precision tolerance in force per atom of 10 5 was used for Coulombic interactions. Berendsen barostat with a time constant of 1fs and damping factor of 1000 was used to control the pressure and Nose-Hoover thermostat with a time constant of 1ps was used to control the temperature. The total length of the equilibration runs is shown in Table 6. Potential of Mean Force calculation: The potential of mean force (W) is the free energy change as a function of reaction coordinates between two states, here the distance between the nanoparticles in vacuum or in the solvent: W(r) = r [ ( )] 0.5 F A F B. r dr (5) where, r is the unit vector pointing from particle A to B and is given as, r = r B r A r B r A (6) 5

6 Table 6: Equilibration run length at the largest solute separation, and equilibration and production NPT run lengths for selected pair separations considered in this study. System Equilibration Equilibration Production per window at 30Å (ns) ns ns C Bare CNT Graphane C Propyl CNT Graphane The term within the ensemble average is the solvation mean force. F A and F B, represents the sum of all forces acting upon the nano particle A and B. The two solutes were initially placed at a relatively large separation ( Å) and were free to rotate under the influence of the solvent forces. During the umbrella sampling MD simulation we evaluate the average solvation force at different pair separation values as described in Equation 5. The umbrella sampling window is then moved by gradually pulling the two solutes along the x-direction from the larger to smaller pair separations at a rate of 0.1Å per ps. Using the above equilibrated initial configuration, further equilibration runs were performed at selected separations for 2-3 ns, followed by a production run of 3-6ns in the NPT ensemble. The mean force was computed every timestep during the production run. About 300 ns runs were therefore used for a typical W(D) curve. In-order to estimate the reproducibility of the computed W(D), the main trajectory was split into two blocks and the W(D) profiles were calculated separately for each block. Interface Areas for a Pair of Adjacent, Finite-Length Cylindrical Solutes When parallel cylindrical solutes of finite length are separated by the distance D < σ, the net liquid/vacuum and solid/vacuum interfaces created upon the steric expulsion of solvent molecules 6

7 are S lv = 2L(D + 2h) + 2{2a(D + 2h) 2[R 2 φ a(r h)]}, S sv = 4RLφ (7) where φ = sin 1 R a. The meaning of distances a and h is explained in Fig. 1 and Eq. 4 of the main text. Eq. 2 of the main text combined with the above expressions provides the criteria for the spontaneity of solvent expulsion in the above geometry. Simulated Potentials of Mean Force and Structures In Figs. 1 and 2, we present the total potential of mean force W(D) (left) and direct contribution to W(D) (right) between pristine carbon particles (Fig. 1) and their propylated counterparts (Fig. 2). In both Figures, W is normalized by the number of carbon atoms comprised in the interacting solute surfaces. 0.0 W(D) / kjmol (a) total, bare Graphane CNT C (b) direct, bare D / Å D / Å Figure 1: The variation of (a) the total, and (b) the direct contribution to the potential of mean force W as a function of the pair separation for the bare solutes (C 60, CNT and graphane) in SPC/E water. On the x-axis we plot the separation D = r σ s, where, σ s is the excluded volume diameter of the solute, i.e. 2.5 Å for graphane and 10.1 Å for CNT and C 60. r is the center to center distance between the nano particles. W(D) is normalized by the number of atoms on the opposing surfaces of the solutes, 30 for C 60, 183 for CNT, and 255 for graphane. The normalization used in Fig. 3 of the main text and in Figs. 1 and 2 of the SI adjusts W(D) with respect to the size of the interacting surfaces (measured in the number of carbon atoms). However, only a fraction of these surfaces is actually involved in the interaction between curved 7

8 2 0 W(D) / kjmol (a) total, propylated Graphane CNT C (b) direct, propylated D / Å D / Å Figure 2: The variation of (a) the total potential of mean force W, and (b) the direct contribution to W as a function of the pair separation D for the solutes (C 60, CNT and graphane) functionalized by propyl chains. D = r σ s and σ s is the excluded volume diameter of the solute: 10.5 Å for the platelets and Å for fullerenes and CNT-s. r is the center to center distance between the nano particles. W(D) is normalized by the number of chains on the opposing surfaces of the solutes (60 on CNT, 19 on graphane and 12 on fullerene. particles. To account for both the differences in particle size and shape, Li et al. proposed a different renormalization 11 aimed at revealing the relative significance of the solvent-induced term in the total potential of mean force. In this approach, the solvent-induced W(D) between the fullerenes is compared to the result for the CNT-s or platelets, divided by the ratio of the direct W(D) between respective particles at the position of global minimum (Figs. 1b and 2b in the SI) and the corresponding quantity for the fullerenes. The results of this renormalization are shown in Fig. 3 of the SI. Here, the repulsive solvent-induced contribution increases from the platelets to nanotubes to fullerenes in agreement with the expectations from the mean-field analysis (Eq. 1), and with the related results from ref. 11 Fig. 4 illustrates the density profiles in systems with propyl-coated, evaporation-prone nanoparticles at small separations. Spontaneous evacuation of the intervening region is indicated in the propylated graphene and CNT systems at 4 Å separations while only a mild depletion is observed between propylated fullerene particles. 8

9 W * (D) / kjmol bare Graphane CNT C D / Å Figure 3: The solvent mediated contribution to the potential of mean force W as a function of the pair separation D for the pristine graphitic solutes (C 60, CNT and graphane). For a better comparison between the results for the different solute species, W is normalized by the ratios of the direct particle interaction for given species and the direct interaction between fullerene (C 60 ) particles taken at the position of maximal direct attraction. The procedure has been shown, 11 to account for the differences in both the particle sizes and geometries of solute species. D = r σ s and σ s is the excluded volume diameter of the solute: 2.5 Å for the platelets and 10.1 Å for fullerenes and CNT-s. r is the center to center distance between the nano particles. 9

1.0 2.81 Å ρ / gcm 3 0.8 0.6 0.4 0.2 0.0 1.

0 30 20 10 0 10 20 30 x (Å) 1.4 1.2 4.36 Å 1.

8 0.6 0.4 0.2 0.0 30 20 10 0 10 20 30 x (Å) 3.0 2.5 5.

of the propylated C 60 (blue), CNT (green) and

10 Å ρ / gcm Å ρ / gcm x (Å) Å 1.0 ρ / gcm Å ρ / gcm x (Å) Å ρ / gcm ρ / gcm Å x (Å) Figure 4: The variation of the water density along the x direction at pair separations corresponding to the dry and wet states of the propylated C 60 (blue), CNT (green) and graphane (red). The simulation snapshots corresponds to the dry and wet states of the respective systems. 1 10

11 References (1) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, (2) Jorgensen, W. L.; Maxwell, D. S.; Rives, T. J. Development and Testing of the OPLS All- Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, (3) Vanzo, D.; Bratko, D.; Luzar, A. Wettability of Pristine and Alkyl-Functionalized Graphane. J. Chem. Phys. 2012, 137, (4) Sofo, J.; Chaudhari, A. S.; Barber, G. D. Graphane: A Two-Dimensional Hydrocarbon. Phys. Rev. B 2007, 75, (5) Boukhvalov, D. W.; Katsnelson, M. I.; Lichtenstein, A. I. Hydrogen on Graphene: Electronic Structure, Total Energy, Structural Distortions and Magnetism from First-Principles Calculations. Phys. Rev. B 2008, 77, (6) Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K.; Novoselov, K. S. Control of Graphene s Properties by Reversible Hydrogenation: Evidence for Graphane. Science 2009, 323, (7) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33. (8) Fowler, P.; Manolopoulos, D. An Atlas of Fullerenes; 1995; Clarendon Press. (9) Schwerdtfeger, P.; Wirz, L.; Avery, J. Program Fullerene. page=fullerenes. (10) Plimpton, S. J. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117,

12 (11) Li, L.; Bedrov, D.; Smith, G. D. Water-induced Interactions Between Carbon Nanoparticles. J. Phys. Chem. B 2006, 110,

Supporting Information for Solid-liquid Thermal Transport and its Relationship with Wettability and the Interfacial Liquid Structure

Supporting Information for Solid-liquid Thermal Transport and its Relationship with Wettability and the Interfacial Liquid Structure Bladimir Ramos-Alvarado, Satish Kumar, and G. P. Peterson The George