Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 4396−4400
pubs.acs.org/JPCL
Interdependent Roles of Electrostatics and Surface Functionalization on the Adhesion Strengths of Nanodiamonds to Gold in Aqueous Environments Revealed by Molecular Dynamics Simulations Liangliang Su,† Jacqueline Krim,† and Donald W. Brenner*,‡ †
Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, United States Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States
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‡
S Supporting Information *
ABSTRACT: Molecular dynamics simulations demonstrate that adhesion strengths as a function of charge for aqueous nanodiamonds (NDs) interacting with a gold substrate result from an interdependence of electrostatics and surface functionalization. The simulations reveal a water layer containing Na+ counterions between a negative ND with surface −COO− functional groups that is not present for a positively charged ND with −NH3+ functional groups. The closer proximity of the positive ND to the gold surface and the lack of cancelation of electrostatic interactions due to counterions and the water layer lead to an electrostatic adhesion force for the positive ND that is nearly three times larger than that of the negative ND. Prior interpretations of experimental tribological studies of ND−gold systems suggested that electrostatics or surface functionalization could be responsible for observed adhesion strength differences. The present work demonstrates how these two effects work together in determining adhesion for this system.
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differences in their performance. To explain the observations, they suggested that the functional groups on the ND, rather than the sign of the charge itself, may control their tribological performance. To better understand the role of charge and functionalization of NDs on their adhesion to gold,7 we have carried out allatom molecular dynamics simulations of octahedral NDs with different charged surface functional groups interacting with a gold surface. To mimic the experiment, the negatively and positively charged NDs had carboxyl (−COO−) and amino (−NH3+) surface functionalization, respectively. ND−solvent electron transfer that can lead to net charging of diamond surfaces with only hydrogen termination was not considered in our model.10 The electrostatic interactions between the gold surface and the NDs, counterions, and water solvent were modeled with a charge equilibration scheme that produces induced charges on the metal. To separate the effects of electrostatic interactions on the adhesion and sliding properties of the NDs interacting with the gold surface from those of the functional groups and nonbonding adhesion, the simulations were carried out with and without the induced substrate charges. The NDs were modeled as a ∼4 nm apex-to-apex diameter octahedron with 478 surface atoms on six exposed {111}
he addition of nanoparticles to liquid lubricants often leads to changes in tribological performance.1,2 Although for the majority of reported cases the nanoparticles improve lubrication performance by reducing friction and wear, there are also cases where adding nanoparticles increases the friction coefficient.3 The detailed physical mechanisms leading to these beneficial or detrimental properties remain to be fully explored.4−6 In a recent set of experiments by Liu et al.,7 for example, the uptake and tribological performance of positively and negatively charged nanodiamonds8,9 (NDs) on a gold surface were measured by a quartz-crystal microbalance (QCM). Two sets of experimental conditions were explored, the QCM immersed in an aqueous solution without a counter face and the QCM immersed in an aqueous solution in contact with stainless-steel ball bearings. It was concluded that negatively charged NDs are more weakly bound to the gold substrate compared with the positive NDs and that the negatively charged NDs are displaced from the gold−stainlesssteel contact while the positively charged NDs remain at the interface. Treating the ND−gold interaction as a point charge and an ideal metal, the adhesion should be independent of the charge sign. Hence to better understand these results, a more sophisticated model is needed that goes beyond simple electrostatic interactions. In a follow-up study, Curtis et al. explored the nanometer- and macroscopic-scale tribological characteristics of alumina and stainless-steel surfaces immersed in aqueous suspensions of positively (hydroxylated) or negatively (carboxylated) charged NDs3 and reported strong © XXXX American Chemical Society
Received: June 11, 2018 Accepted: July 20, 2018 Published: July 20, 2018 4396
DOI: 10.1021/acs.jpclett.8b01814 J. Phys. Chem. Lett. 2018, 9, 4396−4400
Letter
The Journal of Physical Chemistry Letters
This simulation used the LAMMPS code23 and a time step of 2 fs at constant volume and temperature via the Nosé− Hoover thermostat24,25 at 298 K. The induced charge distribution in gold was updated every 10 time steps using a Python code external to LAMMPS. The system was equilibrated for 2 ns, followed by the application of a force of 14.14 eV/Å on the ND particles along the [011̅] direction toward the substrate to slide the NDs along the substrate surface, as in the experiment.7 After 200 ps, the additional force was removed and the system was equilibrated for another 200 ps. A force was then applied to the ND in the direction either away from the surface or along the [010] direction along the surface, and the minimum force needed to move the ND in these directions was recorded. Illustrated in Figures 1 and 2 are snapshots from the simulations after equilibration that show views from the side and from the substrate toward the ND, respectively. The ND has a small difference in orientation with respect to the simulation cell between Figure 1A,B. Figures 1A and 2A are from the simulations of a negatively charged ND, whereas Figures 1B and 2B correspond to a positively charged ND. In both cases, there is an ordered layering of the water molecules in the direction normal to the substrate at the water−gold interface in the region around the ND, in agreement with prior studies15,26−30 and both types of NDs adhere to the gold surface. However, the water molecules and dissolved counterions are absent from the interface between the positive ND and gold surface (as illustrated in Figure 2B), so that the amino groups of the positive ND are directly adjacent to the gold surface. In contrast, a water layer containing Na+ counterions is formed between the interface of the negative ND and gold surface (as illustrated in Figure 2A) so that the water molecules and counterions remain around the carboxyl groups of the negative ND between the ND and the gold surface. Listed in Table 2 are the total forces determined from the simulations needed to remove or slide the ND on the gold surface. Multiple simulations were run, and the lower and upper bounds on the table correspond to the smallest force that removed or slid the ND and the largest force for which the ND did not move, respectively. The simulations predict a difference in behavior for the charged NDs and that this difference depends on the electrostatic interactions with the induced charges in the gold, as characterized by the difference in forces with and without these charges. Without the induced charges, the minimum forces to pull a negatively charged ND off the gold surface are ∼30% larger than those needed for the
facets, each of which has an area of 4.3 nm2. For negatively and positively charged NDs, six surface carbon atoms on each facet were randomly chosen and bonded to an ionized carboxyl (−COO−) or amino group (−NH3+), respectively. The remaining surface carbon atoms were terminated by hydrogen. This density of ionized functional groups is associated with a zeta potential of ∼45 mV,11 consistent with the experimental measurements discussed above.7 The solvent was simulated with the TIP3 water model,12 with bond angles and lengths constrained to be rigid with the SHAKE algorithm.13 To maintain system charge neutrality, 48 Na+ or Cl− counterions were added to the solvent for the simulations of the negative or positive NDs, respectively. Nonbonded interactions were modeled by Lennard-Jones (LJ) and long-range Coulombic terms. The latter were calculated using a particle−particle particle-mesh solver with a cutoff of 9.0 Å.14 The LJ parameters σij and ϵij were determined using the Lorentz−Berthelot combining rules σij = (σi + σj)/2 and ϵij = ϵiϵj . The LJ potential parameters and partial charges of water, Na+, Cl−, and gold atoms are summarized in Table 1.12,15,16 The ND atoms, including the functional groups, were modeled with the optimized potentials for liquid simulations force field.17−21 Table 1. Parameters for the Lennard-Jones Potential and Coulombic Interaction H O Na+ Cl− Au
q (e units)
σ (Å)
ϵ (eV)
0.417 −0.834 1.000 −1.000
0.4000 3.1507 2.4393 4.4777 2.6290
0.001995 0.006596 0.003792 0.001544 0.22942
The induced charges in the gold substrate were modeled using an adaptation of the charge equilibration model previously used.22 See the Supporting Information for details. The gold substrate was modeled by a fixed face-centered cubic lattice with lattice constant 4.08 Å, thickness 1.2 nm, and an exposed (100) surface. The water molecules, ions, and ND particles were maintained in a cubic box with dimensions 81.564 × 81.564 × 61.230 Å3 containing 13 266 explicit water molecules. Periodic boundaries were used in the two directions perpendicular to the substrate.
Figure 1. Illustrations of cross section snapshots from the ND/gold simulations. The teal, red, and blue spheres represent gold, carbon, and hydrogen atoms, respectively, the brown spheres represent the solvated counterions, the white rods represent water molecules, and the green and yellow spheres represent the surface functional groups. (A) Negative ND and (B) positive ND. 4397
DOI: 10.1021/acs.jpclett.8b01814 J. Phys. Chem. Lett. 2018, 9, 4396−4400
Letter
The Journal of Physical Chemistry Letters
Figure 2. Same as in Figure 1 but viewed from the substrate along the surface normal direction. (A) Negative ND and (B) positive ND.
molecules near the surface but away from the ND as a function of the normal distance from the gold surface. These densities are normalized to the corresponding bulk values. The shaded areas illustrate the regions that on average are occupied by the surface functional groups. The left solid line of the hatched region represents the average position of the ND surface carbon atoms. For the negatively charged NDs, the vertical dashed line denotes the average position of the counterions between the substrate and the ND. The layering of the water parallel to the gold surface in the regions surrounding the NPs is apparent in the density plots. Also apparent from Figure 3A is that without induced charges in the gold substrate the counterions reside between the substrate and the negatively charged ND at a distance away from the gold surface that matches the distance of the first water layer in the absence of the ND. When the induced charges in the substrate are included, Na+ counterions move 0.5 Å away from the gold surface, whereas the ND moves 0.2 Å closer to the substrate such that the counterions and ends of the functional groups are almost aligned. This apparently helps to optimize the total electrostatics when induced charges are modeled. In both cases, the width of the region normal to the surface occupied by the −COO− functional groups remains the same at ∼2.85 Å. The structure illustrated by Figure 4 for the positively charged ND is very different from the negative ND. In this case, the region that is occupied by the first water layer in the absence of the ND is replaced by the −NH3+ surface groups. These surface groups extend 1.9 Å from the ND surface, which
Table 2. Forces Required To Pull the ND from the Surface or To Drag the ND along the Surfacea force without induced charges (eV/Å) negative-ND positive-ND negative-ND positive-ND
force with induced charges (eV/Å)
Removing the ND Normal to the Surface 3.31 ± 0.12 6.18 2.47 ± 0.07 17.37 Sliding the ND along the Surface 1.27 ± 0.09 2.94 1.03 ± 0.07 6.57
± 0.05 ± 0.10 ± 0.12 ± 0.10
a
Units are eV/Å.
positively charged ND. Similarly, the force to drag a ND along the surface is ∼20% larger for the negative ND compared with the positive ND. With the induced charges, the magnitude of the removal and sliding forces goes up for both types of ND. For the negative ND, for example, the removal and sliding forces go up by a factor of 1.8 and 2.3, respectively. For the positive ND these removal and sliding forces go up by a factor of 7 and 6.4, respectively, so that both forces become appreciably larger for the positive ND compared with the negative ND. Figures 3 and 4 further illustrate the ND−gold structure for the negatively and positively charged NDs, respectively. Figures 3A and 4A are from the system without induced charges in the gold, whereas the configurations represented in Figures 3B and 4B are from simulations that included the induced charges. The solid and dotted lines give the density of the oxygen and hydrogen atoms, respectively, of the water
Figure 3. Water density normalized by the bulk density in the region surrounding a ND (i.e., not under the ND) along the direction normal to the surface. Solid lines: oxygen atoms. Dashed lines: hydrogen atoms. The shaded areas illustrate the regions that on average are occupied by the −COO− functional groups. The left solid line of the hatched region represents the average position of the ND surface carbon atoms. The vertical dashed line denotes the average position of the counterions between the substrate and the ND. (A) From the simulation without electrostatics from induced charges in the gold. (B) From the simulations including the electrostatic effects. 4398
DOI: 10.1021/acs.jpclett.8b01814 J. Phys. Chem. Lett. 2018, 9, 4396−4400
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The Journal of Physical Chemistry Letters
Figure 4. Same as Figure 3, except from the simulations of the positive ND. (A) From the simulation without electrostatics from induced charges in the gold. (B) From the simulations that include the electrostatic effects.
is about two-thirds of the length of the −COO− functional groups on the negative ND. Without an intermediate water layer or counterions like those predicted by the simulation for the negative ND, including the electrostatic interactions with the positive ND from induced charges in the gold substrate moves the functional groups 0.4 Å closer to the substrate. This is twice the distance that the electrostatics move the functional groups on the negative ND toward the gold. Hence the closer proximity of the positive ND and the lack of cancelation of electrostatic interactions due to the water layer and contained counterions lead to the larger electrostatic adhesion of the positive ND compared with the negative ND determined from these simulations and inferred from experiment.7 Reported in this Letter are results from a series of molecular dynamics simulations that provide an explanation for the dependence of adhesion strength on charge for aqueous NDs on a gold substrate inferred from prior experiments.7 Prior interpretations of experimental studies suggested that electrostatics or surface functionalization could be the primary source of the differences in adhesion, although details were not understood. The simulations presented here suggest that a molecular water layer containing Na+ counterions exists between gold surfaces and negative NDs with −COO− functional groups that is not present for positive NDs with −NH3+ functional groups. Moreover, this water layer is responsible for the weaker adhesion of the negative NDs compared with the positive NDs through a reduction in ND− gold electrostatic interactions arising from the water layer and contained counterions.
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Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based on work supported by the National Science Foundation under grant no. DMR-1535082. Helpful discussions with A. Smirnov, C. Curtis, A. Marek, B. Acharya, M. Winkle, B. Reich, and O. Shenderova are also acknowledged.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b01814. Details of the charge equilibration method and adapted
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REFERENCES
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model for calculating induced charges (PDF)
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Liangliang Su: 0000-0002-2079-2987 4399
DOI: 10.1021/acs.jpclett.8b01814 J. Phys. Chem. Lett. 2018, 9, 4396−4400
Letter
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DOI: 10.1021/acs.jpclett.8b01814 J. Phys. Chem. Lett. 2018, 9, 4396−4400
