Effects of -H and -OH Termination on Adhesion of Si-Si Contacts Examined Using Molecular Dynamics and Density Functional Theory.

The contact between nanoscale single-crystal silicon asperities and substrates terminated with -H and -OH functional groups is simulated using reactive molecular dynamics (MD). Consistent with previous MD simulations for self-mated surfaces with -H terminations only, adhesion is found to be low at full adsorbate coverages, be it self-mated coverages of mixtures of -H and -OH groups, or just -OH groups. As the coverage reduces, adhesion increases markedly, by factors of ∼5 and ∼6 for -H-terminated surfaces and -OH-terminated surfaces, respectively, and is due to the formation of covalent Si-Si bonds; for -OH-terminated surfaces, some interfacial Si-O-Si bonds are also formed. Thus, covalent linkages need to be broken upon separation of the tip and substrate. In contrast, replacing -H groups with -OH groups while maintaining complete coverage leads to negligible increases in adhesion. This indicates that increases in adhesion require unsaturated sites. Furthermore, plane-wave density functional theory (DFT) calculations were performed to investigate the energetics of two Si(111) surfaces fully terminated by either -H or -OH groups. Importantly for the adhesion results, both DFT and MD calculations predict the correct trends for the relative bond strengths: Si-O > Si-H > Si-Si. This work supports the contention that prior experimental work observing strong increases in adhesion after sliding Si-Si nanoasperities over each other is due to sliding-induced removal of passivating species on the Si surfaces.

Interfacial Properties of Linear Alkane/Nitrogen Binary Mixtures: Molecular Dynamics Vapor-Liquid Equilibrium Simulations.

Molecular dynamics simulations were used to investigate the vapor-liquid equilibria (VLE) and interfacial properties of binary mixtures of N2 with either ethane, propane, n-decane, or n-dodecane. Alkanes and N2 were modeled by using the TraPPE-UA and Rivera force fields, respectively. The typically used Lorentz-Berthelot combining rules resulted in liquid phases that are too N2-rich compared to experiment. To improve the accuracy of VLE predictions, the hydrocarbon-nitrogen interactions were fine-tuned, and these improved parameters were used to investigate interfacial properties. Scaling the interaction strength between nitrogen and -CH3 and -CH2- groups by factors of 0.95 and 0.85, respectively, relative to the Lorentz-Berthelot value, was found to minimize error in pressure-composition phase diagrams. These scaling parameters gave excellent agreement with experimental phase diagrams for mixtures of N2 with ethane, propane, or n-dodecane over a range of state points. For ethane/N2 and n-decane/N2 mixtures, trends in surface tension as a function of temperature and pressure are correctly reproduced, although the simulated values are slightly too high compared to experimental values. To assess how the accuracy of hydrocarbon-N2 interaction strength impacts interfacial property predictions, we have compared density profiles and surface tension using several different scaling factors. Using the Lorentz-Berthelot combining rules rather than optimized parameters gave the same qualitative trends, although some quantitative results, such as liquid-phase N2 mole fraction, were found to differ by a factor of ∼1.5. Using the optimized interaction parameters, interfacial behavior was examined by calculating density and free energy profiles. Nitrogen molecules preferentially adsorb at the interfacial region between the liquid and vapor phases. This interfacial adsorption becomes less energetically favorable as either the temperature, pressure, or length of the alkane chain increases.

Covalent Bonding and Atomic-Level Plasticity Increase Adhesion in Silicon-Diamond Nanocontacts.

Nanoindentation and sliding experiments using single-crystal silicon atomic force microscope probes in contact with diamond substrates in vacuum were carried out in situ with a transmission electron microscope (TEM). After sliding, the experimentally measured works of adhesion were significantly larger than values estimated for pure van der Waals (vdW) interactions. Furthermore, the works of adhesion increased with both the normal stress and speed during the sliding, indicating that applied stress played a central role in the reactivity of the interface. Complementary molecular dynamics (MD) simulations were used to lend insight into the atomic-level processes that occur during these experiments. Simulations using crystalline silicon tips with varying degrees of roughness and diamond substrates with different amounts of hydrogen termination demonstrated two relevant phenomena. First, covalent bonds formed across the interface, where the number of bonds formed was affected by the hydrogen termination of the substrate, the tip roughness, the applied stress, and the stochastic nature of bond formation. Second, for initially rough tips, the sliding motion and the associated application of shear stress produced an increase in irreversible atomic-scale plasticity that tended to smoothen the tips' surfaces, which resulted in a concomitant increase in adhesion. In contrast, for initially smooth tips, sliding roughened some of these tips. In the limit of low applied stress, the experimentally determined works of adhesion match the intrinsic (van der Waals) work of adhesion for an atomically smooth silicon-diamond interface obtained from MD simulations. The results provide mechanistic interpretations of sliding-induced changes and interfacial adhesion and may help inform applications involving adhesive interfaces that are subject to applied shear forces and displacements.

Impact of Molecular Structure on Properties of n-Hexadecane and Alkylbenzene Binary Mixtures.

Because of the complexity of petroleum-based fuels, researchers typically use simplified mixtures, known as surrogates, to study combustion behavior and to attempt to identify how physical properties are related to combustion. The process of determining the surrogate composition to yield a desired set of thermophysical properties can be a complicated and time-consuming task. As a result, the use of computer simulations to narrow the number of possible surrogate compositions is beginning to be explored. Herein, molecular dynamics (MD) simulations are used to model binary mixtures of n-hexadecane with either benzene, toluene, n-ethylbenzene, n-propylbenzene, or n-butylbenzene. Calculated densities are in quantitative agreement with experimental values. With the exception of the mixtures containing benzene, simulated excess molar volumes are also in very good agreement with measured values. Isentropic bulk moduli are in qualitative agreement with experiment, and reproduce interesting trends observed in the experimental data. Specifically, minima in the bulk moduli at intermediate compositions of several of the alkylbenzenes are correctly reproduced. In addition, the structures of the fluids are also examined. For mixtures of n-hexadecane with alkylbenzenes with longer chains, the orientation of the aromatic rings is not substantially impacted by composition. In contrast, increasing n-hexadecane content increases the ratio of parallel to perpendicular arrangements of benzene and toluene molecules. In those mixtures, this change in orientation of the aromatic rings could be responsible for the minima observed in the bulk moduli data. These results show that MD simulations can assist in development of fuel surrogates, both by predicting thermophysical properties and by providing insight into how molecular structure and composition affect those properties.

Atomic-scale wear of amorphous hydrogenated carbon during intermittent contact: a combined study using experiment, simulation, and theory.

In this study, we explore the wear behavior of amplitude modulation atomic force microscopy (AM-AFM, an intermittent-contact AFM mode) tips coated with a common type of diamond-like carbon, amorphous hydrogenated carbon (a-C:H), when scanned against an ultra-nanocrystalline diamond (UNCD) sample both experimentally and through molecular dynamics (MD) simulations. Finite element analysis is utilized in a unique way to create a representative geometry of the tip to be simulated in MD. To conduct consistent and quantitative experiments, we apply a protocol that involves determining the tip-sample interaction geometry, calculating the tip-sample force and normal contact stress over the course of the wear test, and precisely quantifying the wear volume using high-resolution transmission electron microscopy imaging. The results reveal gradual wear of a-C:H with no sign of fracture or plastic deformation. The wear rate of a-C:H is consistent with a reaction-rate-based wear theory, which predicts an exponential dependence of the rate of atom removal on the average normal contact stress. From this, kinetic parameters governing the wear process are estimated. MD simulations of an a-C:H tip, whose radius is comparable to the tip radii used in experiments, making contact with a UNCD sample multiple times exhibit an atomic-level removal process. The atomistic wear events observed in the simulations are correlated with under-coordinated atomic species at the contacting surfaces.

Simulated adhesion between realistic hydrocarbon materials: effects of composition, roughness, and contact point.

The work of adhesion is an interfacial materials property that is often extracted from atomic force microscope (AFM) measurements of the pull-off force for tips in contact with flat substrates. Such measurements rely on the use of continuum contact mechanics models, which ignore the atomic structure and contain other assumptions that can be challenging to justify from experiments alone. In this work, molecular dynamics is used to examine work of adhesion values obtained from simulations that mimic such AFM experiments and to examine variables that influence the calculated work of adhesion. Ultrastrong carbon-based materials, which are relevant to high-performance AFM and nano- and micromanufacturing applications, are considered. The three tips used in the simulations were composed of amorphous carbon terminated with hydrogen (a-C-H), and ultrananocrystalline diamond with and without hydrogen (UNCD-H and UNCD, respectively). The model substrate materials used were amorphous carbon with hydrogen termination (a-C-H) and without hydrogen (a-C); ultrananocrystalline diamond with (UNCD-H) and without hydrogen (UNCD); and the (111) face of single crystal diamond with (C(111)-H) and without a monolayer of hydrogen (C(111)). The a-C-H tip was found to have the lowest work of adhesion on all substrates examined, followed by the UNCD-H and then the UNCD tips. This trend is attributable to a combination of roughness on both the tip and sample, the degree of alignment of tip and substrate atoms, and the surface termination. Continuum estimates of the pull-off forces were approximately 2-5 times larger than the MD value for all but one tip-sample pair.

Bond-order potentials with split-charge equilibration: application to C-, H-, and O-containing systems.

A method for extending charge transfer to bond-order potentials, known as the bond-order potential/split-charge equilibration (BOP/SQE) method [P. T. Mikulski, M. T. Knippenberg, and J. A. Harrison, J. Chem. Phys. 131, 241105 (2009)], is integrated into a new bond-order potential for interactions between oxygen, carbon, and hydrogen. This reactive potential utilizes the formalism of the adaptive intermolecular reactive empirical bond-order potential [S. J. Stuart, A. B. Tutein, and J. A. Harrison, J. Chem. Phys. 112, 6472 (2000)] with additional terms for oxygen and charge interactions. This implementation of the reactive potential is able to model chemical reactions where partial charges change in gas- and condensed-phase systems containing oxygen, carbon, and hydrogen. The BOP/SQE method prevents the unrestricted growth of charges, often observed in charge equilibration methods, without adding significant computational time, because it makes use of a quantity which is calculated as part of the underlying covalent portion of the potential, namely, the bond order. The implementation of this method with the qAIREBO potential is designed to provide a tool that can be used to model dynamics in a wide range of systems without significant computational cost. To demonstrate the usefulness and flexibility of this potential, heats of formation for isolated molecules, radial distribution functions of liquids, and energies of oxygenated diamond surfaces are calculated.

Merging bond-order potentials with charge equilibration.

A method is presented for extending any bond-order potential (BOP) to include charge transfer between atoms through a modification of the split-charge equilibration (SQE) formalism. Variable limits on the maximum allowed charge transfer between atomic pairs are defined by mapping bond order to an amount of shared charge in each bond. Charge transfer is interpreted as an asymmetry in how the shared charge is distributed between the atoms of the bond. Charge equilibration (QE) assesses the asymmetry of the shared charge, while the BOP converts this asymmetry to the actual amount of charge transferred. When applied to large molecules, this BOP/SQE method does not exhibit the unrealistic growth of charges that is often associated with QE models.

Friction between solids.

The theoretical examination of the friction between solids is discussed with a focus on self-assembled monolayers, carbon-containing materials and antiwear additives. Important findings are illustrated by describing examples where simulations have complemented experimental work by providing a deeper understanding of the molecular origins of friction. Most of the work discussed herein makes use of classical molecular dynamics (MD) simulations. Of course, classical MD is not the only theoretical tool available to study friction. In view of that, a brief review of the early models of friction is also given. It should be noted that some topics related to the friction between solids, i.e. theory of electronic friction, are not discussed here but will be discussed in a subsequent review.

Atomic-scale friction on diamond: a comparison of different sliding directions on (001) and (111) surfaces using MD and AFM.

Atomic force microscopy (AFM) experiments and molecular dynamics (MD) simulations were conducted to examine single-asperity friction as a function of load, surface orientation, and sliding direction on individual crystalline grains of diamond in the wearless regime. Experimental and simulation conditions were designed to correspond as closely as state-of-the-art techniques allow. Both hydrogen-terminated diamond (111)(1 x 1)-H and the dimer row-reconstructed diamond (001)(2 x 1)-H surfaces were examined. The MD simulations used H-terminated diamond tips with both flat- and curved-end geometries, and the AFM experiments used two spherical, hydrogenated amorphous carbon tips. The AFM measurements showed higher adhesion and friction forces for (001) vs (111) surfaces. However, the increased friction forces can be entirely attributed to increased contact area induced by higher adhesion. Thus, no difference in the intrinsic resistance to friction (i.e., in the interfacial shear strength) is observed. Similarly, the MD results show no significant difference in friction between the two diamond surfaces, except for the specific case of sliding at high pressures along the dimer row direction on the (001) surface. The origin of this effect is discussed. The experimentally observed dependence of friction on load fits closely with the continuum Maugis-Dugdale model for contact area, consistent with the occurrence of single-asperity interfacial friction (friction proportional to contact area with a constant shear strength). In contrast, the simulations showed a nearly linear dependence of the friction on load. This difference may arise from the limits of applicability of continuum mechanics at small scales, because the contact areas in the MD simulations are significantly smaller than the AFM experiments. Regardless of scale, both the AFM and MD results show that nanoscale tribological behavior deviates dramatically from the established macroscopic behavior of diamond, which is highly dependent on orientation.

Expressions for the stress and elasticity tensors for angle-dependent potentials.

The stress and elasticity tensors for interatomic potentials that depend explicitly on bond bending and dihedral angles are derived by taking strain derivatives of the free energy. The resulting expressions can be used in Monte Carlo and molecular dynamics simulations in the canonical and microcanonical ensembles. These expressions are particularly useful at low temperatures where it is difficult to obtain results using the fluctuation formula of Parrinello and Rahman [J. Chem. Phys. 76, 2662 (1982)]. Local elastic constants within heterogeneous and composite materials can also be calculated as a function of temperature using this method. As an example, the stress and elasticity tensors are derived for the second-generation reactive empirical bond-order potential. This potential energy function was used because it has been used extensively in computer simulations of hydrocarbon materials, including carbon nanotubes, and because it is one of the few potential energy functions that can model chemical reactions. To validate the accuracy of the derived expressions, the elastic constants for diamond and graphite and the Young's Modulus of a (10,10) single-wall carbon nanotube are all calculated at T = 0 K using this potential and compared with previously published data and results obtained using other potentials.

Elastic constants of diamond from molecular dynamics simulations.

The elastic constants of diamond between 100 and 1100 K have been calculated for the first time using molecular dynamics and the second-generation, reactive empirical bond-order potential (REBO). This version of the REBO potential was used because it was redesigned to be able to model the elastic properties of diamond and graphite at 0 K while maintaining its original capabilities. The independent elastic constants of diamond, C(11), C(12), and C(44), and the bulk modulus were all calculated as a function of temperature, and the results from the three different methods are in excellent agreement. By extrapolating the elastic constant data to 0 K, it is clear that the values obtained here agree with the previously calculated 0 K elastic constants. Because the second-generation REBO potential was fit to obtain better solid-state force constants for diamond and graphite, the agreement with the 0 K elastic constants is not surprising. In addition, the functional form of the second-generation REBO potential is able to qualitatively model the functional dependence of the elastic constants and bulk modulus of diamond at non-zero temperatures. In contrast, reactive potentials based on other functional forms do not reproduce the correct temperature dependence of the elastic constants. The second-generation REBO potential also correctly predicts that diamond has a negative Cauchy pressure in the temperature range examined.

Odd and even model self-assembled monolayers: links between friction and structure.

The friction between an amorphous carbon tip and two n-alkane monolayers has been examined using classical molecular dynamics simulations. The two monolayers have the same packing density, but the chains comprising each monolayer differ in length by one -CH2- unit. The simulations show that the monolayers composed of C13 chains have higher friction than those composed of C14 chains when sliding in the direction of chain cant; the difference in friction becomes more pronounced as the load is increased. Examination of the contact forces between the chains and the tip, along with conformational differences between the two chain types, lends insight into the friction differences.

Effect of filling on the compressibility of carbon nanotubes: predictions from molecular dynamics simulations.

The compressibility of filled and empty (10, 10) carbon nanotubes (CNTs) is examined using classical molecular dynamics simulations. The filled nanotubes contain C60, CH4, Ne, n-C4H10, and n-C4H7 molecules that are covalently cross-linked to the inner CNT walls. In addition, nanotubes filled with either a hydrogen-terminated carbon nanowire or a carbon nanotube of comparable diameter is also considered. The forces on the atoms are calculated using a many-body reactive empirical bond-order potential and the adaptive intermolecular reactive empirical bond-order potential for hydrocarbons. The butane-filled system shows a unique yielding behavior prior to buckling that has not been observed previously. Cross-linking the molecules to the inner CNT walls is not predicted to affect the stiffness of the filled nanotube systems and removes the yielding response. The mechanical response of the nanowire filled CNT is remarkably similar to the response of the similarly sized multiwalled CNT.

Contact forces at the sliding interface: mixed versus pure model alkane monolayers.

Classical molecular dynamics simulations of an amorphous carbon tip sliding against monolayers of n-alkane chains are presented. The tribological behavior of tightly packed, pure monolayers composed of chains containing 14 carbon atoms is compared to mixed monolayers that randomly combine equal amounts of 12- and 16-carbon-atom chains. When sliding in the direction of chain cant under repulsive (positive) loads, pure monolayers consistently show lower friction than mixed monolayers. The distribution of contact forces between individual monolayer chain groups and the tip shows pure and mixed monolayers resist tip motion similarly. In contrast, the contact forces "pushing" the tip along differ in the two monolayers. The pure monolayers exhibit a high level of symmetry between resisting and pushing forces which results in a lower net friction. Both systems exhibit a marked friction anisotropy. The contact force distribution changes dramatically as a result of the change in sliding direction, resulting in an increase in friction. Upon continued sliding in the direction perpendicular to chain cant, both types of monolayers are often capable of transitioning to a state where the chains are primarily oriented with the cant along the sliding direction. A large change in the distribution of contact forces and a reduction in friction accompany this transition.

Molecular-scale tribology of amorphous carbon coatings: effects of film thickness, adhesion, and long-range interactions.

Classical molecular dynamics simulations have been conducted to investigate the atomic-scale friction and wear when hydrogen-terminated diamond (111) counterfaces are in sliding contact with diamond (111) surfaces coated with amorphous, hydrogen-free carbon films. Two films, with approximately the same ratio of sp(3)-to-sp(2) carbon, but different thicknesses, have been examined. Both systems give a similar average friction in the load range examined. Above a critical load, a series of tribochemical reactions occur resulting in a significant restructuring of the film. This restructuring is analogous to the "run-in" observed in macroscopic friction experiments and reduces the friction. The contribution of adhesion between the probe (counterface) and the sample to friction was examined by varying the saturation of the counterface. Decreasing the degree of counterface saturation, by reducing the hydrogen termination, increases the friction. Finally, the contribution of long-range interactions to friction was examined by using two potential energy functions that differ only in their long-range forces to examine friction in the same system.

Compression of carbon nanotubes filled with C60, CH4, or Ne: predictions from molecular dynamics simulations.

The effect of filling nanotubes with C60, CH4, or Ne on the mechanical properties of the nanotubes is examined. The approach is classical molecular dynamics using the reactive empirical bond order (REBO) and the adaptive intermolecular REBO potentials. The simulations predict that the buckling force of filled nanotubes can be larger than that of empty nanotubes, and the magnitude of the increase depends on the density of the filling material. In addition, these simulations demonstrate that the buckling force of empty nanotubes depends on temperature. Filling the nanotube disrupts this temperature effect so that it is no longer present in some cases.