Guangtu Gao

Elucidating atomic-scale friction using molecular dynamics and specialized analysis techniques

Because all quantities associated with a given atom are known as a function of time, molecular dynamics simulations can provide unparalleled insight into dynamic processes. Many quantities calculated from simulations can be directly compared to experimental values, while others provide information not available from experiment. For example, the tilt and methyl angles of chains within a self-assembled monolayer and the amount of hydrogen in a diamond-like carbon (DLC) film are measurable in an experiment. In contrast, the atomic contact force on a single substrate atom, i.e., the force on that atom due to the tip atoms only, and the changes in hybridization of a carbon atom within a DLC film during sliding are not quantities that are currently obtainable from experiments. Herein, the computation of many quantities, including the ones discussed above, and the unique insights that they provided into compression, friction, and wear are discussed.

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.

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.

Atomistic Factors Governing Adhesion between Diamond, Amorphous Carbon and Model Diamond Nanocomposite Surfaces

Complementary atomic force microscopy (AFM) measurements and molecular dynamics (MD) simulations were conducted to determine the work of adhesion for diamond (C)(111)(1 × 1) and C(001)(2 × 1) surfaces paired with carbon-based materials. While the works of adhesion from experiments and simulations are in reasonable agreement, some differences were identified. Experimentally, the work of adhesion between an amorphous carbon tip and individual C(001)(2 × 1)–H and C(111)(1 × 1)–H surfaces yielded adhesion values that were larger on the C(001)(2 × 1)–H surface. The simulations revealed that the average adhesion between self-mated C(001)(2 × 1) surfaces was smaller than for self-mated C(111)(1 × 1) contacts. Adhesion was reduced when amorphous carbon counterfaces were paired with both types of diamond surfaces. Pairing model diamond nanocomposite surfaces with the C(111)(1 × 1)–H sample resulted in even larger reductions in adhesion. These results point to the importance of atomic-scale roughness for adhesion. The simulated adhesion also shows a modest dependence on hydrogen coverage. Density functional theory calculations revealed small, C–H bond dipoles on both diamond samples, with the C(001)(2 × 1)–H surface having the larger dipole, but having a smaller dipole moment per unit area. Thus, charge separation at the surface is another possible source of the difference between the measured and calculated works of adhesion.

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 Youngs 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.

Molecular Dynamics Simulations of Tribology

Publisher Summary This chapter provides an overview of the molecular dynamics (MD) technique and reactive potentials with special regard to their use in investigating atomic-scale friction. In MD simulations, atoms are treated as discrete particles whose trajectories are followed by numerically integrating the classical equations of motion. After the geometry and boundary conditions of the system are specified and the initial position and velocity of each atom are given, a numerical integration is carried out. Typical timesteps range between 0.1 and about 15 femtoseconds, depending on the largest vibrational frequency of the model system. Instantaneous values of quantities such as energy, force, velocity, strain, and stress can be calculated at regular intervals and saved for postsimulation analysis. Atomistic simulation of a large number of atoms using molecular dynamics is a powerful tool for understanding the fundamental mechanisms of friction and tribology. The underpinning of such calculations is the assumed atomic interaction potential. The most desirable circumstance would be to take the atomic interactions directly from first-principle calculations; however, such calculations are orders of magnitude too slow for the sheer number of energy evaluations required to study a system of reasonable size and practical interest.

The Tribology of Carbon, Hydrogen, and Silicon-Containing Solid Lubricants (Keynote)

Constant temperature molecular dynamics simulations and the adaptive intermolecular reactive empirical bond-order potential energy function [1] (AIREBO) were used to examine the tribology of model self-assembled monolayers (SAMs) attached to diamond substrates. Two types of monolayers were examined. One was composed of alkane chains containing 14 carbons atoms and the other was composed of equal mixtures of 12 and 16 carbon-atom chains. The simulations have yielded unique insight into the origin of the friction differences between the two monolayer systems.

Friction and Wear Studies of Hydrogenated Amorphous Carbon Films Containing Silicon

The ratios of sp2 to sp3 content for a series of hydrogenated amorphous carbon-silicon systems were determined using molecular dynamics simulation. The values of elastic modulii were then determined for each system using constant tension and constant temperature molecular dynamics simulation method. The relationship between sp2 to sp3 content and modulii was investigated by varying Si and H content in the films. The thermal conductivity and heat capacity were also calculated for each system. A series of sliding simulations was used to determine which properties had the greatest effects on the resulting friction and wear behavior of the films.