J. David Schall

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.

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.

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.

Recent developments and simulations utilizing bond-order potentials

Bond-order potentials (BOPs) have been used successfully in simulations of a wide range of processes. A brief overview of bond-order potentials is provided which focuses on the reactive empirical bond-order (REBO) potential for hydrocarbons (Brenner et al 2002 J. Phys.: Condens. Matter 14 783) and the large number of useful potentials it has spawned. Two specific extensions of the REBO potential that make use of its formalism are discussed. First, the 2B-SiCH potential (Schall and Harrison 2013 J. Phys. Chem. C 117 1323) makes the appropriate changes to the hydrocarbon REBO potential so that three atom types, Si, C, and H, can be modeled. Second, we recently added the electronegative element O, along with the associated charge terms, to the adaptive intermolecular REBO (AIREBO) potential (Stuart et al 2000 J. Chem. Phys. 112 6472). The resulting qAIREBO potential (Knippenberg et al 2012 J. Chem. Phys. 136 164701) makes use of the bond-order potential/split-charge (BOP/SQE) equilibration method (Mikulski et al 2009 J. Chem. Phys. 131 241105) and the Lagrangian approach to charge dynamics (Rick et al 1994 J. Chem. Phys. 101 6141). The integration of these two techniques allows for atomic charges to evolve with time during MD simulations: as a result, chemical reactions can be modeled in C-, O-, and H-containing systems. The usefulness of the 2B-SiCH potential for tribological investigations is demonstrated in molecular dynamics (MD) simulations of axisymmetric tips composed of Si and SiC placed in sliding contact with diamond(1 1 1) surfaces with varying amounts of hydrogen termination. The qAIREBO potential is used to investigate confinement of sub-monolayer coverages of water between nanostructured surfaces.

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.

Correcting for Tip Geometry Effects in Molecular Simulations of Single-Asperity Contact

Molecular simulation is a powerful tool for studying the nanotribology of single-asperity contacts, but computational limits require that compromises be made when choosing tip sizes. To assess and correct for the finite size effects, complementary finite element (FE) and molecular statics (MS) simulations examining the effects of tip size (height and radius) on contact stiffness and stress were performed. MS simulations of contact between paraboloidal tips and a flat, rigid diamond substrate using the 2B-SiCH reactive empirical bond-order potential were used to generate force–displacement curves and stress maps. Tips of various radii and heights, truncated by a rigid boundary, were formed from carbon- and silicon-containing materials so that they possessed differing elastic properties. Results were compared to FE simulations with matching geometries and elastic properties. FE analysis showed that the rigid boundary at the back of the tip influences the contact stiffness strongly, deviating from the Hertz model for small tip heights and radii. By examining the relationships between force, tip height, tip radii, and elastic properties obtained with FE simulations, a map interpolation method is presented that accounts for the effect of tip size and enables the extraction of Young’s modulus from MS force–displacement data. Furthermore, the FE results show that the effect of the finite size of the tip on contact stress is less pronounced than its effect on stiffness. The MS simulations also demonstrate that stress propagation within the tip is significantly impacted by the structure of the tip.

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.

Review of force fields and intermolecular potentials used in atomistic computational materials research

Molecular simulation is a powerful computational tool for a broad range of applications including the examination of materials properties and accelerating drug discovery. At the heart of molecular simulation is the analytic potential energy function. These functions span the range of complexity from very simple functions used to model generic phenomena to complex functions designed to model chemical reactions. The complexity of the mathematical function impacts the computational speed and is typically linked to the accuracy of the results obtained from simulations that utilize the function. One approach to improving accuracy is to simply add more parameters and additional complexity to the analytic function. This approach is typically used in non-reactive force fields where the functional form is not derived from quantum mechanical principles. The form of other types of potentials, such as the bond-order potentials, is based on quantum mechanics and has led to varying levels of accuracy and transferability. When selecting a potential energy function for use in molecular simulations, the accuracy, transferability, and computational speed must all be considered. In this focused review, some of the more commonly used potential energy functions for molecular simulations are reviewed with an eye toward presenting their general forms, strengths, and weaknesses.Molecular simulation is a powerful computational tool for a broad range of applications including the examination of materials properties and accelerating drug discovery. At the heart of molecular simulation is the analytic potential energy function. These functions span the range of complexity from very simple functions used to model generic phenomena to complex functions designed to model chemical reactions. The complexity of the mathematical function impacts the computational speed and is typically linked to the accuracy of the results obtained from simulations that utilize the function. One approach to improving accuracy is to simply add more parameters and additional complexity to the analytic function. This approach is typically used in non-reactive force fields where the functional form is not derived from quantum mechanical principles. The form of other types of potentials, such as the bond-order potentials, is based on quantum mechanics and has led to varying levels of accuracy and transferabilit...

Engaging Underrepresented Undergraduates in Engineering Through a Hands-On Automotive-Themed REU Program

Since the summer of 2006, the department of Mechanical Engineering at Oakland University (OU) has been organizing a research experience for undergraduates (REU) program that has been successful at recruiting underrepresented undergraduates in engineering — women in particular. Funded in 2006–2009 and in 2010–2013 through the National Science Foundation REU program and the Department of Defense ASSURE program, this summer REU program focuses on automotive and energy-related research projects. The main purpose of this paper is to share our 6-year experience of organizing and running a summer REU program and to report on the outcomes and short/medium-term assessment results of the program. Also included are some recommendations that we would make to further enhance the success of similar REU programs. We believe that this type of information could prove to be of value to other REU program directors and faculty seeking to organize similar programs.Copyright