Tribological simulation

Another important issue associated with tribological simulations involves the definition of the system to be studied. For example, a simple tribological system consists of two atomically flat, defect-free surfaces sliding past one another. Because of computational convenience, it is common... 

In this chapter, we discuss how to perform meaningful tribological simulations by avoiding the potential pitfalls that were mentioned above. In the next section, some theoretical aspects of friction between solids will be explained. Then an overview of algorithms that have been used in the simulation of tribological phenomena is provided. Selected case studies will be presented in the last section. 

A typical model system used in tribological simulations is shown in Figure 8. In this system, two walls are separated by a fluid and shear is applied by pulling the top wall with an external device, whereas the bottom wall is held fixed. In atomic-level simulations, the two walls correspond to atomically discrete surfaces and the fluid is composed of atoms or molecules, which represent lubricants or contaminants. 

We start by discussing various means of incorporating surface roughness into the model systems in order to perform more realistic simulations. The means of subjecting the system to shear and load are discussed below. Thermostats are then discussed. Finally, we consider cases in which one can neglect the walls and treat the system as a bulk fluid. We finish with a discussion of different computational methodologies that are used in tribological simulations. 

In this section, we give a brief overview of theoretical methods used to perform tribological simulations. We restrict the discussion to methods that are based on an atomic-level description of the system. We begin by discussing generic models, such as the Prandtl-Tomlinson model. Below we explore the use of force fields in MD simulations. Then we discuss the use of quantum chemical methods in tribological simulations. Finally, we briefly discuss multiscale methods that incorporate multiple levels of theory into a single calculation. 

Most atomic-scale tribological simulations use force fields (FFs) to describe the interactions between atoms. A huge amount of literature exists regarding the development and use of FFs, and we will not attempt to cover this vast topic here. Instead, we will point out aspects of FFs and their use that are relevant to tribological simulations. The reader interested in a more general discussion of FFs is directed to the chapters by Bowen and Allinger58 and Dinur and Flagler59 in volume 2 of this series and by Landis et al. in volume 6.60... 

The calculation of electrostatic interactions in FF-based tribological simulations also requires care. The typical model used in tribological simulations consists of two surfaces separated by a fluid, with the whole system subject to periodic boundary conditions (PBCs). If we define the system such that the surfaces extend in the x — y plane, it seems only natural to apply PBCs in these two dimensions. Flowever, care must be taken when treating the third dimension z, which lies normal to the surfaces. Specifically, one must ensure that the length of the simulation cell in the z direction is large enough to leave... 

In general, two types of first-principles tribological simulations have been reported in the literature. The first type of simulation is based on static energy calculations in which the dynamics of the system are not considered.68,69 A typical simulation would be set up as follows. An initial structure is generated where the two surfaces are aligned in the desired configuration and fixed at some constant separation distance D. The structure is relaxed, and the energy is recorded. Then the top is layer is moved by some small distance relative to... 

The second approach used in first-principles tribological simulations focuses on the behavior of the sheared fluid. That is, the walls are not considered and the system is treated as bulk fluid, as discussed. These simulations are typically performed using ab initio molecular dynamics (AIMD) with DFT and plane-wave basis sets. A general tribological AIMD simulation would be run as follows. A system representing the fluid would be placed in a simulation cell repeated periodically in all three directions. Shear or load is applied to the system using schemes such as that of Parrinello and Rahman, which was discussed above. In this approach, one defines a (potentially time-dependent) reference stress tensor aref and alters the nuclear and cell dynamics, such that the internal stress tensor crsys is equal to aref. When crsys = aref, the internal and external forces on the cell vectors balance, and the system is subject to the desired shear or load. 

The last few years have seen an explosion in the number of atomic-level tribological simulations aimed not just at understanding fundamental aspects of friction, but also at determining the frictional properties of systems used in real-world applications. In this section, we will discuss selected studies in an effort to demonstrate how the principles discussed earlier in this chapter are used in practice. Unfortunately, it is not possible to consider all of the important, high-caliber research within the space of this chapter. Instead, we focus on a few key areas that encompass both fundamental and applied research in computational tribology. 

An emerging subdiscipline of tribological simulation involves the study of tribochemical reactions—that is, reactions that are activated by pressure and shear. These reactions alter the structure of lubricants and films that are used to protect surfaces from wear. Understanding the effects of these reactions on the intended behavior of these films is of utmost importance. However, simulation studies of tribochemical reactions have been impeded by the difficulty in accurately describing changes in chemical bonding. In a limited number of cases, this can be achieved with the use of reactive FFs, as noted above, whereas in other cases, one must resort to expensive quantum chemical calculations. In this section, we will describe two studies where such methods were used to examine tribochemical reactions. 

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