Adhesion effects in material transfer in mechanical contacts
Introduction
Contacts are an integral part of many modern technologies; from electrical switches to micro-electro-mechanical systems (MEMS) to printing-based alternatives to lithographic patterning (e.g. micro-contact printing [1], [2]). The evolution of materials/surfaces upon contact is difficult to predict in detail because of the complex interplay of many phenomena, such as elasticity, plastic deformation, chemical reactions, adhesion, material transfer, etc. This is further complicated by the fact that contact phenomena are inherently multi-scale [3], [4]. While progress has been made in understanding the cascade of scales from the smallest asperity contacts to macroscopic contact [3], [5], the most significant gap in our understanding is on the nanoscale, where single asperity contact first occurs.
This paper presents a series of molecular dynamics simulations of single asperity contact where a single parameter is varied – the work of adhesion between the two surfaces. Besides presenting the first systematic work in this area, this study provides simple heuristic and analytical results that can be widely applied to understanding material transfer in contacts. A wide range of experimental observations, on both the nano and macro scales have demonstrated that material transfer from one surface to another is a very common feature of contact phenomena. In some cases, material transfer is desirable while, in other cases, it is not. For example, material transfer upon contact enables contact patterning, as described in Refs. [1], [2], [6]. Material transfer is also key to the mechanical alloying of powders in, for example, ball milling [7]. However, in both of these applications, it is important to note that the right materials transfer from one surface to the other. In contact patterning, it would be undesirable to remove and transfer the die material. Similarly, in ball milling, transfer of material from the balls to the powder would result in contamination of the powder being milled [7], [8]. In the operation of MEMS devices (e.g., MEMS radio frequency switches), material transfer from one of the contacts to the other (debris formation) can greatly degrade the reliability and durability of such devices [9].
In addition to contact/separation problems, material transfer is also frequently observed in sliding of surfaces over one another [10], [11], [12]. There is ample evidence [13] to suggest that the degree of material transfer is strongly influenced by the adhesion between the surfaces of the different materials. This is not surprising since, in the limit that the two surfaces have no adhesive interactions with each other, no material transfer will occur during contact and separation. Modification of the adhesion properties of the opposing surfaces is widely used as a means of extending device lifetimes by limiting material transfer [14], [15], [16] (e.g., putting thiols or other molecular species on metals surfaces).
The goal of the present research is to clarify the role of adhesion on material transfer when two surfaces are pushed together and then separated. To this end, a series of atomistic simulations are performed, in which the properties of the two materials composing the opposing surfaces are identical except for the (ideal work of) adhesion, which can be varied over a large range. This is accomplished by modifying the interactions between the two materials in order to change the interface energetics. A series of molecular dynamics (MD) simulations are performed, in which a single, hemispherical asperity is pushed into contact with a flat surface and then pulled apart at a fixed velocity. The force–displacement relation, the number of atoms transferred and the morphology of the asperity during a single loading and unloading cycle for systems with different interfacial energies are monitored. The atomic interactions are described using an embedded atom method (EAM) potential for gold, but extended to describe variable interface energies between the material on the lower side of the contact (arbitrarily labeled A) and the upper side of the contact (B). In this way, materials A and B are identical in every way except that the A/B interface has a positive, finite energy. It is found that one can vary the amount of material transfer from approximately 1/2 of the volume of the asperity to no material transfer at all. In order to analyze the simulation results, the relationship between the potential parameters and the interface energy/work of adhesion is calculated. From these results, a simple analytical relation that determines whether material transfer will occur or not is derived. The present work is further put into perspective by careful comparisons of the results with the predictions of Johnson, Kendal and Roberts [17] (JKR theory). The present analysis yields a predictive model for material transfer upon contact.
Section snippets
Simulation method
The present study examines the contact between a single asperity and an initially flat surface, as illustrated in Fig. 1. The goal is to understand the role of adhesion between the two surfaces on the asperity contact, deformation and material transfer. This study is performed within a MD framework in which the equations of motion of all atoms are integrated forward in time using a velocity–Verlet algorithm [18] with a constant time step (Δt = 0.5 fs). The number of atoms (N) is fixed. The
Results
The present study examines contact behavior as a function of the strength of interfacial adhesion as described through the potential parameter α. A preliminary version of a subset of the present results was published originally in [24]. For each α, a simulation is performed in which a surface with a single asperity is pushed against another flat surface and then the two are pulled apart. Fig. 2 shows the relationship between the potential parameter α and the work of adhesion Γ for the
Analysis
Examination of the contact morphologies following loading and unloading to separation (Fig. 3) shows that when Γ ⩾ 881.81 erg/cm2 (i.e., Figs. 3a–d), there is significant material transfer from one surface to the other upon contact separation. By contrast, when Γ ⩽ 735 erg/cm2 (i.e., Figs. 3e–i), no material transfer occurs. An additional series of contact and separation simulations for works of adhesion between these limits, 735 < Γ (erg/cm2) < 880, in order to identify more precisely the critical work
Conclusions
A series of MD simulations of the contact and separation of a surface containing an initially hemispherical asperity of material A and a flat substrate of a different material B were performed. Simulations were performed for several different A/B interfacial energies, while leaving all other material properties fixed. It was found that work of adhesion has little effect on the force–displacement relation when the two materials are pushed together (contact followed by large-scale plastic
Acknowledgments
The authors gratefully acknowledge useful discussions and prior collaborations with Dr. Pil-Ryung Cha. This work was supported through the Materials Research Science and Engineering program of the National Science Foundation, Grant DMR 0213706.
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