Capillary adhesion and friction –An approach with the AFM Circular Mode

Introduction
Chapter 1. From Tribology to Nanotribology
1. Introduction to tribology – Macro and Microscopic approaches to the laws of friction
1.1. Laws of Amontons and Coulomb
1.2. Bowden and Tabor adhesion model
2. Contact mechanics – Single asperity contacts
2.1. Fully elastic: The Hertz model
2.2. Including adhesive forces: The JKR model
2.3. The Derjaguin-Muller-Toporov (DMT) model
2.4. Maugis model
2.5. Comparison of the models
3. Nanotribology
3.1. Interactions in a nano-contact
3.2. New approaches for investigations at the nanoscale
3.3. Nanoscale friction
4. Recent experimental results on dynamic friction
4.1. Friction independent of the sliding velocity
4.2. A power-law dependence of the friction on the sliding velocity
4.3. Friction force versus the sliding velocity variation – Slope change from increasing to decreasing
4.4. Logarithmic dependence of friction force on the sliding velocity
5. Capillary condensation
5.1. From water molecules to capillary bridges
5.2. Kinetics of capillary condensation of water bridges
5.3. Humidity dependence of a capillary force
5.4. Roughness dependence of a capillary force
6. Conclusion
Chapter 2. The Circular AFM Mode
1. Motivation
2. Circular mode Implementation
3. Circular motion parameters
4. Circular motion in the horizontal plane of the sample
5. Advantages of the Circular mode
6. Applications of the Circular mode
7. Conclusion
Chapter 3. Velocity dependence of adhesion in a sliding nanometer-sized contact – A Circular mode study
1. Combining the Circular mode with the conventional force distance mode
2. Experimental procedure
3. Experimental data- adhesion force values at different sliding velocities
4. Adhesion force dependence on the sliding velocity
5. Measurements performed with same physical chemical properties at different humidities
6. Reversibility of the behavior
7. Theoretical approach of the influence of the sliding velocity on capillary adhesion
8. Conclusion
Chapter 4. Capillary adhesion versus friction – Preliminary results
1. Measuring lateral force spectra with the Circular mode
2. Friction with the normal load
3. Friction force versus ln (V) at a constant normal load
4. Variation of the friction coefficient with the sliding velocity
5. Interplay between capillary adhesion and dissipation in a contact
General Conclusion
Annex 1.Atomic Force Microscopy
1. Principle of the AFM
2. The AFM probe – Measuring interaction forces
3. The Photodiode detector – measuring cantilever deflection
4. The Piezoelectric tube
5. The Feedback loop
6. Topographic image and resolution
7. Calibration
Annex 2. Circular AFM mode for investigating polymer nanotribological or nanoadhesive properties
Annex 3. Force Volume Mode
1. Force volume mode
Annex 4. Lock-In-Amplifier
1. The lock-in technique
Table of Symbols
REFERENCES

Chapter 1. From Tribology to Nanotribology

We briefly review the historical background relative to the macroscopic friction and present an overview of contact mechanic in the case of two solids in direct contact before focusing on the nanotribological branch of tribology which studies friction phenomenon at the nanometer scale. We begin by introducing the surface forces resulting from the interaction at close proximity. A second part of this chapter discusses the theoretical explanations of friction at the nanometer scale focusing on the thermally activated process of capillary condensation, and an analytical background on the interplay of the contacts surface characteristics such as roughness, and different environmental condition such as humidity with the capillary force, and finally we give a overview on the previous experimental research conducted for investigating the dependence of the friction force on the sliding velocity .

1. Introduction to tribology – Macro and Microscopic approaches to the laws of friction
The term  »tribology » was suggested by Peter Jost in May of 1966 as a name for the research based on the phenomena associated to the contact and relative motion of surfaces. The pursuit for knowledge about origins of friction, lubrication, adhesion, and wear is not a recent scientific activity. Indeed, tribology is one of the oldest fields of interest, dating back from the creation of fire through frictional heating to the current efforts of creating nanodevices.
Furthermore, much attention has been paid to study the physical and chemical origin of these phenomena in order to obtain and design ways and means for minimizing losses such as energy dissipation and material degradation that can cause huge economic losses [9, 10].
In spite of the enormous amount of macroscopic tribological research so far, mainly of empirical nature, a clear fundamental understanding of friction still does not exist [11, 12] .
The main reason for this lack of fundamental insight is the inherent difficulty to study interactions that take place at the buried interface of two contacting bodies. A macroscopic contact between two apparently flat solid surfaces consists in practice of a large number of micro- contacts between the asperities that are present on both contacting surfaces [13], as schematically illustrated in Figure 1.1. This notion inspired Frank Philip Bowden [14] in 1950 to the following analogy: « Putting two solids together is rather like turning Switzerland upside down and standing it on Austria – the area of intimate contact will be small « .

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