Polymer Adhesion, Friction, and Lubrication E-Book

Hongbo Zeng

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1350

Veröffentlichungsjahr: 2013

Beschreibung

Specifically dedicated to polymer and biopolymer systems, Polymer Adhesion, Friction, and Lubrication guides readers to the scratch, wear, and lubrication properties of polymers and the engineering applications, from biomedical research to automotive engineering. Author Hongbo Zeng details different experimental and theoretical methods used to probe static and dynamic properties of polymer materials and biomacromolecular systems. Topics include the use of atomic force microscopy (AFM) to analyze nanotribology, polymer thin films and brushes, nanoparticles, rubber and tire technology, synovial joint lubrication, adhesion in paper products, bioMEMS, and electrorheological fluids.

Leseprobe

Table of Contents

TITLE PAGE

COPYRIGHT PAGE

PREFACE

CONTRIBUTORS

1 FUNDAMENTALS OF SURFACE ADHESION, FRICTION, AND LUBRICATION

1.1 INTRODUCTION

1.2 BASIC CONCEPTS

1.3 ADHESION AND CONTACT MECHANICS

1.4 FRICTION

1.5 ROLLING FRICTION

1.6 LUBRICATION

1.7 WEAR

1.8 REAL CONTACT AREA

1.9 MODERN TOOLS IN TRIBOLOGY

1.10 COMPUTER SIMULATIONS IN TRIBOLOGY

ACKNOWLEDGMENT

REFERENCES

2 ADHESION AND TRIBOLOGICAL CHARACTERISTICS OF ION-CONTAINING POLYMER BRUSHES PREPARED BY CONTROLLED RADICAL POLYMERIZATION

2.1 INTRODUCTION

2.2 CONTROLLED SYNTHESIS OF ION-CONTAINING POLYMER BRUSHES

2.3 WETTABILITY OF POLYELECTROLYTE BRUSHES

2.4 ADHESION AND DETACHMENT BETWEEN POLYELECTROLYTE BRUSHES

2.5 WATER LUBRICATION AND FRICTIONAL PROPERTIES OF POLYELECTROLYTE BRUSHES

2.6 CONCLUSIONS

REFERENCES

3 LUBRICATION AND WEAR PROTECTION OF NATURAL (BIO)SYSTEMS

3.1 INTRODUCTION

3.2 BOUNDARY LUBRICATION

3.3 FLUID FILM LUBRICATION

3.4 MULTIMODAL LUBRICATION

3.5 WEAR

3.6 BIOMIMETIC AND ENGINEERING APPROACHES OF BIOLUBRICATION

ACKNOWLEDGMENT

REFERENCES

4 POLYMER BRUSHES AND SURFACE FORCES

4.1 INTRODUCTION

4.2 SOME GENERIC PROPERTIES OF POLYMER BRUSHES

4.3 SLIDING OF HIGH-Tg POLYMER BRUSHES: THE SEMIDILUTE TO VITRIFIED TRANSITION

4.4 SLIDING MECHANISM AND RELAXATION OF SHEARED BRUSHES

4.5 COMPRESSION, SHEAR, AND RELAXATION OF MELT BRUSHES

4.6 SHEAR SWELLING OF POLYMER BRUSHES

4.7 TELECHELIC BRUSHES

4.8 POLYELECTROLYTE BRUSHES IN AQUEOUS MEDIA

4.9 ZWITTERIONIC POLYMER BRUSHES

4.10 SUMMARY

ACKNOWLEDGMENTS

APPENDIX: SELF-REGULATION AND VELOCITY DEPENDENCE OF BRUSH–BRUSH FRICTION

REFERENCES

5 ADHESION, WETTING, AND SUPERHYDROPHOBICITY OF POLYMERIC SURFACES

5.1 INTRODUCTION

5.2 ADHESION BETWEEN POLYMERIC SURFACES

5.3 WETTING OF POLYMERS

5.4 FABRICATION OF SUPERHYDROPHOBIC POLYMERIC MATERIALS

5.5 SURFACE CHARACTERIZATION

5.6 CONCLUSIONS

ACKNOWLEDGMENTS

REFERENCES

6 MARINE BIOADHESION ON POLYMER SURFACES AND STRATEGIES FOR ITS PREVENTION

6.1 INTRODUCTION

6.2 PROTEIN ADSORPTION ON SOLID SURFACES

6.3 POLYMER COATINGS RESISTANT TO MARINE BIOFOULING

6.4 CONCLUSION

ACKNOWLEDGMENTS

REFERENCES

7 MOLECULAR ENGINEERING OF PEPTIDES FOR CELLULAR ADHESION CONTROL

7.1 INTRODUCTION: CELLS, BIOMACROMOLECULES, AND LIPIDATED PEPTIDES

7.2 BIOMATERIALS

7.3 CHEMISTRY TOOLS

7.4 SELF-ASSEMBLY OF LIPIDATED PEPTIDES: PEPTIDE AMPHIPHILES ENGINEERING

7.5 BIOMIMETIC PEPTIDE AMPHIPHILE SURFACE ENGINEERING CASE STUDIES

7.6 NEURAL STEM CELLS ON SURFACES: A DEEPER LOOK AT CELL ADHESION CONTROL

7.7 OVERVIEW OF MOLECULAR ENGINEERING DESIGNS FOR CELLULAR ADHESION

7.8 CONCLUSION

ACKNOWLEDGMENTS

REFERENCES

8 A MICROCOSM OF WET ADHESION: DISSECTING PROTEIN INTERACTIONS IN MUSSEL ATTACHMENT PLAQUES

8.1 INTRODUCTION

8.2 MUSSEL ADHESION

8.3 SURFACE FORCES APPARATUS

8.4 ASSESSING PROTEIN CONTRIBUTIONS BY SFA

8.5 CONCLUSIONS

ACKNOWLEDGMENTS

REFERENCES

9 GECKO-INSPIRED POLYMER ADHESIVES

9.1 INTRODUCTION

9.2 BIOLOGICAL INSPIRATIONS

9.3 MECHANICAL PRINCIPLES OF STRUCTURED ADHESIVE SURFACES

9.4 GECKO-INSPIRED ADHESIVES AND THEIR FABRICATION

9.5 APPLICATIONS OF BIOINSPIRED ADHESIVES

9.6 FUTURE DIRECTIONS: UNSOLVED CHALLENGES AND POSSIBLE APPLICATIONS

REFERENCES

10 ADHESION AND FRICTION MECHANISMS OF POLYMER SURFACES AND THIN FILMS

10.1 INTRODUCTION

10.2 ADHESION AND CONTACT MECHANICS

10.3 ADHESION OF GLASSY POLYMERS AND ELASTOMERS

10.4 EXPERIMENTAL ADVANCES IN ADHESION AND FRICTION BETWEEN POLYMER SURFACES AND THIN FILMS

10.5 ADHESION AND FRACTURE MECHANISM OF POLYMER THIN FILMS: FROM LIQUID TO SOLID-LIKE BEHAVIORS

10.6 ADHESION AND FRICTION BETWEEN ROUGH POLYMER SURFACES

10.7 FRICTION BETWEEN IMMISCIBLE POLYMER MELTS

10.8 HYDROPHOBIC INTERACTIONS BETWEEN POLYMER SURFACES

10.9 PERSPECTIVES AND FUTURE RESEARCH AVENUES

ACKNOWLEDGMENT

REFERENCES

11 RECENT ADVANCES IN RUBBER FRICTION IN THE CONTEXT OF TIRE TRACTION

11.1 INTRODUCTION

11.2 BACKGROUND ON RUBBER FRICTION AND TIRE TRACTION

11.3 RECENT INNOVATIONS ON TIRE TREAD COMPOUNDS

11.4 RUBBER FRICTION UNDER STATIONARY SLIDING ON ROUGH SURFACES

11.5 RUBBER FRICTION UNDER NONSTATIONARY CONDITIONS

11.6 INTERFACIAL EFFECTS ON RUBBER FRICTION

11.7 RUBBER FRICTION INVOLVING TEXTURED SURFACES

11.8 FIELD MEASUREMENTS WITHIN A FRICTIONAL CONTACT

11.9 OTHER STUDIES ON OR RELATED TO RUBBER FRICTION

11.10 CONCLUDING REMARKS

REFERENCES

12 POLYMERS, ADHESION, AND PAPER MATERIALS

12.1 INTRODUCTION

12.2 POLYMER NATURE OF PAPER

12.3 FUNCTIONAL POLYMERS AND SIZING AGENTS USED IN PAPERMAKING

12.4 POLYMER ADHESION AND THE FORMATION OF PAPER

12.5 POLYMER ADHESION MEASUREMENT

12.6 SUMMARY AND PERSPECTIVES

REFERENCES

13 CARBOHYDRATES AND THEIR ROLES IN BIOLOGICAL RECOGNITION PROCESSES

13.1 INTRODUCTION

13.2 RECENT ADVANCES IN THE FIELD OF CARBOHYDRATE CHEMISTRY

13.3 MOLECULAR INTERACTIONS OF CARBOHYDRATES IN CELL RECOGNITION

13.4 TECHNIQUES USED IN THE IDENTIFICATION OF CARBOHYDRATE INTERACTIONS IN CELL RECOGNITION

13.5 CONCLUSIONS AND FUTURE TRENDS

REFERENCES

14 THE IMPACT OF BACTERIAL SURFACE POLYMERS ON BACTERIAL ADHESION

14.1 BACTERIAL ADHESION

14.2 THE IMPACT OF BACTERIAL SURFACE POLYMERS ON BACTERIAL ADHESION

14.3 METHODS AND MODELS FOR UNDERSTANDING INTERACTION MECHANISMS OF BACTERIAL ADHESION

REFERENCES

15 ADHESION, FRICTION, AND LUBRICATION OF POLYMERIC NANOPARTICLES AND THEIR APPLICATIONS

15.1 INTRODUCTION

15.2 APPLICATIONS OF POLYMERIC NANOPARTICLES

15.3 METHODS OF PREPARATION OF POLYMERIC NANOPARTICLES (PNPs)

15.4 ADHESION OF PNP

15.5 ADSORPTION OF POLYMERIC NANOPARTICLES

15.6 FRICTION OF PNP

15.7 SUMMARY

REFERENCES

16 ELECTRORHEOLOGICAL AND MAGNETORHEOLOGICAL MATERIALS AND MECHANICAL PROPERTIES

16.1 ELECTRORHEOLOGICAL AND MAGNETORHEOLOGICAL HISTORY

16.2 ER/MR PHENOMENON

16.3 ER/MR MATERIALS

16.4 ER/MR EFFECT MODELS

16.5 PROPERTIES OF ER/MR FLUIDS UNDER SHEARING, TENSION, AND SQUEEZING

16.6 TRANSIENT RESPONSE TO FIELD STRENGTH, SHEAR RATE, AND GEOMETRY

16.7 SHEAR THICKENING IN ER/MR FLUIDS AT LOW SHEAR RATES

16.8 APPLICATIONS

REFERENCES

INDEX

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved

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Library of Congress Cataloging-in-Publication Data:

Polymer adhesion, friction, and lubrication / edited by Hongbo Zeng, University of Alberta, Edmonton, AB, Canada.

pages cm

 Includes index.

 ISBN 978-0-470-91627-8 (cloth)

 1. Tribology. 2. Adhesion. 3. Friction. 4. Lubrication and lubricants. I. Zeng, Hongbo (Professor in Chemical engineering), editor.

 TJ1075.P65 2012

 620.1'92042–dc23

2012031792

PREFACE

The word tribology originates from the Greek word tribos, which means “friction, rub, grind,” “to wear away,” or “science of friction.” Tribology is the study of science and technology on interacting surfaces in relative motion which includes various interfacial phenomena such as adhesion, friction, lubrication, and wear, as well as technical applications of tribological knowledge. The origin, study, and application of tribology can be traced back to at least 1000 years ago. Leonardo da Vinci (1452–1519) was the first who stated the two laws of friction and introduced the concept of coefficient of friction as the ratio of the friction force to normal load. Guillaume Amontons (1663–1705) published his rediscovery of the laws of friction in 1699 and Charles-Augustin de Coulomb (1736–1806) proposed a third law in 1781. These pioneers developed the three well-known laws in friction (see Chapter 1) which still apply to many engineering problems today. Since then, research on tribology has steadily progressed, particularly over the past half century with the development of contact mechanics models and advanced characterization techniques. The classical Hertz contact theory describes the elastic deformation of bodies in contact, but neglects the adhesion force. Several improved models were developed by taking into account the effect of surface adhesion, including the Johnson–Kendall–Roberts (JKR) model, Derjaguin–Muller–Toporov (DMT) model, and Maugis–Pollock model. Development of modern tools, such as surface forces apparatus (SFA) in the 1960s and 1970s by Tabor, Winterton, and Israelachvili, and atomic force microscope (AFM) in the 1980s by Binnig, Quate, and Gerber, has significantly advanced the understanding of molecular and surface interactions (e.g., adhesion, friction, and lubrication) for numerous materials, engineering, and biological systems in air, vacuum, and liquid media. The landmark work by Israelachvili and Adams in 1976 and 1978 on surface forces between two mica surfaces in aqueous salt solutions showed good agreement with the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory down to a separation distance of few nanometers for the first time, below which an additional repulsive force was also observed mainly due to hydration force. Professor Israelachvili later refined the SFA technique and experimental methodologies and also developed many other techniques for the static and dynamic measurement of molecular and materials properties in tribology, which have been widely used for the understanding of colloidal dispersions, biological systems, polymer science and engineering, and other interfacial phenomena. The rapid development of computer technologies and methodologies within the past two decades also enables simulation and modeling of very complex tribological processes at the nano-, molecular, and atomic scales.

The research and applications of polymer tribology can be traced back to hundreds of years ago, while important progress was first made by Schallamach and other researchers in the 1940s and the 1950s on rubbers and elastomers as important engineering materials in modern automotive industry. In the early work on tribological properties of nonelastomeric polymers, Shooter, Thomas, and Tabor systematically investigated the friction and wear of both symmetric (polymer on polymer) or asymmetric (polymer on metal) cases for various linear polymers such as Teflon, polyethylene, polystyrene, nylon, polyvinyl chloride and polymethyl methacrylate, and the results confirmed that contact area was proportional to the normal load as originally proposed by Bowden and Tabor for metals. Since then, substantial progress has been made in the understanding of polymer adhesion, friction, lubrication, and wear. Professors Bowden and Tabor at the Cavendish Laboratory, University of Cambridge, essentially laid the foundation for modern understanding of tribology, and their classical book Friction and Lubrication of Solids has been widely referred by tribologists worldwide.

The tribological behaviors (i.e., adhesion, friction, lubrication, and wear) of different materials depend on their intrinsic chemical, physical, and mechan­ical properties, and environmental factors (e.g., temperature, surrounding media), as well as operational conditions (e.g., load, pressure, relative speed). The tribological behaviors of polymers can be much more complex than simple molecular systems due to their large molecular weights, complex chemical structures, and, in most cases, temperature-/time-/rate-dependent properties and molecular interactions. Many researchers, such as Professors P.G. de Gennes, A. Gent, E. Kramer, M. Tirrell, J. Israelachvili, H. Brown, J. Klein, H. Waite, K. Friedrich, L. Léger, N. Spencer, H. Spikes, B. Briscoe, C. Hui, B. Bhushan, H. Hervet, K. Shull, E. Raphael, C. Creton, and their colleagues, have made tremendous progress in the basic understanding of adhesion, friction, and lubrication mechanisms of polymers over the last few decades. The advances span a wide area of knowledge and technology from molecular and surface interactions of elastomers, viscoelastic polymers, polymer thin films, polymer brushes, and biomacromolecules to design of micro- and nanomechanical systems and bioinspired materials. There is an extensive literature on various aspects of the adhesion, friction, and lubrication of different kinds of polymers in peer-reviewed journals and conference proceedings. Many excellent books have also been written in the fields, although they were not specifically dedicated to polymer materials and cover all the three areas (i.e., adhesion, friction, and lubrication).

This book has 16 chapters, which present the current state of the art concerning the adhesion, friction, and lubrication in various polymeric and biomacromolecular systems at the molecular, nano-, and microscale, and also covers the fundamental theories and experimental techniques commonly used in the fields. This book is suitable for third and fourth year undergraduate, graduate students, postdoctoral fellows, industrial practitioners, and professional trainers in the fields of polymer science and engineering, materials science, colloid and interface science, nanotechnology, bioengineering, chemical engineering, and chemistry who are interested in the topics. It is the authors’ hope that this book (or selected chapters) can serve as a useful textbook or course materials for students/researchers new to the fields as well as a helpful reference book for researchers and industrial practitioners who have worked in the fields for certain years.

I wish to thank all of my former and present colleagues and students who have contributed to my learning of surface adhesion, friction, lubrication, and polymer science. I am very grateful to Professors Jacob N. Israelachvili, Matthew Tirrell, Herbert Waite, Jacob Klein, Atsushi Takahara, Metin Sitti, Erika Eiser, Rafael Tadmor, Wuge H. Briscoe, Sitaraman Krishnan, Michael Nosonovsky, Yu Tian, Ravin Narain, Dong Soo Hwang, Mustafa Akbulut, Boxin Zhao, Yang Liu, Xiao-Dong Pan, Yonggang Meng, Shizhu Wen, and their coworkers for their strong support and excellent contributions to the book. I would also like to acknowledge Professors Jacob N. Israelachvili, Matthew Tirrell, Edward J. Kramer, Glenn H. Fredrickson, and Philip Alan Pincus who greatly inspired me to pursue a career in surface science and polymer science.

HONGBO ZENGUniversity of AlbertaMay 18, 2012

CONTRIBUTORS

Mustafa Akbulut, Artie McFerrin Department of Chemical Engineering, Materials Science and Engineering Program, Texas A&M University, College Station, TX

Badriprasad Ananthanarayanan, Department of Bioengineering, University of California, Berkeley, CA

Dhamodaran Arunbabu, Department of Chemical Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, Ontario, Canada

Keshwaree Babooram, Department of Chemical and Materials Engineering, Alberta Innovates Centre for Carbohydrate Science; and Section Sciences, Faculté Saint-Jean, University of Alberta, Edmonton, AB, Canada

Xavier Banquy, Department of Chemical Engineering, University of California, Santa Barbara, CA

Wuge H. Briscoe, School of Chemistry, University of Bristol, Bristol, UK

Meng Chen, Procter and Gamble Technology, Beijing, China

Eric Danner, Department of Molecular, Cell and Developmental Biology, University of California, Santa Barbara, CA

Saurabh Das, Department of Chemical Engineering, University of California, Santa Barbara, CA

Erika Eiser, Department of Physics, University of Cambridge, Cambridge, UK

Ali Faghihnejad, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada

George W. Greene, Materials Department, University of California, Santa Barbara, CA

Dong Soo Hwang, Materials Research Laboratory, POSTECH Ocean Science and Technology Institute, Pohang University of Science and Technology, Pohang, South Korea

Tatsuya Ishikawa, Graduate School of Engineering, Kyushu University, Fuku­oka, Japan

Jacob N. Israelachvili, Materials Department and Department of Chemical Engineering, University of California, Santa Barbara, CA

Nir Kampf, Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, Israel

Bassem Kheireddin, Artie McFerrin Department of Chemical Engineering, Materials Science and Engineering Program, Texas A&M University, Col­lege Station, TX

Jacob Klein, Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, Israel

Motoyasu Kobayashi, Japan Science and Technology Agency, ERATO, Takahara Soft Interfaces Project, Kyushu University, Fukuoka, Japan

Sitaraman Krishnan, Department of Chemical and Biomolecular Engineering, Clarkson University, Potsdam, NY

Dong Woog Lee, Department of Chemical Engineering, University of California, Santa Barbara, CA

Yang Liu, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada

Brendan McDonald, Department of Chemical Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, Ontario, Canada

Yonggang Meng, State Key Laboratory of Tribology, Tsinghua University, Beijing, China

Yiit Mengüç, Mechanical Engineering and Robotics Institute, Carnegie Mellon University, Pittsburgh, PA

Mehdi Mortazavi, Department of Mechanical Engineering, College of Engineering and Applied Science, University of Wisconsin-Milwaukee, Milwaukee, WI

Ravin Narain, Department of Chemical and Materials Engineering, Alberta Innovates Centre for Carbohydrate Science, University of Alberta, Edmonton, Canada

Michael Nosonovsky, Department of Mechanical Engineering, College of Engineering and Applied Science, University of Wisconsin-Milwaukee, Milwaukee, WI

Xiao-Dong Pan, Bridgestone Americas Center for Research and Technology, Akron, OH

Uri Raviv, Department of Chemistry, Hebrew University, Jerusalem, Israel

Nadine R. Rodriguez-Martinez, Department of Molecular, Cell and Developmental Biology, University of California, Santa Barbara, CA

Metin Sitti, Mechanical Engineering and Robotics Institute, Carnegie Mellon University, Pittsburgh, PA

Won Hyuk Suh, Department of Bioengineering, University of California, Berkeley, CA

Rafael Tadmor, Department of Chemistry, Hebrew University, Jerusalem, Israel

Atsushi Takahara, Japan Science and Technology Agency, ERATO, Takahara Soft Interfaces Project; Graduate School of Engineering; and Institute for Materials Chemistry and Engineering, Kyushu University, Fukuoka, Japan

Yu Tian, State Key Laboratory of Tribology, Tsinghua University, Beijing, China

Matthew Tirrell, Department of Bioengineering, University of California, Berkeley, CA; Institute for Molecular Engineering, University of Chicago, Chicago, IL

Larissa Tsarkova, DWI an der RWTH Aachen e.V., Aachen, Germany

J. Herbert Waite, Department of Molecular, Cell and Developmental Biology, University of California, Santa Barbara, CA

Wei Wei, Materials Research Laboratory, University of California, Santa Barbara, CA

Shizhu Wen, State Key Laboratory of Tribology, Tsinghua University, Beijing, China

Jing Yu, Department of Chemical Engineering, University of California, Santa Barbara, CA

Hongbo Zeng, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada

Ming Zhang, Artie McFerrin Department of Chemical Engineering, Materi­als Science and Engineering Program, Texas A&M University, College Station, TX

Boxin Zhao, Department of Chemical Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, Ontario, Canada

1

FUNDAMENTALS OF SURFACE ADHESION, FRICTION, AND LUBRICATION

Ali Faghihnejad and Hongbo Zeng

1.1 INTRODUCTION

The word tribology originates from the Greek word tribos, meaning rubbing. Tribology is the science of study of interacting surfaces in relative motion which encompasses interfacial phenomena such as friction, lubrication, adhesion, and wear. It spans a wide area of knowledge and technology from molecular and surface interactions to design of micro- and nano-mechanical systems. Although the term tribology has emerged only since 1966, the history behind it goes back to the prehistoric era, when man learned how to use force of friction for the generation of fire by rubbing two pieces of wood or flint stones against each other [1]. Later, the tribological achievements of early civilizations in developing wheeled vehicles, mills, rolling bearings, and the use of lubricants for transporting heavy stones were great advancements in the course of history. After the Industrial Revolution, the need for better machinery boosted the experimental and theoretical studies on different aspects of tribology such as bearing design, better lubricants, and so forth. The beginning of the twentieth century was accompanied by early investigations of friction and lubrication on the microscopic scale and development of theories on the molecular scale [1–3]. The development of modern tools such as surface forces apparatus (SFA) in the 1960s and 1970s, atomic force microscope (AFM) in the 1980s, and computers which allow molecular simulation of tribological processes has greatly enhanced the research and knowledge in the broad field of tribology. One of the most exciting and rapidly growing areas of tribology research is biotribology, which covers a vast range of interests from live cell interfaces, artificial implants, and joint lubrication [4]. The importance of the research in tribology becomes more vital when it comes to economy, where more attention to friction and wear could save billions of dollars per year [5]. In this chapter, some basic concepts such as intermolecular and surface forces and surface energy are first discussed because of their fundamental importance in tribological processes. The basic principles of adhesion, friction, rolling friction, lubrication, and wear are discussed in Section 1.3. Section 1.4, Section 1.5, Section 1.6, and Section 1.7, respectively. The concept of real contact area is reviewed in Section 1.8 and some of the modern tools that are used extensively in tribological studies are discussed in Section 1.9. Finally, a brief review of the computer simulations in tribology is given in Section 1.10.

1.2 BASIC CONCEPTS

1.2.1 Intermolecular and Surface Forces

As tribology deals with two interacting surfaces in relative motion, the type of interaction that governs between the two surfaces is determinative of their tribological behavior. The intermolecular and surface forces can be attractive or repulsive and their range of action and magnitude can be very different. The types of forces operating between two surfaces depend on the nature of the interacting surfaces and medium between them. A comprehensive review of intermolecular and surface forces is beyond the scope of this chapter and only a brief overview is given here. The major types of nonspecific intermolecular and surface forces are listed in Table 1.1.

TABLE 1.1 Major Types of Nonspecific Intermolecular and Surface Interactions

Type of Interaction

Main Features

VDW

A force existing between all bodies. Usually attractive, and can be repulsive.

Electrostatic (coulomb, ionic, double layer)

A force existing between charged molecules/surfaces in liquid. Attractive or repulsive

Steric

A quantum mechanical force that is normally short range and increases very sharply as the two molecules get close (depending on geometry/shape or conformation of the interacting molecules)

Thermal fluctuation (i.e., osmotic, entropic, protrusion)

A temperature-dependent force associated with entropic confinement of molecular groups. Usually repulsive

Hydrophobic

An attractive interaction between hydrophobic molecules or surfaces in water. Usually long range

Solvation

Forces associated with local structuring of solvent molecules between interacting surfaces. For water, it is normally called hydration force.

Hydrogen bonding

A special electrostatic attractive interaction involving positively charged H atoms covalently bonded to electronegative atoms (e.g., N, O).

The van der Waals (VDW) forces exist between any two molecules or surfaces which can be attractive or repulsive, but always attractive between similar molecules. The VDW forces originate from interaction between electric dipole moments of the molecules. There are three major contributions to VDW forces: (1) a force between two permanent dipoles (Keesom interaction), (2) a force between a permanent dipole and a corresponding induced dipole (Debye interaction), and (3) a force between two instantly induced dipoles (London dispersion forces) [6]. The VDW interaction energy between two molecules or surfaces is given by

(1.1) 

and the corresponding force becomes:

(1.2) 

where D is the separation distance between the two molecules or surfaces, and CVDW is a constant depending on the optical properties and geometry of the interacting bodies. The VDW interaction energy between two macroscopic bodies can be calculated assuming the interaction to be additive. Thus by integrating the interaction energy of all the molecules in one body with all the molecules in the other body, the two-body interaction energy would be obtained. The result of such analysis is summarized in Table 1.2 for different geometries in terms of Hamaker constant A,

(1.3) 

where ρ1 and ρ2 are the number density of the molecules in bodies 1 and 2, respectively. The Hamaker constant for two macroscopic bodies 1 and 2 interacting across a medium 3 is given by the Lifshitz theory as follows [7]:

(1.4) 

where kB is the Boltzmann constant (1.381 × 10−23 J/K), ε is the dielectric permittivity, n is the refractive index, hP is the Planck’s constant (6.626 × 10−34 m2 kg/s), and νe is the main electronic absorption frequency.

TABLE 1.2 VDW and Electric Double-Layer Interaction Potential between Two Macroscopic Bodies of Different Geometries with Separation Distance D (D << R), and the Force Is Given by F(D) = −dE(D)/dD

The electrostatic double-layer force is another major interaction that exists between two charged entities or surfaces in liquid solutions. When surfaces are charged in an electrolyte solution, the long-range, double-layer force comes to play a role. The electrostatic double-layer interaction energy between two similarly charged surfaces as a function of their separation is given by:

(1.5) 

where CDL is a constant that depends on geometry of the surfaces, solution conditions, and surface charge densities. The parameter 1/κ is the Debye length which depends only on electrolyte conditions (i.e., type and concentration) and temperature. The Debye length is the characteristic decay length of the electrostatic double-layer interaction and decreases with increasing ionic strength of the solution, which is given as:

(1.6) 

where ε0 is the dielectric permittivity of free space, εs is the dielectric constant of solution, e0 is the elementary charge of a single electron, ρ∞i is the number density of ith ion in the bulk solution, and zi is the valancy of the ith ion. The electric double-layer interaction energy for similar constant potential surfaces of different geometries in symmetrical electrolyte solutions (e.g., NaCl and MgSO4) is given in Table 1.2 in terms of an interaction constant Z defined as [7]:

(1.7) 

where Ψ0 is the surface potential in millivolts and z is the electrolyte valency.

The sum of the VDW and double-layer forces between two surfaces form the so-called DLVO theory, after Derjaguin and Landau [8], and Verwey and Overbeek [9]. The VDW and double-layer forces depend differently on separation distance, the former being a power law while the latter an exponential law. VDW force is almost insensitive to solution conditions while double-layer force is significantly affected. As a result of these differences, DLVO forces can be repulsive or attractive depending on separation distance, solution conditions, and surface properties.

Steric and bridging forces normally occur between surfaces covered by large chain molecules (i.e., polymers, proteins) that can extend out into the solution. The net interaction between two polymer-covered surfaces includes the polymer–polymer and polymer–surface interactions, of which the former normally leads to steric forces while the latter leads to bridging forces. Polymer molecules can attach to a surface via either physical forces (physisorption) or chemical bonds (chemisorption). The state/conformation of an adsorbed polymer chain on a surface depends on parameters such as solution conditions, temperature, and type of adsorption. If a polymer is completely soluble in a solvent, then the polymer chain is expanded and conversely, in a poor solvent, the polymer chain tends to shrink. A polymer molecule is known as an ideal chain or freely connected chain if the monomers of the polymer chain are able to rotate freely about each other in any direction and their movement is not affected by the monomer–monomer interaction. In this state, the polymer molecule has a random coil conformation and its dimension is defined by the radius of gyration (Rg) as:

(1.8) 

where l is the monomer length and N is number of monomer units in polymer chain. The solubility and state of a polymer in a solvent also depends on temperature. The temperature in which a polymer molecule acts like a freely connected chain (R = Rg) is known as the theta temperature (Tθ) and a solvent at T = Tθ is known as theta solvent. The surface coverage Γ which is the number of adsorbed polymer chains per unit area is defined as:

(1.9) 

where d is the mean distance between the attachment points of adsorbed polymer chains. As two polymer-covered surfaces approach each other, a repulsive osmotic force is experienced between them, which is known as steric repulsion. The origin of this repulsive force is the unfavorable entropy associated with confining polymer chains between the two surfaces. When the surface coverage is low (d > Rg), also known as the mushroom regime, the repulsive steric interaction energy between two flat surfaces is given by [7]:

(1.10) 

For high surface coverage (d < Rg) known as the brush regime, the repulsive steric force per unit area (pressure) between two flat surfaces is given by the Alexander–de Gennes equation as [7, 10]:

(1.11)

where L is the thickness of the brush layer. The first term in Equation 1.11 is the osmotic repulsion and the second term is the elastic stretch energy of the chains. When two polymer-covered surfaces approach, the net interaction also depends on the forces between the polymer and the opposite surface that can be either repulsive or attractive. If the interaction between polymer and the opposite surface is attractive, then it is normally referred to as the bridging forces. In general, the bridging forces depend on the type of interaction (i.e., specific or nonspecific) between the polymer and the surface. Therefore, there is no single expression available for describing bridging forces, although linear or exponential dependence on distance have been observed in certain systems [7].

Hydrophobic force normally refers to the attractive force between two hydrophobic particles, surfaces, or molecules in water and aqueous solutions. Hydrophobic force has been reported to be much stronger than the theoretically expected VDW force. Experimental force measurements between various hydrophobic surfaces have intended to reveal the long-range nature of the force and corresponding strong adhesion force between the surfaces [11]. The magnitude of the hydrophobic force also depends on hydrophobicity of the surface, which is usually quantified by water contact angle measurement. The surfaces are normally considered to be hydrophobic if the water contact angle exceeds 90°. Nevertheless, the origin of the hydrophobic force is not fully understood yet. Some of the suggested mechanisms include cavitation due to the metastability of a thin aqueous film separating the hydrophobic surfaces [12, 13], correlated dipole interactions [14], rearrangements of water molecules near hydrophobic surfaces [15], and the bridging of nanobubbles [16, 17].

Other intermolecular and intersurface interactions that are important in understanding the various tribological phenomena include, but are not limited to, thermal fluctuation forces, solvation forces, and hydrogen bonding. The reader is referred to other references for a more detailed discussion of the topic [7, 18].

1.2.2 Surface Energy

It is useful to introduce the concept of surface energy which will be used throughout the discussion. The energy required to separate unit areas of two surfaces 1 and 2 from contact is referred to as work of adhesion (W12), and for identical surfaces it is called work of cohesion (W11). The energy required to increase the surface area of medium 1 by unit area is surface energy or surface tension (γ1), which is related to the work of cohesion by Equation 1.12:

(1.12)

For solids, the term surface energy is mostly used, which has the unit of energy per unit area (J/m2), and for liquids, the term surface tension is usually used in units of force per unit length (N/m). The two terms are dimensionally and numerically the same although the term surface energy is more general in the sense that it can be applied to both liquids and solids. The surface tension of a liquid is the magnitude of the force exerted parallel to the liquid surface divided by the length of the line over which the force acts, which is determined by the cohesive forces between liquid molecules. The surface energy represents the excess energy that the molecules on the surface posses compared to molecules in the bulk of a material. There is a direct relationship between the surface energy and intermolecular forces of a material. The intermolecular forces that determine the boiling point and latent heat of a material also define its surface energy [7, 19]. Therefore, it is expected that materials with high boiling point usually have high surface energy (e.g., for mercury: γ = 485 mJ/m2, TB = 357°C) and lower boiling point substances have lower surface energy (e.g., for neon: γ = 3.8 mJ/m2, TB = −246°C). The surface energies and chemical structures of some common materials are given in Table 1.3. For surfaces between which attractive forces can be accounted for by conventional VDW forces, the surface energy can be approximated by Equation 1.13 [7]:

(1.13)

where r is the interatomic or intermolecular center-to-center distance (r/2.5∼0.165 nm is commonly used) and A is the Hamaker constant. Equation 1.13 predicts the surface energy of nonpolar and nonmetallic compounds well. For metals, another attractive surface interaction (i.e., metallic bond) also exists, which is much stronger than conventional VDW forces and is due to electron exchange interactions at short separations. The metallic bonds are responsible for the much higher surface energy of metals compared to other materials (see Table 1.3). Moreover, the surface energy of metals and crystalline materials is very sensitive to the lattice mismatches. Since the atoms of two mismatched lattices cannot pack together as closely as that of two perfectly matched lattices, the adhesion energy of mismatched interface is usually significantly lower [7, 20]. Other contributions to the surface energy can be from charge exchange interactions such as acid–base and hydrogen bonding.

TABLE 1.3 Surface Energy and Chemical Structure of Some Common Materials

Data compiled from different sources, including Knovel.com and Reference [7].

Material

Surface Energy

γ

(mJ/m

2

)

Chemical Structure

Gold

1140

Au

Silver

903

Ag

Tungsten

2500

W

Aluminium

914

Al

Copper

1285

Cu

Mercury

486

Hg

Neon

3.8

Ne

Argon

9.4

Ar

Oxygen

10.7

O

2

Water

73.7

H

2

O

Acetone

23.7

Acetic acid

27.5

Benzene

28.88 ± 0.03

o-Xylene

30.10 ± 0.3

m-Xylene

28.90 ± 0.1

p-Xylene

28.37 ± 0.1

Toluene

28.5 ± 0.3

Phenol

40.9 ± 0.3

Chlorobenzene

33.19 ± 0.1

Ethylbenzene

29.20 ± 0.2

Cyclohexane

25

n-Hexatriacontane

21

Polytetrafluoroethylene (PTFE)

19

Polystyrene (PS)

43

Nylon 4

48.5

Nylon 6

38.4

Nylon 6-6

43

Nylon 7-7

43

Nylon 9-9

36

Nylon 12

35.8

Polyethylene terephthalate (PET)

43

Poly(butylene isophthalate)

47.8

Poly methy methacrylate (PMMA)

39

Low density polyethylene (LDPE)

35

Polyvinyl chloride (PVC)

42

Polyvinylidene chloride (PVDC)

43

Polyvinyl fluoride (PVF)

35

Polyvinylidene fluoride (PVDF)

25

Poly(trifluoroethylene)

22

Poly(chloroprene)

43.6

Poly(vinyl acetate)

36.5

Poly(vinyl alcohol)

37

Amylose

37

Amylopectin

35

Cellulose (from cotton)

42

Ethyl cellulose

32

Nitrocellulose

38

The surface and interfacial energies also determine the shape of a liquid droplet on a surface. One of the most widely used methods for measuring surface energy of a material is based on measuring the liquid droplet contact angel θ. If a droplet of liquid 2 forms a contact angle θ on a surface of material 1 in a medium 3, the interfacial energies are related by the well-known Young’s equation as:

(1.14)

If medium 3 is air, Equation 1.14 can be simplified to:

(1.15)

Only γ2 and θ can be directly measured by experiments, and thus there are two unknowns in Equation 1.15: γ12 and γ1. Different approaches have been suggested to resolve this problem. Zisman et al. [21, 22] found that a plot of cosθ versus γ2 for a homologous series of liquids (so-called Zisman plot) usually generates a straight line and the intercept of such plot with the horizontal line cosθ = 1 is called the critical surface tension γc, which can be approximated as the solid surface energy γ1. This approach should be used with caution as it is assumed that when cosθ = 1, γ12 is zero, which may not be necessarily true.

Another widely used method was developed by van Oss et al. [23] In the van Oss method, the surface energy is comprised of two terms which take into account the relative contributions from Lifshitz–VDW (γLW) and Lewis acid–base (γAB) interactions as:

(1.16)

The Lewis acid–base component of the surface energy is defined such that it comprises all the electron–acceptor and electron–donor interactions given by:

(1.17)

Based on Equation 1.16 and Equation 1.17, the Young’s equation can be written as:

(1.18)

Therefore, at least three different liquids should be used in contact angle measurements to obtain the three components of the surface tension of solid , , in Equation 1.18 and thus the total surface energy in Equation 1.16.

1.3 ADHESION AND CONTACT MECHANICS

Adhesion is the process of attraction between two particles or surfaces which brings them into contact. For the attracted particles or surfaces of the same material, this process is normally referred to as cohesion. Although at first sight there might not be any direct relation between tribology and adhesion (while one deals with surfaces in relative motion, the other tends to bring them into contact), adhesion plays a crucial role in tribological phenomena, specifically friction and wear. Adhesion also plays an important role in a wide range of practical applications from adhesives, to cold welding of metals, to biomedical applications. Research on developing better adhesives in automotive and aerospace industries has continued for decades. Understanding the adhesion mechanisms of cells, bacteria, and proteins on biomedical surfaces is critical for the advances of biotechnology and biomedical science. In this section, the classical theoretical models for the adhesion or contact of two elastic surfaces are reviewed, which are commonly known as contact mechanics theories for analyzing surface deformations, stress distribution, and strength of the adhesion between two surfaces in contact.

1.3.1 Hertz Model

The deformation of two elastic surfaces in contact was first studied by Hertz in 1886 [24]. Hertz assumed that no adhesion was present between the two contacting surfaces, and analyzed the stress distribution and contact geometry of two spheres as a function of compressive load (F⊥). Based on the Hertz theory, the radius a of contact area under compressive load F⊥ is given by Equation 1.19 for two spheres of radii R1 and R2, Young’s moduli E1 and E2, and Poisson ratio υ1 and υ2 , where R and K are given by Equation 1.20 and Equation 1.21:

(1.19)

(1.20)

(1.21)

And the pressure or normal stress distribution within the contact area is given by:

(1.22)

where x = r/a (see Fig. 1.1). According to Equation 1.22, pressure at the center of contact region (x = 0) is P(0) = (3F⊥/2πa2) that is 1.5 times of the mean pressure across the contact area. Hertz studied the contact of glass spheres by using an optical microscope and verified his theory experimentally. Based on the Hertz theory, there is infinite repulsion between the surfaces at D = 0; thus, during the unloading process, the surfaces separate when contact area decreases to zero as the compressive load reduces to zero (see Eq. 1.19).

Figure 1.1 The main features of classical contact mechanics theories.

(Modified based on Horn, R.G.; Israelachvili, J.N.; Pribac, F. (1987) Journal of Colloid and Interface Science, 115, 480-492.) © Elsevier.

1.3.2 Johnson–Kendall–Roberts Model

The main limitation of the Hertz theory is that it neglects the surface energy in the contact of two surfaces. For the first time, in 1921, Griffith pointed out the role of surface energy in elastic contact and fracture of solids [25]. He stated that during the formation of a crack in an elastic body, work must be done to overcome the attractive forces between the molecules of the two sides of the crack. He further pointed out that if the width of a crack is greater than the radius of the molecular action, the molecular attractions are negligible across the crack except near its end. Thus, Griffith stated that the conventional theory of elasticity is capable of analyzing the stresses correctly at all points of an elastic body except those near the end of a crack where molecular attractions cannot be neglected. For the same reason, there was a lot of controversy about the stress distribution and surface deformation at the edge of contact region until almost five decades after Griffith’s paper (see Fig. 1.1) [26–32]. Although Griffith pointed out that surface forces deform the crack and affect the energy balance of the system, he did not quantify the model. The Hertz theory failed to predict the contact mechanics experiments performed by Johnson et al. using glass and rubber spheres: at low loads, the contact area was shown to be much bigger than that predicted by the Hertz theory and during the unloading process the contact radius reached a finite value before detachment [33]. Almost a century after the Hertz model, in 1971, Johnson, Kendall, and Roberts (JKR) proposed a model for contact of elastic surfaces which takes into account the role of surface forces [33]. They analyzed the contact between two elastic spheres and stated that equilibrium condition can be obtained when Equation 1.23 is satisfied:

(1.23)

The total energy of the system (UT) consists of three terms: the stored elastic energy, the mechanical energy under the applied load, and the surface energy. The appropriate expressions for these three components were derived and put into Equation 1.23 to obtain the relation shown in Equation 1.24, where Wad is the adhesion energy and Wad = 2γ for two surfaces of the same materials:

(1.24)

When Wad = 0 (non-adhesive), the Equation 1.24 (JKR theory) reduces to Equation 1.19 (Hertz theory). At zero load (F⊥ = 0), the contact area is finite and given by:

(1.25) 

The adhesion force (or so-called pull-off force) is the force required to separate the spheres from adhesive contact. The corresponding adhesion force between the spheres based on JKR theory is given by:

(1.26) 

And the normal stress distribution within the contact area is given by Equation 1.27, where x = r/a (see Fig. 1.1):

(1.27)

1.3.3 Derjaguin–Muller–Toporov Model

As shown in Equation 1.27, at the edge of contact region (i.e., x = 1), the normal stress is tensile and infinite in magnitude, which causes each surface to bend through a right angle along the contact edge. To resolve this unphysical situation, Derjaguin, Muller, and Toporov (DMT) [34] proposed another model for contact mechanics. According to DMT theory, adhesion arises from attractive surface forces but the surface shape outside the contact area is assumed to be Hertzian and not deformed by the surface forces. The stress distribution within the contact area is also assumed to be the same as that in Hertz theory. In the DMT model, the contact radius is given by Equation 1.28 and the adhesion (pull-off) force is given by Equation 1.29:

(1.28)

(1.29)

1.3.4 Maugis Model

For a while there was some debate on which theory (JKR or DMT) is more suitable to explain the contact area dependence on the load [26–29]. Several models were proposed to show that either of the two theories (JKR and DMT) was a limiting case of a more general approach [30–32, 35, 36]. In these analyses, the intermolecular interaction between single asperities was described by a potential function. For examples, Muller et al. [31, 35] used a Lennard–Jones and Maugis [32] used a Dugdale potential function. In a unified model proposed by Maugis, the transition from JKR to DMT contact is determined by a dimensionless parameter, which is proportional to the parameter proposed by Tabor in 1977, generally known as the so-called Tabor number (Ta) shown in Equation 1.30 [26, 37],

(1.30)

where z0 is the equilibrium separation between the two surfaces in contact, and Wad = 2γ for the cohesion case. The Tabor number depends on the size of interacting particles, their elastic properties, and the characteristic length of molecular interaction of the materials. For soft materials with large surface energy and radius (i.e., Ta >> 1), JKR theory applies; while for hard materials with low surface energy and small radius (i.e., Ta <<1), DMT model would be more appropriate. The main features of contact mechanics theories are summarized in Figure 1.1.

1.3.5 Indentation

One of the most widely used methods for determining hardness and elastic modulus of materials is through indentation measurements. Basically an in­denter is pushed against a sample surface through a complete cycle of loading and unloading, and the load–displacement profile is used to determine the hardness and elastic modulus. The indentation depth δi is the change in distance of the centers of the two approaching bodies from their (first contact and) undeformed state (see Fig. 1.1). The indentation experiments can be used to measure the mechanical properties of both bulk material and thin films or surface layers at the submicroscopic and nanoscales. For a cylindrical flat punch of radius a indenting an elastic material of Young’s modulus E and Poisson’s ration ν under applied load F⊥, assuming no shear stress between the punch and the material surface, the indentation depth δi is given by Equation 1.31. Equation 1.31 shows that the indentation of a flat punch on an elastic plane is proportional to the applied load, which also assumes that the contact area πa2 is constant and independent of the load during indentation:

(1.31)

The indentation depth δi of two elastic spheres in contact as given by different contact mechanics theories is given in Equation 1.32:

(1.32a)

(1.32b)

In typical indentation experiments, a rigid punch is used such that deformation of the punch during the loading–unloading cycle is usually not significant. For simple punch geometries, Sneddon proposed that the relationship between load F⊥ and elastic displacement δi can be generally written as [38, 39]:

(1.33) 

where c1 and c2 are constants. The typical values of c2 parameter are c2 = 1 and 1.5 for cylindrical and spherical punches, respectively. One of the most widely used relationships for analyzing the indentation load-displacement data is given as [40]:

(1.34)

where S = (dF⊥/dδi) is the slope of the unloading-displacement curve during initial stages of the unloading as measured experimentally, K is the com­bined modulus of indenter and specimen defined in Equation 1.21, and AP is the projected area of elastic contact, which is usually assumed to be equal to the optically measured area of the hardness impression. The hardness of the sample material is given by:

(1.35) 

where F⊥,max is the maximum indentation load. As shown in Equation 1.34, reliable determination of elastic modulus depends on accurate measurement of unloading slope S and projected area Ap. For the measurement of unloading slope, S, Oliver and Pharr proposed a power law relationship to describe the unloading data as [40]:

(1.36)

where the parameters c3, c4, and c5 can be determined by common fitting procedures. The unloading slope S can be calculated by differentiating Equation 1.36 and computing the derivative at the maximum load F⊥,max and displacement δi,max. The projected area Ap at maximum load F⊥,max depends on the geometry of the indenter and the depth of contact. Oliver and Pharr assumed that the geometry of the indenter can be described by an area function FA(D), which relates the cross-sectional area of the indenter to the distance from the tip D. The projected contact area AP at the maximum load can then be obtained as [40]:

(1.37) 

The method of Oliver and Pharr has been widely used for the characterization of mechanical properties of different materials by indentation techniques, of which the latest refinements and advances have been reported in a recent review [41].

1.3.6 Effect of Environmental Conditions on Adhesion

All of the adhesion and contact models previously discussed assume contact between perfectly smooth surfaces. In reality, many factors can affect the contact of two surfaces, including contamination, load, surface roughness, and liquid films. Dust contamination can severely reduce the adhesion of metallic surfaces by preventing direct metallic contact [42, 43]. In an early study on gold surfaces, Williamson et al. found that if surface roughness is larger than the size of dust particles, then dust had little effect in preventing metallic contact. In contrast, if the dust particle protrudes the surface, it prevents intimate metallic contact and thus decreases the adhesion [42].

The presence of small amount of condensable vapors in the atmosphere is another parameter which can affect adhesion. The phenomenon of condensation of vapor molecules around the contact joints between the surfaces is known as capillary condensation and can have substantial effect on adhesive properties of surfaces. The condensed vapor forms a liquid meniscus between the two surfaces. As a result of the surface tension of liquid and curva­ture effect, a pressure difference occurs between the inside and outside of the meniscus known as Laplace pressure. The Laplace pressure of the meniscus pulls the two surfaces together and contributes to the adhesion force. The resulting adhesion force between a sphere of radius R on a flat surface in the presence of the liquid meniscus is given by:

(1.38)

where θ is the contact angle of liquid on solid surface, γL is the surface energy of the liquid, and γSL and γSV are interfacial tensions of solid–liquid and solid–vapor interfaces, respectively. Usually γLcosθ exceeds γSL and Equation 1.38 reduces to [7]:

(1.39)

Thus adhesion force in the presence of the liquid meniscus is mainly determined by the surface energy of the liquid. Adhesion experiments that were done in an atmosphere of different vapors corroborate Equation 1.39 [44]. Recent experiments on the effects of relative humidity on adhesion have shown that adhesion regimes changes with humidity. Below a threshold relative humidity, adhesion is mainly determined by VDW forces and above that by capillary condensation [45, 46]. However, it should be noted that when the condensation continues and the Kelvin radius exceeds the sphere radius R (i.e., the particle becomes effectively immersed in excess liquid), the adhesion often turns to be very low due to the disappearance of the capillary term in Equation 1.38.

1.3.7 Adhesion of Rough Surfaces

Surface roughness is another critical parameter on adhesion. Generally, adhesion is conversely related to roughness for elastic surfaces [47–51]. The probability of intimate contact between two surfaces decrease with surface roughness, which therefore decreases the adhesion. Greenwood and Williamson [52] modeled a rough surface on which the asperities are assumed to have the same radius β and a Gaussian distribution of asperity heights z with mean height ω and standard deviation σ, as shown in Equation 1.40. It was assumed that the contact of each asperity follows the Hertzian model:

(1.40)

In 1975, Fuller and Tabor analyzed the adhesion between elastic solids and the effect of roughness. The asperities on the rough surfaces were assumed to follow the Gaussian distribution (similar to the Greenwood–Williamson model) and the contact of each asperity followed the JKR model [48]. Fuller and Tabor showed that the adhesion decreases with the “adhesion parameter” (1/Δc), defined as:

(1.41) 

where Δγ = γ1 + γ2 − γ12. Fuller and Tabor’s model is valid only when the real contact area is much lower than the apparent contact area (see Section 1.7) and that contact breaks uniformly across the apparent contact area, but in real situations separation of surfaces from contact could be accompanied by crack propagation [53]. Other researchers applied different approaches such as using single-parameter characterization [48], double-parameter characterization [54], and fractals [55, 56] to model the surface roughness and the corresponding adhesion force. Nevertheless, there is no general mathematical model for defining the surface roughness. Recent experimental measurement and theoretical modeling on adhesion of rough surfaces [56–59] showed an exponential relation between load F⊥ and intersurface separation u as Equation 1.42, where u0 is a constant:

(1.42)

According to recent experiments and theoretical modelings, the adhesion force decays exponentially with RMS surface roughness ς as [7]:

(1.43) 

where ς0 is a constant and FJKR is the JKR adhesion force for smooth surfaces (ς = 0).

1.3.8 Adhesion Hysteresis

Another important aspect of adhesion process is hysteresis effects. Adhesion hysteresis is the difference between contact properties (e.g., contact area) during loading and unloading cycles. Adhesion hysteresis is usually defined as [60]:

(1.44) 

where γA is the advancing surface energy during loading and γR is the receding surface energy on unloading. Δγ is a measure of energy dissipation during a complete loading–unloading cycle. Thus the adhesion energy hysteresis per unit area is given by:

(1.45)

For purely elastic material with no adhesion hysteresis, contact radius versus load curve would be essentially reversible for loading and unloading processes (see for example Eq. 1.24). However, for viscoelastic materials, the loading and unloading (contact radius vs. load) curves deviate as a result of hysteresis. The origin of hysteresis effects can be the inherent instabilities and irreversibilities associated with loading–unloading cycles or molecular rearrangements and interdigitations at the interface [61]. Recent experiments on polymer surfaces have revealed that polymers of lower molecular weight (MW) show higher adhesion and adhesion hysteresis due to the higher degrees of dynamic molecular rearrangements and interdigitation at the interface [62–64].

1.4 FRICTION

1.4.1 Amontons’ Laws of Friction

The early investigations in the broad field of tribology were more focused on friction. One of the first scientific studies on tribology was performed by Leonardo da Vinci (1452–1519), whose friction experiments resulted in statements that are mostly known as the Amontons’ laws of friction, namely:

i. The friction force is directly proportional to the applied load.

ii. The friction force is independent of the apparent contact area.

The first law of Amontons is usually written mathematically as:

(1.46) 

where F|| is friction force, F⊥ is the normal load that presses the surfaces together, and μ is the coefficient of friction. In order to make the results of different experiments comparable to each other, it is a common practice to report the results of friction experiments in terms of coefficient of friction rather than friction force itself. Euler was the first one who distinguished between two modes of friction: static friction and dynamic friction [53]. The force needed to initiate relative movement of two bodies initially at rest is referred to as static friction force. When two bodies are in motion against each other, the force that resists the movement is referred to as dynamic or kinetic friction. Generally, the kinetic friction is lower than the static friction, but the values may depend on the actual experimental conditions [47]. The values of coefficient of friction for some common materials and systems are given in Table 1.4.

TABLE 1.4 Typical Values of the Coefficient of Friction for Material 1 Sliding on Material 2 at Different Environmental Conditions [7, 47]

The role of surface texture in friction and the concept of asperity interaction were first introduced by Amontons in 1699 [1]. Later, in 1785, Coulomb investigated the role of surface area, nature of materials in contact, normal load, and contact time upon friction, mostly for wooden surfaces. Coulomb also studied the relationship between static and kinetic friction, and the third law of friction is often attributed to him which states:

iii. Kinetic friction is independent of the sliding velocity.

Amontons’ laws of friction were originally concluded mostly based on experiments on wooden surfaces, which were later found to be valid for many other surfaces. However, it should be noted that Amontons’ laws of friction are empirical laws, and exception to Amontons’ laws have been observed in many systems and in various nanometric scenarios, as discussed further in this chapter.

1.4.2 The Basic Models of Friction

In spite of about 500 years of scientific study on friction, a theory has not yet been developed which can describe all experimental data available and predict friction between any two surfaces. A wide range of materials already have been tested in friction experiments such as wood [1, 65, 66], metals [67–69], crystalline solids [70–72], graphite [73–76], diamond [72, 73, 75, 77], mica [78–80], polymers [62–64, 81–83], and many more [49, 84–87]. A valuable list of available resources about friction can be referred to a recent review paper by Krim [88]. As pointed out by Dowson [1], there have been four major models or approaches in the long history of friction study, as follows:

i. The geometrical or mechanistic model. The geometrical or mechanistic model dominated most of friction studies until the beginning of the twentieth century. In this approach, asperity interaction and forces needed for asperities to slip over each other are believed to be the origin of the friction force. The work of early investigators, including Amontons and Coulomb, who believed in the mechanical view of friction, is extensively reviewed by Dowson [1]. Briefly, it was believed that mechanical interlocking of asperities resists the motion of two bodies against each other and the work of frictional force is equal to the work done against the normal load in separating the asperities and sliding them over each other. Therefore, the effect of lubrication in reducing friction was explained by the assumption that lubricants fill the irregularities and gaps between these asperities. However, the geometrical or mechanistic approach could not explain a variety of experimental observations. For example, friction between two highly polished smooth metallic surfaces is higher than unpolished surfaces as a result of cold welding of asperities. If the interlocking of asperities was the origin of friction, one should expect the unpolished surface to have higher friction. Another example is that adsorbed films and monolayers on different surfaces can greatly change the friction while essentially maintaining the same surface roughness.

ii. The molecular or adhesive model. Ewing [47] and Hardy [2] were among the first to propose that the origin of friction is the surface forces and molecular adhesion at the interface. According to Hardy, lubricants reduce the molecular field of force between the solid surfaces, which in turn reduces the friction. Prandtl [1] and Tomlinson [89] considered the role of adhesion in the friction process and tried to analyze the friction at the molecular level. According to Tomlinson, when two surfaces are moved against each other, molecules are forced into each other’s atomic fields and then separated, which is accompanied by energy dissipation that was considered to be the origin of the friction force. Derjaguin took into account the role of intermolecular forces, quantified the concept proposed by Tomlinson, and derived the following relation for friction force [3]:

(1.47) 

where Areal is the real contact area and P and P0 are the mean stresses representing external forces (external load) and molecular adhesion, respectively.

iii. The deformation or ploughing model. In the deformation or ploughing model, friction is attributed to the force required to move hard asperities through or over another surface. Let A0 be the sum of the area of indenting asperities perpendicular to the direction of sliding and H′ be the mean stress required to shear the junction; the friction force would be given by:

(1.48)

Let H be the yield stress of the softer material and note that normal load is applied on real contact area, one would have:

(1.49) 

Therefore, the coefficient of friction becomes:

(1.50)

In Equation 1.50, it is assumed that H is equal to H′, which is a realistic assumption in most cases [47]. In order to quantify the A0/Areal ratio, the geometry of the asperities must be known. For example, for conical asperities that make an angle θ to the direction of sliding, the coefficient of friction is [1]:

(1.51)

Similar expressions have been also derived for other geometries [1, 47].

iv. Combined adhesive and ploughing model. In the fourth approach (combined adhesive and ploughing model), it is believed that both adhesion and ploughing contribute to the friction force. Friction experiments on different metals [67, 69, 90] have shown that deformation and wear occur not only on the surface but to a great depth beneath the surface of the material. Thus friction is not simply a surface phenomenon that can affect the molecules on the surface but also can lead to deformations far beneath the surface molecular layer of the material. Therefore, in order to explain the observed phenomena, it was proposed that friction is due to both adhesion and ploughing. Thus, the proposed mechanism for the metallic friction is as follows: when two surfaces are put into contact, adhesion and cold welding occur at the points of real contact and during sliding; force is required to shear these metallic junctions and also to plough out the metal [47]. Thus friction force can be expressed as:

(1.52)

The ploughing term is given by Equation 1.48 and the shearing term can be written as:

(1.53) 

where s is the tangential stress required to shear the junctions. Thus coefficient of friction becomes:

(1.54) 

Replacing the corresponding value of A0/Areal from Equation 1.51, the coefficient of friction for conical asperities may be expressed as:

(1.55) 

Experiments on metals [47] have shown that the shearing usually occurs within the softer material, therefore the coefficient of friction is mostly determined by the physical properties (s and H) of the softer one of two sliding materials. Experimental [67, 91, 92] and theoretical [93–96] research has been done to investigate the relative contribution of either adhesion or ploughing to the total friction force. Generally, the ploughing term is more dependent on the geometry of the slider and the depth of the indentation in comparison with the adhesion term [47, 94, 96]. Nevertheless, the role of adhesion seems to dominate the ploughing in friction between metals, although it is difficult to be generalized categorically [1].The total friction force (Eq. 1.52) can be also written as:

(1.56)

The first term in Equation 1.56 is referred to as the load-controlled contribution which mainly depends on the structure and topography of the surfaces, while the second term is known as the adhesion-controlled contribution which depends on both the topography and the intermolecular forces between the surfaces [7]. Equation 1.56 also shows that for adhesion-controlled friction (i.e., at low loads), the friction force is not directly proportional to normal load as predicted by Amontons’ first law.The relationship between adhesion and friction has also been studied by using the SFA technique [97–99]. It was found that friction is directly proportional to the adhesion hysteresis rather than adhesion itself. The relation between adhesion hysteresis and friction is schematically shown in Figure 1.2. The friction between two surfaces, as they move relatively by an elemental distance δ, can be divided into a full adhesion cycle: separating the surfaces, moving by distance δ, and then bringing them down to contact. The adhesion energy hysteresis per unit area during this adhesion cycle is given by Equation 1.45