3.1 Adhesion theory of friction

Adhesion theory of friction explains how molecular interactions between surfaces influence friction and wear. It focuses on the real contact area, adhesive bonds, and surface properties to understand friction phenomena in engineering applications.

This theory provides insights into designing low-friction systems and predicting material behavior. It considers factors like surface roughness, material properties, and environmental conditions to explain friction forces and wear mechanisms in various tribological contexts.

Fundamentals of adhesion theory

• Adhesion theory explains friction phenomena by focusing on molecular interactions between contacting surfaces
• Provides a framework for understanding how surface properties influence friction and wear in engineering applications
• Crucial for designing low-friction systems and predicting material behavior in tribological contexts

Definition of adhesion

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• Attractive force between two surfaces in close contact
• Occurs due to intermolecular forces (van der Waals, electrostatic, chemical bonding)
• Measured by the work required to separate two adhered surfaces
• Plays a significant role in friction, especially for clean and smooth surfaces

Historical development

• Originated in the mid-20th century as an alternative to purely mechanical friction theories
• Bowden and Tabor pioneered the concept of adhesion-based friction in the 1940s
• Evolved through contributions from researchers like Derjaguin, Tomlinson, and Johnson
• Gained prominence with advancements in surface science and nanotechnology

Key principles

• Friction force arises from breaking adhesive bonds formed at contact points
• Real contact area is much smaller than apparent contact area due to surface roughness
• Adhesion strength depends on material properties, surface conditions, and environmental factors
• Plastic deformation of asperities contributes to increased real contact area and adhesion

Adhesive forces in friction

Types of adhesive bonds

• Primary bonds: strong chemical bonds (covalent, ionic, metallic)
  • Form during severe plastic deformation or high-temperature conditions
  • Contribute significantly to friction and wear in extreme environments
• Secondary bonds: weaker physical bonds (van der Waals, hydrogen bonding)
  • Dominate adhesion in most engineering applications
  • Easily formed and broken during sliding contact

Molecular interactions

• Van der Waals forces: universal attraction between molecules
  • Include dispersion, dipole-dipole, and induced dipole interactions
  • Strength decreases rapidly with distance (proportional to $1/r^6$)
• Electrostatic forces: arise from charge separation or polarization
  • Can be attractive or repulsive depending on surface charges
  • Significant in materials with high dielectric constants or in dry environments
• Capillary forces: liquid bridges forming between surfaces
  • Occur due to condensation of water vapor in humid conditions
  • Can dramatically increase adhesion and friction, especially for hydrophilic surfaces

Surface energy concepts

• Surface energy ($\gamma$): energy required to create a unit area of new surface
• Work of adhesion ($W_{ad}$): energy released when two surfaces come into contact
  • Expressed as $W_{ad} = \gamma_1 + \gamma_2 - \gamma_{12}$, where $\gamma_{12}$ is the interfacial energy
• Relates to wettability and contact angle measurements
• Higher surface energy materials tend to exhibit stronger adhesion and friction

Microscopic contact areas

Real vs apparent contact

• Apparent contact area: macroscopic area of contact between two surfaces
• Real contact area: sum of discrete microscopic contact points (asperities)
  • Typically 0.1-1% of the apparent contact area for most engineering surfaces
  • Determines the actual load-bearing capacity and friction behavior
• Relationship between real and apparent contact areas influenced by surface topography and applied load

Asperity deformation

• Elastic deformation: occurs at low loads, reversible
  • Described by Hertzian contact theory for simple geometries
  • Contact area proportional to $F^{2/3}$ for spherical asperities
• Plastic deformation: occurs when local stresses exceed yield strength
  • Results in permanent changes to surface topography
  • Contact area becomes directly proportional to applied load ($A \propto F$)
• Transition from elastic to plastic deformation depends on material properties and asperity geometry

Contact area growth

• Increases with applied load due to flattening of asperities
• Time-dependent growth observed in some materials (creep effects)
• Influenced by surface roughness, material hardness, and environmental factors
• Can lead to increased adhesion and friction over time in static contacts

Adhesion-friction relationship

Friction force components

• Adhesion component: force required to break adhesive bonds at the interface
• Deformation component: energy dissipated through plastic deformation of asperities
• Plowing component: resistance to material displacement during sliding
• Total friction force is the sum of these components, with adhesion often dominating

Adhesion contribution to friction

• Proportional to the real contact area and interfacial shear strength
• Expressed as $F_{adhesion} = A_{real} \times \tau$, where $\tau$ is the shear strength
• Dominant mechanism for smooth, clean surfaces and in vacuum or inert environments
• Can account for up to 80-90% of total friction force in some cases

Shear strength of junctions

• Determined by the weakest interface (bulk material or adhesive bond)
• Influenced by material properties, surface chemistry, and environmental conditions
• Can be affected by temperature, sliding speed, and normal load
• Often exhibits pressure dependence, described by $\tau = \tau_0 + \alpha P$, where $\tau_0$ is the intrinsic shear strength and $\alpha$ is a pressure coefficient

Factors affecting adhesion

Surface roughness

• Inverse relationship between roughness and adhesion strength
• Smoother surfaces provide larger real contact areas, increasing adhesion
• Nanoscale roughness can enhance adhesion through increased surface area
• Optimal roughness exists for specific applications (adhesion control)

Material properties

• Elastic modulus: affects deformation and real contact area
  • Lower modulus materials tend to exhibit higher adhesion
• Hardness: influences plastic deformation and junction growth
• Surface energy: determines the strength of adhesive bonds
• Poisson's ratio: affects stress distribution in contact regions

Environmental conditions

• Humidity: influences capillary forces and surface chemistry
  • Can increase or decrease adhesion depending on material hydrophobicity
• Temperature: affects material properties and chemical reactivity
  • Higher temperatures generally increase adhesion due to softening and enhanced diffusion
• Contaminants: can form barrier layers or act as lubricants
  • Oxide layers on metals often reduce adhesion and friction

Adhesion theory limitations

Criticisms and challenges

• Overestimation of friction forces for many real-world surfaces
• Difficulty in accurately measuring real contact areas
• Neglects dynamic effects and velocity dependence of friction
• Challenges in incorporating surface roughness effects at multiple scales

Alternative friction theories

• Mechanical interlocking theory: focuses on geometric interactions between asperities
• Energy dissipation theory: considers various energy loss mechanisms during sliding
• Molecular-kinetic theory: describes friction as thermally activated molecular processes
• Composite theories: combine elements of adhesion and other mechanisms

Experimental discrepancies

• Friction coefficients often lower than predicted by pure adhesion theory
• Weak correlation between adhesion and friction observed in some systems
• Difficulty in isolating adhesion effects from other friction mechanisms
• Challenges in replicating idealized conditions assumed in theoretical models

Applications in engineering

Tribology and lubrication

• Design of low-friction coatings and surface treatments
  • (DLC coatings, self-assembled monolayers)
• Development of advanced lubricants to minimize adhesion
  • (Nanoparticle additives, ionic liquids)
• Optimization of material pairs for specific tribological applications
  • (Bearing materials, brake pads)

Adhesive wear mechanisms

• Understanding and predicting material transfer during sliding contact
• Developing wear-resistant materials and coatings
• Analyzing wear particle formation and its impact on system performance
• Designing surfaces to minimize adhesive wear in critical components

Surface coating design

• Tailoring surface energy to control adhesion and wettability
• Creating multi-functional coatings for specific tribological requirements
• Optimizing coating thickness and composition for durability
• Developing self-healing coatings to mitigate adhesive wear damage

Measurement techniques

Adhesion force measurement

• Atomic force microscopy (AFM) for nanoscale adhesion measurements
  • Force-distance curves provide quantitative adhesion data
• Surface force apparatus (SFA) for measuring forces between macroscopic surfaces
• Centrifugal adhesion testing for larger components and coatings
• Pull-off tests for measuring adhesion strength of films and coatings

Friction coefficient determination

• Pin-on-disk tribometers for measuring friction under controlled conditions
• Nanotribometers for microscale friction measurements
• In-situ friction measurement techniques (SEM, TEM tribometry)
• Reciprocating friction testers for simulating specific application conditions

Surface characterization methods

• Profilometry for quantifying surface roughness and topography
• X-ray photoelectron spectroscopy (XPS) for surface chemical analysis
• Scanning electron microscopy (SEM) for high-resolution surface imaging
• Contact angle measurements for determining surface energy and wettability

Modeling adhesion-based friction

Analytical approaches

• Maugis-Dugdale model for elastic adhesion between spheres
• JKR (Johnson-Kendall-Roberts) theory for soft, adhesive contacts
• DMT (Derjaguin-Muller-Toporov) model for stiff materials with weak adhesion
• Tabor parameter for determining appropriate adhesion model based on material properties

Numerical simulations

• Finite element analysis (FEA) for complex geometries and material behaviors
• Molecular dynamics (MD) simulations for atomic-scale adhesion and friction processes
• Discrete element method (DEM) for modeling granular materials and particle adhesion
• Multi-scale modeling approaches combining atomistic and continuum methods

Scale-dependent models

• Fractal models for describing surface roughness across multiple scales
• Persson's theory of rubber friction incorporating multi-scale roughness
• Greenwood-Williamson statistical models for asperity contact
• Scale-bridging techniques to link nanoscale adhesion to macroscale friction

Future directions

Nanotribology advancements

• Improved understanding of atomic-scale friction mechanisms
• Development of novel nanoscale lubricants and surface treatments
• Integration of nanotribology principles into macroscale engineering design
• Exploration of quantum effects in nanoscale adhesion and friction

Multi-scale modeling

• Advanced computational techniques for bridging length and time scales
• Integration of machine learning and data-driven approaches in tribology modeling
• Development of predictive models for complex, multi-material systems
• Incorporation of chemical reactivity and tribochemistry into friction models

Emerging materials and surfaces

• Tribological properties of 2D materials (graphene, MoS2)
• Biomimetic surfaces inspired by nature (lotus effect, gecko adhesion)
• Smart materials with adaptive friction and adhesion properties
• Nanocomposite coatings for extreme environment applications