Friction and adhesion: why surfaces grip and how glues hold

Friction is about how hard it is to start and keep two rough solids sliding

Intuition

Push a heavy box across a floor. You have to shove harder to get it moving than to keep it moving. That is the gap between static and kinetic friction. Underneath, the box and floor are two mountain ranges pressed together, touching only at the peaks.

When two solids touch under a normal load, a force is needed to start and to keep tangential movement. Static friction is the force needed to start. Kinetic friction is the force needed to keep moving. Lecture 34 gives three laws:

1. The frictional force is proportional to the applied load.
2. The force is independent of the apparent area of contact.
3. The kinetic frictional force is independent of the sliding velocity.

The unitless friction coefficient $\mu$ sums up the first law:

$\mu = \frac{F}{W}$

$F$ is the friction force and $W$ is the applied load.

Friction has two sources: broken contact bonds and ploughing

The first source is adhesion at the real contact points. Even a super-smooth surface has bumps of about 5 to 10 nm, so only the peaks touch and the true area is smaller than the apparent area. Where they touch, the surfaces are bound by adhesion forces. To slide, you must shear or break those bonds. With $A$ the actual contact area and $s$ the adhesive shear strength:

$F_{ad} = A\,s$

The second source is deformation: bulk deformation, cracking or ploughing when the bumps of one surface push into the other. A normal force $W$ flattens the bumps and increases the real contact area. For plastic deformation:

$A = \frac{W}{\tau_0}$

$\tau_0$ is the yield strength of the interface. This links the two ideas: more load means more real contact, so more bonds to shear, so more friction. That is why the first law holds.

A material can respond elastically (reversible) or viscoelastically (reversible but time-dependent). If one surface is harder, its bumps plough grooves into the softer one. Real friction mixes adhesion and ploughing. The two are not necessarily additive and are usually hard to separate. Blunt bumps are usually assumed to plough very little.

The four classes of surface rub differently

Friction depends on the hardness and strength of each material. The lecture groups surfaces into four classes.

Metals and their oxides. Most metals carry at least a monolayer of oxide, so metal friction is really oxide-oxide, oxide-metal or metal-metal contact. In aluminium the oxide is much harder than the metal. The thin film breaks under small loads, and friction is relatively independent of load. In copper, friction depends on load, which points to a relatively strong oxide matched to the metal.

Relatively isotropic crystals (NaCl, diamond, sapphire, krypton). Softer ones have $\mu$ of 0.5 to 1.0. Hard, brittle ones such as NaCl crack extensively. Diamond and sapphire have low $\mu$ (0.1) that depends on load, because they deform elastically, not plastically. Under very clean conditions $\mu$ for diamond rises to 0.6. This suggests that an adsorbed monolayer of water or a thin oxide acts as a natural lubricant.

Layered crystals (graphite, MoS₂, talc). These are good lubricants. Their large faces have lower surface energy, so the forces along the flat faces are much weaker than at the narrow edges. That gives a lower shear strength and lower $\mu$. For graphite, $\mu = 0.1$ in air and $0.6$ in vacuum, so adsorbed gases probably weaken the grip between the faces.

Polymers. Static friction is significantly greater than kinetic friction, and the static value depends on load. Polymer chains are mobile at an interface and can interpenetrate, which gives strong adhesion and high static friction. Once sliding starts, a thin layer of the low-shear-strength polymer can detach and act as a lubricating film.

Optional aside

The slide on metals (p.8) prints “clean copper has μ = 6.8; copper oxide has μ ~ 0.8”. A value of 6.8 is far above the usual range quoted for the other classes on the lecture. It is kept here exactly as printed. Check the slide if you need to quote it.

Exam detail

Expect to link a class of surface to its friction story: oxide film (metals), elastic deformation (diamond, sapphire), weak faces (layered crystals), and chain interpenetration then a lubricating film (polymers).

Adhesion is the work to pull two materials apart, and real joints fall short of it

Adhesion lets a mechanical force, larger than any friction force, act on two touching objects without them separating. The thermodynamic definition uses the work of adhesion. Pull A and B apart inside a vapour V. The A–B interface is destroyed and two new surfaces (A–V and B–V) appear. $W_{AB}$ is the work per unit area needed to separate them beyond the range of their forces.

$W_{AB} = \gamma_{AV} + \gamma_{BV} - \gamma_{AB}$

Pressing two solids together does not normally make them stick, apart from molecularly smooth crystals such as mica. A glue works because it makes intimate molecular contact, so short-range van der Waals forces can hold the materials together.

The thermodynamic model is the ideal, reversible upper bound. Two things lower real strength. First, flaws in the interfacial zone concentrate stress, so the local stress can far exceed the average and failure starts there. Second, irreversible viscoelastic processes dissipate energy. Surfaces are also rough, so an adhesive traps air bubbles, water or oil droplets and dust, which shrinks the contact area.

Strong adhesion needs close contact and, for polymers, entanglement

Van der Waals forces fall off rapidly with distance, as $1/r^6$. The surfaces must be as close as about 0.2 to 0.5 nm. Close contact is necessary but not sufficient. The lecture’s table of interaction energies (kcal/mol) shows how much a bond type can add:

Type of interaction	Approximate energy range (kcal/mol)
van der Waals: dispersion	5
van der Waals: dipole-dipole	0 to 10
van der Waals: dipole-induced dipole	0 to 0.5
van der Waals: hydrogen bonding	0 to 40
chemical bonds: covalent	15 to 170
chemical bonds: ionic	140 to 250
chemical bonds: metallic	27 to 83

Most adhesives are polymers. Entanglement spreads stress and backs up the intermolecular forces, so the material stretches and resists a much greater force before failing. Without entanglement, chains slide past each other and strength is low.

The lecture sorts adhesion into four categories:

1. A sharp interface with weak interactions, for example nonpolar polyethylene against a polar copolymer. Only dispersion forces act, so the joint is very poor.
2. A sharp interface with specific chemical interactions, for example –OH, –NH– or –COOH groups on a metal oxide. No entanglement is possible, but there is significant strength.
3. Interpenetration of adhesive and substrate, because they mix. Entanglement gives a strong joint even without strong intermolecular forces.
4. Physical or mechanical interlocking, for example a molten polymer flowing into a rough surface.

In a proper joint, failure seldom happens at the interface itself. It occurs in a weak boundary layer near the interface or in the weaker of the two bonded phases.

Recall

Why does pressing a heavier load on a sliding block raise the friction, even though friction does not depend on the apparent area?

More load flattens the bumps, so the real contact area $A = W/\tau_0$ grows. More real contact means more adhesive spots to shear ($F_{ad} = A\,s$). The friction rises with load, not with the visible area.