Van der Waals force

Also called van der Waals bonding, vdW

Everyday term

In plain words

A weak attraction between neighbouring atoms and molecules – strong enough, added up over millions of tiny hairs, to let a gecko walk up a pane of glass. In layered crystals it is what holds the layers together, and it is weak enough that a can be peeled off, which is how many are made from ordinary crystals.

Going deeper

Van der Waals attraction comes from electrons in one layer fluctuating in step with those in the next. It is a hundred times weaker than the bonds inside a layer, which is why layered crystals can be split apart and restacked at will.

Where the attraction comes from

The electrons in any piece of matter are constantly redistributing. At any instant a neutral layer has a small, random electric dipole; that dipole polarises its neighbour, and the induced dipole is oriented so as to attract. Averaged over time the dipoles are zero, but the correlation between them is not, and the leftover is a net attraction – the dispersion or London force, the dominant part of what is loosely called van der Waals bonding.

It is the least directional force in chemistry. A bond points somewhere and prefers a specific angle and length; dispersion does neither. It depends only on how polarisable the two bodies are and how far apart they sit, which is precisely why two layers with nothing chemically in common can be stacked without any of the matching a bonded interface would demand.

A hundred times weaker than the bonds inside

Within a layer, atoms are held by covalent bonds worth electronvolts per atom. Between layers, the binding is tens of millielectronvolts per atom – roughly two orders of magnitude less. That gap is the whole basis of the field. It makes possible with adhesive tape, it makes liquid exfoliation possible with the right solvent, and it means that cleaving a crystal between layers leaves a surface with no , which stays clean and unreactive.

The same asymmetry explains why layered crystals are so in everything else: stiffness, , and often electrical conduction differ enormously in and out of the plane, because the forces holding the structure together in those two directions are not the same kind of force.

The other side of being weak

A bond that is easy to break is also easy to slide. Layers in a stack shear past one another at small forces, which is what makes graphite a , and it is also why the relative position of two layers is a variable rather than a fixed property. exists because of it; reconstruct into domains because of it; twisted stacks relax toward alignment because of it; and a scanning probe can rotate or translate a it was only meant to be imaging.

The theory has its own subtleties. Dispersion is a correlation effect that standard density functional approximations miss entirely, so and binding energies require added or specially constructed functionals, and different choices give noticeably different answers. At larger separations the interaction also becomes retarded – the Casimir regime – where the finite speed of light changes its distance dependence, which matters for the forces between surfaces in nanomechanical devices more than for a bonded stack.

For specialists

The weak, non-directional attraction arising from correlated charge fluctuations (dispersion) and related dipolar terms. In layered crystals it binds adjacent layers with energies of tens of meV per atom, roughly two orders of magnitude below in-plane covalent bonds, which enables exfoliation and the free stacking of dissimilar layers.

Where this comes from

Materials perspective on Casimir and van der Waals interactions Woods et al. · Reviews of Modern Physics 88, 045003 (2016) cited by 404

Chemical bond

The glue that holds atoms together. In a covalent bond two atoms share electrons, as within a sheet of graphene; in an ionic bond one atom hands electrons to another and the resulting charges attract, as in table salt; in a metal the outer electrons are shared by all the atoms at once. Much weaker van der Waals forces hold molecules and the layers of a layered crystal together. A 2D material is a crystal with strong bonds within its layers and only weak ones between them – which is why it can be peeled.

The attractive interactions that hold atoms in molecules and solids, classified by how electrons are shared: covalent bonds, from overlapping orbitals holding shared electron pairs, strong and directional (sp² carbon, Mo–S in TMDCs); ionic bonds, from electron transfer and electrostatic attraction (halides, oxides); metallic bonding, with electrons delocalised in a partly filled band; and the weak, non-directional van der Waals interaction from correlated charge fluctuations, besides hydrogen bonds. Real bonds are mixtures, characterised by electronegativity differences and charge analyses. Layered crystals combine in-plane bonds of several electronvolts with interlayer binding of only about 20 meV per Å² (some 0.3 J/m²), the criterion high-throughput screens use to identify exfoliable compounds.

Full explanation

Dangling bond

A bond left with nothing on the other end, on an atom at a surface that has lost the neighbour it was bonded to inside the crystal. Such bonds grab stray molecules and trap electrons, which is why ordinary surfaces are messy – and why layered crystals, whose sheets keep every bond inside themselves, split into faces that stay clean down to a single layer.

An unsaturated valence orbital at a surface, edge or defect where a covalent bond has been cut. In a bulk semiconductor such as silicon these states lie in the gap, trap charge and pin the Fermi level unless passivated by hydrogen or a grown oxide. The basal plane of a layered crystal has none, which is what allows van der Waals stacking without lattice matching and interfaces with few traps – and also why atomic layer deposition nucleates poorly on it. Edges, grain boundaries and vacancies do carry them, and are where 2D materials are chemically active.

Full explanation

Thermal conductivity

How well a material carries heat from a hot place to a cold one. Graphene and boron nitride carry heat along their sheets better than copper, which is why they are used to spread heat away from hot spots – but across the sheets, and across every interface, heat moves far less easily.

The coefficient κ relating heat flux to temperature gradient, q = −κ∇T, carried in insulators and semiconductors almost entirely by phonons. Layered crystals are extremely anisotropic: graphite conducts about 2000 W/m·K along its layers and a few W/m·K across them; suspended graphene reaches several thousand, graphene on silicon dioxide about 600. Low κ – from heavy atoms, anharmonic bonding and interfaces, as in SnSe – is the goal for thermoelectrics, while the thermal boundary resistance at each interface often limits how fast heat leaves a 2D device.

Full explanation

Solid lubricant

A powder or coating that makes surfaces slide over each other easily without oil. Layered crystals such as graphite, MoS₂, WS₂ and hBN are natural lubricants: their layers are strongly bonded inside but only weakly stuck to each other, so they shear apart and coat the rubbing surfaces with slippery sheets. They work where oil cannot – in a vacuum, in space or at high temperatures – and are among the oldest uses of layered materials.

Lamellar solids whose weak interlayer bonding allows easy shear: graphite (which needs adsorbed water or vapour to lubricate well), MoS₂ and WS₂ (best in vacuum and dry gas, oxidising in humid air), and hBN (stable to high temperature in air). Used as burnished or sputtered films, bonded coatings and additives in oils and greases, they reach friction coefficients of a few hundredths, and in space mechanisms MoS₂ is a standard. At the nanoscale, incommensurate contact between layers can make friction nearly vanish – structural superlubricity, seen when graphite flakes are rotated out of register and in MoS₂ – while friction on atomically thin sheets rises as they get thinner because the sheet puckers ahead of the tip.

Full explanation

Density functional theory (DFT)

The workhorse calculation of materials physics. Rather than following every electron, it works with the electron density and a recipe for how electrons avoid one another – which makes a whole crystal cheap enough to compute, and makes the accuracy depend entirely on that recipe.

Ground-state electronic structure from the density, exact in principle by Hohenberg–Kohn and made practical by the Kohn–Sham equations with an approximate exchange–correlation functional. Two dimensions need care: a vacuum gap wide enough that periodic images stop interacting or a truncated Coulomb interaction, a dispersion correction for interlayer binding, and the knowledge that semi-local functionals underestimate gaps – hybrid functionals narrow that error at far higher cost, and quantitative gaps and optical spectra need GW and Bethe–Salpeter on top.

Full explanation