Hamaker Constant

A material-and-medium-dependent coefficient sets the strength of nonretarded van der Waals dispersion interaction between idealized macroscopic bodies.

Version

v1 · 2026-10-31 · History

Domain-specific #

14506

Domain group

Natural Sciences

Origin domain

Chemistry & Materials Science

Subdomains

Dispersion Forces, Interfacial Physics → Chemistry & Materials Science

Aliases

Hamaker coefficient

Core Idea

The Hamaker constant A packages dispersion-interaction strength for a specified pair of bodies and surrounding medium. In a simple nonretarded pair-additive model, A₁₂ = π²ρ₁ρ₂C₁₂ for a −C₁₂/r⁶ molecular potential. Ideal parallel half-spaces have energy per area −A/(12πD²); a sphere near a plane has approximate energy −AR/(6D) for gap D ≪ radius R. These are conditional geometry laws, not a universal attraction of every real surface.^[1]

How would you explain it like I'm…

Super-Close Sticky Number

When two things get super, super close, there's a tiny pull between them, coming from all their little bits. The Hamaker constant is a number that tells how strong that pull is for those two things, and sometimes whether it pulls or pushes. It depends on both things and on what's in between them, like air or water.

Strength of the Tiny Pull

All objects have a very weak attraction to each other when they are extremely close, coming from their molecules. Scientists use the Hamaker constant, a number, to describe how strong that pull is between two objects. To find the total pull, they combine the Hamaker constant with the objects' shapes and the distance between them — for example, two flat surfaces or a ball near a flat surface. The number depends on both materials and on whatever is between them, like water. It isn't a fixed number for just one material, and at bigger distances or on rough surfaces the simple formulas stop working well.

Dispersion Interaction Coefficient

The Hamaker constant A is an energy-scale coefficient describing the strength (and, with a sign convention, the direction) of the dispersion, or van der Waals, interaction between macroscopic bodies. In Hamaker's pair-additive model, the attraction between molecules, which falls off as 1/r⁶, is added up over all the molecules in two bodies, giving A₁₂ = π²ρ₁ρ₂C₁₂. Geometry and distance then contribute a separate factor: for two flat surfaces, energy per area is −A/(12πD²); for a sphere of radius R near a plane, about −AR/(6D) when D is much smaller than R. A belongs to a pair of materials and their environment, not to a single substance. A liquid between the bodies changes it, and Lifshitz's later theory uses the materials' dielectric response instead of summing pairs. At large distances or for rough, coated surfaces, a single constant may not fit well.

 

The Hamaker constant A is an energy-scale coefficient expressing the strength — and, under a signed convention, the direction — of dispersion interactions between idealized macroscopic bodies. In Hamaker's pair-additive model, a molecular pair potential −C₁₂/r⁶ is integrated over two bodies with number densities ρ₁ and ρ₂, yielding A₁₂ = π²ρ₁ρ₂C₁₂. A geometry- and separation-dependent factor then completes the interaction: in the nonretarded idealization, two flat half-spaces have interaction energy per unit area −A/(12πD²), and a sphere of radius R near a plane has energy approximately −AR/(6D) for D ≪ R. A is not a universal constant of one substance independent of its partner and environment. The factorization into material coefficient and geometric factor is useful but conditional. Hamaker's original 1937 paper already considered two spheres immersed in a liquid, and an intervening medium alters the effective interaction. Lifshitz's later electromagnetic theory computes the interaction from dielectric response rather than summing independent pair potentials. At larger separations retardation, and at real contacts coatings, roughness, and other forces, can make a single distance-independent A or smooth-surface geometry inadequate.

Scope of Application

Hamaker's original 1937 sphere calculation also considered liquid immersion. Valmacco and colleagues measured silica-particle forces across aqueous electrolyte and found fitted A about 2.4×10⁻²¹ J after 1200°C treatment versus (7±5)×10⁻²³ J untreated, with nanoscale roughness influencing the result. Ohnishi and colleagues found different behavior in fluorocarbon monolayers prepared by different methods, including capillary bridging in saturated vapor.^[1][2][3]

Clarity

Specify body–medium–body, separation, geometry and whether A is pair-additive, dielectric-response calculated or fitted effectively. Do not confuse the sphere–plane energy −AR/(6D) with force −AR/(6D²). Retardation, roughness, coatings, electrostatics and capillary forces can defeat a simple constant-A interpretation.^[4][2][3]

Manages Complexity

One coefficient times a geometry factor avoids summing atom pairs anew, but hides medium response, surface condition and competing forces. A simple fit is useful only within its regime; a more detailed model requires dielectric and surface inputs to gain fidelity.^[1][4][2]

Abstract Reasoning

Given a quoted A, identify the two bodies and medium, derive or select the geometry law, and test whether the measured force can be attributed to dispersion. Screening electrical repulsion may isolate A in an experiment but not predict a real unscreened suspension's total interaction. Surface roughness can make “same material” yield different effective fitted values.^[2]

Knowledge Transfer

The portable skeleton is coefficient × geometry under a separability assumption; the domain-bound mechanism is van der Waals dispersion and surface-force measurement. Measurement of force can estimate an effective coefficient under a stated model. Hamaker A is not a generic unitless interaction score.^[1][4]

Neighborhood in Abstraction Space

Hamaker Constant sits in a sparse region of the domain-specific corpus (68^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Statistical Mechanics & Particle Phenomena (19 abstractions)

Nearest neighbors

• Solvent model — 0.84
• Random-Phase Approximation — 0.84
• Surface and Bulk Erosion — 0.84
• Scattering — 0.83
• Flocculation — 0.83

Computed from structural-signature embeddings · 2026-10-31

References

[1] Hamaker, H. C. (1937), “The London–van der Waals Attraction between Spherical Particles”, Physica 4: 1058–1072, doi:10.1016/S0031-8914(37)80203-7. Publisher indexed original and intermittently accessible original PDF. registry ↩a ↩b ↩c ↩d

[2] Valmacco, Valentina, et al. (2016), “Dispersion forces acting between silica particles across water, influence of nanoscale roughness”, Nanoscale Horizons 1: 325–330, doi:10.1039/C6NH00070C. Original publication and force measurements. registry ↩a ↩b ↩c ↩d

[3] Ohnishi, Satomi, Vassili Yaminsky, and H. K. Christenson (2000), “Measurements of the Force between Fluorocarbon Monolayer Surfaces in Air and Water”, Langmuir 16: 8360–8367, doi:10.1021/la000262e. Original abstract in author institution repository; full paper not read in this pass. registry ↩a ↩b

[4] Lifshitz, E. M. (1956), “The Theory of Molecular Attractive Forces between Solids”, Soviet Physics JETP 2: 73–83. Original dielectric-response treatment. registry ↩a ↩b ↩c