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Hamaker Theory (physics)

1937
  • H. C. Hamaker
Laboratory experiment demonstrating Hamaker Theory in physical chemistry of surfaces.

(generated image for illustration only)

A theory that extends the microscopic Van der Waals forces between individual atoms to the macroscopic scale, calculating the total interaction force between bulk objects (e.g., two spheres, a sphere and a plate). It assumes pairwise additivity, integrating the microscopic \(r^{-6}\) potential over the volumes of the interacting bodies. The result is quantified by the Hamaker constant, \(A\).

While London’s theory described the Van der Waals force between two atoms, Hamaker’s theory provided a practical method to calculate the force between macroscopic objects. The core assumption of the theory is pairwise additivity: the total interaction energy between two large bodies is simply the sum (or integral) of all the individual atom-atom interactions. For example, to find the force between a sphere and a flat surface, one would integrate the Lennard-Jones potential for a single atom in the sphere with every atom in the surface, and then integrate that result over all atoms in the sphere.

This integration leads to interaction potentials that decay much more slowly with distance than the microscopic \(r^{-6}\) potential. For instance, the interaction energy between two flat plates varies as \(d^{-2}\), and between a sphere and a plate as \(d^{-1}\), where \(d\) is the separation distance. The strength of this macroscopic interaction is encapsulated in the Hamaker constant, \(A\), which depends on the atomic density of the materials and the microscopic interaction constant (\(C_6\)). While the assumption of pairwise additivity is an approximation (it ignores many-body effects and the influence of the intervening medium), the Hamaker theory provides an invaluable and intuitive framework for understanding adhesion, colloidal stability, and surface forces.

UNESCO Nomenclature: 2209
– Physical chemistry

Type

Theoretical Framework

Disruption

Substantial

Usage

Widespread Use

Precursors

  • London Dispersion Force theory providing the microscopic potential
  • Integral calculus for summing forces over continuous bodies
  • DLVO theory, which incorporates Hamaker’s work to describe colloidal stability
  • Early experimental observations of adhesion and colloidal behavior

Applications

  • colloidal science, as part of DLVO theory to predict the stability of suspensions
  • atomic force microscopy (AFM) to model tip-surface interactions
  • design of microelectromechanical systems (MEMS) to understand and prevent stiction (unwanted adhesion)
  • thin film physics, wetting phenomena, and surface energy calculations

Patents:

NA

Potential Innovations Ideas

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Related to: Hamaker constant, macroscopic Van der Waals, colloid, surface science, adhesion, stiction, atomic force microscopy, DLVO theory, thin film, Lifshitz theory.

Historical Context

Hamaker Theory (physics)

1931
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1937
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1931
1932
1936-01-01
1938
1940
1950
1950

(if date is unknown or not relevant, e.g. "fluid mechanics", a rounded estimation of its notable emergence is provided)

Related Invention, Innovation & Technical Principles

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