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Hamaker Theory (physics)

1937

H. C. Hamaker

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 [latex]r^{-6}[/latex] potential over the volumes of the interacting bodies. The result is quantified by the Hamaker constant, [latex]A[/latex].

While London’s theory described the Van der Waals force between two atoms, Hamaker’s theory provided a practical 方法 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 [latex]r^{-6}[/latex] potential. For instance, the interaction energy between two flat plates varies as [latex]d^{-2}[/latex], and between a sphere and a plate as [latex]d^{-1}[/latex], where [latex]d[/latex] is the separation distance. The strength of this macroscopic interaction is encapsulated in the Hamaker constant, [latex]A[/latex], which depends on the atomic density of the materials and the microscopic interaction constant ([latex]C_6[/latex]). 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 框架 for understanding adhesion, colloidal stability, and surface forces.

化学气相沉积（CVD）, 环境工程, 材料科学, 纳米技术, 物理, 表面张力, 摩擦学

UNESCO Nomenclature: 2209

– Physical chemistry

类型

Theoretical Framework

中断

实质性

使用方法

广泛使用

前体

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

应用

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 (微机电系统) to understand and prevent stiction (unwanted adhesion)
thin film physics, wetting phenomena, and surface energy calculations

专利：

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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.