Hamaker constant

In molecular physics, the Hamaker constant (denoted A; named for H. C. Hamaker) is a physical constant that can be defined for a van der Waals (vdW) body–body interaction:

${\displaystyle A=\pi ^{2}C\rho _{1}\rho _{2},}$

where ρ₁, ρ₂ are the number densities of the two interacting kinds of particles, and C is the London coefficient in the particle–particle pair interaction.¹² The magnitude of this constant reflects the strength of the vdW-force between two particles, or between a particle and a substrate.¹

The Hamaker constant provides the means to determine the interaction parameter C from the vdW-pair potential,

${\displaystyle w(r)={\frac {-C}{r^{6}}}.}$

Hamaker's method and the associated Hamaker constant ignores the influence of an intervening medium between the two particles of interaction. In 1956 Lifshitz developed a description of the vdW energy but with consideration of the dielectric properties of this intervening medium (often a continuous phase).³

The Van der Waals forces are effective only up to several hundred angstroms. When the interactions are too far apart, the dispersion potential decays faster than ${\displaystyle 1/r^{6};}$ this is called the retarded regime, and the result is a Casimir–Polder force.