Hamaker constant

{{short description|Physical constant related to Van der Waals interactions}}

{{Use dmy dates|date=December 2023}}

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

:$A=\backslash pi^2C\backslash rho\_1\backslash rho\_2,$

where {{math|ρ{{sub|1}}, ρ{{sub|2}}}} are the number densities of the two interacting kinds of particles, and {{mvar|C}} is the London coefficient in the particle–particle pair interaction.{{cite journal|author=Hamaker, H. C.|year=1937|title=The London – van der Waals attraction between spherical particles|journal=Physica|volume=4|issue=10|pages=1058–1072|doi=10.1016/S0031-8914(37)80203-7|bibcode=1937Phy.....4.1058H }}{{cite journal|author=Seung-woo Lee and Wolfgang M. Sigmund|title=AFM study of repulsive Van der Waals forces between Teflon AF thin film and silica or alumina|journal=Colloids and Surfaces A: Physicochemical and Engineering Aspects|volume=204|issue=1–3|date=23 May 2002|pages=43–50|doi=10.1016/S0927-7757(01)01118-9}} The magnitude of this constant reflects the strength of the vdW-force between two particles, or between a particle and a substrate.

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

:$w(r)\; =\; \backslash frac\{-C\}\{r^6\}.$

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).{{Cite journal |last=Lifshitz |first=E.M. |date=1956 |title=The Theory of Molecular Attractive Forces between Solids |journal=Soviet Journal of Experimental and Theoretical Physics |volume=2 |pages=73–83}}

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 $1/r^6;$ this is called the retarded regime, and the result is a Casimir–Polder force.