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:

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

where $ρ 1, ρ 2$ are the number densities of the two interacting kinds of particles, and $C$ is the London coefficient in the particle–particle pair interaction.^[1]^[2] 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,

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

References

^ ^a ^b Hamaker, H. C. (1937). "The London – van der Waals attraction between spherical particles". Physica. 4 (10): 1058–1072. Bibcode:1937Phy.....4.1058H. doi:10.1016/S0031-8914(37)80203-7.
^ Seung-woo Lee and Wolfgang M. Sigmund (23 May 2002). "AFM study of repulsive Van der Waals forces between Teflon AF thin film and silica or alumina". Colloids and Surfaces A: Physicochemical and Engineering Aspects. 204 (1–3): 43–50. doi:10.1016/S0927-7757(01)01118-9.
^ Lifshitz, E.M. (1956). "The Theory of Molecular Attractive Forces between Solids". Soviet Journal of Experimental and Theoretical Physics. 2: 73–83.

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[:0-1] Hamaker, H. C. (1937). "The London – van der Waals attraction between spherical particles". Physica. 4 (10): 1058–1072. Bibcode:1937Phy.....4.1058H. doi:10.1016/S0031-8914(37)80203-7.

[2] Seung-woo Lee and Wolfgang M. Sigmund (23 May 2002). "AFM study of repulsive Van der Waals forces between Teflon AF thin film and silica or alumina". Colloids and Surfaces A: Physicochemical and Engineering Aspects. 204 (1–3): 43–50. doi:10.1016/S0927-7757(01)01118-9.

[3] Lifshitz, E.M. (1956). "The Theory of Molecular Attractive Forces between Solids". Soviet Journal of Experimental and Theoretical Physics. 2: 73–83.

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