Casimir-Polder retardation forces

At this point we should darify that the Casimir force is not a really new type of force. It is simply another term for a special case of the van der Waals forces, namely, the retrarded van der Waals force between metallic surfaces. While the terms retarded van der Waals force or retarded London dispersion force are prevalent in the physical chemistry and colloid community, the term Casimir force or Casimir-Polder force has become popular in the physics community. This means that in principle the lifshitz theory is apphcable to describe the Casimir forces. The problem with using Lifshitz theory for ideal metals is the fact that for these the didectric constant diverges (e oo) and therefore the Lifshitz theory breaks down. However, for real metals, the use of the Lifshitz theory is possible with corresponding dielectric models of the metals. 

Casimir HBG, Polder D (1948) The influence of retardation on the londonvan der waals forces. Phys Rev 73 360-372... 

Casimir and Polder also showed that retardation effects weaken the dispersion force at separations of the order of the wavelength of the electronic absorption bands of the interacting molecules, which is typically 10 m. The retarded dispersion energy varies as R at large R and is determined by the static polarizabilities of the interacting molecules. At very large separations the forces between molecules are weak but for colloidal particles and macroscopic objects they may add and their effects are measurable. Fluctuations in particle position occur more slowly for nuclei than for electrons, so the intermolecular forces that are due to nuclear motion are effectively unretarded. A general theory of the interaction of macroscopic bodies in terms of the bulk static and dynamic dielectric properties... 

Casimir, H.B.G. Polder, D. The influence of retardation on the London-van der Waals forces. Physical Review 1948, 73, 360-372 Overbeek, J.T.G. The interaction between colloidal particles. 

Casimir H B G and Polder D 1948 The influence of retardation on the London-van der Waals forces... 

Very recently Casimir and Polder succeeded in giving an exact quantum mechanical -description of the influence of the retardation effects on the London-Van Der Waal s-forces. They found, in fair accord with what was expected by the semi- classical reasoning given above, that a significant reduction of the London-Van Der Waals force between two atoms is felt for distances larger than A/3. When the distance is very large the L o n d o n-energy is proportional to 1/r, instead to 1/r as is found when no account is taken of the retardation. 

Casimir and Polder showed, in 1948, that London s theory must be modified if the molecules are some distance (in molecular terms) apart. This is because the electrostatic forces are not propagated instantaneously but take a finite, if small, time pass between two molecules. The net result of such retarded dispersion forces is that the energy of interaction between two particles with distance between them being greater than 20 nm is proportional to r instead of... 

Clayfield, E. J., E. C. Lumb, and R H. Mackey. 1971. Retarded dispersion forces in colloidal particles—Exact integration of the Casimir and Polder equation. Journal of Colloid and Interface Science 37, no. 2 382-389. doi 10.1016/0021-9797(71)90306-7. 

Force balances which measure, with great precision, the interaction forces between two solid objects, as a function of distance between the two objects, were developed, independently, in Russia and in the Netherlands, especially during the 1950 s (van Oss 1994). Their main initial aim was the experimental verification of the existence of retardation (Casimir and Polder, 1948) of attractive van der Waals forces at distances greater than approximately 10 nm. Experimental proof of the existence of retardation was finally obtmned with an improved force balance (Tabor and Winterton, 1969). The usefulness of the force balance was subsequently vastly improved by Israeladivili and Adams (1978), who extended its application to measurements in liquids (e.g., water), whilst theretofore measurements usually were only done in... 

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