Repulsion?

  Stiction due to the attractive Casimir force is a challenge to design and operation of MEMs.

Can Casimir forces be weakened or made repulsive? [DARPA ; Scientific American]

1. Repulsion via Boundary Conditions

  Scalar Fields with Dirichlet (D) or Neumann (N) boundary conditions:

     Similar boundaries (DD or NN) lead to attraction, while opposing boundaries (DN) result in repulsion.

  In Lifshitz (DLP) theory, this is obtained by an intervening medium with dielectric constant intermediate to the  boundaries, as in the case of liquid helium climbing (wetting) a wall.  (dielectric constants: solid > helium > air).

 "Verification of Lifshitz theory of the van der Waals Potential using liquid-helium films,"

E.S. Sabisky and C.H. Anderson, Phys. Rev. A 7, 790 (1973)

 "Measured long-range repulsive Casimir–Lifshitz forces,"

J. N. Munday, F. Capasso & V. A. Parsegian, Nature 457, 170 (2009) (gold, bromobenzene, silica)

  Opposition of hydrophobic/hydrophilic surfaces in oil-water mixtures close to criticality:

"Critical Casimir forces in colloidal suspensions on chemically patterned surfaces,"

F. Soyka, O. Zvyagolskaya, C. Hertlein, L. Helden, & C. Bechinger, Phys. Rev. Lett. 101, 208301 (2008) (movie)

  

  Immersing MEMs in fluids is not practical.  Is repulsion across vacuum possible?

"Van der Waals forces and zero-point energy for dielectric and permeable materials,"

T.H. Boyer, Phys. Rev. A 9, 2078 (1974) (A perfect conductor repels a perfect magnet)

A material with large permeability is required for repulsion, but in ordinary materials permeability is close to one.

Metamaterials, incorporating arrays of microengineered circuitry mimic, at certain frequencies, a strong magnetic response and have been proposed as candidates for Casimir repulsion across vacuum.

 

   

1. Repulsion via Geometry & Shape

  Abraham-Lorentz (+Casimir) model of electron:

 A spherical conducting shell of radius R , with a uniform charge e .

 "Introductory remarks on quantum electrodynamics," H.B.G. Casimir, Physics 19, 846 (1956)

Casimir's "mousetrap" to catch the fine structure constant:

Balance the repulsive Coulomb energy, with the (presumed attractive) Casimir energy:

"Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle," T.H. Boyer, Phys. Rev. 174, 1764 (1968)

2A = - 0.09235  is negative!  [also obtained by R. Balian and B. Duplantier (1977)]

"Vacuum means of energy-momentum tensor of quantized fields on manifolds of different topology and geometry. I," 

S.G. Mamaev and N.N. Trunov, Sov. Phys. J. (USA) 22, 51 (1979)

The "Casimir energy" of a parallelopiped changes sign with aspect ratio:

  Does this imply a repulisve force?

 

 "Attractive Casimir forces in a closed geometry,"

M. P. Hertzberg, R. L. Jaffe, M. Kardar, and A. Scardicchio, Phys. Rev. Lett. 95, 250402 (2005)

In the physically accessible geometry of a piston, the partition is always attracted to the closer side.

 "Opposites Attract: A Theorem about the Casimir Force,"

O. Kenneth and I. Klich, Phys. Rev. Lett. 97, 160401 (2006) (two halfs of a cut sphere attract)

  Contrained repulsion?

 "Casimir repulsion between metallic objects in vacuum,"

M. Levin, A.P. McCauley, A.W. Rodriguez, M.T.H. Reid, S.G. Johnson,Phys. Rev. Lett. 105, 090403 (2010)