**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 chargee ."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 = - 0.09235is 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)