Adhesion stability of rough elastic films in presence of quantum vacuum fluctuations

Abstract

In this work the influence of vacuum fluctuations through the Casimir effect on the stability of an elastic film conformal onto to a self-affine rough substrate that is brought in close proximity with another parallel plate is studied. By considering the energy balance among adhesion, elastic and Casimir energies, it is shown that beyond certain parameter values (low roughness exponent H and/or high ω/ξ ratio with ω the rms roughness amplitude and ξ the lateral correlation length) the adhesion energy is counter-balanced by the elastic energy, allowing significant contributions in this regime by the Casimir energy. With increasing lateral correlation length ξ and/or decreasing roughness amplitude ω, leading to long wavelength smoothing, the regime of roughness exponents H where the contribution of vacuum fluctuations is significant shifts drastically to a lower value. This occurs so that the short wavelength roughening compensates for the effect of long wavelength smoothing that decreases predominantly the elastic and Casimir energies.

Keywords:

• ADHESION
• STABILITY
• ELASTIC THIN FILMS
• SURFACE ROUGHNESS
• VACUUM FLUCTUATIONS
• MICRO-ELECTROMECHANICAL SYSTEMS