Interplay of roughness/modulation and curvature for surface interactions at proximity

Abstract

We show that roughness or surface modulations change the distance dependence of (power-law) interactions between curved objects at proximity. The modified scaling law is then simply related to the order of the first non-vanishing coefficient of the Taylor expansion of the distribution of separations between the surfaces. The latter can in principle be estimated by scanning measurements, or computed for well characterized modulations, and then used to predict short-distance scaling behavior in disparate experiments. For example, we predict that the radiative heat transfer between a rough sphere and a plate approaches a constant with decreasing separation. Similar saturation is expected for the Casimir force between dielectric or metallic surfaces with appropriate modulations over distinct length scales. 44.40.+a, 68.35.Ct The Proximity Approximation (PA) has long served as a useful guide for estimating interactions between closely spaced objects with curved surfaces. Originally introduced by Derjaguin [1] to compute van der Waals forces between colloidal particles, the PA relates the interaction between curved objects at close separations to the corresponding interaction between two flat surfaces, over an area determined by the local radii of curvature. The PA has been successfully used in experimental studies in a variety of fields, such as quantum Casimir forces [2-4], classical Casimir forces in a fluid near a critical point [5], near field radiative heat transfer [6,7], and interactions among nuclei [8]. Recently it has also been applied to the gravitational force in searches of non-Newtonian gravity [9].In this paper, we utilize PA to investigate scaling of the interaction between two surfaces whose local radii of curvature can be decomposed as the sum of components which vary along the surface on well separated length scales. We note that this situation encompasses the experimentally relevant cases of two large rough objects, such that the correlation length of the roughness is much smaller than the characteristic radius of curvature of the surface, or alternatively the case of a surface with large average radius of curvature modulated by small structures fabricated by the experimenter. We find that at proximity a subtle interplay between roughness/modulation and the global curvature of the surfaces leads to a drastic change in the distance dependence of the interaction, compared to that for perfectly smooth (structureless) surfaces. The modified scaling law is found to depend in a simple way on the order of the first non-vanishing term in the Taylor expansion of the * Present address: 4th Institute for Theoretical Physics, Universität Stuttgart, Germany and Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany height distribution function of the surfaces. The latter is a geometric feature of the surface that can be either computed for well characterized modulations, or experimentally obtained via scanning probes of rough surfaces, and then used to predict the short distance scaling of ...

Forces between Negatively Charged Interfaces in the Presence of Cationic Multivalent Oligoamines Measured with the Atomic Force Microscope

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Patch contribution to near-field radiative energy transfer and van der Waals pressure between two half-spaces

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Effect of concurrent geometry and roughness in interacting surfaces

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