Optimum Roughness for Minimum Adhesion

Surface roughness has a significant affect on adhesion. We used a single-asperity model to describe a smooth tip in contact with a rough surface and predicted that an optimal size of asperity will yield a minimum of adhesion. Experimentally, adhesive forces on silicon wafers with varying roughness were measured using AFM cantilevers with varying tip radii. It was found that minima do exist, and for all tip radii, the adhesion falls significantly for roughness greater than 1–2 nm and drops at higher roughness for larger tips. In addition to RMS roughness, the roughness exponent is another important parameter for the characterization of rough surfaces and its affect on adhesion was also investigated. We developed computer programs to simulate a set of fractal rough surfaces with differing roughness exponents. The adhesive forces between an AFM tip and the fractal surfaces were calculated and the adhesion was seen to decrease as the roughness exponent increases. This work should help minimize MEMS stiction and progress the understanding of nanoscale contact mechanics.

THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

COUNTEREXAMPLES IN FRACTAL ROUGHNESS ANALYSIS AND THEIR PHYSICAL PROPERTIES

We disprove the widely held notion that a surface with nontrivial roughness exponents fluctuates at all scales ("structure within structure") and has nontrivial fractal dimension. Strong counterexamples are Cantor staircases, which have nontrivial roughness exponents, do not fluctuate at all, and have trivial fractal dimension. Weak counterexamples fluctuate intermittently and have nontrivial fractal dimension. Characteristic of all counterexamples is: (i) they consist of terraces of all sizes and exhibit scaling over the entire range of terrace sizes. (ii) they have roughness exponents Hq that vary strongly with order q; (iii) they are self affine, but not all affinities are invertible. The strong variation of Hq drives a strongly varying surface response to different external interactions (different interactions are governed by different orders q) and abrupt changes similar to a phase transition, with Hq playing the role of temperature. A summary of this extraordinary functional tunability and its applications is given.

Self-Affinity Analysis of the Fracture Surfaces of Polypropylene and Opal Glass.

In this work we report the self-affinity analysis of the fracture surfaces of a polymeric semicrystalline material and an opal glass. In the case of the plastic material, samples of isotactic polypropylene (i-PP) were prepared by varying the cooling rate from the melt; this resulted in different spherulite sizes. Samples were then broken in bend test after being immersed in liquid nitrogen. In the case of the opal glass, samples with different sizes of the opacifying particles, obtained by different thermal treatments, were broken in a punch test. In both cases the fracture surfaces were analyzed by both Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM) in the contact mode. Self-affinity analysis was performed by the variable bandwidth method, covering a range of length scales spanning from a few nanometers up to ten micrometers. The roughness exponents are found to be of similar values close to ζ = 0.8 with the correlation length corresponding to the size of the spherulites in the plastic material and to the size of the opacifying particles in the opal glass. These results should be taken into account in the development of multiscale models and simulations of the fracture process of real heterogeneous materials.