The number of measurements of a surface’s topography and the expected variation in adhesion to the surface

Abstract

Variations in roughness on a surface spawn variations in adhesion force between the surface and any particles that contact the surface. To fully characterize the adhesion that will be exhibited when a particle contacts any location on the surface, it is desirable to map the surface with nanoscale detail. Since it is impractical to make nanoscale roughness measurements over the entirety of a surface with a characteristic dimension on the order of centimeters, a relationship between the number of surface measurements and the likely variation in the expected adhesion force is similarly desirable. In this work, the predicted van der Waals force was used to describe the particle adhesion force. The bootstrap statistical method was employed to estimate the error associated with the predicted mean adhesion force between a smooth spherical particle and a rough surface as a function of the number of locations on the surface where the roughness was measured. Specifically, 40 atomic force microscope (AFM) topographical scans (5 × 5 μm) were taken of three different surfaces and used as model surface inputs to an existing van der Waals adhesion force simulator. The simulator described the expected adhesion force resulting from 1200 contacts between the smooth, spherical particle (10 μm diameter) and random locations on each scanned area. After analyzing the results using the bootstrap method, it was determined that the adhesion between the particle and 10–15 scanned areas (out of 40) optimizes the accuracy of the predicted adhesion with respect to the researcher’s labor.