A self-adhesion criterion for slanted micropillars

Abstract

Micropillar arrays see use in many fields such as biochemistry, mechanobiology, microfluidics, and micro/nanotechnology via applications like carbon nanotube forests and bioinspired fibrillar adhesives. In these fields, it is commonly desirable to either pack the micropillars as densely as possible or manufacture them to be as long/compliant possible. A barrier to either aim is the phenomenon of self-adhesion, where adjacent micropillars adhere to each other due to Van der Waals forces. In this paper, with self-adhesion as the limiting constraint, we show that longer, more compliant, and/or more densely packed micropillar arrays can be made by slanting the micropillars. From their typical orthogonal configuration, small inclinations produce an increment in micropillar packing and length up to a critical (optimum) angle, beyond which significant slanting produces a reduction in both. For parameter values typical of bioinspired fibrillar adhesives, we estimate that slanted micropillars arranged in a rectangular (triangular) lattice can improve in density by 10% (20%). Slanted micropillars also have increased compliance to loads applied orthogonally to the substrate (we refer to this as ‘orthogonal compliance’), achieved by engaging bending over axial deformation modes. This is particularly useful in fibrillar adhesives for conformation to surface roughness, hence increasing the overall adhesive strength. Our model provides a quantitative tool for the design of slanted micropillar arrays and computes the resulting enhanced array-properties.