Plowing-Induced Structuring of Compliant Surfaces

Abstract

The structures produced by a sharp tip scraping a compliant surface are modeled in the illustrative case of scan patterns formed by a series of parallel lines. This is made possible by a modified version of the Prandtl model for stick-slip friction, with an interaction energy landscape replicating the morphology of the evolving surface. As a result, a ripple motif emerges with a tilt angle increasing linearly with the distance between the scan lines, except for the region close to the left boundary of the scanned area, where the ripples are oriented at 90°. This region can penetrate considerably to the right, forming a complex branched pattern. These predictions are substantiated by atomic force microscopy nanolithography experiments on polystyrene surfaces at room temperature. A simple and robust theoretical protocol for reproducing earlystage wear processes (potentially going beyond single contacts) is thus made available.

Numerical study of pattern formation in compliant surfaces scraped by a rigid tip

“…We see that the ripple inclination is larger for larger b values. This was already observed in our previous simulations and experimental results in [12]. There it was reported the observation of ripples for b values between 0.2σ and 1.2σ and the increasing of the ripple tilt angle with b in full agreement with numerical results.…”

“…Under these hypotheses, the shape and time evolution of the typical patterns observed on polymer surfaces indented by AFM are well reproduced [12]. In line with [9,12] the numeric simulations have been run with the values σ = 50 nm for the parameter defining the print width, N = 100 nm/s for the indentation rate, and λ = 1.8 nm for the crossover depth. The energy conversion factor involved in Eq.…”

“…where R c is the support position andk is the (anisotropic) effective spring constant or stiffness of the system. For consistency with the experiments described in [12] it is indeed necessary to distinguish between two distinct values k x and k y (corresponding to longitudinal and transverse deformations with respect to the scan direction). The surface interaction energy landscape explored by the tip corresponds to a continuous field which evolves in time due to the penetrating action of the tip itself.…”

“…In a recent investigation [12] and in a preliminary work limited to the scanning of single lines [9] we introduced a mesoscopic dynamic model which allowed us to reproduce the main features of the observed patterns. The model parameters were fitted to experiments performed over polystyrene films using a commercial AFM operated in contact mode and standard silicon probes.…”

“…After reviewing the used model, introduced in [9] and [12], we will rediscuss the simplest case of single scan lines, where we are able to offer an analytical interpretation beyond the numerical results presented so far. Then we will focus on the description and understanding of the ripple emergence process.…”