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

Pedro J Martínez,Juan J Mazo,Enrico Gnecco

doi:10.1103/physreve.103.022802

Abstract

The emergence of surface patterns on the surfaces of compliant materials subject to plowing wear is a complex problem which can be quantitatively characterized, e.g., on polymer surfaces scraped by an atomic force microscope (AFM) tip. Here we explore the applicability of a phenomenological model recently introduced to describe this phenomenon. Based on the competition between the viscoplastic indentation and the elastic shear stress caused by the tip, the model is able to reproduce the wavy features (ripples) observed when the tip is scanned along a series of parallel lines. For low values of the driving velocity v and the spacing b between scan lines, the existence of dotted areas formed by variously oriented pit alignments is observed. Moreover, coexistence of rippled with dotted domains is also observed at suitable parameter values. The formation process of the ripples is also described in detail. The amplitude, period, and orientation of these features are estimated numerically for different values of v and b parameters. We have also revisited the formation of the wavy patterns formed when a single line is scanned, and derived an equation which correctly describes their period and depth, and the static friction as well. This equation is not applicable when several lines are scanned one after the other and the ripples emerge as result of a cooperative process which involves the scanning of several lines.

Highlights

In 1992, Leung and Goh [1] published a pioneering work on the “orientational ordering of polymers by atomic force microscope tip-surface interaction.” As stated in the abstract, they observed that, by action of an atomic force microscope (AFM) tip “nanometer-size structures are induced, resulting in a pattern that is periodic and is oriented perpendicular to the scan direction.” Such wavy patterns, later called ripples, appear as the outcome of the tip motion, which reshapes the polymer surface locally
The emergence of surface patterns on the surfaces of compliant materials subject to plowing wear is a complex problem which can be quantitatively characterized, e.g., on polymer surfaces scraped by an atomic force microscope (AFM) tip
On the one hand the driving velocity causes an increase of the elastic energy, and elastic force, in the system

Summary

Introduction

In 1992, Leung and Goh [1] published a pioneering work on the “orientational ordering of polymers by atomic force microscope tip-surface interaction.” As stated in the abstract, they observed that, by action of an atomic force microscope (AFM) tip “nanometer-size structures are induced, resulting in a pattern that is periodic and is oriented perpendicular to the scan direction.” Such wavy patterns, later called ripples, appear as the outcome of the tip motion, which reshapes the polymer surface locally. Based on the competition between the viscoplastic indentation and the elastic shear stress caused by the tip, the model is able to reproduce the wavy features (ripples) observed when the tip is scanned along a series of parallel lines. For low values of the driving velocity v and the spacing b between scan lines, the existence of dotted areas formed by variously oriented pit alignments is observed.

Results

Conclusion