Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions.

Santiago D Solares

doi:10.3762/bjnano.7.49

Abstract

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip–sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surface as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip–sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information.

Highlights

The accurate characterization of viscoelastic materials with atomic force microscopy (AFM) is of high interest [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], but it is a very difficult task due to the complexity of the material behavior phenomena that govern the AFM observables
A simulation study has been carried out to gain insight into the mechanical behaviors exhibited by viscoelastic materials in the context of AFM imaging
The study is based on an enhanced version of a previously developed quasi-three-dimensional model that treats the surface as a collection of standard-linearsolid viscoelastic elements

Summary

Introduction

The accurate characterization of viscoelastic materials with atomic force microscopy (AFM) is of high interest [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], but it is a very difficult task due to the complexity of the material behavior phenomena that govern the AFM observables. At the scale of an AFM indentation it may be difficult to properly define the surface energy (even conceptually) since the local material constituents (e.g., polymer chains) can significantly differ from their neighbors and can be, to a varying degree, flexible and mobile. At this scale, the surface is not a smooth continuum but may instead contain molecules oriented in various directions, as well molecules trapped in conformations that do not correspond to a global energy minimum (especially in the compressed volume directly under the AFM tip). One could continue extending the list of phenomena that preclude an ideal measurement by considering other issues such as limitations of the measurement method and instrumentation, almost arriving at the conclusion that it is nearly impossible to carry out quantitatively accurate measurements of viscoelasticity with AFM, unless one assumes that the sample follows the simplest continuum behaviors

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Conclusion