An Analytical Model of Nanometer Scale Viscoelastic Properties of Polymer Surfaces Measured Using an Atomic Force Microscope

<p>The United States Air Force and the Department of Defense is increasingly interested in nanomaterials. To study these materials one needs to measure the mechanics of materials on the nanoscale. Over the past few decades the atomic force microscope (AFM) has been used in various methods to establish local surface properties at the nanoscale. In particular surface elasticity measurements are crucial to understanding nanoscale surface properties. Problems arise however when measuring soft surfaces such as polymers and biological specimens because these materials have a more complex viscoelastic response. This research focuses on modeling an AFM dynamic nanoindentation experiment intended to characterize near-surface viscoelastic material parameters. The experiment uses an AFM in dynamic contact mode with a polymer surface to gather frequency dependent amplitude and phase data. A three-dimensional dynamic viscoelastic model of the AFM and surface interaction is developed and then analytically solved in the linear approximation under appropriate physical assumptions based on the physics of the AFM experimental setup. As an illustrative application the analytical solution is coupled with experimental data from a polystyrene material to ascertain surface material properties at the nanoscale. Our solution allows the direct calculation of the storage and loss modulus from experimental data.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>