Applications of a new theory extending continuum mechanics to the nanoscale

Abstract

In this dissertation, we present the Slattery-Oh-Fu theory extending continuum mechanics to the nanoscale and its applications. We begin with an analysis of supercritical adsorption of argon, krypton, and methane on Graphon before we fully develop the theory. We compare our results both with existing experimental data and with prior molecular-based theories. Then, we present the general theory, which is based upon a long history of important developments beginning with Hamaker (1937). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on PDMS. For the contact angle predictions, the results are compatible with previously published experimental data. The results for the contact angle analysis also provide a successful test of a previously derived form of Young??s equation for the true, rather than apparent, common line. We also studied Mode I fracture at nanoscale. While we don??t have experimental data to compare, we get reasonable crack configuration and avoid stress singularity at the crack tip. Coalescence problems are revisited to explore the retardation effects in the computation of intermolecular forces. We get good agreement with experimental results. We conclude with a confidence that this theory can be used as a bridge between continuum mechanics and other molecular-based methods.