Multiscale Modeling of Adsorbed Molecules on Freestanding Microfabricated Structures

This paper outlines a multiscale model to quantitatively describe the chemomechanical coupling between adsorbed molecules and thin elastic films. The goal is to provide clear, quantitative connections between molecular interactions, adsorption distribution, and surface stress, which can be integrated with conventional thin film mechanics to quantify device performance in terms of molecular inputs. The decoupling of molecular and continuum frameworks enables a straightforward analysis of arbitrary structures and deformation modes, e.g., buckling and plate/membrane behavior. Moreover, it enables one to simultaneously identify both chemical properties (e.g., binding energy and grafting density) and mechanical properties (e.g., modulus and film geometry) that result in chemically responsive devices. We present the governing equations for scenarios where interactions between adsorbed molecules can be described in terms of pair interactions. These are used to quantify the mechanical driving forces that can be generated from adsorption of double-stranded DNA and $C60$ (fullerenes). The utility of the framework is illustrated by quantifying the performance of adsorption-driven cantilevers and clamped structures that experience buckling. We demonstrate that the use of surface-grafted polyelectrolytes (such as DNA) and ultracompliant elastomer structures is particularly attractive since deformation can be tuned over a very wide range by varying grafting density and chemical environment. The predictions illustrate that it is possible to construct (1) adsorption-based tools to quantify molecular properties such as polymer chain flexibility and (2) chemically activated structures to control flow in microfluidic devices.