ABSTRACT
Interactions of Adsorbates ................................................................ 386 11.4Surface-Enhanced Cantilever Sensors with Porous Films ........................... 389
11.4.1Mechanics of Cantilevers with Porous Films ................................... 389 11.4.1.1 Deformation and Resonance Frequency ............................ 390 11.4.1.2 Film with Aligned Cylindrical Pores ................................. 392 11.4.1.3Disordered Porous Film ..................................................... 394
11.4.2Deformation of Cantilevers with Porous Films ................................ 395 11.4.3Resonance Frequency Shift of Cantilevers with Porous Films ..................................................................................... 397
11.5 Surface Stress on Rough Surfaces ................................................................ 399 11.5.1Theory of Effective Surface Stress ...................................................400 11.5.2Impact of Surface Geometry ............................................................403
11.6Surface-Enhanced Cantilever Sensors with Rough Surfaces .......................408 11.6.1 Cantilever Bending with Rough Surfaces .........................................408
11.7 Conclusion .................................................................................................... 414 References .............................................................................................................. 414
Microcantilevers have been used as sensors in the processes in physics, chemistry, and biology, and as components in microelectromechanical systems because of their high sensitivity and easy manipulation. The commonly measured output signals of cantilever sensors are their static bending and the resonance frequency shift of vibration. For example, the reaction on the upper or lower surface of a microcantilever beam can bend the cantilever (Figure 11.1), due to the free energy reduction as the result of biomolecular interactions. Therefore, when the free energy on a cantilever surface is reduced, the reduced energy density creates a bending moment that bends the cantilever. Because free energy reduction is the common driving force for all reactions, this mechanical approach has become a common platform for detecting a variety of biomolecular binding such as DNA hybridization, protein-protein interactions, DNA-protein binding, and protein-ligand binding (Kassner et al. 2005). In general, the bending of cantilevers is driven by the eigenstrain and the change of surface stress, while the vibration frequency shift is affected by the mass and surface elasticity. Microcantilever sensors work when contacting with liquid or gas. The adsorbates on them change the surface stress. This change comes from different interacting mechanisms of the adsorbates, such as electrostatic interaction, the van der Waals (vdW) forces, the dipole-dipole interactions, hydrogen bonding, and the changes in the charge distribution of surface atoms, and so on (Yi and Duan 2009). One big challenge in developing microcantilever sensors is to quantify the connections between the properties of adsorbates and the adsorption-induced surface stress. As both static deformation and dynamic frequency are quantities at the continuum level, whereas the interactions exist at the atomic or molecular level, an effective way to address this challenge is to derive the continuum-level descriptions of the surface stress from the molecular-level descriptions of the adsorbate interactions (Yi and Duan 2009).
