Theoretical analysis of resonance frequency change induced by adsorption

Abstract

Microcantilever-based techniques can be used to explore the autonomy and property of molecules (e.g. DNA and single actin filaments) adsorbed on a surface. A theoretical model is presented here to predict the resonance frequency of a cantilever induced by physically adsorbed atoms/molecules. The cantilever is modelled as a sandwich beam containing two surface layers of a finite thickness and a bulk layer between them. It is found that the resonance frequency shift depends sensitively on both the mass and bending stiffness variations of the cantilever induced by the adsorbed atoms/molecules. The adsorptions of O atoms on Si(1 0 0), of O atoms on Au(1 0 0) and of H atoms on Au(1 0 0) are taken as three representative examples. We demonstrate that physisorption can induce distinctly different resonant responses of cantilevers, depending not only on the adatoms but also on the substrate material. This study is helpful for the optimal design of microcantilever-based measurement techniques.

Determining the effects of surface elasticity and surface stress by measuring the shifts of resonant frequencies

“…16) There is no damping in equations (2.7) and (2.12), which is also the case in many studies [3,4,6,7,13,18,19,33]. The presence of damping reduces the resonance, and damping can be determined by the so-called half-power method from the frequency response curve obtained by experiment [45].…”

“…The application of the ansatz that nanostructure = bulk + surface [1] in continuum mechanics leads to the so-called core-shell model [2][3][4][5][6][7][8][9][10][11], in which the core is the bulk and the shell is the surface layer. In a surface layer, the total surface stress (τ ) is given as follows [2,4,5,[8][9][10][11][12][13]: 1) where is the dimensionless strain and C s is the surface modulus.…”

“…By solving this inverse problem, we actually provide a viable experimental method to determine the effects of both surface elasticity and surface stress. Because the surface stress effect is modelled as an axial load on the structure, two different models arise: the concentrated load model [3][4][5][6][7][8]13,16,24,[35][36][37] and the distributed load model [35][36][37]. The difference between these two models is also discussed.…”

“…Figure 1a is a schematic diagram to illustrate the concentrated load model, in which the effect of surface stress is modelled as a concentrated load F applied at the beam free end. The concentrated load model leads to the following governing equation [3][4][5][6][7][8]16,24,[35][36][37]:…”

Adsorption-induced resonance frequency shift in Timoshenko microbeams

“…Hagan et al [15] presented a model to evaluate the beam deflections induced by adsorption and subsequent hybridization of DNA molecules and concluded that the dominant contribution to the deflection arises from hydration forces, instead of conformational entropy or electrostatics. Recently Zhang et al considered the effects of adsorption on the resonance frequency change and bending of microcantilever by adopting the EulereBernoulli beam model [16,17].…”