Detecting the mass and position of an adsorbate on a drum resonator

Abstract

The resonant frequency shifts of a circular membrane caused by an adsorbate are the sensing mechanism for a drum resonator. The adsorbate mass and position are the two major (unknown) parameters determining the resonant frequency shifts. There are infinite combinations of mass and position which can cause the same shift of one resonant frequency. Finding the mass and position of an adsorbate from the experimentally measured resonant frequencies forms an inverse problem. This study presents a straightforward method to determine the adsorbate mass and position by using the changes of two resonant frequencies. Because detecting the position of an adsorbate can be extremely difficult, especially when the adsorbate is as small as an atom or a molecule, this new inverse problem-solving method should be of some help to the mass resonator sensor application of detecting a single adsorbate. How to apply this method to the case of multiple adsorbates is also discussed.

Mass and force sensing of an adsorbate on a string resonator

“…Kehrbusch et al [35] fabricated the vertically aligned silicon resonator and as a result, adsorbates can only land on the top of the column. When both position and mass of an adsorbate are unknown, two or more resonant frequencies are needed to identify the two parameters [9,10,26,36,37]. Even for this two-parameter case, solving the inverse problem is not an easy task: complex statistics [9,10], algorithm [36] and graphic solution [26,37] methods are used.…”

“…In the application of nanomechanical resonator, detecting the adsorbate position is extremely difficult or even impossible when an adsorbate is as small as a protein [9,10], a molecule [7,17] and an atom [8,11]. The stiffness change due to adsorption can result from many sources, for example, surface stress [19,21], the adsorbate stiffness [22,23,24], the stress variation [3,25,26,27], the alloy formation [28,29], swelling [30] and polymer chains interpenetrated by small adsorbate molecules [31], etc. In one word, a lot of things can occur with adsorption, which is the very reason making the in-A c c e p t e d M a n u s c r i p t terpretation on adsorption "notoriously difficult" [7].…”

“…In this study, a generalized method of solving the inverse problem is presented for a string resonator. In the previous studies [4,7,8,9,10,11,26,36], the mechanical resonators are for mass sensing only. By incorporating the adsorbate-induced force in the model, the force sensing function is added.…”

“…There are various mechanisms causing the stress variation inside a nanomechanical resonator. For example, the resonator built-in tensile stress can be relieved by adsorbate absorbing light (photothermal effect) [3], distorting lattice [25,26] and hydroxylation [27], etc. Sometimes the force or stress variation even dominates the shifts of resonant frequencies, which has been used as the sensing mechanism for A c c e p t e d M a n u s c r i p t hydrogen [25] and various ions [27].…”

Measuring the nonlocal effects of a micro/nanobeam by the shifts of resonant frequencies

“…For a given material, a is known as an intrinsic length, but e o is an unknown fitting constant. Besides the applied axial load, there are two major sources contributing to F : surface stress ( Altenbach and Eremeyev, 2011;He and Lilley, 2008;Karabalin et al, 2012;Zhang, 2013;Zhang et al, 2013;Zhang and Zhao, 2014 ) and residual stress ( McFarland and Colton, 2005;Zhang and Zhao, 2015 ), which make F unknown in most micro/nanobeam applications. For the convenience of statement, we let E * I = EI + .…”