Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles

Abstract

Recent advances in nanotechnology have led to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators, which have recently received significant attention from the scientific community. This is not only due to their capability of label-free detection of bio/chemical molecules at single-molecule (or atomic) resolution for future applications such as the early diagnosis of diseases like cancer, but also due to their unprecedented ability to detect physical quantities such as molecular weight, elastic stiffness, surface stress, and surface elastic stiffness for adsorbed molecules on the surface. Most experimental works on resonator-based molecular detection have been based on the principle that molecular adsorption onto a resonator surface increases the effective mass, and consequently decreases the resonant frequencies of the nanomechanical resonator. However, this principle is insufficient to provide fundamental insights into resonator-based molecular detection at the nanoscale; this is due to recently proposed novel nanoscale detection principles including various effects such as surface effects, nonlinear oscillations, coupled resonance, and stiffness effects. Furthermore, these effects have only recently been incorporated into existing physical models for resonators, and therefore the universal physical principles governing nanoresonator-based detection have not been completely described. Therefore, our objective in this review is to overview the current attempts to understand the underlying mechanisms in nanoresonator-based detection using physical models coupled to computational simulations and/or experiments. Specifically, we will focus on issues of special relevance to the dynamic behavior of nanoresonators and their applications in biological/chemical detection: the resonance behavior of micro/nanoresonators; resonator-based chemical/biological detection; physical models of various nanoresonators such as nanowires, carbon nanotubes, and graphene. We pay particular attention to experimental and computational approaches that have been useful in elucidating the mechanisms underlying the dynamic behavior of resonators across multiple and disparate spatial/length scales, and the resulting insight into resonator-based detection that has been obtained. We additionally provide extensive discussion regarding potentially fruitful future research directions coupling experiments and simulations in order to develop a fundamental understanding of the basic physical principles that govern NEMS and NEMS-based sensing and detection applications.

Introduction

The past decade has witnessed the emergence of nanotechnology that enables the development of nanoscale functional devices designed for specific aims such as nanoscale actuation, sensing, and detection [1], [2], [3]. For instance, micro/nano-electro-mechanical system (MEMS/NEMS) devices have allowed the sensitive detection of physical quantities such as spin [4], [5], molecular mass [6], [7], [8], [9], [10], quantum state [11] (see also Refs. [12], [13], [14] which discuss the prospect of NEMS for studying quantum mechanics), thermal fluctuation [15], [16], [17], [18], coupled resonance [19], [20], [21], and biochemical reactions [22], [23], [24], [25], [26]. Among MEMS/NEMS devices, nanomechanical resonators have been recently highlighted for their unprecedented dynamic characteristics as they can easily reach ultrahigh frequency (UHF) and/or very high frequency (VHF) dynamic behavior up to the Giga Hertz (GHz=10⁹ Hz) regime [3], [27], [28], [29]. Reaching this frequency range is critical as it implies that nanoresonators can be directly utilized as an electronic device for radio communications. This high frequency dynamic behavior is achieved by scaling down the size of the resonator because the resonant frequency is proportional to $L^{-2}$, where $L$ is the length of a device. Therefore, if the resonator length is decreased by an order of magnitude, then its resonant frequency is increased by two orders of magnitude. Furthermore, the ability of the resonator to sense or detect physical quantities (i.e. mass, force or pressure) is closely related to its resonant frequency. For example, for sensing mass that is added onto a resonator, the detection sensitivity is given by the relation $\Delta f_n/\Delta m=(1/2m)f_n$ [30], [31], [32], where $f_n$ and $m$ represent the resonant frequency and the effective mass of a device, respectively, while $\Delta f_n$ and $\Delta m$ indicate the resonant frequency shift and the added mass. Clearly, this relationship suggests that as the frequency of the resonator increases, so does its ability to sense or detect ever smaller masses, which implies that UHF/VHF resonators are suitable for ultra-sensitive detection, where the eventual limit of a single atom or molecule is experimentally within reach.

An example of the incredible potential of NEMS resonators can be found in recent works by Roukes and coworkers [6], [7], [10], who first showed the possibility of nanoscale mass spectrometers that enable the measurement of the molecular weight of specific molecules. This implies not only that nanomechanical resonators could be a viable alternative to conventional mass spectrometry techniques such as matrix-assisted desorption/ionization time-of-flight (MALDI-TOF), but also that mass spectrometry could be realized in a lab-on-a-chip [33]. It should be emphasized that NEMS-based sensing is not restricted to small, molecular masses; other important physical quantities such as quantum state [11], spin [4], [5], and force [34], [35], [36] can also be detected using NEMS, which suggests that nanomechanical resonators may allow the realization of lab-on-a-chip sensing toolkits for detecting other relevant physical quantities [1], [3].

In recent years, micro/nanomechanical resonators have also received significant attention for their capability of label-free detection of specific biological molecules [10], [22], [37], [38] and/or cells [25], [39], [40], even at low concentrations, that are relevant to specific diseases such as cancer [41], [42]. However, current biosensing tools such as enzyme-linked immunosorbent assay (ELISA) exhibits a key restriction in that they are unable to accurately detect marker proteins (relevant to specific cancers) in the concentration of ∼1 ng/ml, which is known as the “diagnostic gray zone” [43], in blood serum. On the other hand, micro/nanomechanical resonators are able to easily overcome the “diagnostic gray zone” limitation because of their unprecedented detection sensitivity even at single-molecule resolution [9], [10], [44], which shows that nanomechanical resonators can serve as lab-on-a-chip biosensors enabling the early diagnosis of important diseases like cancer. Moreover, nano/micromechanical resonators show the promising ability to provide the detailed mechanisms of biochemical reactions [23], [24], [26], [45], [46] and/or cell functions [47].

As stated earlier, the excellent performance of nanomechanical resonators for sensing applications is highly correlated with their dynamic characteristics [30], [31], [32]. It is therefore essential to characterize and understand the dynamic behavior of nanomechanical resonators for the novel design of resonator-based sensing toolkits. Furthermore, it has been suggested that nanoresonators are easily able to exhibit unique dynamic features such as nonlinear oscillations [48], [49] and/or coupled resonance [19], [20]. For instance, nanostructures can easily be tuned to oscillate nonlinearly by modulating the actuation force so as to drive the geometrically nonlinear deformation of doubly clamped nanostructures [28], [50], [51]; we note that this would also enable fundamental investigations into various theories underlying the field of nonlinear vibrations. In addition, it has been reported that coupled nanomechanical resonators not only provide unique dynamic features such as coupled oscillation [19], [20], but also enable ultra-sensitive mass detection [21]. These show that unique dynamic features such as nonlinear oscillations and/or coupled resonance could be a new avenue to improve the detection sensitivity of nanoresonators.

Moreover, because nanoresonators are characterized by a large surface-to-volume ratio, surface effects play a critical, but currently not a well-understood role on their dynamic characteristics. Specifically, as the resonator size is scaled down, its surface area is increased which leads to an increase of its surface energy [52], [53], [54], which is defined as the energetic cost to create a new surface. In general, the surface energy $U_S$ depends on the deformation of the surface, and consequently the surface stress can be defined as $\tau =\partial U_S/\partial {\epsilon }_s={\tau }_0+S{\epsilon }_s+O\left({\epsilon }_s^2\right)$ [55], [56], where ${\tau }_0$, ${\epsilon }_s$, and $S$ represents the constant surface stress, surface strain, and surface elastic stiffness, respectively. The surface stress is also inherent to nanostructures due to the fact that surface atoms have fewer bonding neighbors than do bulk atoms; because they are therefore not at equilibrium, they are subject to a surface stress [57], which causes deformation of the surface in the absence of external forces [58], [59], [60]. Both of these explanations strongly suggest that surface effects such as surface stress play a key role on the mechanical properties and thus the resonant frequencies of a nanostructure. Furthermore, because the detection sensitivity is correlated with the resonant frequency of a nanomechanical resonator, the surface stress will inherently have a significant effect on the detection sensitivity for nanoresonators. In addition, for sensing applications, the adsorption of molecules onto the surface of a nanoresonator induces changes of the surface state, and consequently the surface energy (or equivalently the surface stress) by changing the bonding configuration for the surface atoms. Therefore, the effect of surface stress changes that result due to molecular adsorption has to be carefully considered for gaining insight into the detection principle for NEMS. We note that surface effects on the resonance behaviors as well as the detection mechanisms of nanoresonators are a very active and on-going area of research.

The purpose of our review article is to present not only the current state-of-the-art in the development of nanomechanical resonators and their applications in chemical/biological sensing, but also the physical principles that have enabled fundamental insights into the underlying mechanisms for the dynamic characteristics of nanomechanical resonators as well as the detection principles. Specifically, we describe not only the current state-of-the-art experimentally, but also the on-going development in theoretical and computational techniques that are being used to develop a fundamental understanding of NEMS-based resonators across multiple spatial/length scales ranging from atomistics to continua. We first overview the experimental approaches that are used to characterize the dynamic behavior of micro/nanoresonators as well as their applications to sensing chemical and/or biological species. Subsequently, we review the continuum elastic models that are able to explain the fundamental physics of nanomechanical resonators such as nonlinear oscillations, coupled resonance and detection principles. However, these classical continuum elastic models are unable to capture the underlying physics of nanoscale surface effects, which leads us to review recent molecular/multiscale modeling of nanoresonators such as carbon nanotube, nanowire, and graphene in order to understand their nanoscale-driven dynamic behavior and detection principles for resonator-based sensing.

We anticipate that the theoretical and computational models reviewed here will allow one to gain insight into not only the anomalous dynamics observed experimentally (e.g. surface effect coupled resonance behavior) but also the fundamental, novel detection principles for sensing applications. For instance, theoretical and computational models that take surface effects into account are able to explain the resonance behavior of nanocantilevers, which cannot be understood by conventional continuum models that do not account for surface effects. Furthermore, the experimentally observed resonance response of a nanocantilever to biomolecular adsorption has not been well described by conventional detection principles, because the resonant frequency shift for nanoresonators due to biomolecular adsorptions depends on not only the mass of adsorbates but also other unexpected effects, which were not considered in conventional detection principles, such as elastic stiffness of adsorbates [61], [62], the change of surface elastic stiffness [63], [64], [65], and surface stress [63], [64], [65], [66] due to adsorbates. These indicate that theoretical and computational models are complimentary to the experimentally observed unique behavior of nanomechanical resonators and their sensing applications. In addition, theoretical and/or computational models are able to provide milestones for further guidance and design of novel nanoresonators and their sensing applications.

Our review article is organized as follows: Section 2 reviews the current progress in the development of micro/nanoresonators and their related harmonic dynamic behavior such as resonant frequencies and $Q$-factors within the physical background of continuum elasticity. In Section 3, we review micro/nanoresonator-based sensing applications such as chemical and/or biological detection. Furthermore, we provide perspectives and challenges of the current state-of-the-art in resonator-based chemical/biological sensing applications. Section 4 overviews the continuum elastic models that enable the understanding of not only the unique dynamic features such as nonlinear oscillations and coupled resonance but also the novel detection principles such as mass sensing based on coupled resonance and/or nonlinear oscillations. Section 4 also discusses the controversial issues surrounding continuum elastic models for gaining insight into surface stress effects on the resonant frequencies of nanoresonators. Section 5 reviews the current computational approaches based on molecular/multiscale models that have been utilized in order to understand the surface-induced dynamic behavior of nanoresonators that cannot be captured by the standard continuum models discussed in Section 2, and their related sensing applications. We present a future outlook in Section 6, while Section 7 concludes our review with closing remarks.