Abstract
A quartz tuning fork and its qPlus configuration show different characteristics in their dynamic features, including peak amplitude, resonance frequency, and quality factor. Here, we present an electromechanical model that comprehensively describes the dynamic responses of an electrically driven tuning fork and its qPlus configuration. Based on the model, we theoretically derive and experimentally validate how the peak amplitude, resonance frequency, quality factor, and normalized capacitance are changed when transforming a tuning fork to its qPlus configuration. Furthermore, we introduce two experimentally measurable parameters that are intrinsic for a given tuning fork and not changed by the qPlus configuration. The present model and analysis allow quantitative prediction of the dynamic characteristics in tuning fork and qPlus, and thus could be useful to optimize the sensors’ performance.
Highlights
Understanding the dynamics of a probe’s motion is important in order to use the probe as a quantitative force sensor in atomic force microscopy and spectroscopy [1,2]
For tuning forks (TFs), the qPlus configuration [10] is well-approximated as the harmonic oscillator when it is driven mechanically [11,12] so that the qPlus sensor facilitates quantitative force measurement, and it is widely employed for dynamic force spectroscopy [13]
For probes A and B, we found that the qPlus configuration showed much lower values of peak amplitude A0 (Figure 3a), quality factor Q (Figure 3b), and resonance frequency f 0 (Figure 3c) than the original bare TF
Summary
Understanding the dynamics of a probe’s motion is important in order to use the probe as a quantitative force sensor in atomic force microscopy and spectroscopy [1,2]. For probes such as micro-cantilevers and quartz tuning forks (TFs), there have been long-investigated linear and nonlinear dynamics [3,4,5] and associated models [6] of the probes. The dynamic characteristics of the ED-qPlus such as peak amplitude, resonance frequency, and quality factor are very distinct from those of the original form (i.e., bare TF), they are both electrically driven and only one of the two prongs is fixed in the qPlus. Our results could be useful to optimize sensors’ dynamic characteristics for quantitative interaction measurements with qPlus or TF
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