## 3 Results and Discussion
### Characteristics of the Quartz Crystal Microbalance Sensor
#### 3.1.2 Linear Range and Selectivity of the Sensor  
Several studies dealing with QCM sensors have presented a very good linear correlation in frequency shift versus concentrations of target substances within a specific range [27; 28; 29]. In this study, the linearity in the frequency-shift rate versus solution concentration was evaluated using different concentrations of palmitic acid solutions at pH 10.7. The typical patterns of frequency shift at each palmitate concentration and the average absolute values of frequency-shift rates are given in Figure 3a,b, respectively. All samples of 12.5-100 mg/L palmitate, except the blank solution, similarly show linear deceases for the first 150 s, while their decreasing rates rise according to palmitate concentrations. However, 100 mg/L palmitate shows destabilized frequencies soon after the resonance resistance exceeds 1000 \(\Omega\) at approximately 160 s. Similarly 150 mg/L palmit  
Figure 2: **(a)** Typical frequency change patterns during quartz crystal microbalance (QCM) measurements of 100 mg/L palmitic acid at different pH levels, the horizontal axis represents the time from the start of feeding into the flow cell; and (**b**) absolute values of average frequency-shift rates (\(n\) = 3) within the linear ranges (50–150 s). the frequency curves earlier, around 100 s, when the resonance resistance is over 1000 ohm. Taking this into consideration, the maximum detection limit of our sensor might depend on the oscillator's load capacitance. As such, in this study, 0-100 mg/L is regarded as a reliable range for study. Based on the average frequency-shift rates in Figure 3b, there is a high correlation (\(R^{2}\) = 0.9929) between the rates and palmitate concentrations within 0-100 mg/L. Within the linear range, [PERSON]'s Equation (2) is established [29]. \[\Delta m=-C\cdot\Delta f \tag{2}\]  
In this equation, there is a linear relation between mass change on the electrode (\(\Delta m\)) and frequency shift (\(\Delta f\)). Nevertheless [PERSON]'s equation is inaccurate when the mass change is greater than 2% of the mass of the quartz disc [30]. In the present study, the mass change due to the coating is 36 ug/cm\({}^{2}\) and that estimated from [PERSON]'s equation, when measuring 100 mg/L palmitate, is at most 15 ug/cm\({}^{2}\). Thus the total mass change during our experiment is a level below 0.1% of the quartz disc weight. In AD, due to the relatively high concentrations of LCFAs (50-3000 mg/L) at inhibition levels [3; 4; 14], such high sensitivity is not required for the QCM sensor. Meanwhile, selectivity is more important because there are various chemicals similar to LCFAs, such as triglycerides and acetate, in the digestate. Figure 3c illustrates the frequency response to various substances based on the average  
Figure 3: (**a**) Typical frequency change patterns during QCM measurements using different concentrations of palmitate; (**b**) absolute values of average frequency-shift rates (\(n\) = 3) within the linear ranges (50–150 s) at each palmitate concentration; and (**c**) absolute values of average frequency-shift rates (\(n\) = 3) within the linear ranges (50–150 s) obtained from solutions of different model compounds. frequency-shift rates obtained in the same way stated above. All QCM measurements are carried out at pH 10.7. A higher response is clearly observed when the sensor is applied to palmitate-containing solutions. Conversely triolein and acetate show little effect on frequency. In the presence of palmitate and triolein, the QCM sensor shows the same level of response as with palmitate alone. These facts indicate that our QCM sensor can selectively detect palmitate. It is clearly found by observation that triolein is not dissolved and forms a droplet on the surface of the water even at pH 10.7. These droplets of triolein are probably not allowed to flow into the QCM flow cell and thus have no chance to contact the coated film, which is the cause of the low response.