## 3 Results and Discussion  
### Characteristics of the Quartz Crystal Microbalance Sensor  
#### 3.1.1 Effect of Dissociation on Quartz Crystal Microbalance Frequency Responses  
Most short-chain fatty acids, such as acetic and propionic acids, have lower pKa values than the neutral pH level, and are easily dissolved in water or digestate in the form of ions; however, the pKa values of fatty acids increase with their carbon chain length. The pKa of C8-C18 chain-length fatty acids has been determined experimentally by titration. The C8, C10, and C12 fatty acids show pKa values below 7.5, and those of C14, C16, and C18 fatty acids are in the range of 8.1-10.15 at 20 \({}^{\circ}\)C or 25 \({}^{\circ}\)C [23; 24]. As described above, palmitate and oleate are predominant LCFAs in an AD of de-oiled GTW [7]. Therefore most LCFAs are almost insoluble in digestate, having a neutral pH. Usually LCFAs are immiscible and float to the water surface like lipids. In contrast, dissociation at alkaline pH allows LCFAs to dissolve into water and, as a result, LCFAs can be successfully dispersed in digestate or water. In this study, to determine the desirable pH for QCM measurements of palmitate, EPs in titrations with NaOH solution were first investigated using palmitic and oleic acids. The titration curves were obtained using palmitic and oleic acids at 25 \({}^{\circ}\)C and 65 \({}^{\circ}\)C. Palmitic acid has too slow a dissociation rate, making it impossible to obtain a good titration curve using an automatic titrator at 25 \({}^{\circ}\)C, while oleate successfully shows an S-shaped curve. The average pH at the EP of oleate is 10.69 \(\pm\) 0.21 at 25 \({}^{\circ}\)C (\(n\) = 5). By contrast, palmitic acid completely melts at 65 \({}^{\circ}\)C and is easily dissociated by the addition of a NaOH solution, and the aqueous solution shows a transparent appearance. The pH finally reaches 10.5 and the palmitate is still dissociated at room temperature. As a result, the average pH values at EPs are 9.32 \(\pm\) 0.05 (palmitic acid) and 9.48 \(\pm\) 0.19 (oleic acid). These results are similar to those of [PERSON] and [PERSON] [24], suggesting that oleic acid shows a higher pKa than palmitate at 20 \({}^{\circ}\)C. On the basis of this nature, the pH values of the samples in this study were adjusted to 10.7 before testing with the QCM sensor. The QCM response was studied using palmitic acid at different pH levels in the range of 6.0-10.7 to understand the effects of acid dissociation. Figure 2a illustrates typical patterns of frequency shifts at pH values 6.0, 7.5, 9.0, and 10.7 during QCM measurements of 100 mg/L palmitic acid in water. The frequency-shift of the QCM sensor is considered as a mass change of the electrode caused by the absorption of palmitate. The frequency-shift patterns always show linear decreases, except in the initial period. Although in most cases researchers use the values of frequency change after a given period of time, a measurement using a flow cell shows a lag time before sample reach a QCM disc, sometimes resulting in destabilization in sensor response at initial period. Therefore, the absolute values of the slopes of regression lines were calculated using linear portions of frequency curves (basically in the range from 50 s to 150 s) in this study. The bars shown in Figure 2b are the averages of the slopes, indicating decreasing rates in the frequencies. As shown in these figures, the frequency-shift rates are considerably increased in the pH range of 7.5-10.7, crossing the pKa value. The total water-solubility of the palmitic acid including dissociated and nondissociated form (\(C_{tot}^{sat}\)) depends on the pH.