## 2 Materials and Methods
### Method
#### 2.2.2 Dynamic Light Scattering  
The dynamic light scattering method (DLS) was used to investigate the aggregation behavior of the CNHox with various electrolyte concentrations and different amounts of LSZ. The used CNHox suspension was dispersed with an ultrasonic disperser (US-2R, AS ONE Corporation) to disperse the aggregates. Each sample had a total volume of 1 mL with a CNHox concentration of 2 mg/L in a disposable polystyrene cell. Appropriate amounts of the CNHox suspension, deionized water, KCl solution, and LSZ solution were added into the disposable polystyrene cell. All the disposable polystyrene cells used were cleaned by soaking them in NaOH (0.1 M) solution, HCl (0.1 M) solution, and deionized water in that order. After the preparations, each sample in the cell was immediately shaken with a mixer (MVM-10, AS ONE Corporation, Osaka, Japan). Then, the time-resolved dynamic light scattering (DLS) method (Zetasizer Nano-ZS, Malvern Panalytical Ltd, Malvern, UK) was carried out and the temporal change in hydrodynamic size was measured. The results of average hydrodynamic diameter (\(d_{\text{h}}\)) as a function of time (\(t\)) were obtained.  
The relationship between the \(d_{\text{h}}\) of aggregates and the particles' diffusion coefficient (\(D\)) was related by Stokes-Einstein equation:  
\[d_{\text{h}}=\frac{k_{\text{B}}T}{3\pi\eta D}\, \tag{2}\]  
where \(k_{\text{B}}\) is the Boltzmann constant, \(T\) is the absolute temperature, and \(\eta\) is the dynamic viscosity. From the relationship between \(d_{\text{h}}\) and time (\(t\)), the initial increased rate of the hydrodynamic diameter \(\left(\dd{d_{\text{h}}}/\dd{t}\right)_{t\to 0}\) corresponds to the apparent aggregation rate in this experiment, also known as the initial slope. The relationship between the measured particle size and time was fitted with a 3 rd order polynomial equation, and the coefficient of the 1 st order term in the equation was extracted to represent the initial slope \(\left(\dd{d_{\text{h}}}/\dd{t}\right)_{t\to 0}\). The measurements were performed by varying the concentrations of the KCl and LSZ. All the measured values of \(\left(\dd{d_{\text{h}}}/\dd{t}\right)_{t\to 0}\) were normalized to the rate \(\left(\dd{d_{\text{h}}}/\dd{t}\right)_{t\to 0}\) of the fast aggregation regime, where the van der Waals attraction is dominant. The normalized rates can be related to the stability ratio \(W\), defined as follows:  
\[W=\frac{\left(\dd{d_{\text{h}}}/\dd{t}\right)_{t\to 0}\ \of a total of three measurements. The error bars are used to show the standard deviation for each case.  
Figure 3 demonstrates that the CNHox is negatively charged in KCl solutions. The surface of the CNHox has carboxyl groups because of oxidation [18]. Due to the deprotonation of the carboxyl groups, this group can account for the negative charge on the CNHox surface. As the KCl concentration increases, the EPM remains negative in this range but decreases in magnitude, say, charge reversal does not happen. The reason why the magnitude of the zeta potential decreases may be attributed to the electrical double-layer (EDL) screening caused by the increment in KCl concentration. The compression of EDL due to high counterion concentration leads to lower magnitudes of zeta potential.