*2.2. Operations*

Our experiments consist of two parts: (i) a single-pass experiment with a constant voltage charge and (ii) a full-cycle experiment.

As schematically shown in Figure 1b, the experimental setup consists of two containers for fresh and seawater, respectively, two peristaltic pumps (BT100J-1A, HUIYU WEIYE Fluid Equipment Co., Ltd., Beijing, China), a CDLE cell and a potentiostat (PGSTAT30, Metrohm Autolab, Utrecht, The Netherlands) that is used to maintain a constant voltage between the electrodes and measure the change in current.

Before each experiment, the electrodes were short-circuited to ensure that no external charge was left on the electrodes, and the cell was fully flushed by deionized water until the effluent conductivity reached a stable value. The details of the two sets of experiments are summarized in what follows.

(i) Single-pass experiment: The experiments were performed in a single pass mode to investigate the amount of total charge stored on activated electrodes at equilibrium, using NaCl solution with a concentration of 5, 20, 100, 200 and 600 mM, respectively. It consists of two steps. In the charge step, a fixed electrical voltage (0.1 to 1.0 V) was applied to the cell when the feed solution was continuously passing through the cells. The charged positive and negative ions in the solution were then adsorbed into the EDL that was formed near the electrode surface, and as a result of the movement of charged ions, an electric current was generated. This step continued until an equilibrium state was reached. The total electrode charge per mass *Q* (C/g) can, therefore, be calculated by integrating the electric current *I* over the charging time *t*(s) and then divided by the mass of total electrodes in the cell *melec*, as [29]:

$$Q = \frac{\int I dt}{m\_{elcc}}\tag{1}$$

Following the charge step, a zero voltage is immediately applied over a sufficiently long time to remove any ions adsorbed in the electrodes.

To illustrate how the current varies with time in the charge and discharge steps, we show in Figure 2 the current profiles obtained at *Vext* = 0.2, 0.6 and 1.0 V with a solution concentration of 600 mM. It is seen clearly that the current *I* dropped quickly at the initial stage of charging. After around 100 s, the electrodes were nearly saturated with charged ions as the electric current *I* of the circuit has reached a stable value that closes to zero. At this moment, the cell could be deemed to reach an equilibrium state.

**Figure 2.** Electrical current as a function of time during the charging and discharging step. The applied voltage *V* = 0.2, 0.6 and 1.0 V, solution concentration *c* = 600 mM.

The small electric current at the end of the charging step is known as the leakage current *Ilea*, and it should be subtracted from the measured current *Imea* to give the net current *I* = *Imea* − *Ilea*, used in calculating the electrode charge *Q* at equilibrium in Equation (1).

(ii) Full-cycle experiment: in this set of experiments, we used 20 mM and 600 mM NaCl solutions as the freshwater and seawater, respectively. These solutions were supplied intermittently to the CDLE cell by a peristaltic pump at a flow rate of 10 mL/min. To harvest the energy, we connect an external resistance *Rext* = 100 Ω to the cell. As a result, the voltage across the cell can be calculated by: *V* = *Vext* − *I*·*Rext*.

A complete cycle CDLE process consists of four steps (Figure 3). In step 1, the circuit was closed, and the cell, immersed with seawater, was charged by a fixed voltage *Vext* (0.2 to 0.9 V) until the cell potential *V* becomes equal to *Vext*. This is followed by step 2, the circuit was opened, and the freshwater was pumped into the cell to replace the seawater until the cell potential increased to a stable value (*Vf resh*). Then in Step 3, the circuit was closed, and the cell was discharged at the same external voltage *Vext* as it in Step 1, this step continued until the cell potential *V* decreases to the *Vext*. Finally in Step 4, the freshwater in the cell was replaced by the seawater until the cell potential *V* declined to a stable value (*Vsalt*). The surface area enclosed in the cycle in Figure 3 represents, therefore, the extracted energy, i.e.,

$$\mathcal{W} = \oint V(\mathcal{Q}) \mathrm{d}\mathcal{Q}.\tag{2}$$

**Figure 3.** Schematic of the relation between the cell potential and the electrode charge at one CDLE cycle.

The corresponding *V* − *t* profile is exemplified in Figure 4a for the case of *Vext* = 0.2 V, which shows that the equilibrium cell potential can only reach 0.185 V due to the use of a large external resistance load in the circuit. The result with respect to the *Q* − *V* cycle is shown in Figure 4b, which mimics closely the theoretical plot in Figure 3 and therefore suggests the success of our experiments.

**Figure 4.** A full CDLE cycle at the applied voltage *Vext* = 0.2V, *Rext* = 100 Ω, *c f resh* = 20 mM, *csea* = 600 mM. (**a**) Cell potential *V* as a function of time *t*; (**b**) cell potential *V* as a function of electrode charge *Q*.

#### **3. Theory of Electrical Double Layers**

The mechanism behind CDLE is the formation of EDL near the electrode surface and the change in the properties of EDL when the concentration of the solution is changed. Therefore, a proper description of the structural and thermodynamic properties of EDLs at equilibrium is of great importance for understanding the performance of the CDLE technique. For this reason, we may start with a summary of the basic assumptions and simplifications about activated carbon electrodes when applying different EDL models. These include [30–33]:

(i) the electrodes are symmetric, meaning that the applied voltage is equally distributed over each electrode and the adsorption amount of the anion in the anode is equal to that of cation in cathode;

(ii) The electric potential of the anode is opposite to that of the cathode in sign but is equal in magnitude;

(iii) the adsorbed ions are positioned only on the surface of electrode particles, meaning that they cannot become part of the electrode matrix.

With these common considerations, different EDL models have been developed over the years to remedy the inherent defects of the Poisson–Boltzmann theory, as shown schematically in Figure 5 and detailed in what follows for the GCS, MPBS and mD models, respectively.

**Figure 5.** Schematic view of GCS, MPBS and mD models.
