*4.4. Full CDLE Experiment*

The extracted energy per gram *W* in our CDEL experiment is 0.1 to 0.15 J/g at an applied voltage ranging from 0.3 to 0.8 V, which is comparable to the relevant reported energy production of other works, i.e., the *W* ranged from 0.2 to 0.6 J/g at an applied voltage ranging from 0.3 to 0.7 V is reported by D. Brogioli et al. [22], and *W* ≈ 0.11 to 0.22 J/g at *Vext* = 0.4 V reported by Nasir et al. [18]. The reason for the difference in energy production might be attributed to the different CDLE cell design and electrode materials. Note that the results of *Q* vs. *V* obtained in single-pass experiments clearly show that, for a fixed value of *Q*, the reduction in the electrolyte concentration results in higher cell potential. This allows us to extract energy by intermittently exchange seawater and freshwater thorough a CDLE cell. In addition, one may expect that, in a full CDLE cycle, the potential rise ΔV at sept 2 and the energy extracted should both increase monotonically with the applied voltage *Vext*, if the kinetics of the full CDLE cycle is solely controlled by the diffusion of ions within the porous electrodes. However, this not the case. As shown in Figure 15, the experimental results suggest a parabolic curve for both Δ*V* and *W*. The potential rise Δ*V* increases monotonically until it reaches a maximum value at *Vext* = 0.6 V and then followed with a progressive decay with further increase in *Vext*. Correspondingly, the energy extracted, *W*, achieves a maximum value at *Vext* = 0.6 V. This phenomenon was also observed by Jiménez et al. [24] and Iglesias et al. [17] and explained qualitatively by the MPBS model assuming a spherical geometry of solid carbon particles [24]. Our findings do not, however, support the use of such an MPBS model because the results of single-pass experiments, as shown in Figure 14, clearly indicate that both Δ*V* and *W* should monotonically increase with an increase in the applied voltage. The large deviation between experimental data and theoretical prediction at higher applied voltage suggested that using only the equilibrium double layer model itself is not sufficient to describe the performance of a full CDLE cell. An advanced model as the one developed by Rica et al. [27] is then required to include the effect of advection, mass transfer at the electrode/solution interface, ionic diffusion through the electrodes and build-up of EDLs at the micropore space, etc. This work is now undertaken and will be discussed in detail in the near future.

**Figure 15.** (**a**) Potential rise Δ*V* in step 2 of CDLE process as a function of cell voltage. (**b**) Extracted energy of one CDLE cycle at different cell voltage. *Rext* = 100 Ω, *c f resh* = 20 mM, *csea* = 600 mM. The line refers to the theoretical prediction by i-mD model, marks refer to the experiment data and error bars of the experimental data are indicated by horizontal lines through the marked data points.

#### **5. Conclusions**

In this study, a series of single-pass and full-cycle experiments were performed for a self-made CDLE cell in order to exploit its potential to harvest energy from an intermittent exchange of seawater and freshwater. The focus is, however, on the analysis of different EDL models in describing the structural and thermodynamic properties of EDLs at the micropore scale at equilibrium. The results suggest that both GCS and MPBS models involve physically unmeaningful parameters, despite their ability to well reproduce the *Q*–*V* curves (the key performance of the CDLE cell) at different NaCl concentrations. The reason is, perhaps, that both models were applied on the assumption of thin EDLs, which is unreasonable since *λ<sup>D</sup>* - *Hp* in all the cases of interest. By contrast, both the mD and i-mD models consider the strong overlap of EDLs within the micropores of the electrodes, making the diffuse potential constant. As a result, the non-ideal properties of the EDLs were well accounted for with only a few parameters that are physically interpretable. In particular, the i-mD model considers the excess chemical potential as a function of the total concentration of NaCl within the micropores instead of a constant value. This makes i-mD model superior to mD model in describing the performance of the CDLE cell at equilibrium, and therefore should be recommended to be used in the first place.

However, when applied for practical use, it was found that the theoretical calculation of the i-mD model alone gives inconsistent results with the data of the full-cycle CDLE experiments about the dependence of Δ*V* and *W* on the applied voltage. The model and the single-pass experimental results suggest that both Δ*V* and *W* should increase monotonically with the applied voltage, in contrast to a parabolic behavior that was found experimentally with a maximum of *W* located at *Vext* = 0.6 V. The reason for this difference may be attributed to the higher current leakage and the effect of ion size at larger applied voltage [18,24,25]. However, to understand the performance of the full-cycle CDLE cells better, an advanced model is expected to include the effect of advection, mass transfer at the electrode/solution interface, ionic diffusion through the electrodes and i-mD description of EDLs at the micropore space, etc. Thus, the knowledge we obtained from this study provides important guidance towards the application of EDL models in CDLE technology.

**Author Contributions:** Writing—original draft preparation, Z.Z.; writing—review and editing, L.L.; methodology, Z.Z.; data curation, X.B.; simulation, S.M.; supervision, Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Swedish Energy Agency (Energimyndigheten), Sweden, project number 44606-1.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Zhi Zou acknowledges the financial support from China Scholarship Council (CSC).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Nomenclature**


