*Article* **Applicability of Different Double-Layer Models for the Performance Assessment of the Capacitive Energy Extraction Based on Double Layer Expansion (CDLE) Technique**

**Zhi Zou 1, Longcheng Liu 1,2, Shuo Meng 2, Xiaolei Bian <sup>1</sup> and Yongmei Li 3,\***


**Abstract:** Capacitive energy extraction based on double layer expansion (CDLE) is a renewable method of harvesting energy from the salinity difference between seawater and freshwater. It is based on the change in properties of the electric double layer (EDL) formed at the electrode surface when the concentration of the solution is changed. Many theoretical models have been developed to describe the structural and thermodynamic properties of the EDL at equilibrium, e.g., the Gouy–Chapman– Stern (GCS), Modified Poisson–Boltzmann–Stern (MPBS), modified Donnan (mD) and improved modified Donnan (i-mD) models. To evaluate the applicability of these models, especially the rationality and the physical interpretation of the parameters that were used in these models, a series of single-pass and full-cycle experiments were performed. The experimental results were compared with the numerical simulations of different EDL models. The analysis suggested that, with optimized parameters, all the EDL models we examined can well explain the equilibrium charge–voltage relation of the single-pass experiment. The GCS and MPBS models involve, however, the use of physically unreasonable parameter values. By comparison, the i-mD model is the most recommended one because of its accuracy in the results and the meaning of the parameters. Nonetheless, the i-mD model alone failed to simulate the energy production of the full-cycle CDLE experiments. Future research regarding the i-mD model is required to understand the process of the CDLE technique better.

**Keywords:** CapMix; CDLE; electric double layer; salinity difference energy; modified Donnan
