Pore-Size Effect\non Capacitive Energy Extraction from\nthe Salinity Gradient with Porous Electrodes

The microscopic mechanisms through which the pore size\nof electrodes\ninfluences the extraction of salinity gradient energy via a capacitive\ndouble-layer expansion method remain not yet fully understood. Herein,\nwe elucidate the relationship between the extracted energy and the\npore size in the porous electrode using classical density functional\ntheory. The influence of the pore size on energy, capacitance, and\nenergy density is systematically explored, and a nonmonotonic relationship\nbetween the extracted energy and pore size is put forward, which indicates\nthat maximum energy extraction can be attained with an optimal pore\nsize. Moreover, we find that the optimal pore size grows when the\noperating voltage is enhanced, and the corresponding extraction energy\nis also raised. Further analysis reveals that the nonmonotonic dependence\nof energy extraction on the pore size stems from the distinct ion\nadsorption within nanoscale pores immersed in seawater versus freshwater\nsolutions, and the optimal pore size can be determined empirically\nby the pore width at which ion adsorption onto the electrode surface\nin seawater just reaches its saturation. This study not only discloses\nthe microscopic mechanism of pore size influencing energy extraction\nbut also proposes a feasible approach to determining the optimal pore\nsize.