Surface Charge Density in Electrical Double Layer Capacitors with Nanoscale Cathode–Anode Separation

Using a dynamic density functional theory, we study the charging dynamics, the final equilibrium structure, and the energy storage in an electrical double layer capacitor with nanoscale cathode–anode separation in a slit geometry. We derive a simple expression for the surface charge density that naturally separates the effects of the charge polarization due to the ions from those due to the polarization of the dielectric medium and allows a more intuitive understanding of how the ion distribution within the cell affects the surface charge density. We find that charge neutrality in the half-cell does not hold during the dynamic charging process for any cathode–anode separation, and also does not hold at the final equilibrium state for small separations. Therefore, the charge accumulation in the half-cell in general does not equal the surface charge density. The relationships between the surface charge density and the charge accumulation within the half-cell are systematically investigated by tuning the electrolyte concentration, cathode–anode separation, and applied voltage. For high electrolyte concentrations, we observe charge inversion at which the charge accumulation exceeds the surface charge at special values of the separation. In addition, we find that the energy density has a maximum at intermediate electrolyte concentrations for a high applied voltage

Interfacial Microstructure of Neutral and Charged Polymer Brushes: A Density Functional Theory Study

Polymer density functional theory (PDFT) is a computationally efficient and popular statistical mechanics theory of complex fluids for capturing the interfacial microstructure of grafted polymer brushes (PBs). Undoubtedly, the intramolecular and intermolecular interactions in PDFT (e.g., excluded volume interactions and electrostatic interactions) are affected by the grafting behaviors. However, how to treat these interactions coupled with the physical constraints of end-grafted PBs remains unclear in the literature. Even worse, there are remarkable differences in the density profiles of PBs between the predictions from PDFT and simulations. Herein, we propose a PDFT for studying neutral and charged grafted PBs, and provide its rigorous derivation and numerical details. This PDFT is successfully validated, where the density distributions of neutral and weakly charged PBs predicted by the PDFT are in excellent agreement with the results from Monte Carlo (MC) and molecular dynamics (MD) simulations. This work provides a powerful and accurate theoretical method to reveal the interfacial microstructure of grafted PBs

Tuning interfacial ion distribution to improve energy density of supercapacitors

Supercapacitors as energy carriers have the advantages of high-power efficiency and long-term stability. An improvement of their energy density promises a solution to make up for the weakness of secondary batteries at a high rate of applications. Here we report an attempt to improve the energy density of supercapacitor by tuning ions arrangement at the electrode-electrolyte interface. Upon the theoretical analysis with classical density functional theory (CDFT), we find that the capacitance of the supercapacitor is maximized at a mediate con-centration of electrolytes, i.e., 1.0 M, where ions accumulate near the electrode surface and display a few multilayered oscillatory distributions. Further, by adjusting the dielectric constant of electrolyte solution and the electrode surface voltage, the interfacial ion distribution is tuned to optimize the energy density of super -capacitors. The theoretical results are corroborated by designed experiments, confirming the role of interfacial ion distribution in specific capacitance. This study shows that an appropriate interfacial ion distribution is beneficial to obtaining high capacitance, highlighting an unusual solution to improve the energy density of supercapacitors

Tuning interfacial ion distribution to improve energy density of supercapacitors

Supercapacitors as energy carriers have the advantages of high-power efficiency and long-term stability. An improvement of their energy density promises a solution to make up for the weakness of secondary batteries at a high rate of applications. Here we report an attempt to improve the energy density of supercapacitor by tuning ions arrangement at the electrode-electrolyte interface. Upon the theoretical analysis with classical density functional theory (CDFT), we find that the capacitance of the supercapacitor is maximized at a mediate con-centration of electrolytes, i.e., 1.0 M, where ions accumulate near the electrode surface and display a few multilayered oscillatory distributions. Further, by adjusting the dielectric constant of electrolyte solution and the electrode surface voltage, the interfacial ion distribution is tuned to optimize the energy density of super -capacitors. The theoretical results are corroborated by designed experiments, confirming the role of interfacial ion distribution in specific capacitance. This study shows that an appropriate interfacial ion distribution is beneficial to obtaining high capacitance, highlighting an unusual solution to improve the energy density of supercapacitors

Dynamic Adsorption of Ions into Like-Charged Nanospace: A Dynamic Density Functional Theory Study

The adsorption processes of ions into charged nanospace are associated with many practical applications. Whereas a large number of microporous materials have been prepared toward efficient adsorption of ions from solutions, theoretical models that allow for capturing the characteristics of ion dynamic adsorption into like-charged nanopores are still few. The difficulty originates from the overlapping of electric potentials inside the pores. Herein, a theoretical model is proposed by incorporating dynamic density functional theory with modified Poisson equation for investigating the dynamic adsorption of ions into like-charged nanoslits. This model is rationalized by comparing the theoretical predictions with corresponding simulation results. Afterward, by analyzing the adsorption dynamics, we show that the overlapping effect is associated with the pore size, ion bulk concentration, and surface charge density, and it plays a dominant role in the coupling between the total adsorption amount of ions and total adsorption time. Specifically, with weak overlapping effect, the total adsorption amount is intuitively proportional to the total adsorption time; however, when the overlapping effect is strong, the total adsorption amount may be inversely proportional to the total adsorption time, indicating that both high adsorption amount and short adsorption time can be achieved simultaneously. This work provides a meaningful insight toward the rational design and optimization of microporous materials for efficient ion adsorption