Blue Energy and Desalination with Nanoporous Carbon Electrodes: Capacitance from Molecular Simulations to Continuous Models

Capacitive mixing (CapMix) and capacitive deionization (CDI) are currently developed as alternatives to membrane-based processes to harvest blue energy—from salinity gradients between river and sea water—and to desalinate water—using charge-discharge cycles of capacitors. Nanoporous electrodes increase the contact area with the electrolyte and hence, in principle, also the performance of the process. However, models to design and optimize devices should be used with caution when the size of the pores becomes comparable to that of ions and water molecules. Here, we address this issue by simulating realistic capacitors based on aqueous electrolytes and nanoporous carbide-derived carbon (CDC) electrodes, accounting for both their complex structure and their polarization by the electrolyte under applied voltage. We compute the capacitance for two salt concentrations and validate our simulations by comparison with cyclic voltammetry experiments. We discuss the predictions of Debye-Hückel and Poisson-Boltzmann theories, as well as modified Donnan models, and we show that the latter can be parametrized using the molecular simulation results at high concentration. This then allows us to extrapolate the capacitance and salt adsorption capacity at lower concentrations, which cannot be simulated, finding a reasonable agreement with the experimental capacitance. We analyze the solvation of ions and their confinement within the electrodes—microscopic properties that are much more difficult to obtain experimentally than the electrochemical response but very important to understand the mechanisms at play. We finally discuss the implications of our findings for CapMix and CDI, both from the modeling point of view and from the use of CDCs in these contexts.

Popular Summary

Electrical power generation from salinity gradients—achieved by tapping into the energy released as salt water mixes with fresh water—has the potential to become a significant source of clean, renewable energy. One novel strategy is capacitive mixing (CapMix), which produces power from the charging and discharging of a water-immersed capacitor as a result of changes in the surrounding salinity. When run in reverse, this technique also offers an efficient alternative to desalination techniques (known as capacitive deionization, or CDI). Nanoporous carbons have already been successful for energy storage applications and are therefore good candidate materials. However, current models to design and optimize these devices must be used with caution when the size of the pores becomes comparable to that of ions and water molecules. Here, we address this issue using computer simulations on the molecular scale.

We simulate realistic capacitors, accounting for both their complex structure and their polarization by the electrolyte under an applied voltage. We compute the capacitance for two salt concentrations and find excellent agreement with experiments, thus validating our approach. While we find that the two models currently used for designing these devices are not suitable for nanoporous materials, one of those models can be emulated by molecular simulations and used to make reasonable predictions under realistic situations.

While our approach is not a perfect solution—in particular, there is a high computational cost at low salinities—our results show that molecular simulations will be a useful tool for characterizing the performance of nanoporous carbon in both CapMix and CDI applications. Future work could also investigate energy loss during charging and discharging.

Figure 1

The simulated system (top panel) consists of two nanoporous carbon electrodes, with a structure corresponding to carbide-derived carbons synthesized at $800°\mathrm{C}$ (cyan lines) and an aqueous NaCl solution as an electrolyte (here at 1 M; sodium is shown in blue, chloride in orange, oxygen in red, and hydrogen in white). A potential difference of 1 V is applied between the electrodes, and the charge $q$ of each electrode atom fluctuates in response to the instantaneous configuration of the electrolyte (see the color scale in the central panels, where water is not shown). The bottom parts illustrate the electrolyte confined in the electrodes.

Figure 2

Cyclic voltammograms of electrochemical cells based on CDC and aqueous solutions of sodium chloride at concentrations ranging from 0.05 to 1.0 M as electrolytes. The potential scan rate is $1\mathrm{mV}{\mathrm{s}}^{-1}$.

Figure 3

Density profiles along the simulation cell, for an average salt concentration of 0.5 and $1.0\mathrm{M}$ (top and bottom, respectively). The negative (resp. positive) electrode is on the left (resp. right) side of the cell.

Figure 4

Distribution of solvation number for ${\mathrm{Na}}^{+}$ (left panel) and ${\mathrm{Cl}}^{-}$ (right panel) ions in the bulk, negative and positive electrodes, for the 1.0 M system.

Figure 5

Joint distribution of solvation number and d.o.c. of ${\mathrm{Na}}^{+}$ (left panel) and ${\mathrm{Cl}}^{-}$ (right panel) ions in positive (dark blue, red) and negative (light blue, orange) electrodes, for the 1.0 M system. The histograms correspond to the discrete values of the solvation number and to finite intervals of the continuous d.o.c. (of width 2% and 10% for ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$, respectively).

Figure 6

Capacitive mixing thermodynamic cycle, using two electrolytes with different salt concentrations. Segment A: the electrochemical cell is charged under a supply voltage $\mathrm{\Delta }\phi$ in the presence of the more concentrated electrolyte (sea water), corresponding to a large cell capacitance $C_1$. Segment B: the voltage between the electrodes rises when the electrolyte is replaced by the more dilute one (river water, small cell capacitance $C_2$) under open circuit conditions. Segment C: the electrochemical cell is then discharged down to the supply voltage $\mathrm{\Delta }\phi$, before being flushed with a concentrated electrolyte under open circuit conditions (segment D). The energy extracted per cycle, $\mathrm{\Delta }{E}_{\text{cycle}}$, is equal to the area of the shaded region.