Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination

Härtel, Andreas; Janssen, Mathijs; Samin, Sela; Roij, René van

doi:10.1088/0953-8984/27/19/194129

Cited by 54 publications

(110 citation statements)

References 92 publications

(150 reference statements)

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“…In conclusion, on the basis of modified PoissonBoltzmann theory (which was actually corroborated by density functional theory [21] that accounts more accurately for ionic packing effects), we predict a significant voltage increase with temperature for water-filled nanoporous capacitors. We show how this effect can be applied to boost the efficiency of capacitive blue-energy and desalination devices by varying the water temperature along their cyclic processes.…”

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confidence: 72%

Boosting Capacitive Blue-Energy and Desalination Devices with Waste Heat

2014

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We show that sustainably harvesting "blue" energy from the spontaneous mixing process of fresh and salty water can be boosted by varying the water temperature during a capacitive mixing process. Our modified Poisson-Boltzmann calculations predict a strong temperature dependence of the electrostatic potential of a charged electrode in contact with an adjacent aqueous 1∶1 electrolyte. We propose to exploit this dependence to boost the efficiency of capacitive blue engines, which are based on cyclically charging and discharging nanoporous supercapacitors immersed in salty and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. We show that the energy output of blue engines can be increased by a factor of order 2 if warm (waste-heated) fresh water is mixed with cold sea water. Moreover, the underlying physics can also be used to optimize the reverse process of capacitive desalination of water. DOI: 10.1103/PhysRevLett.113.268501 PACS numbers: 92.05.Jn, 82.47.Uv, 84.60.Rb, 92.40.Qk In river mouths an enormous free-energy dissipation of the order of 2 kJ takes place for every liter of fresh river water that mixes with an excess of salty sea water. This so-called "blue energy" can nowadays be harvested due to newly available nanostructured materials such as selective membranes [1,2] and nanoporous electrodes [3,4], as also used in supercapacitors [5]. In fact, several test factories have been built based either on pressure-retarded osmosis using waterpermeable membranes [6,7] or on reverse-electrode dialysis using ion-selective membranes [8], and recently a lot of progress has been made with capacitive mixing processes that involve highly porous carbide derived electrodes [9][10][11]. In all these cases, the spontaneous and irreversible ionic mixing process is intercepted and converted to a voltage difference by an enginelike device, very much in the spirit of a Stirling or Carnot engine that intercepts the spontaneous heat flow between a hot and a cold heat bath and converts it (partially) to the mechanical energy of a rotating flywheel [12]. However, the temperature of the river and sea water has been assumed constant throughout the cycle in all devices considered so far. Given the intrinsic scientific and societal interest in combined chemical-heat engines and heat-to-power converters, the ongoing development and upscaling of blue-energy devices and test factories, and the availability of a lot of waste heat in the form of "warmish" water in the industrial world, it is timely to consider temperature tuning in blue-energy devices. In this Letter we predict that the work extracted from capacitive mixing devices can be boosted by a factor of order 2 if warm fresh water is mixed with cold salty water. Moreover, we show how varying the temperature during a desalination cycle reduces the required energy input substantially, and we predict on the basis of a general thermodynamic argument that adiabatic (dis)charging processes lead to significant temperature changes on the order of several deg...

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confidence: 72%

Boosting Capacitive Blue-Energy and Desalination Devices with Waste Heat

2014

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“…While here we have not considered classical DFT, recent work capturing excluded volume and electrostatic correlations between ions suggests that these effects may increase the energy produced per unit area [31], therefore further overestimating this quantity. Nevertheless, it would be necessary to investigate the predictions of classical DFT under comparable conditions and, ideally, also in more realistic geometries.…”

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confidence: 99%

“…The most commonly used models in these contexts are Debye-Hückel (DH) and Poisson-Boltzmann (PB)-possibly including excluded volume effects-theories [22][23][24][25][26][27][28][29], as well as modified Donnan (mD) models [30]. Recently, a better description of steric effects and electrostatic correlations has also been introduced in this context using classical density functional theory (DFT) [31][32][33].…”

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confidence: 99%

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

et al. 2018

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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 waterand 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.

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“…Approximations enter the theory at the level of (∂Ψ/∂T ) Q , so that more accurate estimates can be found by systematically improving the grand potential Eq. (3), by including, for instance, solvent polarizability [38], a better description of excluded volume interactions [39], and residual ion correlations [29] (see also Appendix C).Though oversimplified ideal-gas reasoning permeates 5 the reversible heating literature [9,11,[13][14][15], the main finding of this Letter is that the thermodynamic identity Eq. (2), and not Eq.…”

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confidence: 92%

Reversible Heating in Electric Double Layer Capacitors

Janssen

Roij

2017

Phys. Rev. Lett.

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A detailed comparison is made between different viewpoints on reversible heating in electric double layer capacitors. We show in the limit of slow charging that a combined Poisson-Nernst-Planck and heat equation, first studied by d'Entremont and Pilon [J. Power Sources 246, 887 (2014)], recovers the temperature changes as predicted by the thermodynamic identity of Janssen et al. [Phys. Rev. Lett. 113, 268501 (2014)], and disagrees with the approximative model of Schiffer et al. [J. Power Sources 160, 765 (2006)] that predominates the literature. The thermal response to the adiabatic charging of supercapacitors contains information on electric double layer formation that has remained largely unexplored.With the relation between heat and entropy formulated by Clausius in 1855, and with the establishment of the importance of ion entropy to the electric double layer (EDL) by Gouy (1910) and Chapman (1913) [1], almost a century passed before reversible, adiabatic heating and cooling was measured in electric double layer capacitors (EDLCs) [2]. Unlike irreversible Joule heating, occurring everywhere in the electrolyte when an EDLC is charged at finite currents, it turns out that the sources of reversible heating are located only within the nanometerrange vicinity of the electrode's surface. Therefore, one needs EDLCs whose surface-to-volume ratio is as high as possible to notice an appreciable reversible temperature variation. This has become possible and relevant in recent years because electrodes can now be manufactured from porous carbon with internal surface areas up to 2000 m 2 g −1 . Electrolyte-filled supercapacitors made from these electrodes are characterized by a high capacitance, fast (dis)charging rates, and high cyclability [3]. These favorable properties have sparked a huge scientific interest in supercapacitors in recent years, and led to various applications [4][5][6][7][8]. The performance of supercapacitors for energy storage usually suffers, however, from increased temperatures causing aging of materials, increased internal resistance, decreased capacitance, parasitic electrochemical reactions, and self discharging [9][10][11]. Efforts were therefore made both in experiments [2, 10-13] and modeling [14][15][16][17] to gain insight in the thermal behavior of supercapacitors. However, a unified understanding of reversible heating effects occurring during EDL buildup is still lacking, and thermal response to charging has not yet been fully exploited. This Letter for the first time quantitatively reconciles two viewpoints on reversible heating. Within the thermodynamic viewpoint, two distinct identities for isentropic processes are discussed, only one of which (we show) agrees with the other, kinetic, viewpoint.For the thermodynamic viewpoint, consider an EDLC on which a potential is imposed by connecting it to a battery. The electrodes then obtain surface charges which are screened by diffuse clouds of counterionic charge (see Fig. 1), hence the ionic configuration entropy decreases. For a thermally ...

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Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination

Cited by 54 publications

References 92 publications

Boosting Capacitive Blue-Energy and Desalination Devices with Waste Heat

Boosting Capacitive Blue-Energy and Desalination Devices with Waste Heat

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

Reversible Heating in Electric Double Layer Capacitors

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