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Capacitive Deionization (CDI) is a water desalination and purification technology based on the theory of electric double layer (EDL) capacitors. The basic principle is that after the low voltage is applied to the electrodes, the charged particles migrate to the two poles respectively under the action of the electric field force and the concentration gradient, and adsorb on the surface of the electrodes to form an electric double layer so as to achieve desalination or purification. We review the science and technology of CDI and describe the range of possible electrode materials and devices. We summarize the range of options for CDI-designs and possible operational modes ,and describe the various theoretical-conceptual approaches to understand the phenomenon of CDI [1-4].
In 1960 the concept of electrochemical demineralization of water was reported by Blair and Murphy . In that study, it was assumed that ions were removed by electrochemical reactions with specific chemical groups on the carbon particles in the electrodes. In 1968 the commercial relevance and long term operation of CDI was demonstrated by Reid. In 1971 Johnson and Newman introduced theory for ion transport in porous carbon electrodes for CDI and ion storage according to a capacitor mechanism . From 1990 onward, CDI attracted more attention because of the development of new electrode materials, such as carbon aerogels and carbon nanotube electrodes . In 1996, Farmer et al. also introduced the term capacitive deionization and used the now commonly abbreviation ‘CDI’ for the first time. In 2004, Membrane Capacitive Deionization was introduced in a patent of Andelman.
The operation of a conventional CDI system cycles through two phases: an adsorption phase where water is desalinated and a desorption phase where the electrodes are regenerated. During the adsorption phase, a potential difference over two electrodes is applied and ions are adsorbed from the water. In the case of CDI with porous carbon electrodes, the ions are transported through the interparticle pores of the porous carbon electrode to the intraparticle pores, where the ions are electrosorbed in the so-called electrical double layers (EDLs). After the electrodes are saturated with ions, the adsorbed ions are released for regeneration of the electrodes. The potential difference between electrodes is reversed or reduced to zero. In this way, ions leave the electrode pores and can be flushed out of the CDI cell resulting in an effluent stream with a high salt concentration, the so-called brine stream or concentrate. Part of the energy input required during the adsorption phase can be recovered during this desorption step .
2.= Adsorption of ions from the brackish water to desalinate it.
(b) Desorption of ions from the brackish water to regenerate the electrodes
Ion adsorption in Electrical Double Layers
Gouy-Chapman-Stern theory for non-overlapping EDLs
Any amount of charge should always be compensated by the same amount of counter-charge. For example, in an aqueous solution the concentration of the anions equals the concentration of cations. However, in the EDLs formed in the intraparticle pores in a carbon-based electrode, an excess of one type of ion over the other is possible, but it has to be compensated by electrical charge in the carbon matrix. In a first approximation, this EDL can be described using the Gouy-Chapman-Stern model, which distinguishes three different layers:
a） The porous carbon matrix, which contains the electrical charge in the carbon structure.
b）A Stern layer is located between the carbon matrix and the diffuse layer. The Stern-layer is a dielectric layer, i.e. it separates two layers with charge, but it does not carry any charge itself.
c) The diffuse layer, in which the ions compensate the electrical charge of the carbon matrix. The ions are diffusively distributed in this layer.
The width of the diffuse layer can often be approximated using the Debye length, characterizing the distance for concentration of counter-ions to decrease by the factor 1/e. To illustrate this, the Debye length is about 3.1 nm at 20 °C and for a 10 mM NaCl solution. This implies that more than 95% of the electrical charge in the carbon matrix is compensated in a diffuse layer with a width of about 9 nm . As the carbon matrix is charged, the charge has to be compensated by ionic charge in the diffuse layer. This can be done by either the adsorption of counter-ions, or the desorption of co-ions (ions with an equal charge sign as the one in the carbon matrix). Electrical Double Layer (model according to the Gouy-Chapman-Stern theory) Besides the adsorption of ionic species due to the formation of EDLs in the intraparticle pores, ions can form a chemical bond with the surface area of the carbon particles as well. This is called specific adsorption, while the adsorption of ions in the EDLs is referred to as non-specific adsorption.
We use some simplifications and assumptions as follows：
a) Assume the system is completely symmetrical
b) Only monovalent symmetrical salt (electrolyte) (1:1) is used for the system
c) The electrode surface is flat In the GCS model, the surface charge density σ is given by [8, 10-13] σ = 4λDc sinh(Δϕd/2), where λD is the Debye length, λD = (8π·c·Nav·λB)−1/2, λB the Bjerrum length (λB = 0.72 nm in water at room temperature), Nav Avogadro’s number, Δϕd the potential difference over the diffuse layer, and c the ionic strength (in mM).
The voltage difference over the Stern layer ΔϕSt relates directly to σ according to Gauss’s law, CSt·ΔϕSt·VT = σ·F, where CSt is the Stern layer capacity. Potentials Δϕd and ΔϕSt are dimensionless and can be multiplied by the thermal voltage VT = RT/F to result in the dimensional voltage. At equilibrium, the sum of Δϕd and ΔϕSt (times VT) equals half of the applied cell potential, Vcell , as we assume that Vcell equally distributes over the two CDI electrodes. The surface charge Σ per gram of total electrode mass is given by multiplying σ by the factor 1/2·am, where am is the specific electrode area available for ion adsorption (in m2/g), while the salt adsorption Γsalt is given by multiplying the salt adsorption surface density [8,12], w = 8λDc sinh2(Δϕd/4), by the same factor. Finally, the charge efficiency is given by Λ = Γsalt/Σ = w/σ = tanh(Δϕd/4) [8,9,12] .
Modified Donnan theory for fully overlapped EDLs
Because the Stern model does not give a good account of the non-planar, we also need to understand the donnan model. The mD-model assumes that EDLs lining the micropore walls are strongly overlapped since the pore size of the micropores is small relative to the Debye length λD, a measure of EDL thickness, thus leading to a constant electrical potential and ion concentration across the pore radius. In addition, non-electrostatic attraction (physi- or chemisorption) for the ions transporting into the micropores is not considered, i.e., it is assumed that ions are not adsorbed onto the carbon surface within electrodes until a non-zero cell voltage is applied, although this is not necessarily true if certain carbon surface groups (e.g., carboxylic groups) exist or coexisting NaCl concentration is low (say, ≤0.1 g L−1) . In the donnan model，the cell voltage is： And then simplify under equilibrium situation, when electrodes are saturated： In the symmetrical condition，we can obtain： Volumetric charge density is related to the stern layer capacitance and the stern layer potential according to Gauss Law 
Membrane capacitive deionization(MCDI)
By inserting two ion exchange membranes, a modified form of CDI is obtained, namely Membrane Capacitive Deionization .This modification improves the CDI cell in several ways : Co-ions do not leave the electrodes during the adsorption phase, as described above (see Ion adsorption in Electrical Double Layers for explanation). Instead, due to the inclusion of the ion exchange membranes, these co-ions will be kept in the interparticle pores of the electrodes, which enhances the salt adsorption efficiency [15, 18, 19]. Since these co-ions cannot leave the electrodes and because the electroneutrality condition applies for the interparticle pores, extra counter-ions must pass through the ion-exchange membranes, which gives rise to a higher salt adsorption as well [15, 18, 19]. Operating MCDI at constant current mode can produce freshwater with a stable effluent concentration (see constant voltage vs. constant current for more information).The required energy input of MCDI is lower than of CDI [15, 18-20].
2.= Capacitive deionization during the adsorption cycle
(b） Membrane capacitive deionization during the adsorption cycle
Flow-electrode capacitive deionization (FCDI)
Flow-electrode capacitive deionization (FCDI) is a novel membrane CDI method that uses a flow-electrode with infinite ion adsorption capacity . The flow-electrode, which replaces the fixed carbon electrode of the conventional CDI, flows through a flow channel carved on the current collectors . The FCDI system shows a continuous desalting behavior and an excellent removal efficiency with respect to salt water with high concentration, such as seawater, because the flow-electrode has infinite ion adsorption capacity in contrast to the electrode used in conventional CDI processes .
Schematic representation of FCDI. The flow-electrode flows continuously between the ion-exchange membrane and the current collectors. They capture ions on the surface of particles under the electric field.
Hybrid capacitive deionization (HCDI)
Another innovative desalination technique is a battery-based desalination process [22-24], in which the electrodes are composed of battery materials. In this system, ions are captured by chemical bonds instead of the electrical double layer in the CDI system. This method is expected to have a high desalination capacity and ion selectivity because the battery materials themselves have a high specific capacity and unique structure. Note that, to date, although the system has shown a high efficiency and desalination capacity, the performance rate of its desalination process is slower than the current CDI systems .
Constant voltage vs. constant current operation mode A CDI cell can be operated in either the constant voltage or the constant current mode.
During the adsorption phase of CDI using constant voltage operation, the salt effluent salt concentration decreases, but after a while, the effluent salt concentration increases again . This can be explained by the fact that the EDLs (in case of a carbon-based CDI system) are uncharged at the beginning of an adsorption step, which results in a high potential difference (electrical driving force on the ions) over the two electrodes. When more ions are adsorbed in the EDLs, the EDL potential increases and the remaining potential difference between the electrodes, which drives the ion transport, decreases. Because of the decreasing ion removal rate, the effluent concentration increases again .
Since the ionic charge transported into the electrodes is equal to the applied electric current, applying a constant current allows a better control on the effluent salt concentration compared to the constant voltage operation mode. However, for a stable effluent salt concentration membranes should be incorporated in the cell design (MCDI), as the electric current does not only induce counter-ion adsorption, but co-ion depletion as well (see Membrane capacitive deionization vs. Capacitive deionization for an explanation) .
The electrodes are placed in a stack with a thin spacer area in between, through which the water flows. This is by far the most commonly used mode of operation and electrodes, which are prepared in a similar fashion as for electrical double layer capacitors with a high carbon mass loading.
In this mode, the feed water flows straight through the electrodes, i.e. the water flows directly through the interparticle pores of the porous carbon electrodes. This approach has the benefit of ions directly migrating through these pores, hence mitigating transport limitations encountered in the flow-by mode .
This geometrical design is comparable to the flow-by mode with the inclusion of membranes in front of both electrodes, but instead of having solid electrodes, a carbon suspension (slurry) flows between the membranes and the current collector. A potential difference is applied between both channels of flowing carbon slurries, the so-called flow electrodes, and water is desalinated. Since the carbon slurries flow, the electrodes do not saturate and therefore this cell design can be used for the desalination of water with high salt concentrations as well (e.g. sea water, with salt concentrations of approximately 30 g/L). A discharging step is not necessary; the carbon slurries are, after leaving the cell, mixed together and the carbon slurry can be separated from a concentrated salt water stream [21, 29-31].
Capacitive deionization with wires
The freshwater stream can be made to flow continuously in a modified CDI configuration where the anode and cathode electrode pairs are not fixed in space, but made to move cyclically from one stream, in which the cell voltage is applied and salt is adsorbed, to another stream, where the cell voltage is reduced and salt is released .
3. Flow-through CDI cell during the adsorption cycle
(b） Flow-electrode CDI cell during the adsorption cycle
For a high performance of the CDI cell, high quality electrode materials are of utmost importance. In most cases, carbon is the choice as porous electrode material. Regarding the structure of the carbon material, there are several considerations. As a high salt electrosorption capacity is important, the specific surface area and the pore size distribution of the carbon accessible for ions should be large. Furthermore, the used material should be stable and no chemical degradation of the electrode (degradation) should occur in the voltage window applied for CDI. The ions should be able to move fast through the pore network of the carbon and the conductivity of the carbon should be high. Lastly, the costs of the electrode materials are important to take into consideration .
Nowadays, activated carbon (AC) is the commonly used material [33-35], as it is the most cost efficient option and it has a high specific surface area. It can be made from natural or synthetic sources. Other carbon materials used in CDI research are, for example, ordered mesoporous carbon , carbon aerogels [7, 37, 38], carbide-derived carbons , carbon nanotubes , graphene and carbon black . Recent work argues that micropores, especially pores < 1.1 nm are the most effective for salt adsorption in CDI . However, activated carbon, at only US$4/kg for commodity carbon and US$15/kg for highly purified, specially selected supercapacitor carbon, remains much cheaper than the alternatives, which cost US$50/kg or more. Larger activated carbon electrodes are much cheaper than relatively small exotic carbon electrodes, and can remove just as much salt for a given current. The performance increase from novel carbons is insufficient to motivate their use at this point, especially since virtually all CDI applications under serious near-term consideration are stationary applications, where unit size is a relatively minor consideration . Nowadays, electrode materials based on redox-chemistry are more and more studied, such as sodium manganese oxide (NMO) and prussian blue analogues (PBA).
Since the ionic content of water is demixed during a CDI adsorption cycle, the entropy of the system decreases and an external energy input is required. The theoretical energy input of CDI can be calculated as follows : where R is the gas constant (8.314 J mol−1 K−1), T the temperature (K), Φv,fresh, the flow rate of the fresh water outflow (m3/s), Cfeed the concentration of ions in the feed water (mol/m3) and Cfresh the ion concentration in the fresh water outflow (mol/m3) of the CDI cell. α is defined Cfeed/Cfresh and β as Cfeed/Cconc, with Cconc the concentration of the ions in the concentrated outflow. In practice, the energy requirements will be significantly higher than the theoretical energy input. Important energy requirements, which are not included in the theoretical energy requirements, are pumping, and losses in the CDI cell due to internal resistances. If MCDI and CDI are compared for the energy required per removed ion, MCDI has a lower energy requirement than CDI . Comparing CDI with reverse osmosis of water with salt concentrations lower than 20 mM, lab-scale research shows that the energy consumption in kWh per m3 freshwater produced can be lower for MCDI than for reverse osmosis [4, 41].
In conclusion, in our view CDI is a challenging and exciting field and even after 50 years of development can still rightfully be considered an emerging technology. Many challenges remain in the understanding of the CDI process, and the search for improved electrode materials and CDI system solutions to enhance desalination performance continues.
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