ThesisPDF Available

The electric double layer put to work -- thermal physics at electrochemical interfaces

Authors:

Abstract

Where charged electrode surfaces meet fluids that contain mobile ions, so-called electric double layers (EDLs) form to screen the electric surface charge by a diffuse cloud of counterionic charge in the fluid phase. This double layer has been studied for over a century and is of paramount importance to many processes in physical chemistry and soft matter physics, as well as in electric double layer capacitors (EDLCs) used for energy storage. With the ongoing development of nanomaterials, electrodes can nowadays be built from porous carbon with internal surface areas up to 2000 m2/g, leading to very high capacitances. However, in EDLCs made from this material, the size of hydrated ions is on the same length scale as their confining geometry. This poses a substantial theoretical challenge, since EDL models must address both the electrostatics and the packing of the ions. To address this challenge, model calculations of different levels of sophistication are presented throughout this thesis. These calculations give access to the capacitance, the relation between the electrostatic potential and the charge on the electrodes’ surface. Particularly, we focus on the interplay between the capacitance and the temperature the electrolyte solution. First, we show that the electrostatic potential at fixed electrode charge rises with electrolyte temperature. This thermal voltage rise is predicted by calculations and observed in experiments, both in the case of an aqueous and an organic solvent. This finding opens the door to thermal energy harvesting with EDLCs. To this end, we propose to convert thermal into electric energy via a charging-heating-discharging-cooling cycle of an EDLC in alternating contact with heat reservoirs at either high or low temperature. The essence of this cycle is the surplus of energy harvested during discharging at high temperature (and associated high potentials) compared to the energy invested during charging at lower temperature (hence lower potentials). As another possible application of the thermal voltage rise, we show that harvesting “blue” energy from the spontaneous mixing process of fresh and salt water can be boosted by varying the water temperature during a capacitive mixing cycle. We show that the energy output of blue engines can be increased by a factor of order two if warm fresh water is mixed with cold seawater. Note that we do not advocate to consume fossil fuels to generate warm water, but rather to use (industrial) waste heat, which is abundantly available. While electrolyte temperature affects EDLC capacitance, the reverse is also true. As a second example of the interplay between temperature and EDLC capacitance, we consider how the charging of an EDLC affects the electrolyte temperature. For a thermally insulated capacitor that is charged quasi-statically, thermodynamics demands via the second law (dS = 0) that the ionic configuration entropy decrease upon EDL formation is counterbalanced by an electrolyte entropy increase: the EDLC heats up. Upon quasi-static adiabatic discharging, the opposite happens: the electrolyte cools while the EDL breaks down. We discuss various earlier models, and propose a new thermodynamic identity that fixes some of their shortcomings.
A preview of the PDF is not available
... Owing to the principle of the energy storage mechanism based on the electric double layer, carbon materials show a positive correlation between the specific capacitance and the specific surface area when applied to supercapacitors [21][22][23]. If the supercapacitor is thermally charged, it is manifested that the expansion of the electric double layer leads to an increase in the voltages of devices, thereby realizing thermoelectric conversion [24,25]. Qiao et al. found that the specific surface area of the electrode has an important influence on the generation of thermoelectric potential [26]. ...
... Heating can expand the electric double layer and can thus increase the voltage between electrodes. The capacity of the hot-state supercapacitors should indeed decline, but the total discharge of electricity will increase, thus realizing thermoelectric conversion [24]. The Seebeck coefficients of ZnG or AC are tested in Figure 5b. ...
Article
Full-text available
Low-grade heat energy recycling is the key technology of waste-heat utilization, which needs to be improved. Here, we use a zinc-assisted solid-state pyrolysis route to prepare zinc-guided 3D graphene (ZnG), a 3D porous graphene with the interconnected structure. The obtained ZnG, with a high specific surface area of 1817 m2 g−1 and abundant micropores and mesopores, gives a specific capacitance of 139 F g−1 in a neutral electrolyte when used as electrode material for supercapacitors. At a high current density of 8 A g−1, the capacitance retention is 93% after 10,000 cycles. When ZnG is used for thermally chargeable supercapacitors, the thermoelectric conversion of the low-grade heat energy is successfully realized. This work thus provides a demonstration for low-grade heat energy conversion.
... However, cooling due to current is possible as well, for instance at the junction of two materials that allow current to pass. Examples are the contact point of two thermoelectric materials (the Peltier effect) [4,5], and the electrical double layer (EDL) in porous electrodes [6][7][8][9][10][11]. Electrostatic heating and cooling in EDLs are both described by the inner product of I and field strength E, a term which can be both positive and negative [9][10][11][12][13][14][15][16][17][18][19][20][21]. When Ohm's law applies and thus current flows in the direction of the field strength, then the classical expression I 2 R results (Joule heating), but when additional driving forces act on the charge carriers, the electric power density I · E does not directly depend on the resistance R and can also be negative, which implies local cooling. ...
... Assuming two ideal salt solutions, with different salinity but the same temperature, when they are mixed without extraction of power, the temperature must stay the same (assuming no heating due to fluid friction). When, instead, electrical energy is extracted in an RED device that is fed with these two solutions, then the solutions that leave the device must have become colder than the inlet streams [20]. This is because when the extracted electrical energy is used to later heat up these exit streams, they must (on average) end up at the same temperature as in the case of no extraction of energy (namely, the same as the temperature of the inlet streams). ...
Preprint
Full-text available
Electrostatic cooling is known to occur in conductors and in porous electrodes in contact with aqueous electrolytes. Here we present for the first time evidence of electrostatic cooling at the junction of two electrolyte phases. These are, first, water containing salt, and, second, an ion-exchange membrane, which is a water-filled porous layer containing a large concentration of fixed charges. When ionic current is directed through such a membrane in contact with aqueous phases on both sides, a temperature difference develops across the membrane which rapidly switches sign when the current direction is reversed. The temperature difference develops because one water-membrane junction cools down, while the other heats up. Cooling takes place when the inner product of ionic current $\textbf{I}$ and field strength $\textbf{E}$ is a negative quantity, which is possible in the electrical double layers that form on the surface of the membrane. Theory reproduces the magnitude of the effect but overestimates the rate by which the temperature difference across the membrane adjusts itself to a reversal in current.
... However, cooling due to current is possible as well, for instance, at the junction of two materials that allow current to pass. Examples are the contact point of two thermoelectric materials (the Peltier effect) [4,5] and the electrical double layer (EDL) in porous electrodes [6][7][8][9][10][11]. Electrostatic heating and cooling in EDLs are both described by the inner product of I and field strength E, a term which can be both positive and negative [9][10][11][12][13][14][15][16][17][18][19][20][21]. When Ohm's law applies and thus current flows in the direction of the field strength, the classical expression I 2 R results (Joule heating), but when additional driving forces act on the charge carriers, the electric power density I · E does not directly depend on the resistance R and can also be negative, which implies local cooling. ...
... Assuming two ideal salt solutions, with different salinity but the same temperature, when they are mixed without extraction of power, the temperature must stay the same (assuming no heating due to fluid friction). When, instead, electrical energy is extracted in an RED device that is fed with these two solutions, the solutions that leave the device must be colder than the inlet streams [20]. This is because when the extracted electrical energy is used to later heat up these exit streams, they must (on average) end up at the same temperature as in the case of no extraction of energy, namely, the same as the temperature of the inlet streams. ...
Article
Full-text available
Electrostatic cooling is known to occur in conductors and in porous electrodes in contact with aqueous electrolytes. Here we present evidence of electrostatic cooling at the junction of two electrolyte phases. These are, first, water containing salt and, second, an ion-exchange membrane, which is a water-filled porous layer containing a large concentration of fixed charges. When ionic current is directed through such a membrane in contact with aqueous phases on both sides, a temperature difference develops across the membrane which rapidly switches sign when the current direction is reversed. The temperature difference develops because one water-membrane junction cools down while the other heats up. Cooling takes place when the inner product of ionic current I and field strength E is a negative quantity, which is possible in the electrical double layers that form on the surface of the membrane. Theory reproduces the magnitude of the effect but overestimates the rate by which the temperature difference across the membrane adjusts itself to a reversal in current.
Article
Full-text available
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, Härtel, and van Roij [Phys. Rev. Lett., 113, 268501 (2014)], and disagrees with the approximative model of Schiffer, Linzen, and Sauer [J. Power Sources 160, 765 (2006)] that predominates the literature.
Article
Full-text available
Thermal energy is abundantly available, and especially low-grade heat is often wasted in industrial processes as a by-product. Tapping into this vast energy reservoir with cost-attractive technologies may become a key element for the transition to an energy-sustainable economy and society. We propose a novel heat-to-current converter which is based on the temperature dependence of the cell voltage of charged supercapacitors. Using a commercially available supercapacitor, we observed a thermal cell-voltage rise of around 0.6 mV/K over a temperature window of 0 °C to 65 °C. Within our theoretical model, this can be used to operate a Stirling-like charge-voltage cycle whose efficiency is competitive to the most-efficient thermoelectric (Seebeck) engines. Our proposed heat-to-current converter is built from cheap materials, contains no moving parts, and could operate with a plethora of electrolytes which can be chosen for optimal performance at specific working temperatures. Therefore, this heat-to-current converter is interesting for small-scale, domestic, and industrial applications.
Article
Full-text available
An enormous dissipation of the order of 2 kJ/L takes place during the natural mixing process of fresh river water entering the salty sea. "Capacitive mixing" is a promising technique to efficiently harvest this energy in an environmentally clean and sustainable fashion. This method has its roots in the ability to store a very large amount of electric charge inside supercapacitor or battery electrodes dipped in a saline solution. Three different schemes have been studied so far, namely, Capacitive Double Layer Expansion (CDLE), Capacitive Donnan Potential (CDP) and Mixing Entropy Battery (MEB), respectively based on the variation upon salinity change of the electric double layer capacity, on the Donnan membrane potential, and on the electrochemical energy of intercalated ions.
Article
Full-text available
Capacitive mixing (CAPMIX) and capacitive deionization (CDI) are promising candidates for harvesting clean, renewable energy and for the energy efficient production of potable water, respectively. Both CAPMIX and CDI involve water-immersed porous carbon electrodes at voltages of the order of hundreds of millivolts, such that counter-ionic packing is important. We propose a density functional theory (DFT) to model the electric double layer which forms near the surfaces of these porous materials. The White-Bear mark II fundamental measure theory (FMT) functional is combined with a mean-field Coulombic and a MSA-type correction to describe the interplay between dense packing and electrostatics, in good agreement with MD simulations. Compared to less elaborate mean-field models our DFT calculations reveal a higher work output for blue-energy cycles and a higher energy demand for desalination cycles.
Article
Supercapacitors are electrochemical energy storage devices that operate on the simple mechanism of adsorption of ions from an electrolyte on a high-surface-area electrode. Over the past decade, the performance of supercapacitors has greatly improved, as electrode materials have been tuned at the nanoscale and electrolytes have gained an active role, enabling more efficient storage mechanisms. In porous carbon materials with subnanometre pores, the desolvation of the ions leads to surprisingly high capacitances. Oxide materials store charge by surface redox reactions, leading to the pseudocapacitive effect. Understanding the physical mechanisms underlying charge storage in these materials is important for further development of supercapacitors. Here we review recent progress, from both in situ experiments and advanced simulation techniques, in understanding the charge storage mechanism in carbon- and oxide-based supercapacitors. We also discuss the challenges that still need to be addressed for building better supercapacitors.
Chapter
The structure of molecular and polymer fluids near surfaces and in thin films is a topic of great fundamental and practical interest which is still not well understood. We present a density functional theory which is a generalization to inhomogeneous polyatomic fluids of Wertheim's thermodynamic perturbation theory for associating fluids. In the local density approximation, this theory takes a very simple form which can be used to study the structure and the thermodynamics of long chains at the free surface. As an application, we compute the variations of the surface tension with temperature and chain length and we investigate the surface segregation effects due to side branching, segment size, or isotopic substitution.
Article
Electrical double layers are ubiquitous; they will inevitably emerge, given mobile charge carriers and an interface. They play a decisive role in well-known problems such as electrochemical reactions, electrokinetics, and colloidal stability and thus have been studied extensively since the very concept of the double layer was postulated by Helmholtz. Furthermore, the transition between different lateral arrangements of counter and co-ions during electrification of narrow pores has been observed in simulations and shown to greatly affect both the capacitance and dynamics of the double layers. These relatively new issues and developments all point to new challenges in understanding the three-dimensional (3D) structures of the double layers controlled by the electrification of surfaces. The new feature of the double layer in ionic liquids is that structural transitions can take place in the adjacent layer to the electrode, even when its ions may not be specifically adsorbed on the electrode.
Article
Extracting electric energy from small temperature differences is an emerging field in response to the transition toward sustainable energy generation. We introduce a novel concept for producing electricity from small temperature differences by the use of an assembly combining ion exchange membranes and porous carbon electrodes immersed in aqueous electrolytes. Via the temperature differences, we generate a thermal membrane potential that acts as a driving force for ion adsorption/desorption cycles within an electrostatic double layer, thus converting heat into electric work. We report for a temperature difference of 30 degrees C a maximal energy harvest of similar to 2 mJ/m(2), normalized to the surface area of all the membranes.
Article
Significance Tremendous low-grade heat is stored in industrial processes and the environment. Efficient and low-cost utilization of the low-grade heat is critical to imminent energy and environmental challenges. Here, a rechargeable electrochemical cell (battery) is used to harvest such thermal energy because its voltage changes significantly with temperature. Moreover, by carefully tuning the composition of electrodes, the charging process is purely powered by thermal energy and no electricity is required to charge it. A high heat-to-electricity conversion efficiency of 2.0% can be reached when it is operated between 20 and 60 °C. Such charging-free characteristic may have potential application for harvesting low-grade heat from the environment, especially in remote areas.