Seebeck, Peltier, and Soret effects: On different formalisms for transport equations in thermogalvanic cells

Thermogalvanic cells convert waste heat directly to electric work. There is an abundance of waste heat in the world and thermogalvanic cells may be underused. We discuss theoretical tools that can help us understand and therefore improve on cell performance. One theory is able to describe all aspects of the energy conversion: nonequilibrium thermodynamics. We recommend to use the theory with operationally defined, independent variables, as others have done before. These describe well-defined experiments. Three invariance criteria serve as a basis for any description: of local electroneutrality, entropy production invariance, and emf's independence of the frame of reference. Alternative formalisms, using different sets of variables, start with ionic or neutral components. We show that the heat flux is not the same in the two formalisms and derive a new relationship between the heat fluxes. The heat flux enters the definition of the Peltier coefficient and is essential for the understanding of the Peltier heat at the electrode interfaces and of the Seebeck coefficient of the cell. The Soret effect can occur independently of any Seebeck effect, but the Seebeck effect will be affected by the presence of a Soret effect. Common misunderstandings are pointed out. Peltier coefficients are needed for the interpretation and design of experiments.

Paper-Based Ionic Thermocouples for Inexpensive and High-Precision Measurement of Temperature

Accurate and yet cost-effective temperature measurements are required in various sectors of academia and industry. Thermocouples (TCs) are most widely used for temperature measurements; however, their low temperature sensitivity and high thermal conductivity should be improved to ensure the reliable measurement of output voltage for small temperature differences. To address this, a paper-based ionic thermocouple (P-iTC) presented here utilizes a pair of paper strips soaked with the electrolytes of potassium ferri-/ferrocyanide and iron (II/III) chloride redox couples, which are used as p- and n-type elements, respectively. The fabricated P-iTC provides 70× higher temperature sensitivity (α, 2.8 mV/K) and 30× lower thermal conductivity (k, 0.8 W/m K) than those of commercial K-type TCs, thereby yielding a remarkably high α/k ratio of 3.5 mV m/W. Reliable sensing performance is measured during three weeks of operation, which indicates that the P-iTC should be stable in long-term operation. To demonstrate the practicality of the P-iTC, a 3 × 3 planar array of P-iTCs is fabricated to monitor the temperature profile of a surface in contact with heat sources. Using pencil-drawn graphite electrodes on paper, a highly cost-effective P-iTC with the material cost of ∼0.5 cents per device is also fabricated, which is successfully used to monitor cold chain temperatures while retaining its excellent temperature-sensing performance.

On the time-dependent electrolyte Seebeck effect

Single-ion Soret coefficients α_i characterize the tendency of ions in an electrolyte solution to move in a thermal gradient. When these coefficients differ between cations and anions, an electric field can be generated. For this so-called electrolyte Seebeck effect to occur, different thermodiffusive fluxes need to be blocked by boundaries-electrodes, for example. Local charge neutrality is then broken in the Debye-length vicinity of the electrodes. Confusingly, many authors point to these regions as the source of the thermoelectric field yet ignore them in derivations of the time-dependent Seebeck coefficient S(t), giving a false impression that the electrolyte Seebeck effect is purely a bulk phenomenon. Without enforcing local electroneutrality, we derive S(t) generated by a binary electrolyte with arbitrary ionic valencies subject to a time-dependent thermal gradient. Next, we experimentally measure S(t) for five acids, bases, and salts near titanium electrodes. For the steady state, we find S ≈ 2 mV K^-1 for many electrolytes, roughly one order of magnitude larger than the predictions based on literature α_i. We fit our expression for S(t) to the experimental data, treating the α_i as fit parameters, and also find larger-than-literature values, accordingly.

Thermoelectric Converters Based on Ionic Conductors

Thermoelectric materials represent a new paradigm for harvesting low-grade heat, which would otherwise be dissipated to the environment uselessly. Relative to conventional thermoelectric materials generally composed of semiconductors or semi-metals, ionic thermoelectric materials are rising as an alternative choice which exhibit higher Seebeck coefficient and lower thermal conductivity. The ionic thermoelectric materials own a completely different thermoelectric conversion mechanism, in which the ions do not enter the electrode but rearrange on the electrode surface to generate a voltage difference between the hot and cold electrodes. This unique character has inspired worldwide interests on the design of ionic-type thermoelectric converters with attractive advantages of high flexibility, low cost, limited environmental pollution, and self-healing capability. Referring to the categories of ionic thermoelectric conversion, some representative ionic thermoelectric materials with their respective characteristics are summarized in this minireview. In addition, examples of applying ionic thermoelectric materials in supercapacitors, wearable devices, and fire warning system are also discussed. Insight into the challenges for the further development of ionic thermoelectric materials is finally provided.

Insight into the effect of the configuration entropy of additives on the Seebeck coefficient

Thermogalvanic cells have attracted considerable attention because of their potential to directly convert waste heat into electricity by using redox reactions under continuous operation with a simple, cost-effective design. An increase in the Seebeck coefficient owing to the interactions between the redox ions and the additives has been reported in recent studies. The configuration entropy of the small additives coordinated to a large ion is calculated to analyze the Seebeck coefficient obtained from the entropy difference between the redox pairs. The recently reported increase in the Seebeck coefficient owing to the introduction of guanidinium (Gdm) or urea into the Fe(CN)64-/Fe(CN)63- electrolyte is analyzed using the theoretical results. Furthermore, qualitative and quantitative analyses were also performed to determine the influence of the affinity for the additives on the entropy difference of the redox couples and on the Seebeck coefficient. This study also demonstrates the enhancement in the Seebeck coefficient caused by a membrane isolating the binding species into an appropriate hot/cold zone.

Noor NL, Abdullah N. Ultra-high Seebeck coefficient of a thermal sensor through entropic optimisation of ligand length of Fe(ii) spin-crossover (SCO) materials

In this work, we present a spin-crossover (SCO) complex molecular formulation [Fe(Lⁿ)₂](BF₄)₂ in an electrochemical single couple solution. A Seebeck voltage arises when an electrochemical single couple solution is subjected to a temperature difference, resulting in a single couple reaction at either terminal of the electrochemical cell. The ultrahigh Seebeck coefficients were obtained due to a number of molecular optimisation strategies. The [Fe(L¹⁶)₂](BF₄)₂ complex demonstrated a maximum Seebeck coefficient of 8.67 mV K⁻¹, achieved through a six-pronged approach to maximise entropy during the transition from low spin (LS) to high spin (HS) through: (i) a change in spin state, (ii) a change in physical liquid crystalline state, (iii) the spin Seebeck effect, (iv) the kosmotropic and chaotropic effect, (v) the fastener effect and (vi) thermal heat absorbance. A reduction of the Seebeck coefficient to 1.68 mV K⁻¹ during the HS–LS transition at higher temperatures is related to the single spin state transition entropy change. In summary, this paper presents a systematic study to identify the contributing factors in the production of a sensor with an ultrahigh Seebeck coefficient for energy harvesting through the optimisation of its molecular entropy elements.

The molecular optimisation strategies exhibit ultrahigh Seebeck coefficient through a six-pronged approach to maximise entropy during the transition from low spin (LS) to high spin (HS).

Thermoelectricity and Thermodiffusion in Magnetic Nanofluids: Entropic Analysis

An analytical model describing the thermoelectric potential production in magnetic nanofluids (dispersions of magnetic and charged colloidal particles in liquid media) is presented. The two major entropy sources, the thermogalvanic and thermodiffusion processes are considered. The thermodiffusion term is described in terms of three physical parameters; the diffusion coefficient, the Eastman entropy of transfer and the electrophoretic charge number of colloidal particles, which all depend on the particle concentration and the applied magnetic field strength and direction. The results are combined with well-known formulation of thermoelectric potential in thermogalvanic cells and compared to the recent observation of Seebeck coefficient enhancement/diminution in magnetic nanofluids in polar media.

Thermo-electrochemical cells for waste heat harvesting - progress and perspectives

Thermo-electrochemical cells (also called thermocells) are promising devices for harvesting waste heat for the sustainable production of energy. Research into thermocells has increased significantly in recent years, driven by advantages such as their ability to continuously convert heat into electrical energy without producing emissions or consuming materials. Until relatively recently, the commercial viability of thermocells was limited by their low power output and conversion efficiency. However, there have lately been significant advances in thermocell performance as a result of improvements to the electrode materials, electrolyte and redox chemistry and various features of the cell design. This article overviews these recent developments in thermocell research, including the development of new redox couples, the optimisation of electrolytes for improved power output and high-temperature operation, the design of high surface area electrodes for increased current density and device flexibility, and the optimisation of cell design to further enhance performance.

Synthesis and characterization of protic ionic liquids as thermoelectrochemical materials

PILs have been designed and synthesized for energy harvesting applications. The module exhibited a maximum S_e value of 420 μV K⁻¹ which is the highest reported for PILs with the I⁻/I₃⁻ redox couple.

Protic ionic liquid-based thermoelectrochemical cells for the harvesting of waste heat

The ability to efficiently harvest heat as a source of sustainable energy would make a significant contribution to reducing our current reliance on fossil fuels. Waste heat sources, such as those produced in industrial processes or through geothermal activity, are extensive, often continuous, and at present severely underutilised. Thermoelectrochemical cells offer an alternative design to the traditional semiconductor-based thermoelectric devices and offer thepromise of continuous and cheap operation at moderate temperatures, low maintenance and with no carbon emissions. They utilise two electrodes, held at different temperatures, separated by an electrolyte containing a redox couple. It is the temperature dependence of the electrochemical redox potential that generates the potential difference across the device as a result of the appliedtemperature difference. The magnitude of this redox potential temperature dependence is given by the Seebeck coefficient, Se. Until recently, research into thermoelectrochemical cells had primarily focused on aqueous media, predominantly with the Fe(CN)63-/4- redox couple.[1] However, the good thermal and electrochemical stability, non-volatility and non-flammability ofmany ionic liquids make them promising alternative electrolytes for these devices. The use of ionic liquid (IL) electrolytes offers potential advantages that include increased thermoelectrochemical device efficiencies and lifetimes and the ability to utilise low temperature (often “waste”) heat sources in the 100 – 200 °C temperature range.[2] Here we discuss our research into the use of the Fe(CN)63-/4- redox couple in protic IL electrolytes, with different amounts of added water, in a thermoelectrochemical device with platinum and single walled carbon nanotube (SWNT) electrodes.

Seebeck coefficients in ionic liquids--prospects for thermo-electrochemical cells

Measurement of Seebeck coefficients in a range of ionic liquids (ILs) suggests that these electrolytes could enable the development of thermoelectric devices to generate electrical energy from low-grade heat in the 100-150 °C range.

Thermal diffusion in solutions of electrolytes

A conductimetric method for following the small concentration changes that occur when a temperature gradient is maintained in an aqueous electrolyte is described. The solution is contained in a Perspex cell between silver end-plates which are faced with platinized platinum and kept at temperatures differing by about 10°C. A further connexion to the cell (a ‘centretap’) is made through a small lateral hole equidistant from the ends. The cell is incorporated in an audio-frequency Wheatstone bridge and movement of solute from one half of the cell to the other is followed by measuring the ratio of their resistances. For a convection-free system, the Soret coefficient (σ) may be derived either from the initial rate of change of the ratio or from its value in the steady state. It is found experimentally that there are discrepancies between the two estimates of σ, and also related anomalies in the rate of change of concentration, which can be ascribed to convection. It can be shown that the initial rate observations should be free from convection errors, and the effect of convection on the steady state can be analysed by dimensional methods. The observed discrepancies are correlated with the relevant properties of the solutions in the manner suggested by this analysis. The Soret coefficients of eighteen 1:1 salts in 0⋅01 m aqueous solution and at mean temperature 25⋅0°C have been determined by this method. Some additional measurements have been made at 34⋅7°C and at other concentrations in the range 0⋅002 to 0⋅02m. Three salts of other valency types (potassium, thallous and cadmium sulphates) have also been studied. The molar heats of transport of the salts ( Q *) have been calculated from the Soret coefficients. The results show that Q * (i) is an additive function of contributions characteristic of the constituent ions in dilute (0⋅01 M) solutions of 1:1 electrolytes, (ii) increases markedly on raising the mean temperatures from 25⋅0 to 34⋅7°C, in agreement with the results of Alexander (1954) and Longsworth (1957) (iii) increases appreciably on dilution below 0⋅01 M, indicating that heats of transport are influenced by long-range inter-ionic forces.