Diffuse charge dynamics in ionic thermoelectrochemical systems

Recent advances in ionic thermoelectric systems and theoretical modelling

Converting waste heat from solar radiation and industrial processes into useable electricity remains a challenge due to limitations of traditional thermoelectrics. Ionic thermoelectric (i-TE) materials offer a compelling alternative to traditional thermoelectrics due to their excellent ionic thermopower, low thermal conductivity, and abundant material options. This review categorizes i-TE materials into thermally diffusive and thermogalvanic types, with an emphasis on the former due to its superior thermopower. This review also highlights the i-TE materials for creating ionic thermoelectric supercapacitors (ITESCs) that can generate significantly higher voltages from low-grade heat sources compared to conventional technologies. Additionally, it explores thermogalvanic cells and combined devices, discussing key optimization parameters and theoretical modeling approaches for maximizing material and device performance. Future directions aim to enhance i-TE material performance and address low energy density challenges for flexible and wearable applications. Herein, the cutting-edge of i-TE materials are comprehensively outlined, empowering researchers to develop next-generation waste heat harvesting technologies for a more sustainable future.

Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport

The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model∂ t ρ ( x , t ) = ∂ x 2 ρ ( x , t ) - ρ ( x , t ) (also known as the Debye-Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order 0 < α < 1 , and the second-order space derivative with the Riesz-Feller fractional derivative of order 0 < β < 2 . Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox's H-function that we evaluate for different values of α and β .

Thermal diffusion of ionic species in charged nanochannels

Diffusion of ions due to temperature gradients (known as thermal diffusion) in charged nanochannels is of interest in several engineering fields, including energy recovery and environmental protection. This paper presents a fundamental investigation of the thermal diffusion of sodium chloride in charged silica nanochannels performed by molecular dynamics (MD). The results reveal the effects of nanoconfinement and surface charges on the sign and magnitude of the Soret coefficient. It is shown that the sign and magnitude of the Soret coefficient are controlled by the structural modifications of the interfacial solutions. These modifications include the ionic solvation and hydrogen bond structure induced by the nanoconfinement and surface charges. The results show that both nanoconfinement and surface charges can make the solutions more thermophilic. Furthermore, the thermal diffusion of solutions in boundary layers is significantly different from that of solutions in bulk fluid, contributing to the overall difference between the thermal diffusivity of pore fluid and that associated with bulk fluid. The findings provide further understanding of thermal diffusion in nano-porous systems. The proposed MD simulation methodology is applicable to a wider category of coupled heat and mass transfer problems in nanoscale spaces.

Giant and bidirectionally tunable thermopower in nonaqueous ionogels enabled by selective ion doping

Ionic thermoelectrics show great potential in thermal sensing owing to their ultrahigh thermopower, low cost, and ease in production. However, the lack of effective n-type ionic thermoelectric materials seriously hinders their applications. Here, we report giant and bidirectionally tunable thermopowers within an ultrawide range from −15 to +17 mV K⁻¹ in solid ionic liquid–based ionogels. Particularly, a record high negative thermopower of −15 mV K⁻¹ is achieved in the ternary ionogel, rendering it among the best n-type ionic thermoelectric materials under the same condition. A thermopower regulation strategy through ion doping to selectively induce ion aggregates to enhance ion-ion interactions is proposed. These selective ion interactions are found to be decisive in modulating the sign and magnitude of the thermopower in the ionogels. A prototype wearable device integrated with 12 p-n pairs is demonstrated with a total thermopower of 0.358 V K⁻¹, showing promise for ultrasensitive thermal detection.

Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions

An approach to investigate the physical parameters related to ion thermodiffusion in aqueous solutions is proposed herein by calculating the equilibrium hydration free energy and the self-diffusion coefficient as a function of temperature, ranging from 293 to 353 K, using molecular dynamics simulations of infinitely diluted ions in aqueous solutions. Several ion force field parameters are used in the simulations, and new parameters are proposed for some ions to better describe their hydration free energy. Such a theoretical framework enables the calculation of some single-ion properties, such as heat of transport, Soret coefficient, and mass current density, as well as properties of salts, such as effective mass and thermal diffusion, Soret and Seebeck, coefficients. These calculated properties are compared with experimental data available from optical measurements and showed good agreement revealing an excellent theoretical predictability of salt thermodiffusion properties. Differences in single-ion Soret and self-diffusion coefficients of anions and cations give rise to a thermoelectric field, which affects the system response that is quantified by the Seebeck coefficient. The fast and slow Seebeck coefficients are calculated and discussed, resulting in values with mV/K order of magnitude, as observed in experiments involving several salts, such as K⁺Cl^-, Na⁺Cl^-, H⁺Cl^-, Na⁺OH^-, TMA⁺OH^-, and TBA⁺OH^-. The present approach can be adopted for any ion or charged particle dispersed in water with the aim of predicting the thermoelectric field induced through the fluid. It has potential applications in designing electrolytes for ionic thermoelectric devices in order to harvest energy and thermoelectricity in biological nanofluids.

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.

Magnetically tuned thermoelectric behavior of Zn-doped magnetite nanofluids

In the present work, magneto thermoelectric behavior of the Zn-doped magnetite nanofluids is reported. Thermal and electrical conductivity studies have been done, compared and determined to be in line with the theoretical models. Thermoelectric voltage measurements have been carried out in the fluid samples for quite a number of temperature differences at various magnetic fields, and the Seebeck coefficient is calculated from the obtained measurements. It is observed that the fluid samples, which includes magnetite nanoparticle with zinc dopant concentration x = 0.2 shows better enhancement in electrical conductivity, mild enhancement in thermal conductivity and higher Seebeck coefficient value among all the samples. Also, a higher enhancement of 26% is observed in the Seebeck coefficient value of the same sample with an application of 770 G magnetic field. Hence, this is identified as a potential candidate for energy harvesting purposes such as thermoelectric generators in automobile systems, industries and etc.

Structural, Thermodiffusive and Thermoelectric Properties of Maghemite Nanoparticles Dispersed in Ethylammonium Nitrate

Ethylammonium nitrate (ionic liquid) based ferrofluids with citrate-coated nanoparticles and Na + counterions were synthesized for a wide range of nanoparticle (NP) volume fractions ( Φ ) of up to 16%. Detailed structural analyses on these fluids were performed using magneto-optical birefringence and small angle X-ray scattering (SAXS) methods. Furthermore, the thermophoretic and thermodiffusive properties (Soret coefficient S T and diffusion coefficient D m ) were explored by forced Rayleigh scattering experiments as a function of T and Φ . They were compared to the thermoelectric potential (Seebeck coefficient, Se) properties induced in these fluids. The results were analyzed using a modified theoretical model on S T and Se adapted from an existing model developed for dispersions in more standard polar media which allows the determination of the Eastman entropy of transfer ( S ^ NP ) and the effective charge ( Z 0 e f f ) of the nanoparticles.

Thermophoresis of biological and biocompatible compounds in aqueous solution

With rising popularity of microscale thermophoresis for the characterisation of protein-ligand binding reactions and possible applications in microfluidic devices, there is a growing interest in considering thermodiffusion in the context of life sciences. But although the understanding of thermodiffusion in non-polar mixtures has grown rapidly in recent years, predictions for associated mixtures like aqueous solutions remain challenging. This review aims to give an overview of the literature on thermodiffusion in aqueous systems, show the difficulties in theoretical description that arise from the non-ideal behaviour of water-mixtures, and highlight the relevance of thermodiffusion in a biological context. We find that the thermodiffusion in aqueous systems is dominated by contributions from heat of transfer, hydrogen bond interactions and charge effects. However, the separation of these effects is often difficult, especially in case of biological systems where a systematic exclusion of contributions may not be feasible.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Magnetically enhancing the Seebeck coefficient in ferrofluids

The influence of the magnetic field on the Seebeck coefficient (Se) was investigated in dilute magnetic nanofluids (ferrofluids) composed of maghemite magnetic nanoparticles dispersed in dimethyl-sulfoxide (DMSO). A 25% increase in the Se value was found when the external magnetic field was applied perpendicularly to the temperature gradient, reminiscent of an increase in the Soret coefficient (S _T, concentration gradient) observed in the same fluids. In-depth analysis of experimental data, however, revealed that different mechanisms are responsible for the observed magneto-thermoelectric and -thermodiffusive phenomena. Possible physical and physico-chemical origins leading to the enhancement of the fluids' Seebeck coefficient are discussed.

Transient response of an electrolyte to a thermal quench

We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q,c, and the thermovoltage V_{T} for early (t≪τ_{T}) and late (t≫τ_{T}) times as compared to the relaxation time τ_{T} of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and V_{T}) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t≪τ_{T} regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, V_{T} exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)JCPSA60021-960610.1063/1.4923199].

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

We revisit a classical problem of theoretical electrochemistry: the response of an electric double-layer capacitor (EDLC) subject to a small, suddenly applied external potential. We solve the Debye-Falkenhagen equation to obtain exact expressions for key EDLC quantities: the ionic charge density, the ionic current density, and the electric field. In contrast to earlier works, our results are not restricted to the long-time asymptotics of those quantities. The solutions take the form of infinite sums whose successive terms all decay exponentially with increasingly short relaxation times. Importantly, this set of relaxation times is the same among all aforementioned EDLC quantities; this property is demanded on physical grounds but not generally achieved within approximation schemes. The scaling of the largest relaxation timescale τ_{1}, that determines the long-time decay, is in accordance with earlier results: Depending on the Debye length, λ_{D}, and the electrode separation, 2L, it amounts to τ_{1}≃λ_{D}L/D for L≫λ_{D} and τ_{1}≃4L^{2}/(π^{2}D) for L≪λ_{D}, respectively (with D being the ionic diffusivity).