Thermoelectric effects in ion conducting membranes and perspectives for thermoelectric energy conversion

A theoretical understanding of ionic current through a nanochannel driven by a viscosity gradient

HYPOTHESIS

Different thermodynamic forces owing to the gradient of temperature, electrical potential, or concentration can drive ionic current through charged membranes. It has been recently shown that a viscosity gradient can drive an electrical current through a negatively charged nanochannel (Wiener and Stein, arXiv: 1807.09106). A model description of this phenomenon, based on the Maxwell-Stefan equation will help unravel the dominating physical mechanisms in so-called visco-migration.

THEORY

To understand the physical mechanisms underlying this phenomenon, we employed the Maxwell-Stefan equation to develop a 1D model and obtain a relation between the flux of solvents and the driving forces. Viscosity gradients are known to drive transport, but the development of an electrical current has not been theoretically described prior to this work.

FINDINGS

Our 1D model shows that the ionic current depends on the ideality of the solvent, though both ideal and non-ideal scenarios demonstrated good agreement with experimental data. We employed the model to understand the impact of solution bulk ionic strength and pH on the drift of ionic species with same reservoirs solution properties. Our modeling results unveiled the significant impact of bulk solution properties on the drift of ions which is in agreement with the experiments. Moreover, we have shown that the diffusion gradient along the nanochannel contributes significantly into driving ionic species if we even apply a small ionic concentration gradient to both reservoirs. Our modeling results may pave the way for finding novel applications for drift of ions in a diffusion gradient, which can be induced by connecting reservoirs of different viscosity fluids.

Non-isothermal flow of an electrolyte in a charged nanochannel

Electrokinetic flows are generally analyzed, assuming isothermal conditions even though such situations are hard to be achieved in practice. In this paper, the flow of a symmetric electrolyte in a charged nanochannel subjected to an axial temperature gradient is investigated using molecular dynamics simulations. We analyze the relative contribution of the Soret effect, the thermoelectric effect, and the double layer potential in the electrical double layer for various surface charges and temperature gradients. We find the flow driven by thermal gradient is analogous to electroosmotic flow. The thermophoretic motion of the electrolyte is significant for negative surface charge than the positive surface charge. The vibrational spectrum of graphene is calculated to delineate the effect of the surface charge polarity on the observed thermophoretic motion of the electrolyte. A unique structure of interfacial water layer is observed for the positive and negative surface charges. We attribute the presence of these structures to the differences in water-carbon interactions existing for various surface charge polarity. For an applied thermal gradient in the range 2.6 K nm-1 to 8 K nm-1, we observe a continuous net flow with average velocities reaching up to 9.4 m s-1 inside the channel for a negative surface charge of -0.101 C m-2. The results indicate that in a charged graphene-based nanochannel, temperature gradients can be employed to induce streaming current, depending on the relative influence of the Soret effect and the double layer potential.

Perspectives on Thermoelectric Energy Conversion in Ion-Exchange Membranes

By thermoelectric power generation we mean the creation of electrical power directly from a temperature gradient. Semiconductors have been mainly used for this purpose, but these imply the use of rare and expensive materials. We show in this review that ion-exchange membranes may be interesting alternatives for thermoelectric energy conversion, giving Seebeck coefficients around 1 mV/K. Laboratory cells with Ag|AgCl electrodes can be used to find the transported entropies of the ions in the membrane without making assumptions. Non-equilibrium thermodynamics can be used to compute the Seebeck coefficient of this and other cells, in particular the popular cell with calomel electrodes. We review experimental results in the literature on cells with ion-exchange membranes, document the relatively large Seebeck coefficient, and explain with the help of theory its variation with electrode materials and electrolyte concentration and composition. The impact of the membrane heterogeneity and water content on the transported entropies is documented, and it is concluded that this and other properties should be further investigated, to better understand how all transport properties can serve the purpose of thermoelectric energy conversion.

Can charged colloidal particles increase the thermoelectric energy conversion efficiency?

We show that charged colloidal particles can be used to increase the thermoelectric energy conversion of a thermocell.

Thermoelectricity in Confined Liquid Electrolytes

The electric field in an extended phase of a liquid electrolyte exposed to a temperature gradient is attributed to different thermophoretic mobilities of the ion species. As shown herein, such Soret-type ion thermodiffusion is not required to induce thermoelectricity even in the simplest electrolyte if it is confined between charged walls. The space charge of the electric double layer leads to selective ion diffusion driven by a temperature-dependent electrophoretic ion mobility, which-for narrow channels-may cause thermovoltages larger in magnitude than for the classical Soret equilibrium.