Giant Thermoelectric Response of Confined Electrolytes with Thermally Activated Charge Carrier Generation

The thermoelectric response of thermally activated electrolytes (TAEs) in a slit channel is studied theoretically and by numerical simulations. The term TAE refers to electrolytes whose charge carrier concentration is a function of temperature, as recently suggested for ionic liquids and highly concentrated aqueous electrolyte solutions. Two competing mechanisms driving charge transport by temperature gradients are identified. For suitable values of the activation energy that governs the generation of charge carriers, a giant thermoelectric response is found, which could help explain recent experimental results for nanoporous media infiltrated with TAEs.

Figure 1

(a) Schematic of a narrow-confined space of half-width $h$, bounded by two parallel plates and connecting two reservoirs maintained at temperatures $T_0$ and $T_e(=T_0+\mathrm{\Delta }T)$, with subscripts 0 and $e$ denoting the properties at the left (cold) and the right (hot) reservoir, respectively. Debye layers with a characteristic temperature-dependent thickness of ${\kappa }^{-1}$ form at the channel walls. (b) An axial gradient in the cross-section averaged counterion concentration develops through the superposition of two competing effects. First, there is the temperature dependence of the wall-normal diffusion and electromigration fluxes. The temperature dependence already exists at constant effective charge carrier concentration (green dashed line). This effect, however, is overridden when in addition the temperature-dependent effective charge carrier concentration (yellow solid line) is considered. The $x$ axis extends over the entire length of the channel.

Figure 2

(a) Seebeck coefficient (in units of $k_B/e$) as a function of the nondimensional Debye parameter $({\kappa }_{0}h)$ for a TAE $(-S)$ and a DE $(S_{\mathrm{DE}})$. Results based on the DH approximation (lines) are compared with results from the full numerical simulation of the coupled PNP equations (symbols). The solid lines (and the corresponding symbols) correspond to $\zeta =5\mathrm{mV}$, the dotted lines (and the corresponding symbols) represent $\zeta =50\mathrm{mV}$. (b) Dependence of the Seebeck coefficient on the wall boundary conditions. A constant surface charge density $q$ (symbols) or $\zeta$ potential (lines) is imposed at the bounding walls. Green circles, $q=-0.27\times {10}^{-4}\mathrm{C}/{\mathrm{m}}^2$; blue stars, $q=-2.5\times {10}^{-4}\mathrm{C}/{\mathrm{m}}^2$; green solid line, $\zeta =10\mathrm{mV}$; blue dashed line, $\zeta =70\mathrm{mV}$. The activation energy considered here corresponds to $[{\mathrm{C}}_2\mathrm{mim}][{\mathrm{NTf}}_2]$ [10].

Figure 3

Dependence of the Seebeck coefficient on the activation energy and $\zeta$ potential at ${\kappa }_{0}h=0.1$. Results based on the numerical evaluation of Eq. (S28) [15] (symbols) are compared with the DH approximation (solid lines).