Transient-state methods to determine all the mass/charge transport properties of a material

Abstract

All the mass/charge transport properties of a material with, e.g., single-type ions (i) and electrons (e) as mobile charged components may be documented exhaustively and succinctly in terms of a coupling coefficient matrix L of the Onsagerian causality as

$\left(\begin{array}{c}{J}_i\\ J_e\end{array}\right)=\left(\begin{array}{ccc}{L}_{\mathrm{ii}}& L_{\mathrm{ie}}& L_{\mathrm{iT}}\\ L_{\mathrm{ei}}& L_{\mathrm{ee}}& L_{\mathrm{eT}}\end{array}\right)\left(\begin{array}{c}-\nabla {\eta }_i\\ -\nabla {\eta }_e\\ -\nabla T\end{array}\right)$,

where J_k and η_k stand for the flux and electrochemical potential, respectively, of the mobile charged-component k(=i,e), and T the absolute temperature. Due to the Onsager reciprocity and the L-matrix transformation rule,

$L_{\mathrm{ie}}=L_{\mathrm{ei}};\left(\begin{array}{c}{L}_{\mathrm{iT}}\\ L_{\mathrm{eT}}\end{array}\right)=\left(\begin{array}{cc}{L}_{\mathrm{ii}}& L_{\mathrm{ie}}\\ L_{\mathrm{ei}}& L_{\mathrm{ee}}\end{array}\right)\left(\begin{array}{c}{\overline{\stackrel{̄}{S}}}_i\\ {\overline{\stackrel{̄}{S}}}_e\end{array}\right)$,

where ${\overline{\stackrel{̄}{S}}}_k$is the transported entropy of k, the sum of its partial entropy, ${\bar{S}}_k$and entropy-of-transport, $S_k^{\ast }$ or${\overline{\stackrel{̄}{S}}}_k\equiv {\bar{S}}_k+S_k^{\ast };S_k^{\ast }\equiv \frac{q_k^{\ast }}{T}$

with $q_k^{\ast }$ being the reduced heat-of-transport of k(=i,e). In this paper, we will introduce the transient-state methods to determine, once and for all, all the mass/charge transport properties $L=\left(L_{\mathrm{ii}},L_{\mathrm{ie}},L_{\mathrm{ei}},L_{\mathrm{ee}},L_{\mathrm{iT}},L_{\mathrm{eT}}\right)$, together with their experimental implementations based on isothermal semi-blocking-induced and nonisothermal temperature-gradient induced chemical polarizations. Finally, we will present a few examples of complete documentation and demonstrate how to retrieve the mass/charge transport properties of interest.