On the Lark-Horovitz equation for ion selective membrane electrodes and its derivation

The principles of non-equilibrium thermodynamics are used to allow for entropy production due to the current transfer across regions of varying composition in electrochemical cells containing a membrane between electrolyte solutions and, optionally, a liquid junction. By this approach, a general equation is derived for the response of a cell as a whole, rather than for separate contributions to it. The equation is applied to cells with solid-electrolyte membranes of different types, as exemplified by alkali aluminosilicate glasses responsive to alkali metal cations, the pre-conditioned silicate glasses responsive to hydrogen ions, and lanthanum trifluoride responding to fluoride ions. Among the more significant results of the applications is a generalized form of the Lark-Horovitz equation for two ionic charge carriers in a sublattice of opposite charge sign. However, its derivation is circumscribed by the conditions of a uniform charge density of the sublattice and equal charge numbers and coordination numbers of the carriers. The degree to which these conditions are met by specific membranes is discussed from the structural chemistry point of view. As a special feature of hydrogen ion-responsive silicate glasses accounting for the extremely fast response, the concept of a pH-sensitive silica network is introduced on the basis of the previously found interrelationships between the bond lengths Si–OH, Si–OSi, and Si–NBO in hydrous alkali silicates, where NBO means a non-bridging oxygen coordinated by hydrogen bonds and/or alkali cations.