Transference function for electro-insertion reactions in blue energy devices and acid-base machines

We propose a model in the frequency domain to determine kinetic and thermodynamic parameters directed to ion electro-insertion in host matrices, aiming to couple reaction mechanisms and mass transport in transference functions. We use Maclaurin series to expand the electrical current as a function of the potential and the ion concentration gradient within the host matrix, to obtain an analytical solution in the frequency domain. The parameters associated with non-faradaic processes can also be inserted in the transference function. The model can aid better comprehension of energy harvesting from blue energy devices and acid-base machines: dissipated energy, maximum work, practical work, potential rise, and efficiency can be estimated for different combinations of ionic concentration in solution. We investigate sodium ion electro-insertion in a copper Prussian blue analogue as an example of application of the model. The method presented here may contribute to the proposition of host matrices with suitable properties. In turn, the proposed host matrices will help to improve how these devices and machines perform, thereby ensuring that energy harvesting is efficient, and that environmental preservation is stimulated.