In order to enhance the capacity of a charge storage device, nanostructures such as one-dimensional (1-D) carbon nanotubes (CNTs) have often been employed, much of the time with the effect of increasing the surface area exposed to electrolyte or enhancing the electrode inter-connections and reducing the electrical resistance.  Previous work also demonstrated the need for new physics based on lower dimensional density of states (DoS), as would occur in CNTs or graphene [1].  Here, for nanostructured battery electrodes, we propose a new current-voltage (I-V) model based on 2D and 1D DoS, and compare with related experiments. The model is broadly based on Marcus-Hush-Chidsey (MHC) kinetics and is aimed to extend the utility of the MHC formulations, to a larger class of materials and situations. We employ an integral expression for current, which involves the DoS, the Fermi-Dirac function, and the Arrhenius rate law as the basis.  Our model provides better agreement to measured chronopotentiometry data on Li-ion batteries with nanostructured organic polymer electrodes, compared to previous analysis.  An interesting feature of our model is the prediction in one-dimensional nanostructures of electrical current oscillations in the I-V curve, corresponding to the gradual population (and de-population) of each successive sub-band, provided that the sub-band widths are comparable to the reorganization energy. We posit that the consideration of a variable/non-constant DOS in MHC electrokinetics may yield tests of dimensional character and concomitant contribution to electrochemical systems.

[1] H. Yamada and P. R. Bandaru, Appl. Phys. Lett. 102, 173113 (2013), ibid 104, 213901 (2014).