## To further investigate the electrode kinetics the apparent

For short tubes the thermodynamic limit does not apply; they ADX 10059 can be charged only in multiples of the unit charge, and correspondingly the electrochemical potential increases in steps during charging. Thus these tubes behave like quantum dots.

Our model can be extended in various ways; the most obvious extension would consider two kinds of ions with opposite charges. Another possibility would be to include a solvent, which would require more extensive DFT calculations.

AcknowledgementI thank Dr. Elizabeth Santos, Ulm University, for useful comments. I also thank the referees of the first version for asking so many questions, especially about the entropy.

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Keywords

Lithium ion batteries; Cathode materials; Rhombohedral structure; Li3−xNaxV2(PO4)3

1. Introduction

As well-known, electric devices can run well under a stable power supply from lithium-ion batteries, which indicates that the electrode material should provide a single and stable working potential plateau during charge/discharge cycles. However, monoclinic Li3V2(PO4)3 exhibits three charge/discharge potential plateaus with two lithium ions insertion/extraction in the potential range from 3.0 to 4.3 V. In contrast, rhombohedral Li3V2(PO4)3 exhibits only one potential plateau in the same potential range [14]. Therefore, rhombohedral Li3V2(PO4)3 shows the superiority as cathode material.