Two-Dimensional Modeling of Columnar TiO2 Nanostructured Electrodes

Titanium dioxide (TiO₂) has recently emerged as a potential anode material for lithium ion batteries due to its low cost, abundance, and high chemical stability. There has been considerable interest in nanostructured thin films for this application since they offer higher surface area and thus better performance compared to bulk films. The performance of the anodes has previously been correlated to the morphology of these nanostructures¹. Single crystalline columnar structures were shown to exhibit enhanced specific rate capacity compared to the polycrystalline granular structures for the same structure height due to sluggish diffusion kinetics in the presence of grain boundaries. Further, the performance of the columnar and granular nanostructures depended on the height of the structures.

It has been reported that nanostructured TiO₂ exhibits a higher capacity to store lithium due to inherent structural distortions at the nanoscale²; however, very little work has been done to mathematically correlate the nanostructure morphology to the capacitive performance of this material. Previous modeling studies of lithiation in silicon electrode nanowires have utilized atomistic and diffusion impedance models to understand Li dynamics in structures of various geometries^3,4. The primary focus of most studies has been on intercalation-induced stress development and its effects on overall electrode performance, which can require finite element analysis software such as COMSOL^5,6. Stress generation is an important concern in silicon due to high volumetric expansion (350%), but for TiO₂, stress is a minor concern since the volume expansion upon lithiation in anatase TiO₂ is only 4%.

In this work, we will use a continuum-based approach^7-9 to predict capacity of a TiO₂ electrode for certain charging rates. To accomplish this, mathematical simulations of columnar titanium TiO₂ nanostructured electrodes will be performed. The mesoscale 2D cylindrical model will be based on Butler-Volmer kinetics at the solid-electrolyte interface, which couples lithium transport in the electrolyte with insertion into the solid porous nanostructure¹⁰. The present study will attempt to simulate the effects of both columnar aspect ratio and Li diffusion in granular structures on electrode capacity at different charging rates by using experimentally derived parameters. For example, the number of grains (i.e., grain boundaries) in synthesized columnar structures will be correlated to an effective diffusivity to be used in the model, and results will be compared to existing experimental charging data. Height and aspect ratio will then be varied to determine if there exists an optimum size for these nanostructures.

Acknowledgements

This paper is based upon work supported in part under the U.S.-India Partnership to Advance Clean Energy-Research (PACE-R) for the Solar Energy Research Institute for India and the United States (SERIIUS), funded jointly by the U.S. Department of Energy (Office of Science, Office of Basic Energy Sciences, and Energy Efficiency and Renewable Energy, Solar Energy Technology Program, under Subcontract DE-AC36-08GO28308 to the National Renewable Energy Laboratory, Golden, Colorado) and the Government of India, through the Department of Science and Technology under Subcontract IUSSTF/JCERDC-SERIIUS/2012 dated 22nd Nov. 2012.

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