INVESTIGATION OF MAGNESIUM ION CHARGE STORAGE MECHANISM IN MANGANESE DIOXIDE

Magnesium (Mg) battery is considered as a promising candidate for the next generation battery technology that could potentially replace the current lithium (Li)-ion batteries due to the following factors. Magnesium possesses a higher volumetric capacity than commercialized Li-ion battery anode materials. Additionally, the low cost and high abundance of Mg compared to Li makes Mg batteries even more attractive. Moreover, unlike metallic Li anodes which have a tendency to develop a dendritic structure on the surface upon the cycling of the battery, Mg metal is known to be free from such a hazardous phenomenon. Due to these merits of Mg as an anode, the topic of rechargea¬ble Mg batteries has attracted considerable attention among researchers in the last few decades. However, the aforementioned advantages of Mg batteries have not been fully utilized due to the serious kinetic limitation of Mg2+ diffusion process in many hosting compounds which is believed to be due to a strong electrostatic interaction between divalent Mg2+ ions and hosting matrix. This serious kinetic hindrance is directly related to the lack of cathode materials for Mg battery that provide comparable electrochemical performances to that of Li-based system. Manganese oxide (MnO2) is one of the most well studied electrode materials due to its excellent electrochemical properties, including high Li+ ion capacity and relatively high operating voltage (i.e., ~ 4 V vs. Li/Li+ for LiMn2O4 and ~ 3.2 V vs. Mg/Mg2+). However, unlike the good electrochemical properties of MnO2 realized in Li-based systems, rather poor electrochemical performances have been reported in Mg based systems, particularly with low capacity and poor cycling performances. While the origin of the observed poor performances is believed to be due to the aforementioned strong ionic interaction between the Mg2+ ions and MnO2 lattice resulting in a limited diffusion of Mg2+ ions in MnO2, very little has been explored regarding the charge storage mechanism of MnO2 with divalent Mg2+ ions. This dissertation investigates the charge storage mechanism of MnO2, focusing on the insertion behaviors of divalent Mg2+ ions and exploring the origins of the limited Mg2+ insertion behavior in MnO2. It is found that the limited Mg2+ capacity in MnO2 can be significantly improved by introducing water molecules in the Mg electrolyte system, where the water molecules effectively mitigated the kinetic hindrance of Mg2+ insertion process. The combination of nanostructured MnO2 electrode and water effect provides a synergic effect demonstrating further enhanced Mg2+ insertion capability. Furthermore, it is demonstrated in this study that pre-cycling MnO2 electrodes in water-containing electrolyte activates MnO2 electrode, after which improved Mg2+ capacity is maintained in dry Mg electrolyte. Based on a series of XPS analysis, a conversion mechanism is proposed where magnesiated MnO2 undergoes a conversion reaction to Mg(OH)2 and MnOx and Mn(OH)y species in the presence of water molecules. This conversion process is believed to be the driving force that generates the improved Mg2+ capacity in MnO2 along with the water molecule’s charge screening effect. Finally, it is discussed that upon a consecutive cycling of MnO2 in the water-containing Mg electrolyte, structural water is generated within the MnO2 lattice, which is thought to be the origin of the observed activation phenomenon. The results provided in this dissertation highlight that the divalency of Mg2+ ions result in very different electrochemical behaviors than those of the well-studied monovalent Li+ ions towards MnO2.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.