Ying Zhao

Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles

This work is supported by the “Excellence Initiative” of the German Federal and State Governments and the Graduate School of Computational Engineering at the Technische Universitat Darmstadt. The author Xu would particularly like to thank the Adolf Messer Foundation for awarding her the Adolf Messer Prize and for the financial support.

Variational boundary conditions based on the Nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled Cahn–Hilliard equation

The primal variational formulation of the fourth-order Cahn–Hilliard equation requires C1-continuous finite element discretizations, e.g., in the context of isogeometric analysis. In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn–Hilliard equation in primal variables. Our formulation is based on the symmetric variant of Nitsches method, does not introduce additional degrees of freedom and is shown to be variationally consistent. In contrast to strong enforcement, the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree. In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions. Unfitted Cartesian B-spline meshes constitute an effective alternative to boundary-fitted isogeometric parametrizations for constructing C1-continuous discretizations, in particular for complex geometries. We combine our variational boundary condition formulation with unfitted Cartesian B-spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode. This example, involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces, demonstrates the flexibility of variational boundary conditions in the context of higher-order unfitted isogeometric discretizations.

Lithiation across interconnected V2O5 nanoparticle networks

Electrochemical reactions within Li-ion batteries occur far from equilibrium and are accompanied by considerable heterogeneity. Many electrode materials undergo phase transformations upon insertion of cations. The sequence and propagation of these phase transformations determine energy dissipation and the proportion of actively intercalating materials, which play a vital role in influencing characteristics such as cyclability, degradation, and hysteresis. The heterogeneity within electrode materials stems in large measure from local variations of structure, surface states, and position within the electrode; these factors are poorly understood given limited studies of local structure. Here, we show based on scanning transmission X-ray microscopy studies of Li-ion intercalation within interconnected V2O5 particle networks that interconnects between cathode particles strongly influence the transport of Li-ions and the resulting spatial propagation of phase transformations across the network. Considerable phase heterogeneity is observed across interfaces that are rationalized based on phase field models that suggest that the propagation of Li-rich domains occurs preferentially across a single particle instead of concurrent lithiation and nucleation of Li-rich domains across the entire network. Further phase heterogeneity arises from defects and secondary growth of Li-rich phases at nanowire tips. These findings suggest that mesoscale architectures can potentially be designed with appropriately positioned interconnects to maximize the proportion of actively intercalating regions and to ensure equilibration of local current densities.

Modeling of phase separation across interconnected electrode particles in lithium-ion batteries

Lithium transport and phase separation in and across interconnected electrode particles are investigated in this paper. This paper signifies the influential role of particle size variation on battery performance with phase-separating electrodes. In this work, a model is developed which accounts for lithium transport in the particles, phase separation, and interface reactions across the particle network. The implementation in 3D is carried out using the B-spline based finite cell method for a straightforward treatment of the Cahn–Hilliard equation and a flexible representation of particle geometry. Representative examples based on scanning transmission X-ray microscopy (STXM) images are simulated to discuss the factors that will influence phase separation during non-equilibrium lithiation and delithiation, as well as relaxation towards equilibrium. The simulations reveal that particles with a slight advance during (de-)lithiation at the beginning will strengthen their advance at the expense of neighboring particles, in a “winner-takes-all” fashion. Moreover, rapid reaction can suppress phase separation, both inside a single particle and across the particle network. Lastly, both particle size and size variation in electrodes composed of phase-separating materials ought to be small to avoid intra- and inter-particle phase separation. This study can serve as a guide for the design of battery electrodes composed of phase-separating materials.