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With the development of ferroelectric memories, it is becoming increasingly important to understand the ferroelectric switching behaviors at small applied electric fields. In this letter, we use a discretized phase-field model to systematically investigate the intrinsic threshold electric field (TEF) to drive flat 180$^\circ$ and 90$^\circ$ domain walls (DWs), and show that the results are qualitatively consistent with existing first-principle studies and experiments at cryogenic temperature. In addition, this work suggests that the activation electric field (AEF) observed in experiments at room temperature can be interpreted as the average of TEF behaviors of DWs with different curvatures, rather than explained by the traditional thermal nucleation theory. This work improves the understanding of DW motion kinetics at small applied fields, and shows that the mesh size and orientation are both important for the phase-field modeling of the above process.

Ion concentration polarization (CP, current-induced concentration gradient adjacent to a charge-selective interface) has been well studied for single-phase mixed conductors (e.g., liquid electrolyte), but multiphase CP has been rarely addressed in literature. In our recent publication, we proposed that CP above certain threshold currents can flip the phase distribution in multiphase ion-intercalation nanofilms sandwiched by ion-blocking electrodes. We call this phenomenon as multiphase polarization (MP). We then proposed that MP can further lead to nonvolatile interfacial resistive switching (RS) for asymmetric electrodes with ion-modulated electron transfer, which theory can reproduce the experimental results of LTO memristors. In this work, we derive a comprehensive 2D phase-field model for coupled ion-electron transport in ion-intercalation materials, with surface effects including electron transfer kinetics, non-neutral wetting, energy relaxation, and surface charge. Then we use the model to study MP. We present time evolution of phase boundaries, and analyze the switching time, current, energy, and cyclic voltammetry, for various boundary conditions. We find that the switching performance can be improved significantly by manipulating surface conditions and mean concentration. Finally, we discuss the prospects of MP-based memories and possible extensions of the current model.

Nonvolatile resistive-switching (RS) memories promise to revolutionize hardware architectures with in-memory computing. Recently, ion-interclation materials have attracted increasing attention as potential RS materials for their ion-modulated electronic conductivity. In this Letter, we propose RS by multiphase polarization (MP) of ion-intercalated thin films between ion-blocking electrodes, in which interfacial phase separation triggered by an applied voltage switches the electron-transfer resistance. We develop an electrochemical phase-field model for simulations of coupled ion-electron transport and ion-modulated electron-transfer rates and use it to analyze the MP switching current and time, resistance ratio, and current-voltage response. The model is able to reproduce the complex cyclic voltammograms of lithium titanate (LTO) memristors, which cannot be explained by existing models based on bulk dielectric breakdown. The theory predicts the achievable switching speeds for multiphase ion-intercalation materials and could be used to guide the design of high-performance MP-based RS memories.

Shock electrodialysis (shock ED), an emerging electrokinetic process for water purification, leverages the new physics of deionization shock waves in porous media. In previous work, a simple leaky membrane model with surface conduction can explain the propagation of deionization shocks in a shock ED system, but it cannot quantitatively predict the deionization and conductance (which determines the energy consumption), and it cannot explain the selective removal of ions in experiments. This two-part series of work establishes a more comprehensive model for shock ED, which applies to multicomponent electrolytes and any electrical double layer thickness, captures the phenomena of electroosmosis, diffusioosmosis, and water dissociation, and incorporates more realistic boundary conditions. In this paper, we will present the model details and show that hydronium transport and electroosmotic vortices (at the inlet and outlet) play important roles in determining the deionization and conductance in shock ED. We also find that the results are quantitatively consistent with experimental data in the literature. Finally, the model is used to investigate design strategies for scale up and optimization.

Shock electrodialysis is a recently developed electrochemical water treatment method which shows promise for water deionization and ionic separations. Although simple models and scaling laws have been proposed, a predictive theory has not yet emerged to fit experimental data and enable system design. Here, we extend and analyze existing "leaky membrane" models for the canonical case of a steady shock in cross flow, as in recent experimental prototypes. Two-dimensional numerical solutions are compared with analytical boundary-layer approximations and experimental data. The boundary-layer theory accurately reproduces the simulation results for desalination, and both models predict the data collapse of the desalination factor with dimensionless current, scaled to the incoming convective flux of cations. The numerical simulation also predicts the water recovery increase with current. Nevertheless, both approaches cannot quantitatively fit the transition from normal to over-limiting current, which suggests gaps in our understanding of extreme electrokinetic phenomena in porous media.

In this paper, we deal with limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2 by studying expansions of the first order Melnikov functions near the loop and coefficients in these expansions. More precisely, we prove that the perturbed system can have 11, 13, 14 or 16 limit cycles in a neighborhood of the loop under certain conditions. Finally, we give an example to illustrate the effectiveness of our main results., Comment: 49 pages, 3 figures