ABSTRACT
We establish the kinetics of ballistic-to-diffusive (BD) transition observed in two-dimensional random walk using directional statistics. Directional correlation is parameterized using the walker's turning angle distribution, which follows the commonly adopted wrapped Cauchy distribution (WCD) function. During the BD transition, the concentration factor (ρ) governing the WCD shape is observed to decrease from its initial value. We next analytically derive the relationship between effective ρ and time, which essentially quantifies the BD transition rate. The prediction of our kinetic expression agrees well with the empirical datasets obtained from correlated random walk simulation. We further connect our formulation with the conventionally used scaling relationship between the walker's mean-square displacement and time.
ABSTRACT
It has been demonstrated that atomic layer deposition (ALD) provides an initially safeguarding, uniform ultrathin film of controllable thickness for lithium-ion battery electrodes. In this work, CeO2 thin films were deposited to modify the surface of lithium-rich Li1.2Mn0.54Ni0.13Co0.13O2 (LRNMC) particles via ALD. The film thicknesses were measured by transmission electron microscopy. For electrochemical performance, â¼2.5 nm CeO2 film, deposited by 50 ALD cycles (50Ce), was found to have the optimal thickness. At a 1 C rate and 55 °C in a voltage range of 2.0-4.8 V, an initial capacity of 199 mAh/g was achieved, which was 8% higher than that of the uncoated (UC) LRNMC particles. Also, 60.2% of the initial capacity was retained after 400 cycles of charge-discharge, compared to 22% capacity retention of UC after only 180 cycles of charge-discharge. A robust kinetic of electrochemical reaction was found on the CeO2-coated samples at 55 °C through electrochemical impedance spectroscopy. The conductivity of 50Ce was observed to be around 3 times higher than that of UC at 60-140 °C. The function of the CeO2 thin-film coating was interpreted as being to increase substrate conductivity and to block the dissolution of metal ions during the charge-discharge process.
