We present an electrochemical model of a lithium iron phosphate/graphite (LFP/C 6 ) cell that includes combined aging mechanisms: (i) Electrochemical formation of the solid electrolyte interphase (SEI) at the anode, leading to loss of lithium inventory, (ii) breaking of the SEI due to volume changes of the graphite particles, causing accelerated SEI growth, and (iii) loss of active material due to of loss percolation of the liquid electrolyte resulting from electrode dry-out. The latter requires the introduction of an activity-saturation relationship. A time-upscaling methodology is developed that allows to simulate large time spans (thousands of operating hours). The combined modeling and simulation framework is able to predict calendaric and cyclic aging up to the end of life of the battery cells. The aging parameters are adjusted to match literature calendaric and cyclic aging experiments, resulting in quantitative agreement of simulated nonlinear capacity loss with experimental data. The model predicts and provides an interpretation for the dependence of capacity loss on temperature, cycling depth, and average SOC. The introduction of a percolation threshold in the activity-saturation relationship allows to capture the strong nonlinearity of aging toward end of life ("sudden death").

Lithium-ion batteries show a complex thermo-electrochemical performance and aging behavior. This paper presents a modeling and simulation framework that is able to describe both multi-scale heat and mass transport and complex electrochemical reaction mechanisms. The transport model is based on a 1D + 1D + 1D (pseudo-3D or P3D) multi-scale approach for intra-particle lithium diffusion, electrode-pair mass and charge transport, and cell-level heat transport, coupled via boundary conditions and homogenization approaches. The electrochemistry model is based on the use of the open-source chemical kinetics code CAN-TERA, allowing flexible multi-phase electrochemistry to describe both main and side reactions such as SEI formation. A model of gas-phase pressure buildup inside the cell upon aging is added. We parameterize the model to reflect the performance and aging behavior of a lithium iron phosphate (LiFePO 4 , LFP)/graphite (LiC 6 ) 26650 battery cell. Performance (0.1-10 C discharge/charge at 25, 40 and 60 • C) and calendaric aging experimental data (500 days at 30 • C and 45 • C and different SOC) from literature can be successfully reproduced. The predicted internal cell states (concentrations, potential, temperature, pressure, internal resistances) are shown and discussed. The model is able to capture the nonlinear feedback between performance, aging, and temperature. Mathematical modeling and numerical simulation have become standard techniques in lithium-ion battery research and developmentfrom the atomistic scale up to the system scale. [1][2][3][4][5] Historically, most lithium-ion cell models are based on the work of John Newman and coworkers who developed a one-dimensional model of electrochemistry and mass and charge transport in porous electrodes on the ∼100 μm scale, 6 which was later extended by transport in the active materials particles on the ∼1 μm scale, giving rise to 1D + 1D or "pseudo-2D" (P2D) models. 7,8 This type of model is widely used today. Extensions include solid electrolyte interphase (SEI) formation, 9 aging mechanisms, 10,11 impedance simulations, 12 and multi-phase chemistry in lithium-air 13,14 and lithium-sulfur 15 cells. Temperature has a strong influence on the performance and lifetime of a lithium-ion battery. A straightforward approach has been to include heat sources and heat conductivity to the standard P2D type models. [16][17][18] However, temperature gradients typically occur on a higher scale, that is, the mm and cm scale of a single cell, as compared to electrode scale described by typical P2D models. Therefore, model extensions to the cell scale are necessary. Consequently, scale-coupling methods have been developed that describe both, electrochemistry on the electrode-pair scale, and heat transport on the cell scale more efficiently. Scale coupling usually uses independent computational domains on the various scales coupled through adequate boundary conditions. As a result, models with various dimensionalities have been presented, for example, 3D + 1D + 1D (cell scale...

No abstract

The role of attentional focusing in motor tasks has been highlighted frequently. The "internal-external" dimension has emerged, but also the spatial distance between body and attended location. In two experiments, an extended attentional focus paradigm was introduced to investigate distality effects of attentional foci on balance performance. First, the distality of the coordinates of the point of focus was varied between a proximal and distal position on an artificial tool attached to the body. Second, the distance of the displayed effect on the wall was varied between a 2.5 and 5 m condition. Subjects were instructed to focus on controlling either a proximal or distal spot on a tool attached to their head, represented by two laser pointers. Subsequently, they needed to visually track their own body-movement effect of one of the laser pointers at a wall while completing various single leg stance tasks. Center of pressure (COP) sway was analyzed using a linear method (classic sway variables) as well as a nonlinear method (multiscale entropy). In addition, laser trajectories were videotaped and served as additional performance outcome measure. Experiment 1 revealed differences in balance performance under proximal compared to distal attentional focus conditions. Moreover, experiment 2 yielded differences in balance-related sway measures and laser data between the 2.5 and 5 m condition of the visually observable movement effect. In conclusion, varying the distality of the point of focus between proximal and distal impacted balance performance. However, this effect was not consistent across all balance tasks. Relevantly, the distality of the movement effect shows a significant effect on balance plus laser performance with advantages in more distal conditions. This research emphasizes the importance of the spatial distality of movement effects for human behavior.