Retraction Note: Theoretical Limits of Energy Density in Silicon-Carbon Composite Anode Based Lithium Ion Batteries.

This article has been retracted.

Theoretical Limits of Energy Density in Silicon-Carbon Composite Anode Based Lithium Ion Batteries.

Silicon (Si) is under consideration as a potential next-generation anode material for the lithium ion battery (LIB). Experimental reports of up to 40% increase in energy density of Si anode based LIBs (Si-LIBs) have been reported in literature. However, this increase in energy density is achieved when the Si-LIB is allowed to swell (volumetrically expand) more than graphite based LIB (graphite-LIB) and beyond practical limits. The volume expansion of LIB electrodes should be negligible for applications such as automotive or mobile devices. We determine the theoretical bounds of Si composition in a Si-carbon composite (SCC) based anode to maximize the volumetric energy density of a LIB by constraining the external dimensions of the anode during charging. The porosity of the SCC anode is adjusted to accommodate the volume expansion during lithiation. The calculated threshold value of Si was then used to determine the possible volumetric energy densities of LIBs with SCC anode (SCC-LIBs) and the potential improvement over graphite-LIBs. The level of improvement in volumetric and gravimetric energy density of SCC-LIBs with constrained volume is predicted to be less than 10% to ensure the battery has similar power characteristics of graphite-LIBs.

Real-time optical diagnostics of graphene growth induced by pulsed chemical vapor deposition.

The kinetics and mechanisms of graphene growth on Ni films at 720-880 °C have been measured using fast pulses of acetylene and real-time optical diagnostics. In situ UV-Raman spectroscopy was used to unambiguously detect isothermal graphene growth at high temperatures, measure the growth kinetics with ∼1 s temporal resolution, and estimate the fractional precipitation upon cooldown. Optical reflectivity and videography provided much faster temporal resolution. Both the growth kinetics and the fractional isothermal precipitation were found to be governed by the C2H2 partial pressure in the CVD pulse for a given film thickness and temperature, with up to ∼94% of graphene growth occurring isothermally within 1 second at 800 °C at high partial pressures. At lower partial pressures, isothermal graphene growth is shown to continue 10 seconds after the gas pulse. These flux-dependent growth kinetics are described in the context of a dissolution/precipitation model, where carbon rapidly dissolves into the Ni film and later precipitates driven by gradients in the chemical potential. The combination of pulsed-CVD and real-time optical diagnostics opens new opportunities to understand and control the fast, sub-second growth of graphene on various substrates at high temperatures.

Incremental growth of short SWNT arrays by pulsed chemical vapor deposition.

Very short arrays of continuous single-wall carbon nanotubes (SWNTs) are grown incrementally in steps as small as 25 nm using pulsed chemical vapor deposition (CVD). In-situ optical extinction measurements indicate that over 98% of the nanotubes reinitiate growth on successive gas pulses, and high-resolution transmission electron microscopy (HR-TEM) images show that the SWNTs do not exhibit segments, caps, or noticeable sidewall defects resulting from repeatedly stopping and restarting growth. Time-resolved laser reflectivity (3-ms temporal resolution) is used to record the nucleation and growth kinetics for each fast (0.2 s) gas pulse and to measure the height increase of the array in situ, providing a method to incrementally grow short nanotube arrays to precise heights. Derivatives of the optical reflectivity signal reveal distinct temporal signatures for both nucleation and growth kinetics, with their amplitude ratio on the first gas pulse serving as a good predictor for the evolution of the growth of the nanotube ensemble into a coordinated array. Incremental growth by pulsed CVD is interpreted in the context of autocatalytic kinetic models as a special processing window in which a sufficiently high flux of feedstock gas drives the nucleation and rapid growth phases of a catalyst nanoparticle ensemble to occur within the temporal period of the gas pulse, but without inducing growth termination.

Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity.

We introduce a model of cavitation based on the multiphase Lattice Boltzmann method (LBM) that allows for coupling between the hydrodynamics of a collapsing cavity and supported solute chemical species. We demonstrate that this model can also be coupled to deterministic or stochastic chemical reactions. In a two-species model of chemical reactions (with a major and a minor species), the major difference observed between the deterministic and stochastic reactions takes the form of random fluctuations in concentration of the minor species. We demonstrate that advection associated with the hydrodynamics of a collapsing cavity leads to highly inhomogeneous concentration of solutes. In turn these inhomogeneities in concentration may lead to significant increase in concentration-dependent reaction rates and can result in a local enhancement in the production of minor species.

Dynamic compound wavelet matrix method for multiphysics and multiscale problems.

The paper presents the dynamic compound wavelet method (dCWM) for modeling the time evolution of multiscale and/or multiphysics systems via an "active" coupling of different simulation methods applied at their characteristic spatial and temporal scales. Key to this "predictive" approach is the dynamic updating of information from the different methods in order to adaptively and accurately capture the temporal behavior of the modeled system with higher efficiency than the (nondynamic) "corrective" compound wavelet matrix method (CWM), upon which the proposed method is based. The system is simulated by a sequence of temporal increments where the CWM solution on each increment is used as the initial conditions for the next. The numerous advantages of the dCWM method such as increased accuracy and computational efficiency in addition to a less-constrained and a significantly better exploration of phase space are demonstrated through an application to a multiscale and multiphysics reaction-diffusion process in a one-dimensional system modeled using stochastic and deterministic methods addressing microscopic and macroscopic scales, respectively.

Bifurcation analysis of bubble dynamics in fluidized beds.

We use a low-dimensional, agent-based bubble model to study the changes in the global dynamics of fluidized beds in response to changes in the frequency of the rising bubbles. The computationally based bifurcation analysis shows that at low frequencies, the global dynamics is attracted towards a fixed point since the bubbles interact very little with one another. As the frequency of injection increases, however, the global dynamics undergoes a series of bifurcations to new behaviors that include highly periodic orbits, chaotic attractors, and intermittent behavior between periodic orbits and chaotic sets. Using methods from time-series analysis, we are able to approximate nonlinear models that allow for long-term predictions and the possibility of developing control algorithms.

Dynamic interacting bubble simulation (DIBS): an agent-based bubble model for reacting fluidized beds.

In this paper we explore the global dynamics of an agent-type model for bubbles in gas-fluidized beds and demonstrate that these features are consistent with experimentally observed behavior. The model accounts for the simultaneous interactions of thousands of individual bubbles and includes mass-transfer and first-order reactions between the gas and solids so that the impact of the dynamics is reflected in reactant conversion. We start with model parameters that have been demonstrated to produce time average behavior consistent with experimental reactor measurements. By observing the temporal variations of spatially averaged bubble properties, we are able to clearly distinguish the onset of global low-dimensional features that appear to be consistent with previous observations. The most prominent of these features is a large-scale oscillation that exhibits intermittency with power-law scaling in the vicinity of a critical gas flow. We show that the oscillation occurs as the result of a globally synchronized horizontal movement of the bubbles toward the center of the reactor. The oscillation appears to be consistent with the occurrence of the so-called "slugging" phenomenon, which is known to have large effects on fluidized bed reactor performance. Although this model can clearly be further improved, its success in replicating several of the key features of slugging indicates that this approach can serve as a useful tool for understanding and possibly controlling fluidized bed dynamics. We also conjecture that this model may be useful for more generally understanding the occurrence of global features in high-dimensional, multi-agent systems.