Analysis of Transient Hydrogen Uptake by Metal Alloy Particles

This paper describes a new approach to solving the equations comprising the shrinking core model for diffusion and reaction of a chemical species in a solid spherical particle. The reactant adsorbs on the particle surface, diffuses into the particle\u27s interior, and reacts with the particle to form a solid product. The shrinking core model assumes a fast reaction rate compared to reactant diffusion so that the reaction is localized in the interfacial zone between the unreacted solid core and the surrounding shell of reacted product. Analytical solutions of the governing conservation equations usually invoke the pseudo-steady state (PSS) approximation which neglects the transient mass accumulation and diffusion-induced convection terms in the continuity equation for the diffusing reactant. However, small particle radii and slow reactant diffusion cast doubt on the validity of the PSS approximation. Dimensional analysis reveals an approximation that is less restrictive than PSS, yet enables a semi-analytical solution for the diffusing reactant distribution and interface velocity. For sufficiently large values of the surface mass fraction of the diffusing reactant, the PSS approximation leads to serious errors in the time dependence of the interface position and fractional conversion. However, our estimate of the surface mass fraction of hydrogen in LaNi5 particles suggests the validity of the PSS approximation for hydriding of metal alloy particles. The shrinking core model thus enables an estimate of hydrogen diffusivity in metal alloy particles

The Effect of Particle Size on the Discharge Performance of a Nickel-Metal Hydride Cell

We investigate the effect of particle size on the discharge performance of a nickel-metal hydride cell with a mathematical model. Electrodes with uniform as well as with nonuniform particle sizes are studied. With uniform particle size, the dependence of the particle-to-particle resistance on the particle size is taken into account. The optimal particle size depends on the discharge rate. Moreover, we show that under certain conditions it is advantageous to use a nonuniform particle size. In general, the higher the discharge current density, the more the particle size affects the electrode performance

Rheology of Aqueous Suspensions of Polystyrene Latex Stabilized by Grafted Poly(Ethylene Oxide)

A water-soluble carbodiimide has been used to end-graft aminated poly (ethylene oxide)(PEO) chemically onto colloidal polystyrene particles. Two particle sizes (115 and 347 nm diameter) and two PEO molecular weights (112 000 and 615 000 g mol–1) were combined to give suspensions with four different ratios of polymer layer thickness to particle radius. Electrophoresis demonstrated that the PEO was grafted, not just adsorbed. Dynamic light scattering showed that the adsorbed and grafted layers had similar structures and that non-ionic surfactant perturbed the PEO configurations. Steady shear and oscillatory rheometry indicated that long-ranged polymeric forces between particles governed the variation of viscosity and storage modulus with applied stress and PS volume fraction. Hard-sphere and effective hard-sphere scaling helps rationalize the rheological behaviour in terms of the variation of the polymeric force among the different suspensions and hydrodynamic deformation of the polymer layers

Measurement of Thin Liquid Film Drainage Using a Novel High-Speed Impedance Analyzer

This work describes the design and implementation of a new instrument, called the thin film impedance analyzer, which measures the rate of drainage of thin oil films. The instrument forms an oil film by elevating a planar oil–water interface into a water drop hanging from a stainless steel capillary tube immersed in the oil. The instrument measures the magnitude of the impedance of the matter between the capillary tube and a screen electrode immersed in the lower water phase. Under appropriate conditions, the capacitance of the oil film dominates the impedance. The instrument records the increase in the magnitude of the admittance associated with the draining and thinning of the oil film. The features of the drainage curves vary considerably with the type, amount, and location of surfactants in the oil and water phases, as well as with user-specified values of drop volume, drop equilibration time, and extent of drop compression. For this reason, the instrument has utility as a screening tool for selecting surfactants for emulsion formulations. Potential future uses include accelerated prediction of emulsion stability and extraction of oil–water interfacial rheological parameters

Measurement of thin liquid film drainage using a novel high-speed impedance analyzer

This work describes the design and implementation of a new instrument, called the thin film impedance analyzer, which measures the rate of drainage of thin oil films. The instrument forms an oil film by elevating a planar oil–water interface into a water drop hanging from a stainless steel capillary tube immersed in the oil. The instrument measures the magnitude of the impedance of the matter between the capillary tube and a screen electrode immersed in the lower water phase. Under appropriate conditions, the capacitance of the oil film dominates the impedance. The instrument records the increase in the magnitude of the admittance associated with the draining and thinning of the oil film. The features of the drainage curves vary considerably with the type, amount, and location of surfactants in the oil and water phases, as well as with user-specified values of drop volume, drop equilibration time, and extent of drop compression. For this reason, the instrument has utility as a screening tool for selecting surfactants for emulsion formulations. Potential future uses include accelerated prediction of emulsion stability and extraction of oil–water interfacial rheological parameters

Modeling the Effect of Plasticizer on the Viscoelastic Response of Crosslinked Polymers Using the Tube-Junction Model

Plasticizers modify the mechanical properties of polymericmaterials. The effects of plasticizers on glass transition temperatures can be most clearly observed in isochronal temperature sweep profiles of viscoelastic dynamic moduli. However, no simple mathematical models of plasticization are available to those who wish to design and employ plasticized materials in specific applications. We extend a phenomenological, molecular-level model (known as the tube–junction model) for crosslinked polymers to describe the effect of plasticizers on dynamic moduli. We show that the increase in free volume fraction due to the presence of the plasticizer can account for the shift in the glass transition in dynamic moduli. We also show that the secondary effects of plasticizers on the shape of the temperature sweep profiles can be explained in terms of increased width of the distribution of activation energies associated with intermolecular frictional forces

Molecular-Level Modeling of the Viscoelasticity of Crosslinked Polymers: Effect of Time and Temperature

We present a new molecular-level picture of chain dynamics for describing the viscoelasticity of crosslinked polymers. The associated mathematical model consists of a time-dependent momentum balance on a representative polymer segment in the crosslinked network, plus phenomenological expressions for forces acting on the segments. These include a cohesive force that accounts for intermolecular attraction, an entropic force describing the thermodynamics governing chain conformations, and a frictional force that captures the temperature dependence of relative chain motion. We treat the case of oscillatory uniaxial deformation. Solution of the model equations in the frequency domain yields the dynamic moduli as functions of temperature and frequency. The model reproduces all of the qualitative features of experimental dynamic modulus data across the complete spectrum of time and temperature, spanning the glassy zone, the β transition, the dynamicglass transition, and the rubbery zone. All of the model parameters can be evaluated through the use of independent experimental data. Comparison of model predictions with experimental data yields good quantitative agreement outside of the glass transition region

AC Impedance Studies on Metal Hydride Electrodes

The metal hydride (MHx) electrode is the negative electrode in one of the most advanced secondary batteries (i.e.,nickel/metal hydride). The objective of this study is to obtain insight on the mechanism of the hydriding/dehydridingreaction in the battery by using the electrochemical impedance spectroscopy (EIS) technique. An equivalent circuit for the MHx electrode reaction is proposed. The rate capability of charge and discharge of the MHx electrode is determined by thekinetics of the charge-transfer reaction at the alloy surface, which is mainly represented by the EIS responses in the lowfrequency region. Transient and pseudo-steady-state analyses (cyclic voltammetry and potential vs. current density behavior)qualitatively and quantitatively support the EIS results. EIS studies on electrodes with (i) three types of bindingadditives, (ii) varying amounts of active material, and (iii) two types of alloys as active materials demonstrate the usefulnessof this technique for developing electrodes with the optimum composition and structure

Solvent Diffusion Model for Aging of Lithium-Ion Battery Cells

This work presents a rigorous continuum mechanics model of solvent diffusion describing the growth of solid-electrolyte interfaces (SEIs) in Li-ion cells incorporating carbon anodes. The model assumes that a reactive solvent component diffuses through the SEI and undergoes two-electron reduction at the carbon-SEI interface. Solvent reduction produces an insoluble product, resulting in increasing SEI thickness. The model predicts that the SEI thickness increases linearly with the square root of time. Experimental data from the literature for capacity loss in two types of prototype Li-ion cells validates the solvent diffusion model. We use the model to estimate SEI thickness and extract solvent diffusivity values from the capacity loss data. Solvent diffusivity values have an Arrhenius temperature dependence consistent with solvent diffusion through a solid SEI. The magnitudes of the diffusivities and activation energies are comparable to literature values for hydrocarbon diffusion in carbon molecular sieves and zeolites. These findings, viewed in the context of recent SEI morphology studies, suggest that the SEI may be viewed as a single layer with both micro- and macroporosity that controls the ingress of electrolyte, anode passivation by the SEI, and cell performance during initial cycling as well as long-term operatio

Modeling the Effects of Electrode Composition and Pore Structure on the Performance of Electrochemical Capacitors

This work presents a mathematical model for charge/discharge of electrochemical capacitors that explicitly accounts for particle-packing effects in a composite electrochemical capacitor consisting of hydrous RuO2 nanoparticles dispersed within porous activated carbon. The model is also used to investigate the effect of nonuniform distributions of salt in the electrolyte phase of the electrode in the context of dilute solution theory. We use the model to compare the performance of capacitors with electrodes made from different activated carbons and to investigate the effects of varying carbon content and discharge current density. Even at low discharge current density, concentration polarization in the electrodes results in underutilization of the electrodes\u27 charge-storage capability, and thus decreased performance. Among various types of activated carbons, those with large micropore surface areas and low meso- and macropore surface areas are preferred because they give high double-layer capacitance and favor efficient packing of RuO2 nanoparticles, thus maximizing faradaic pseudocapacitance. Increasing the electrode carbon content decreases the delivered charge and energy density, but the reductions are not severe at moderate carbon content and high discharge current. This suggests the possibility of optimizing the carbon content to minimize cost while achieving acceptable discharge performance