521 research outputs found
Intercalation dynamics in lithium-ion batteries
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 153-160).A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeable-battery electrode materials. It is based on the Cahn-Hilliard equation coupled to reaction rate laws as boundary conditions to handle the transfer of ions between the crystal and the electrolyte. In this thesis, I carefully derive a second set of boundary conditions--necessary to close the original PDE system--via a variational analysis of the free energy functional; I include a thermodynamically-consistent treatment of the reaction rates; I develop a semi-discrete finite volume method for numerical simulations; and I include a careful asymptotic treatment of the dynamical regimes found in different limits of the governing equations. Further, I will present several new findings relevant to batteries: Defect Interactions: When applied to strongly phase-separating, highly anisotropic materials such as LiFePO4, this model predicts phase-transformation waves between the lithiated and unlithiated portions of a crystal. This work extends the analysis of the wave dynamics, and describes a new mechanism for current capacity fade through the interactions of these waves with defects in the particle. Size-Dependent Spinodal and Miscibility Gaps: This work demonstrates that the model is powerful enough to predict that the spinodal and miscibility gaps shrink as the particle size decreases. It is also shown that boundary reactions are another general mechanism for the suppression of phase separation.(cont.) Multi-Particle Interactions: This work presents the results of parallel simulations of several nearby crystals linked together via common parameters in the boundary conditions. The results demonstrate the so-called "mosaic effect": the particles tend to fill one at a time, so much so that the particle being filled actually draws lithium out of the other ones. Moreover, it is shown that the smaller particles tend to phase separate first, a phenomenon seen in experiments but difficult to explain with any other theoretical model.by Damian Burch.Ph.D
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Model-based Experimental Design in Electrochemistry
The following thesis applies an experimental design framework to investigate properties
of electron transfer kinetics and homogeneous catalytic reactions. The approach is
model-based and the classical Butler-Volmer description is chosen to describe the
fundamental electrochemical reaction at a conductive interface. The methodology
focuses on two significant design variables: the applied potential at the electrode and
mass transport mode induced by physical arrangement.
An important problem in electrochemistry is the recovery of model parameters from
output current measurements. In this work, the identifiability function is proposed
as a measure of correspondence between the parameters and output variable. Under
diffusion-limit conditions, plain Monte Carlo optimization shows that the function is
globally non-identifiable, or equivalently the correspondence is generally non-unique.
However by selecting linear voltammetry as the applied potential, the primary parameters in the Butler-Volmer description are theoretically recovered from a single set
of data. The result is accomplished via applications of Sobol ranking to reduce the
parameter set and a sensitivity equation to inverse these parameters.
The use of hydrodynamic tools for investigating electron transfer reactions is next
considered. The work initially focuses on the rotating disk and its generalization - the
rocking disk mechanism. A numerical framework is developed to analyze the latter,
most notably the derivation of a Levich-like expression for the limiting current. The
results are then used to compute corresponding identifiability functions for each of
the above configurations. Potential effectiveness of each device in recovering kinetic
parameters are straightforwardly evaluated by comparing the functional values. Furthermore, another hydrodynamic device - the rotating drum, which is highly suitable
for viscous and resistive solvents, is theoretically analyzed. Combined with previous
results, this rotating drum configuration shows promising potential as an alternative
tool to traditional electrode arrangement.
The final chapter illustrates the combination of modulated input signal and appro-
priate mass transport regimes to express electro-catalytic effects. An AC voltammetry
technique plays an important role in this approach and is discussed step-by-step from
simple redox reaction to the complete EC′ catalytic mechanism. A general algorithm
based on forward and inverse Fourier transform functions for extracting harmonic
currents from the total current is presented. The catalytic effect is evaluated and
compared for three cases: macro, micro electrodes under diffusion control condition
and in micro fluidic environments. Experimental data are also included to support
the simulated design results
Direct Numerical Simulations
To understand and model the turbulent behavior of flowing fluids is one of the most fascinating, intriguing, annoying, and most important problems of engineering and physics. Admittedly most of the fluid flows are turbulent. In the known universe, turbulence is evident at the macroscopic scale and the microscopic scale in identical proportions. Turbulence is manifested in many places, such as: a plethora of technological devices, atmospheres and ocean currents, astronomical or galactic motions, and biological systems like circulation or respiration. With the continuum as an assumption, the equations that define the physics of fluid flow are the Navier-Stokes equations modeled during the mid-19th Century by Claude-Louis Navier and Sir George Gabriel Stokes. These equations define all flows, even turbulent flows, yet there is no analytical solution to even the simplest turbulent flow possible. However, the numerical solution of the Navier-Stokes equation is able to describe the flow variable as a function of space and time. It is called direct numerical simulations (DNS), which is the subject matter of this book
Continuum scale modelling and complementary experimentation of solid oxide cells
Solid oxide cells are an exciting technology for energy conversion. Fuel cells, based on solid oxide technology, convert hydrogen or hydrogen-rich fuels into electrical energy, with potential applications in stationary power generation. Conversely, solid oxide electrolysers convert electricity into chemical energy, thereby offering the potential to store energy from transient resources, such as wind turbines and other renewable technologies. For solid oxide cells to displace conventional energy conversion devices in the marketplace, reliability must be improved, product lifecycles extended, and unit costs reduced. Mathematical models can provide qualitative and quantitative insight into physical phenomena and performance, over a range of length and time scales. The purpose of this paper is to provide the reader with a summary of the state-of-the art of solid oxide cell models. These range from: simple methods based on lumped parameters with little or no kinetics to detailed, time-dependent, three-dimensional solutions for electric field potentials, complex chemical kinetics and fully-comprehensive equations of motion based on effective transport properties. Many mathematical models have, in the past, been based on inaccurate property values obtained from the literature, as well as over-simplistic schemes to compute effective values. It is important to be aware of the underlying experimental methods available to parameterise mathematical models, as well as validate results. In this article, state-of-the-art techniques for measuring kinetic, electric and transport properties are also described. Methods such as electrochemical impedance spectroscopy allow for fundamental physicochemical parameters to be obtained. In addition, effective properties may be obtained using micro-scale computer simulations based on digital reconstruction obtained from X-ray tomography/focussed ion beam scanning electron microscopy, as well as percolation theory. The cornerstone of model validation, namely the polarisation or current-voltage diagram, provides necessary, but insufficient information to substantiate the reliability of detailed model calculations. The results of physical experiments which precisely mimic the details of model conditions are scarce, and it is fair to say there is a gap between the two activities. The purpose of this review is to introduce the reader to the current state-of-the art of solid oxide analysis techniques, in a tutorial fashion, not only numerical and but also experimental, and to emphasise the cross-linkages between techniques
Asymptotic analysis of extreme electrochemical transport
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 237-244).In the study of electrochemical transport processes, experimental exploration currently outpaces theoretical understanding of new phenomena. Classical electrochemical transport theory is not equipped to explain the behavior of electrochemical systems in the extreme operating conditions required by modern devices. In this thesis, we extend the classical theory to examine the response of two electrochemical systems that form the basis for novel electrochemical devices. We first examine the DC response of an electrochemical thin film, such as the separator in a micro-battery, driven by current applied through reactive electrodes. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer which mediates Faradaic reactions with Butler-Volmer kinetics. Our analysis differs from previous studies in two significant ways. First, we impose the full nonlinear, reactive boundary conditions appropriate for electrolytic/galvanic cells.(cont.) Since surface effects become important for physically small systems, the use of reactive boundary conditions is critical in order to gain insight into the behavior of actual electrochemical thin films that are sandwiched between reactive electrodes, especially at high current densities. For instance, our analysis shows that reaction rate constants and the Stern-layer capacitance have a strong influence on the response of the thin film. Second, we analyze the system at high current densities (far beyond the classical diffusion-limited current) which may be important for high power-density applications. At high currents, we obtain previously unknown characterizations of two interesting features at the cathode end of the cell: (i) a nested boundary layer structure and (ii) an extended space charge region. Next, we study the response of a metal (i.e., polarizable) colloid sphere in an electrolyte solution over a range of applied electric fields.(cont.) This problem, which underlies novel electrokinetically driven microfluidic devices, has traditionally been analyzed using circuit models which neglect bulk concentration variations that arise due to double layer charging. Our analysis, in contrast, is based on the Nernst-Planck equations which explicitly allow for bulk concentration gradients. A key feature of our analysis is the use of surface conservation laws to provide effective boundary conditions that couple the double layer charging dynamics, surface transport processes, and bulk transport processes. The formulation and derivation of these surface conservation laws via boundary layer analysis is one of the main contributions of this thesis. For steady applied fields, our analysis shows that bulk concentrations gradients become significant at high applied fields and affect both bulk and double layer transport processes. We also find that surface transport becomes important for strong applied fields as a result of enhanced absorption of ions by the double layer.(cont.) Unlike existing theoretical studies which focus on weak applied fields (so that both of these effects remain weak), we explore the response of the system to strong applied fields where both bulk concentration gradients and surface transport contribute at leading order. For the unsteady problem at applied fields that are not too strong, we find that diffusion processes, which are necessary for the system to relax to steady-state, are suppressed at leading-order but appear as higher-order corrections. This result is derived in a novel way using time-dependent matched asymptotic analysis. Unfortunately, the dynamic response of the system to large applied fields seems to introduce several complications that make the analysis (both mathematical and numerical) quite challenging; the resolution of these challenges is left for future work. Both of these problems require the use of novel techniques of asymptotic analysis (e.g., multiple parameter asymptotic expansions, surface conservation laws, and time-dependent asymptotic matching) and advanced numerical methods (e.g., pseudospectral methods, Newton-Kantorovich method, and direct matrix calculation of Jacobians) which may be applicable elsewhere.by Kevin Taylor Chu.Ph.D
Physics of Ionic Conduction in Narrow Biological and Artificial Channels
The book reprints a set of important scientific papers applying physics and mathematics to address the problem of selective ionic conduction in narrow water-filled channels and pores. It is a long-standing problem, and an extremely important one. Life in all its forms depends on ion channels and, furthermore, the technological applications of artificial ion channels are already widespread and growing rapidly. They include desalination, DNA sequencing, energy harvesting, molecular sensors, fuel cells, batteries, personalised medicine, and drug design. Further applications are to be anticipated.The book will be helpful to researchers and technologists already working in the area, or planning to enter it. It gives detailed descriptions of a diversity of modern approaches, and shows how they can be particularly effective and mutually reinforcing when used together. It not only provides a snapshot of current cutting-edge scientific activity in the area, but also offers indications of how the subject is likely to evolve in the future
Development of predictive models of flow induced and localized corrosion
Corrosion is a serious industrial concern. According to a cost of corrosion study released in 2002, the direct cost of corrosion is approximately $276 billion dollars in the United States – approximately 3.1% of their Gross Domestic Product. Key influences on the severity of corrosion include: metal and electrolyte composition, temperature, turbulent flow, and location of attack. In this work, mechanistic models of localized and flow influenced corrosion were constructed and these influences on corrosion were simulated.A rigourous description of mass transport is paramount for accurate corrosion modelling. A new moderately dilute mass transport model was developed. A customized hybrid differencing scheme was used to discretize the model. The scheme calculated an appropriate upwind parameter based upon the Peclet number. Charge density effects were modelled using an algebraic charge density correction. Activity coefficients were calculated using Pitzer’s equations. This transport model was computationally efficient and yielded accurate simulation results relative to experimental data. Use of the hybrid differencing scheme with the mass transport equation resulted in simulation results which were up to 87% more accurate (relative to experimental data) than other conventional differencing schemes. In addition, when the charge density correction was used during the solution of the electromigration-diffusion equation, rather than solving the charge density term separately, a sixfold increase in the simulation time to real time was seen (for equal time steps in both simulation strategies). Furthermore, the charge density correction is algebraic, and thus, can be applied at larger time steps that would cause the solution of the charge density term to not converge.The validated mass transport model was then applied to simulate crevice corrosion initiation of passive alloys. The cathodic reactions assumed to occur were crevice-external oxygen reduction and crevice-internal hydrogen ion reduction. Dissolution of each metal in the alloy occurred at anodic sites. The predicted transient and spatial pH profile for type 304 stainless steel was in good agreement with the independent experimental data of others. Furthermore, the pH predictions of the new model for 304 stainless steel more closely matched experimental results than previous models.The mass transport model was also applied to model flow influenced CO2 corrosion. The CO2 corrosion model accounted for iron dissolution, H+, H2CO3, and water reduction, and FeCO3 film formation. The model accurately predicted experimental transient corrosion rate data.Finally, a comprehensive model of crevice corrosion under the influence of flow was developed. The mass transport model was modified to account for convection. Electrode potential and current density in solution was calculated using a rigourous electrode-coupling algorithm. It was predicted that as the crevice gap to depth ratio increased, the extent of fluid penetration also increased, thereby causing crevice washout. However, for crevices with small crevice gaps, external flow increased the cathodic limiting current while fluid penetration did not occur, thereby increasing the propensity for crevice corrosion
Electrochemical-Thermal Modeling of Lithium-ion Batteries
Incorporating lithium-ion (Li-ion) batteries as an energy storage system in electric devices including electric vehicles brings about new challenges. In fact, the design of Li-ion batteries has to be optimized depending on each application specifications to improve the performance and safety of battery operation under each application and at the same time prevent the batteries from quick degradation. As a result, accurate models capable of predicting the behavior of Li-ion batteries under various operating conditions are necessary. Therefore, the main objective of this research is to develop a battery model that includes thermal heating and is suitable for large-sized prismatic cells used in electric vehicles.
This works starts with developing a dual-extended Kalman filter based on an equivalent circuit model for the battery. The dual-extended Kalman filter simultaneously estimates the dynamic internal resistance and state of the charge of the battery. However, the estimated parameters are only the fitted values to the experimental data and may be non-physical. In addition, this filter is only valid for the operating conditions that it is validated against via experimental data. To overcome these issues, physics-based electrochemical models for Li-ion batteries are subsequently considered.
One drawback of physics-based models is their high computational cost. In this work, two simplified one-dimensional physics-based models capable of predicting the output voltage of coin cells with less than 2.5% maximum error compared to the full-order model are developed. These models reduce the simulation computational time more than one order of magnitude. In addition to computational time, the accuracy of the physico-chemical model parameter estimates is a concern for physics-based models. Therefore, commercial LiFePO4 (LFP) and graphite electrodes are precisely modelled and characterized by fitting experimental data at different charge/discharge rates (C/5 to 5C). The temperature dependency of the kinetic and transport properties of LFP and graphite electrodes is also estimated by fitting experimental data at various temperatures (10 ºC, 23 ºC, 35 ºC, and 45 ºC).
Since the spatial current and temperature variations in the large-sized prismatic cells are significant, one-dimensional models cannot be used for the modeling of these prismatic cells. In this work, a resistor network methodology is utilized to combine the one-dimensional models into a three-dimensional multi-layer model. The developed model is verified by comparing the simulated temperatures at the surface of the prismatic cell (consist of LFP as the positive and graphite as the negative electrode) to experimental data at different charge/discharge rates (1C, 2C, 3C, and 5C). Using the developed model the effect of tab size and location, and the current collector thickness, on the electrochemical characteristics of large-sized batteries is evaluated. It is shown that transferring tabs from the edges and the same side (common commercial design) to the center and opposite sides of the cell, and extending them as much as possible in width, lowers the non-uniformity variation in electrochemical current generation
Mikrovian elektrolyyttisen täyttöpinnoitus: malli prosessimonitoroinnin kehitystä varten
Mikrovia on monikerrospiirilevyn yhden levyn läpi kulkeva reikä.
Täyttämällä tämä reikä kuparilla muodostetaan yhteys kahdessa eri piirilevykerroksessa kulkevien johdinpiirien välille.
Mikroviateknologia yhdistettynä moderniin piirisuunnitteluun mahdollistaa piirilevyjen johdintiheyden kasvattamisen ja näin ollen piirilevyjen sekä niille rakentuvien laitteiden pienentämisen.
Viareiät täytetään elektrolyyttisesti rikkihappo-kuparisulfaatti-liuoksesta.
Täyttöpinnoitusprosessissa mikrovia täyttyy täydellisesti kuparimetallilla ja reiän kohdalle jää peilikirkas kuparipinta valmiiksi seuraavan piirilevykerroksen ladontaa varten.
Prosessin onnistuminen edellyttää kuparin pinnoittumista elektrolyyttiliuoksesta piirilevylle hallitun epätasaisesti siten, että kuparia pelkistyy eniten sinne, missä pinnassa on syvin reikä ja vähemmän sinne, missä pinta on tasainen tai siinä on kohouma.
Ilmiö saadaan aikaan erityisten pinnoituslisäaineiden avulla.
Mikroviojen pinnoitusastetta ei voida pinnoituksen aikana mitenkään mitata ja prosessin lunnonilmiöt huomioon ottava malli on ainut rationaalinen tapa arvioida pinnoituksen etenemistä.
Tässä diplomityössä on kehitetty täyttöpinnoitusprosessin malli, joka luo perustan prosessin mallipohjaiselle ohjaukselle.
Työssä esitellään pinnoitusprosessiin liittyvät perusilmiöt: diffuusion ja migraation aiheuttama massansiirto, sähkökemiallisen reaktion jännite-virta-tasapaino sekä läpivientireiän muodon muuttumisen vaikutukset.
Kirjallisuusosassa käydään läpi monipuolisesti eri pinnoituslisäaineet sekä prosessissa esiintyvät pintakemialliset ilmiöt.
Työssä kehitetty malli on toteutettu elementtimenetelmää käyttäen.
Malli ottaa huomioon kaikki pinnoitusprosessin oleelliset fysikaaliset ja kemialliset ilmiöt sekä mallituskohteen muodonmuutokset.
Myös pinnoituslisäaineiden vaikutus sisältyy malliin.
Malli ennustaa pinnoitusprosessin vaatiman pinnoitusajan annetuissa prosessiolosuhteissa kohtalaisesti.
Täyttöpinnoitusprosessin monimutkaisuuden sekä prosessiin liittyvien liikesalaisuuksien takia työn tulosta voidaan pitää hyödyllisenä.
Kehitetty malli on sinällään käyttövalmis ja työn myötä täyttöpinnoitusprosessien ongelmakenttä on kartoitettu ja sen systemaattinen ratkaisu voi jatkua.
Työn lopuksi kerrotaan tärkeimmät jatkotutkimuksen kohteet sekä niihin liittyvät koe- ja tutkimussuunnitelmat
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