Methods-A Potential-Dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts
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Sequestration of CO 2 within stable mineral carbonates (e.g., CaCO 3 ) represents an attractive emission reduction strategy because it offers a leakage-free alternative to geological storage of CO 2 in an environmentally benign form. However, the pH of aqueous streams equilibrated with gaseous streams containing CO 2 (pH < 4) are typically lower than that which is required for carbonate precipitation (pH > 8). Traditionally, alkalinity is provided by a stoichiometric reagent (e.g., NaOH) which renders these processes environmentally hazardous and economically unfeasible. This work investigates the use of regenerable ion-exchange materials to induce alkalinity in CO 2 -saturated aqueous solutions such that the pH shift required for mineralization occurs without the need for stoichiometric reagents. Na + -H + exchange isotherms (at [H + ] = 10 −8 –10 −1 M) and rates were measured for 13X and 4A zeolites and TP-207 and TP-260 organic exchange resins in batch equilibrium and fixed-bed exchange experiments, respectively. At solutions equilibrated with CO 2 at 1.0 atm (pH = 3.9), H + exchange capacities for the materials were similar (1.7–2.4 mmol H + /g material) and resulted in pH increases from 3.9 to greater than 8.0. Multi-component mixtures using Ca 2+ and Mg 2+ cations (at 10 −3 –10 −1 M) in CO 2 -saturated water were used to probe competitive ion exchange. The presence of divalent cations in solution inhibited H + exchange, reducing capacities to as low as 0.2 mmol H + /g for both resins and zeolites. Dynamic H + exchange capacities in fixed-bed ion exchange columns were similar to equilibrium values for resins (∼1.5 mmol/g) and zeolites (∼0.8 mmol/g) using inlet solutions that were equilibrated with gaseous streams of CO 2 at 1.0 atm. However, exchange kinetics were limited by intraparticle diffusion as indicated by the increased rate parameters with increasing inlet flow rates (20–160 cm 3 min −1 ). Experimental calcite precipitation from mixing the alkaline CO 3 2− -rich water solution obtained from the ion-exchange column with a simulated liquid waste stream solution achieved thermodynamic maximum yields. The results from these studies indicate that ion exchange processes can be used as an alternative to the addition of stoichiometric bases to induce alkalinity for the precipitation of CaCO 3 , thereby opening a pathway toward sustainable and economic mineralization processes.
The adsorption of sulfamethoxazole (SMX) onto a NaOH-activated pine wood-derived biochar was investigated via batch experiments and models. Surprisingly, the maximum adsorption capacity of activated biochar for SMX (397.29 mg/g) was superior than those of pristine biochars from various feedstock, but comparable to those of commercially available activated carbons. Elovich kinetic and Freundlich isotherm models revealed the best fitted ones for the adsorption of SMX onto the activated biochar indicating chemisorptive interaction occurred on surface of the activated biochar. In addition, the intraparticle diffusion limitation was thought to be the major barrier for the adsorption of SMX on the activated biochar. The main mechanisms for the activated biochar would include hydrophobic, π-π interactions and hydrogen bonding. This was consistent with the changes in physicochemical properties of the activated biochar (e.g., increase in sp 2 and surface area, but decrease in the ratios of O/C and H/C).
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Effective design of heterogeneous catalytic systems requires careful coordination of physiochemical phenomena that span orders or magnitude in length and time scales. Multiscale modelling and simulation tools can provide useful insight for understanding and improving the performance of such systems. Mesoporous silica catalyst support materials present a versatile platform wherein support attributes may be tuned to control transport phenomena throughout the system. In this study we develop an integrated multiscale modelling approach for the conversion of ethanol to butadiene over a SBA-16 mesoporous silica supported catalyst. We use molecular dynamics simulations to calculate domain specific diffusivities of reactants and products in the various domains of SBA-16's nanostructure. This is used to calculate a resultant effective diffusivity through its microstructure using finite element method (FEM) models of the tessellated unit cell. The resultant intraparticle effective diffusivity enables the development of a reduced-order reactor level FEM model that is able to implicitly account for the SBA-16's transport effects without the explicit consideration of its detailed geometry. Experimental bench-scale conversion data for the ethanol to butadiene process over SBA-16 is used to extract intrinsic kinetic rate constants for a simplified reaction mechanism using this reduced order bench-scale reactor FEM model. The model is able to reproduce experimental trends in conversion and activity lifetimes. The impact of varying key support attributes such as pore-size and particle size on catalytic activity lifetimes is then explored. We demonstrate the utility of this multi-scale modelling strategy in guiding catalyst design for the development of rational strategies to improve the performance of heterogeneous supported catalytic systems.
Here we present a methodology for modeling multi-step reaction rates in porous catalyst particles for use in CFD-DEM and two fluid models. Single-step effectiveness factors based on a Thiele modulus, while useful, cannot accurately capture the cascading reaction systems common in high temperature vapor-phase chemical reactors like fluidized catalytic cracking units and catalytic biomass fast pyrolysis systems. Instead, multi-step effectiveness vectors derived from steady-state solutions to the governing reaction-diffusion equations are needed. Solutions for various catalyst shapes are presented, including spheres, cylinders, and prisms. Computational challenges inherent in repeated evaluation of reaction rates with diffusion limitations are discussed, and an efficient implementation based on pre-computed lookup tables is proposed and demonstrated on a simulation of a fluidized bed reactor. Open-source code is provided for the compilation of reaction rate tables for use in ODE, DEM, and two-fluid models.
Crystalline silicotitanate (CST) ion exchanger is planned to be used to remove cesium (137Cs) from the aqueous phases of Hanford tank wastes in preparation for vitrification at the Waste Treatment and Immobilization Plant (WTP) Pretreatment Facility. Column scale up testing was conducted to evaluate performance of Cs exchange onto the CST. Batch contact testing was conducted to assess exchange kinetics of Cs exchange at four different CST PSDs. Column testing was conducted at three column sizes, small (2.5% full height), medium (12% full height), and full height, to assess Cs load performance behavior. Testing at the small scale was compared to actual Hanford tank waste testing to verify the validity of simulant tests to accurately represent full height column performance. A change in CST particle size was essential in scaling the small column dynamics up to full scale. Based on these results, a determination of intraparticle and film diffusion impacts on overall mass transfer coefficients will allow future modeling of the breakthrough performance at a range of process conditions.
The fusion step in the formation of colloidal quantum dot molecules, constructed from two core/shell quantum dots, dictates the coupling strength and hence their properties and enriched functionalities compared to monomers. Herein, studying the monomer size effect on fusion and coupling, we observe a linear relation of the fusion temperature with the inverse nanocrystal radius. This trend, similar to that in nanocrystal melting, emphasizes the role of the surface energy. The suggested fusion mechanism involves intraparticle ripening where atoms diffuse to the reactive connecting neck region. Moreover, the effect of monomer size and neck filling on the degree of electronic coupling is studied by combined atomistic-pseudopotential calculations and optical measurements, uncovering strong coupling effects in small QD dimers, leading to significant optical changes. Understanding and controlling the fusion and hence coupling effect allows tailoring the optical properties of these nanoscale structures, with potential applications in photonic and quantum technologies.
Alkaline pretreatment of herbaceous feedstocks such as corn stover prior to mechanical refining and enzymatic saccharification improves downstream sugar yields by removing acetyl moieties from hemicellulose. However, the relationship between transport phenomena and deacetylation kinetics is virtually unknown for such feedstocks and this pretreatment process. Here, we report the development of an experimentally validated reaction–diffusion model for the deacetylation of corn stover. A tissue-specific transport model is used to estimate transport-independent kinetic rate constants for the reactive extraction of acetate, hemicellulose and lignin from corn stover under representative alkaline conditions (5–7 g L -1 NaOH, 10 wt% solids loadings) and at low to mild temperatures (4–70°C) selected to attenuate individual component extraction rates under differential kinetic regimes. The underlying transport model is based on microstructural characteristics of corn stover derived from statistically meaningful geometric particle and pore measurements. These physical descriptors are incorporated into distinct particle models of the three major anatomical fractions (cobs, husks and stalks) alongside an unsorted, aggregate corn stover particle, capturing average Feret lengths of 917–1239 μm and length-to-width aspect ratios of 1.8–2.9 for this highly heterogeneous feedstock. Individual reaction–diffusion models and their resulting particle model ensembles are used to validate and predict anatomically-specific and bulk feedstock performance under kinetic-controlled vs. diffusion-controlled regimes. In general, deacetylation kinetics and mass transfer processes are predicted to compete on similar time and length scales, emphasizing the significance of intraparticle transport phenomena. Critically, we predict that typical corn stover particles as small as ~2.3 mm in length are entirely diffusion-limited for acetate extraction, with experimental effectiveness factors calculated to be 0.50 for such processes. Debilitatingly low effectiveness factors of 0.021–0.054 are uncovered for cobs—implying that intraparticle mass transfer resistances may impair observable kinetic measurements of this anatomical fraction by up to 98%. These first-reported quantitative maps of reaction vs. diffusion control link fundamental insights into corn stover anatomy, biopolymer composition, practical size reduction thresholds and their kinetic consequences. These results offer a guidepost for industrial deacetylation reactor design, scale-up and feedstock selection, further establishing deacetylation as a viable biorefinery pretreatment for the conversion of lignocellulosics into value-added fuels and chemicals.
Solid-state lithium diffusion dynamics are critical for the rate capability and longevity of Li-ion batteries. Conventionally, nanoscale lithium diffusion within individual battery particles has been simplified as being primarily driven by concentration gradients, despite the associated processes inducing local lattice expansion, contraction, and strain fields. Using operando scanning transmission soft X-ray microscopy with high spatial resolution and chemical sensitivity to track nanoscale intraparticle lithium transport, and post-cycling Bragg coherent diffraction X-ray imaging to directly reveal three-dimensional intraparticle strain fields, we uncover strain-associated lithium transport dynamics within single-crystalline LiNi 1/3 Mn 1/3 Co 1/3 O 2 (scNMC) particles during cycling. Contrary to the expected thermodynamic solid-solution behavior of scNMC, our observations reveal near-uniform but fluctuating regions of lithium-dense and lithium-dilute areas during cycling. These fluctuations suggest that nanoscale lithium diffusion can proceed counter to concentration gradients. Additionally, we demonstrate that an increased presence of lithium-dilute regions near the surface enhances lithium surface insertion kinetics, emphasizing the importance of controlling surface lithium distribution to improve rate performance. Our study provides insights into nanoscale solid-state ion transport, with potential applications in batteries, solid-state fuel cells, and memristors.
One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. To that end, this talk investigates the formation of stress-induced fracture within polycrystalline cathode particles and the impact on capacity loss. Physically based cathode aging dynamics is simulated in a 3D, continuum-level chemo-mechanical model. The model captures anisotropic Li diffusion within a single polycrystalline particle comprised of hundreds to thousands of randomly oriented grains. A recent addition to this model includes electrolyte infiltration, which occurs when the electrolyte seeps into surface cracks within the particle. The model predicts that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains are misaligned, they expand a different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicts that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicates that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. The principle contribution of this research is the use of an anisotropic chemo-mechanical model to test how particle geometry affect capacity fade, which predicts that particle size has a stronger effect on capacity fade than grain size and ultimately that small particles with large grains have the least capacity fade.
One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. Unfortunately, this requires simulation of thousands of charge/discharge cycles, which can be rather time consuming depending on the fidelity of the simulation. The purpose of this talk is to discuss a new modeling framework that couples a high-resolution, continuous damage model (CDM) to a single particle model (SPM) resulting in a good combination of speed and fidelity. In previous work, a 3D, continuum-level chemo-mechanical model was developed to investigate cracking within a single cathode particle comprised of hundreds to thousands of randomly oriented grains. The CDM predicted that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains were misaligned, they expanded different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicted that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicted most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicated that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. This led to a need for simulating fatigue-like mechanism that degrade the battery over longer time scales. In order to reach the time scales, need to resolve fatigue-like degradation, the CDM needs to be complemented by a faster model. Therefore, recent efforts have been focused on using results from the CDM to inform parameters within the SPM. These parameters are homogenization factors that are associated with diffusion, particle radius, and/or exchange current density. By coupling the CDM to the SPM, the aging simulation is broken up into two domains: short-term and long-term degradation. The short-term degradation occurs over a single cycle and is handled by the CDM due of its high fidelity, but relatively expensive computational cost. Such mechanism include break-in crack caused by mismatches in grain orientation. The long-term degradation occurs over tens of cycles and is handled by the SPM due it's computational efficiency. Most of the fatigue-like mechanism fall into this category. The eventual goal of this modeling framework is to upscale to a psudo-2D model allowing for full electrode simulation, which are informed by high-fidelity grain-scale simulations.