Diffusion-controlled Reaction Model Research Articles

A mechanistic investigation of the Li10GeP2S12|LiNi1-x-yCoxMnyO2 interface stability in all-solid-state lithium batteries

All-solid-state batteries are intensively investigated, although their performance is not yet satisfactory for large-scale applications. In this context, the combination of Li10GeP2S12 solid electrolyte and LiNi1-x-yCoxMnyO2 positive electrode active materials is considered promising despite the yet unsatisfactory battery performance induced by the thermodynamically unstable electrode|electrolyte interface. Here, we report electrochemical and spectrometric studies to monitor the interface evolution during cycling and understand the reactivity and degradation kinetics. We found that the Wagner-type model for diffusion-controlled reactions describes the degradation kinetics very well, suggesting that electronic transport limits the growth of the degradation layer formed at the electrode|electrolyte interface. Furthermore, we demonstrate that the rate of interfacial degradation increases with the state of charge and the presence of two oxidation mechanisms at medium (3.7 V vs. Li+/Li < E < 4.2 V vs. Li+/Li) and high (E ≥ 4.2 V vs. Li+/Li) potentials. A high state of charge (>80%) triggers the structural instability and oxygen release at the positive electrode and leads to more severe degradation.

Photovoltaic Effect in Phthalocyanine-Based Organic Solar Cells: 2. Trapping of Molecular Excitons by Impurities

Trapping of molecular excitons (MEs) by ionizing impurities is a fast initial step of the photovoltaic effect in organic solar cells. Values for the ME trapping rate constant at a fixed impurity concentration NI have been found in terms of the model of diffusion-controlled bimolecular reactions. The model takes into account two pathways of quasi-steady-state ME trapping, contact and bulk capture (caused by dipole–dipole interaction with an impurity), which are determined by the ME diffusion length lS, the minimum radius of approach of partners a0, and the Forster radius RS. The trapping quantum yield at RS > a0 is YS = (1 + b)−1, where b−1 ≈ 4π(2lDRS)3/2NI. Possible doping conditions when YS ~ 1 at NI ~ 1018 cm−3 are discussed.

Reduction kinetics of hematite ore fines with H2 in a rotary drum reactor

Porous hematite ore was prepared by the dehydration of low-grade limonite ore with high moisture content. In this study, the mechanisms and kinetics of the isothermal reduction of hematite ore fines by hydrogen–nitrogen gas mixtures were investigated using a rotary drum reactor in the temperature range of 700–900 °C. The reduction rate and degree of reduction initially increased with H2 content and temperature, and subsequently, the reduction rate decreased with the increasing reduction reactions of iron oxide. Our results indicate that the dehydration significantly increases the specific surface area of the original limonite ore, creating nanopores. We found that the reduction of hematite (Fe2O3) to metallic iron (Fe) was controlled by a first-order reaction model (one-dimensional formation and growth of nuclei) below 850 °C. However, at 900 °C, the reaction initially followed the above model and then shifted to follow a diffusion-controlled reaction model in the final stages of reduction owing to the low diffusion rate of oxygen in the formed dense iron layer. The value of the apparent activation energy for the overall reduction process of hematite to metallic iron was ~51 kJ/mol.

Enhanced recycling and utilization of mullite from coal fly ash with a flotation and metallurgy process

Abstract The recycling and utilization of mullite in coal fly ash (CFA) gives rise to environmental and economic profits. The optimal experimental conditions for enhanced recycling of mullite with a flotation and metallurgy process are studied by factorial designs, and further analyzed by thermodynamic and dynamics calculations, and XRD/SEM characterizations. The unburned carbon is firstly removed from the CFA assisted with effective humic acid surfactant in the froth flotation step. The maximum removal rate of carbon is 93.20 ± 0.05%. Then the digesting of glass phase in carbon-free product with mixed acid solutions (HF: H2SO4 = 3:1) is employed in the metallurgy step. The influencing intensity of digesting factor on glass phase decreases in order of acid concentration, agitation intensity, reaction time, reaction temperature. The digesting kinetics of glass phase in mixed acid solution is belonging to diffusion-controlled reaction model. The maximum digesting rate of glass phase can be 97.40 ± 0.16%. The mineralogical phase of the digested residue is mainly mullite. The performance of the refractory obtained from the water-cleaned mullite-enriched product meets the production requirements of refractory materials. This potential process would provide an effective approach for the separation and recycling of valuable components from CFA in further industry applications.

Reactive sintering process of ferromagnetic MnBi under high magnetic fields

The magnetic field effect on the reactive sintering process of MnBi was investigated. Magnetic-field-induced enhancement of the reaction was found to be exhibited at the initial stages. The coercivity field decreased with an increase in the in-field annealing time. The kinetics of the reaction were in good agreement with the diffusion-controlled reaction model. It is suggested that the decrease in activation energy at the initial stages of reaction increased the amount of formed MnBi phases, resulting in enhancement of the reaction Mn + Bi to MnBi phase by in-field reactive sintering.

Quantum Yield of Cyclobutane Pyrimidine Dimer Formation Via the Triplet Channel Determined by Photosensitization.

UV-induced formation of the cyclobutane pyrimidine dimer (CPD) lesion is investigated by stationary and time-resolved photosensitization experiments. The photosensitizer 2'-methoxyacetophenone with high intersystem crossing efficiency and large absorption cross-section in the UV-A range was used. A diffusion controlled reaction model is presented. Time-resolved experiments confirmed the validity of the reaction model and provided information on the dynamics of the triplet sensitization process. With a series of concentration dependent stationary illumination experiments, we determined the quantum efficiency for CPD formation from the triplet state of the thymine dinucleotide TpT to be 4 ± 0.2%.

Predicting the quench sensitivity of Al–Zn–Mg–Cu alloys: A model for linear cooling and strengthening

In this work the quench sensitivity of Al–Zn–Mg–Cu alloys is studied through continuous cooling at constant rates of a range of alloys using differential scanning calorimetry (DSC), transmission electron microscopy (TEM), scanning electron microscopy (SEM) and hardness testing. The DSC, TEM and SEM data show that the cooling reactions are dominated by a high temperature reaction (typically ~450°C down to ~350°C) due mostly to S-Al2CuMg phase formation, a medium temperature reaction (~350°C down to ~250°C) due predominantly to η-Mg(Al,Cu,Zn)2 phase formation and a lower temperature reaction (~250°C down to ~150°C) due to a Zn–Cu rich thin plate phase. A new, physically-based model is constructed to predict rates of all reactions, enthalpy changes and resulting yield strength in the artificially aged condition. The model incorporates a recently derived model for diffusion-controlled reactions based on the extended volume fraction concept as well as recent findings from first principles modelling of enthalpies of the relevant phases. The model shows a near perfect correspondence with data on all 6 alloys studied extensively by cooling DSC and hardness testing, and allows prediction of the influence of the 3 major elements and 3 dispersoid forming elements on quench sensitivity.

Analysis of nucleation and growth with the model for diffusion-controlled precipitation reactions based on the extended volume concept

Recently (Starink, 2014) a new model for diffusion-controlled precipitation reactions based on the extended volume concept was derived. The model leads to an analytical equation describing the relation between the fraction transformed, α, the reaction time, t, and the reaction exponent, n, as:α={exp(-2(k1t)n)-1}/(2(k1t)n)+1 In the present work, new analysis methods are derived which allow determination of the reaction exponent n. The new methods are applied to analysis of nucleation and it is shown that generally during a reaction with growth in 3 dimensions there are only 2 modes: either the nucleation rate in the extended volume is constant or it is negligibly small. A new approach to the interaction of diffusion-controlled growth and nucleation is proposed to rationalise these findings. The exponential decay of the average solute content predicted by the new model is further analysed and compared with a range of experimental data and contrasted with other models. The new model is found to correspond excellently to these solute decay data.

Copper, zinc, and iron bioleaching from polymetallic sulphide concentrate

Bioleaching of low-grade complex Cu–Zn–Pb–Fe–Ag–Au sulphide concentrate (of Majdanpek ore body, RTB Bor, Serbia) was carried out in an aerated bioleach reactor in the presence of mesophilic mixed bacterial culture of Acidithiobacillus ferrooxidans, Acidithiobacillus thiooxidans, and Leptospirillum ferrooxidans. A mesophilic acidophiles culture was isolated from the acidic solution of the underground copper mine of Bor, Serbia. The nutrient medium was 9K at pH 1.6. 87% of the particles were <10 µm in size, with a pulp density of 8% (w/v). Bioleaching efficiencies of 89% for zinc, 83% for copper, and 68% for iron can be achieved in the examined conditions. Kinetic analysis shows that the change in leaching corresponds to the Spencer-Topley kinetic model for diffusion-controlled topochemical reactions.

A new model for diffusion-controlled precipitation reactions using the extended volume concept

In this work a new model for diffusion-controlled precipitation reactions is derived, analysed and tested against a wide range of data. The model incorporates elements of the extended volume concept and combines this with a new treatment of soft impingement of diffusion fields. The model derivation involves an integration over iso-concentration regions in the parent phase in the extended volume, which leads to a single analytical equation describing the relation the fraction transformed, α, and the extended volume fraction, αext, as: α={exp(−2αext)−1}/(2αext)+1. The model is compared to a range of new and old data on diffusion-controlled reactions including precipitation reactions and exsolution reactions, showing a very good performance, outperforming classical and recent models. The model allows new interpretation of existing data which, for the first time, show a consistent analysis, in which Avrami constants, n, equal values that are always consistent with transformation theory.

Dissolution kinetics of Si and Al from montmorillonite in carbonic acid solution

AbstractThe reaction between carbonic acid and montmorillonite minerals was studied in order to provide a theoretical basis for analyzing changes in the physical properties of coal seams after CO2 injection and for optimizing CO2 pumping parameters. A single montmorillonite mineral of purity &gt;90 % was selected and subjected to reactions at 25, 35, and 45 °C in carbonic acid solutions of varying acidity. The Si and Al concentrations in the solutions and the structure and elemental compositions of the montmorillonite before and after the reactions were analyzed using a spectrophotometer, an X-ray diffractometer, and an energy-dispersive X-ray spectrometer; kinetic reaction models were established for the dissolution of Si and Al in carbonic acid solutions in order to estimate the apparent activation energy of Si dissolution under different acidity conditions. The results indicate that Al dissolved rapidly and soon reached solubility equilibrium. On the other hand, Si concentration in the solutions increased rapidly and then gradually declined with vibrations, with maximum values at 25, 35, and 45 °C, which were observed at approximately 96, 72, and 48 h, respectively. In addition, Si dissolution fitted the diffusion-controlled reaction model well; as the pH value decreased, the apparent activation energy of Si dissolution decreased, and Si became easier to dissolve. Furthermore, it was concluded that as a weak acid, carbonic acid causes little damage to the mineral structure of montmorillonite.

Reaction kinetics study of CdTe thin films during CdCl 2 heat treatment

In order to investigate the effect of CdCl 2 heat treatment on the physical properties of CdTe thin films grown by a sputtering method, the CdTe thin films were coated with CdCl 2. The recrystallization, grain growth, randomization, and reaction kinetics were investigated by monitoring the phase transition of CdCl 2-heat-treated CdTe specimens during temperature ramp annealing or isothermal soaking by using in-situ time-resolved high-temperature X-ray diffraction. The results of annealing show that the recrystallizations of CdTe (1 1 1) and other planes do not occur simultaneously, but sequentially in terms of temperature. The results of isothermal soaking imply that the Avrami diffusion-controlled reaction model fits well with the experimental data. This proves that the CdCl 2 diffusion process is the dominant factor in the CdTe recrystallization mechanism.

Non-isothermal reaction kinetics of lithium cobalt oxide

The reaction kinetics of the formation of LiCoO 2 during solid-state reaction was investigated using a non-isothermal approach at constant heating rates. The conversion ratios of the starting material of LiCoO 2 were calculated from thermogravimetric measurements. Analysis based on the differential method revealed that two diffusion-controlled models described the probable reaction mechanisms. The utilized integral method corroborated the fact that the reaction kinetics of the formation of LiCoO 2 was governed by Ginstling's diffusion-controlled reaction model. The activation energy of the formation of LiCoO 2 was calculated to be 163.6 kJ/mol. A combination of the differential and integral methods was demonstrated to effectively elucidate the reaction kinetics of ceramics and accurately determine the associated kinetic parameters.

Fluctuating reaction rate and non-exponential blinking statistics in single-enzyme kinetics

Extending the Michaelis–Menten kinetic scheme, we consider a three-state diffusion-controlled reaction model to investigate the effects of fluctuating reaction rate on the blinking statistics of single-enzyme catalytic reactions. As a result of conformational changes, the barrier-height and the reaction rate for the bottleneck enzymatic reaction could fluctuate in time, leading to non-exponential blinking statistics. To illustrate model applications, some reported experimental data for single β-galactosidase molecules were reanalyzed here to extract useful kinetic parameters.

The effects of anomalous diffusion on power-law blinking statistics of CdSe nanorods

In this study of fluorescence blinking statistics for nanorods, we present a diffusion-controlled reaction model that leads to a more general formula: t(-m) exp[-(Gammat)(n)]. This formula describes a short-time power law with a crossover to a stretched exponential decay at later times. Based on quantum Brownian motion for a coupled central harmonic oscillator coupled to heat bath oscillators, we show that the position distribution follows anomalous diffusion with time-dependent diffusion coefficient and drift coefficient. The first and the second moments of the energy fluctuations are shown to be related to the exponent m and n for the blinking statistics.

Fluorescence intermittency of silicon nanocrystals and other quantum dots: A unified two-dimensional diffusion-controlled reaction model

We present a unified model involving two-dimensional diffusion-controlled reactions of both slow and fast reaction coordinates to elucidate the dynamic origin of fluorescence intermittency observed not just in quantum dots but also in organic chromphores and biomolecules. This improved model also solves the puzzling behavior of Si nanocrystals which display an unusually large m (exceeding 2) for the power-law decay of t(-m) and provides remedies for the deficiencies in existing models.

Kinetic Analysis of Thermite Reactions in Al-MoO3 Nanocomposites

Reactions in energetic Al-MoO 3 nanocomposites prepared by arrested reactive milling were investigated by scanning calorimetry and heated filament ignition experiments. The calorimetry data were processed to obtain kinetic parameters describing the reaction between Al and MoO 3 . The reaction was treated as a combination of four subreactions, which were described by a combination of a diffusion-controlled reaction model and first-order reactions. The activation energies determined in this study allowed the comparison to reference values for the decomposition of MOO 3 and the diffusion of oxygen through an Al 2 O 3 product layer. The kinetic model was extrapolated to high heating rates in the 10 3 -10 6 K/s range and compared to ignition data. It was concluded that ignition of Al-MoO 3 nanocomposites prepared by arrested reactive milling is primarily controlled by oxygen diffusion in Al 2 O 3 .

Electron Transfer Kinetics between PQQ-dependent Soluble Glucose Dehydrogenase and Mediators

Steady-state kinetic parameters between PQQ-dependent soluble glucose dehydrogenase (PQQ-sGDH) and mediators were evaluated based on a theory of bioelectrocatalysis. Quinones showed bi-molecular reaction constants in the order of 1010 M−1 s−1 as the limiting values, while the values of Os-complexes were two or three orders smaller. The magnitude of the limiting values was interpreted in terms of the long-range electron transfer in the active center as well as the diffusion-controlled reaction model.

Controlled Initiation of Enzymatic Reactions in Micrometer-Sized Biomimetic Compartments

We present a technique to initiate chemical reactions involving few reactants inside micrometer-scale biomimetic vesicles (10(-12) to 10(-15) L) integral to three-dimensional surfactant networks. The shape of these networks is under dynamic control, allowing for transfer and mixing of two or several reactants at will. Specifically, two nanotube-connected vesicles were filled with reactants (substrate and enzyme, respectively) by microinjection. Initially, the vesicles are far apart and any diffusive mixing (on relevant experimental time scales) between the contents of the separated vesicles is hindered because of the narrow diameter and long axial extension of the nanotube. To initiate a reaction, the vesicles were brought close together, the nanotube was consumed by the vesicles and at a critical distance, the nanotube-vesicle junctions were dilated leading to formation of one spherical reactor, and hence mixing of the contents. We demonstrate the concept using a model enzymatic reaction, which yields a fluorescent product (two-step hydrolysis of fluorescein diphosphate by alkaline phosphatase), where product formation was measured as a function of time using a FRAP fluorescence microscopy protocol. By comparing the enzymatic activity with bulk measurements, the enzyme concentration inside the vesicle could be determined. Reactions could be followed for systems having as few as approximately 15 enzyme molecules confined to a reactor vesicle. To describe the experiments we use a simple diffusion-controlled reaction model and solve it using a survival probability approach. The agreement with experiment is qualitative, but the model describes the trends well. It is shown that the model correctly predicts (i) single-exponential decay after a few seconds, and (ii) that the substrate decay constant depends on the number of enzymes and geometry of reaction container. The numerical correction factor Lambda is introduced in order to ensure semiquantitative agreement between experiment and theory. It was shown that this numerical factor depends weakly on vesicle radius and number of enzymes, thus it is sufficient to determine this factor only once in a single calibration measurement.

Kinetics of Electron Attachment to Reverse Micelles

The kinetics of the attachment of isooctane solvated electrons to the water pools of reverse micelles (water/ AOT/isooctane) has been studied by ultrafast time-resolved spectroscopy. The electrons generated in isooctane by photoionization (three photons of 400 nm) are observed to rapidly attach to reverse micelles, resulting in hydrated electrons in the water pools of the reverse micelles. The measured electron attachment rates (inferred from attachment yields) show a greater dependence on reverse micelle size than that predicted by a diffusioncontrolled reaction model. Evidence is presented that highly delocalized, excess electron states of the water pool play an important role in the attachment process.