Three-dimension Diffusion Research Articles

Recycling of spent LiFePO4 batteries by oxidizing roasting: Kinetic analysis and thermal conversion mechanism

The recycling of spent lithium-ion batteries has gained increasing attention due to its economic and environmental benefits. The oxidizing roasting has been preliminarily proven to be a feasible method to pre-treat and recycle spent LiFePO4 battery. However, the kinetics and thermal conversion mechanism of spent LiFePO4 battery during oxidizing roasting process remains indefinable and needs to be elucidated. Therefore, the kinetic analysis and thermal conversion mechanism of the spent LiFePO4 battery during the oxidizing roasting process were investigated in this study. The results indicated that the oxidizing roasting process of the electrode materials (LiFePO4 and C) could be divided into four weight loss stages, and the maximum weight loss took place in the third weight loss stage (500–800 °C). The model-free methods (Flynn-Wall-Ozawa and Kissinger-Akahira-Sunose models) could well describe the oxidizing roasting process, and the corresponding Eα obtained were 257.38 and 255.35 kJ/mol respectively. The model-fitting methods showed that the three-dimension diffusion model was the most suitable kinetic reaction model for the electrode materials oxidizing roasting process. The graphite in the electrode materials could be easily oxidized to CO2 (the major gaseous product). Besides, the LiFePO4 was firstly oxidized and converted into Li3Fe2(PO4)3 and Fe2O3. Then the Li3Fe2(PO4)3 was decomposed into Li3PO4 and P2O5. Finally, P2O5 could react with Fe2O3 to form FePO4. The physical state of oxidizing roasting products changed from powder to molten state from 600 to 800 °C because of the lower melting point temperature of Li3Fe2(PO4)3, and the oxidizing roasting temperature was suggested to be controlled below 800 °C. The final products obtained from the oxidizing roasting process of the spent LiFePO4 battery electrode materials were Li3Fe2(PO4)3, FePO4 and Li3PO4. This study provides a comprehensive understanding of the kinetics and thermal conversion mechanism during spent LiFePO4 battery oxidizing roasting recovery process.

Thermokinetics of mass-loss behavior on direct reduction of copper slag by waste plastic char

The effective utilization of waste plastics is the key technology for environmental protection. Waste plastic char was proposed as a reductant for recovering valuable metals from copper slag. Reaction reactivity, mass-loss behavior and thermokinetics of copper slag were studied by FTIR and thermogravimetric analyzer. The main functional groups of waste plastic char are benzene ring, C-O and –OH. Mass-loss behavior evaluation method was proposed based on calculating and detection of sample’s total mass-loss and reductant mass-loss.With temperature increasing, reaction mechanism transformed. Three-dimension diffusion and interface’s chemical reaction rate are restrictive steps for the first and the second reaction regime, respectively. For waste plastic char, activation energy of the first regime and second regime are about 289.5 ~ 276.2 kJ/mol and 584.5 ~ 709.9 kJ/mol, respectively. CaO changed the second regime’s activation energy. When CaO added, activation energy of waste plastic char and coal decreased by 119.8 ~ 121.5 kJ/mol and 100.0 ~ 113.6 kJ/mol respectively. Waste plastic char presents better reduction reactivity in the second reduction regime than coal. This research makes it possible for recycling of municipal organic wastes and iron containing slags.

Hydrogen generation characteristics of steel slag-steam high temperature reaction in terms of particle size

The iron species in the lower valence state in steel slag are capable of thermochemical H2O splitting and producing hydrogen energy. The defining of the slag reactivity with varying particle size distributions was put forward. The results showed the hydrogen generation rate was primarily dependent on temperature and particle size. The kinetics analysis revealed a typical self-retardation reaction behavior for the fine slag, due to the clogging of macropores upon oxidation. In comparison, the reaction kinetics of the coarser slag were described well by three-dimension diffusion model and exhibited better resistance against the rate decline. The coarser slag had much more grain junctions and fewer fraction of RO phases distributed at the particle surface. Due to the lack of free surfaces, the volume expansion derived from the oxidation of RO phase would cause larger mismatch stresses at grain boundaries, and further trigger the cracks formation.

A statistical mechanical model for drug release: Relations between release parameters and porosity

A lattice gas model is proposed for investigating the release of drug molecules on devices with semi-permeable, porous membranes in two and three dimensions. The kinetic of this model was obtained through the analytical solution of the three-dimension diffusion equation for systems without membrane and with Monte Carlo simulations. Pharmaceutical data from drug release is usually adjusted to the Weibull function, exp[−(t∕τ)b], and the dependence of adjusted parameters b and τ is usually associated, in the pharmaceutical literature, with physical mechanisms dominating the drug dynamics inside the capsule. The relation of parameters τ and b with porosity λ are found to satisfy, a simple linear relation for between τ and λ−1, which can be explained through simple physically based arguments, and a scaling relation between b and λ, with the scaling coefficient proportional to the system dimension.

Pyrolysis performance, kinetic, thermodynamic, product and joint optimization analyses of incense sticks in N2 and CO2 atmospheres

Thermogravimetric and pyrolysis-gas chromatography/mass spectrometry analyses were performed to quantify the pyrolysis performances, kinetics, thermodynamics, products and optimization of incense sticks (IS) in N2 and CO2 atmospheres at five heating rates. The increased heating rate caused a lagged IS pyrolysis, moving its curves to a higher temperature. According to four model-free methods, activation energy estimates ranged from 34.17 to 439.19 kJ· mol−1 and 28.46–187.34 kJ· mol−1 in the N2 and CO2 atmospheres, respectively. The three-dimension diffusion (spherical symmetry) (D3) was determined using the Horowitz-Metzger method as the most probable degradation mechanism in both atmospheres. The main pyrolytic products were found as benzene and its derivatives whose mass accounted for 49.94% of the total 18 products. Significant two-way interaction effects were found between temperature, heating rate, and atmosphere type on the three responses of remaining mass, derivative thermogravimetry, and differential scanning calorimetry (p = 0.001). The best joint optimization was obtained at 899.5 °C with the heating rate of 5 °C·min−1 in the CO2 atmosphere and was more sensitive to the increased heating rate in the N2 than CO2 atmosphere.

MODELLING THE INDOOR RADIATION DOSES: A REVIEW AND PERSPECTIVE.

Theoretical models to calculate the indoor gamma and radon doses are reviewed, refined and applied. The model for gamma doses is built based on the relative effects of the different room elements that control the amount of radiation. The relative doses are calculated by the MCNP5 simulation software. The gamma sources are due to the natural radiation from the 238U series, 232Th series and the radionuclide 40K. An application of the model that involves all the considered elements is demonstrated. The elements are the thickness of the walls, the density of the building material, the dimensions of the room, the existence of other rooms surrounding the room under study, the split of some walls into two portions, the existence of internal thin partial walls inside the room, the existence of windows and doors, and the incompleteness of the secular equilibrium in the 238U decay series due to radon release from the building materials. The model for radon doses is built based on Fick's laws. The radon surface exhalation rate from a wall and that from a building material sample are calculated from a one-dimension and three-dimension diffusion description by Fick's second law, respectively. The two rates are compared, and the radon indoor concentration and inhalation doses are formulated.

On FTCS Approach for Box Model of Three-Dimension Advection-Diffusion Equation

This paper describes a numerical solution for mathematical model of the transport equation in a simple rectangular box domain. The model of street tunnel pollution distribution using two-dimension advection and three-dimension diffusion is solved numerically. Because of the nature of the problem, the model is extended to become three-dimension advection and three-dimension diffusion to study the sea-sand mining pollution distribution. This model with various advection and diffusion parameters and the boundaries conditions is also solved numerically using a finite difference (FTCS) method.

Thermal degradation of typical plastics under high heating rate conditions by TG-FTIR: Pyrolysis behaviors and kinetic analysis

Pyrolysis of plastics has gained more attention recently due to the advantages of environmental protection and energy conversion. In this study, low-density polyethylene (LDPE), polypropylene (PP) and polyvinyl chloride (PVC) were studied under high heating rate conditions to investigate pyrolysis behaviors and find the most suitable kinetic reaction mechanisms. The TG and DTG curves for LDPE were similar to those for PP, but different from those for PVC. It was found that high heating rate led to the shifting of initial, end and peak temperatures to higher values. The FTIR results showed the main products of LDPE and PP were alkanes and alkenes, and the major products of PVC were HCl, alkenes and a small number of aromatic compounds. A comparative study of model-free methods like Ozawa-Flynn-Wall (OFW), Kissinger-Akahira-Sunose (KAS) and Friedman method were discussed to calculate activation energy. Kinetic reaction mechanisms were predicted by using model-fitting methods including Coats-Redfern and Criado method. The pyrolysis reaction mechanism of LDPE was summarized as contracting sphere model, PP was summarized as contracting cylinder model, whereas that of PVC was concluded that two-dimension nucleation for the first stage and three-dimension diffusion (Jander) for the second stage.

Nitridation enhancement of TiSi2 powders by addition of nickel

The nitridation enhancement of a TiSi2 powder by nickel addition was examined. The quantities of the added metal were comprised between 2.5 and 25mol.%, the balance being TiSi2. The isothermal heat treatments were made at 1100 °C for durations up to 40 h under normal pressure and continuous flow of pure nitrogen. Comparing to pure TiSi2 powder, an improvement of the conversion in TiN and Si3N4 is obtained for compositions containing 10.0; 12.5 and 15.0 mol.% of nickel. According to the quaternary Ti-Si-Ni-N phase diagram, nickel was found to form Ni4Ti4Si7 compound. Thermogravimetric analysis of these three compositions showed the existence of three successive stages during the conversion. First, an initiate reaction occurred with a very weak weight gain. Then, the second stage exhibited an acceleration of the weight gain. Those two stages are both controlled by nucleation and growth, as represented by the kinetic equation [-ln(1-α)]1/2 = k.t. Finally, the reaction is limited by three-dimension diffusion, as represented by the kinetic equation: [1-(1-α)1/3]2 = k.t. From this behavior, an activation mechanism is proposed.

Formation kinetics of Na2SnO3 from SnO2 and Na2CO3 roasted under CO-CO2 atmosphere

A novel method for Na2SnO3 preparation from SnO2 and Na2CO3 roasted under CO-CO2 atmosphere in a solid state has been successfully developed. In this study, the formation kinetics of Na2SnO3 was investigated. The formation of Na2SnO3 was controlled by the first-order interfacial chemical reaction at 800°C under 10vol% CO content; as the temperature increased to 850°C–900°C, it was controlled by the three-dimension (Ginstling and Brounshtein) diffusion through the product layer at the early reaction stage. The rate constant increased with the increasing of temperature. Furthermore, the rate controlling characterizations of three-dimension diffusion were also discussed.

Deuterium absorption properties of Zr–xCu alloys prepared by SPS

Zirconium is a kind of deuterium absorption materials and can be used as a candidate deuterium carrier in the nuclear fusion industry. However, it usually cracks after deuterium absorption and fails in its application. For the prevention of cracks, copper particles with good ductility were added into the zirconium by spark plasma sintering (SPS) synthesis method. The results showed that the addition of the Cu element affected the cracking behavior of Zr–xCu alloys significantly. With the addition of the 5%Cu no cracking was observed, and an addition of the 10%Cu lead to an observation of a few large cracks within the second phase, compared in size to the small cracks that appeared in Zr. Moreover, the addition of the Cu element decreased the deuterium absorption capacity of the Zr–xCu alloys and changed the deuterium absorption mechanism from three-dimension diffusion in the Zr alloy to chemical reaction in the Zr–10%Cu alloy. The pressure–composition–temperature (PCT) curves showed that all the Zr alloys had two plateau pressures at 900 °C, and the addition of Cu had an effect on the plateau pressure. After 10 cycles of deuterium absorption–desorption, Zr–5%Cu sample kept a integrity morphology with no cracking at low magnification, on the contrary Zr–10%Cu sample broken into pieces, though both of them kept a higher relative deuterium absorption capacity than that of Zr.

Thermal behavior of waste tea pyrolysis by TG-FTIR analysis

To investigate the kinetic behavior and the release of evolved gases in the pyrolysis process for waste tea, the technique of TG-FTIR at different heating rates was introduced in this study. The mass loss of the waste tea was divided into two steps: the volatilization of water at the temperature lower than 210 °C, and the volatilization of CO2 and organic compounds at the temperature range of 210–550 °C. FTIR (Fourier transform infrared) analysis indicated that CO2was the main gas released from the thermal degradation of waste tea. Moreover, the evolved gases from the waste tea also included H2O, CH3COOH, C6H5OH, CC and so on. Three model-free models and three model-fitting models were applied to investigate the pyrolysis process of waste tea. According to the values of the activation energy by the three model-free models and the correlation coefficient from model-fitting models, the activation energy (207.96 kJ/mol ∼ 222.6 kJ/mol) and pre-exponential factor were determined for the pyrolysis of waste tea. The results of the model-fitting models indicated that three-dimension diffusion (spherical symmetry) model conformed to the pyrolysis mechanism of waste tea well.

Effect of Fluctuation of Electrolyte Flow Rate in Hydrogen Entry Cell on Hydrogen Permeation into Steel Sheet

The sensitive measurement of hydrogen permeated into the steel is the key of issue not only to investigate the kinetics of hydrogen embrittlement of the steel but also to develop the prevention surface from the hydrogen embrittlement. Conventionally, a Devanathan-Stachurski (DS) double electrochemical cell [1] was used to measure the hydrogen permeation into the sheet specimen. However, it was a relatively difficult to measure the localized permeation of the specimen. It has been expected to develop the more sensitive method to detect the local hydrogen permeation into the steel specimen. The authors have modified the DS cell for hydrogen permeation measurement into a steel sheet to flow an electrolyte solution in the hydrogen entry side [2]. Sinusoidal fluctuation of the electrolyte flow rate resulted in the conduction of fluctuations of not only hydrogen evolution current in the entry cell but also hydrogen detection current in the exit cell. Amplitude of the detection current wave was dependent on a frequency of the fluctuation and decreased with increase in the frequency. Furthermore, a phase shift of the detection current wave from the evolution current wave was observed and it was strongly depended on the frequency. The phase shift of the detection current wave was significantly sensitive to the thickness and diffusion coefficient of the sheet [3]. The DS cell with a micro-capillary cell and the flow rate fluctuation was also applied to measure the local hydrogen permeation behavior into the steel sheet. The phase shift on a single grain of the steel sheet was two times larger than that on two grains, indicating that the hydrogen permeation was accelerated due to existence of the grain boundary of the sheet. From the comparison with theoretical diffusion equation of hydrogen into the steel [4], it was revealed that the diffusion coefficient on the grain boundary was at least two times larger than that on the single grain. These results suggested that the metallurgical structure of steel substrate strongly influenced to the permeation. However, it was difficult to the solve analytically the diffusion problem for the two- or three-dimension permeation. The authors have applied a finite element method (FEM) for the two- or three-dimension diffusion problem. A numerical calculation of FEM revealed successfully that the electrolyte fluctuation appeared the phase shift of current waves depending on the thickness and diffusivity of the substrate. The difference in phase shift due to local diffusivity was also simulated as well as the size effect of local substrate where hydrogen was permeated. The results will be reported in the paper.

Kinetics of titanium nitride synthesized with Ti and N2

The kinetics of titanium nitride synthesized with Ti and N2 at different temperatures were examined by differential scanning calorimetry and thermogravimetry. The maximum conversion degrees after 4h were 0.55, 0.76, 0.93, and 0.96 at 800, 900, 1000, and 1100°C, respectively. The reaction mechanism was analyzed through both model fitting method and ln–ln analysis method. Results showed that the reaction was initially controlled by nucleation and growth, as represented by the kinetic equation: [−ln(1−a)]4=kt, Then the reaction was controlled by three-dimension diffusion, as represented by the kinetic equation: [1−(1−a)1/3]2=kt. Activation energies for the two stages were 214.84 and 124.01kJ/mol respectively.

Pyrolysis behavior and kinetic study of phenol as tar model compound in micro fluidized bed reactor

Thermal cracking characteristic of phenol as the model compound of biomass tar was investigated on a micro fluidized bed reactor. Pyrolysis kinetics for individual gaseous component, including hydrogen, methane, carbon monoxide and carbon dioxide were determined based on the iso-conversional and model-fitting approaches. Results indicated that carbon monoxide accounted for the biggest percentage of the total gas yield during pyrolysis of phenol. The evolution profiles of hydrogen energy and carbon monoxide were more affected by reaction temperature compared to methane and carbon dioxide. In the major conversion fraction from 20% to 80%, the apparent activation energies of methane (49.67 kJ/mol) and carbon dioxide (30.87 kJ/mol) were lower than that of hydrogen (145.2 kJ/mol) and carbon monoxide (53.35 kJ/mol). The most probable reaction mechanism for the formation of hydrogen and methane was three-dimension diffusion while chemical reaction and contracting sphere could describe the generation of carbon monoxide and carbon dioxide, respectively.

Thermal analysis kinetics of thermal decomposition of nickel–viscose composite fiber

In this study, the thermal decompositions of nickel composite fibers (NCF) under different atmospheres of flowing nitrogen and air were investigated by XRD, SEM–EDS, and TG–DTG techniques. Non-isothermal studies indicated that only one mass loss stage occurred over the temperature regions of 298–1,073 K in nitrogen. The mass loss was from the decomposition. But after this decomposition, nickel was oxidized in air, when the temperature was high enough. In nitrogen media, the model-free kinetic analysis method was applied to calculate the apparent activation energy (E a) and pre-exponential factor (A). The method combining Satava–Sestak equation with one TG curve was used to select the suitable mechanism functions from 30 typical kinetic models. Furthermore, the Coats–Redfern method was used to study the NCF decomposition kinetics. The study results showed that the decomposition of NCF in nitrogen media was controlled by three-dimension diffusion; mechanism function was the anti-Jander equation, the apparent activation energy (E a) and the pre-exponential factor (A) were 172.3 kJ mol−1 and 2.16 × 109 s−1, respectively. The kinetic equation could be expressed as following: $$ \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \frac{{ 2. 1 6\times 1 0^{ 9} }}{\beta }{ \exp }\left( {\frac{ - 2 0 7 2 4. 1}{T}} \right)\left\{ {\frac{ 3}{ 2}(1 + \alpha )^{2/3} [(1 + \alpha )^{1/3} - 1]^{ - 1} } \right\}. $$

Thermal decomposition kinetics of magnesite from thermogravimetric data

Thermal decomposition kinetics of magnesite were investigated using non-isothermal TG-DSC technique at heating rate (beta) of 15, 20, 25, 35, and 40 K min(-1). The method combined Friedman equation and Kissinger equation was applied to calculate the E and lgA values. A new multiple rate iso-temperature method was used to determine the magnesite thermal decomposition mechanism function, based on the assumption of a series of mechanism functions. The mechanism corresponding to this value of F(a), which with high correlation coefficient (r-squared value) of linear regression analysis and the slope was equal to -1.000, was selected. And the Malek method was also used to further study the magnesite decomposition kinetics. The research results showed that the decomposition of magnesite was controlled by three-dimension diffusion; mechanism function was the anti-Jander equation, the apparent activation energy (E), and the pre-exponential term (A) were 156.12 kJ mol(-1) and 10(5.61) s(-1), respectively. The kinetic equation was

Thermodynamics and kinetics of the dehydration reaction of FePO4·2H2O

Abstract The thermal decomposition kinetics of FePO4·2H2O in dynamical air atmosphere was studied by mean TG–DTG–DTA. The stage and product of the thermal decomposition were determined. A number of kinetic models and calculation procedures were used to determine the kinetic triplet and thermodynamic parameters characterizing the dehydration process. The obtained activation energy and most kinetic model indicate the single kinetic mechanism and three-dimension diffusion as “Ginstling–Brounstein equation (D4 model)”, respectively. The thermodynamic functions (ΔH*, ΔG* and ΔS*) of the dehydration reaction are calculated by the activated complex theory and indicate that the process is non-spontaneous without connecting with the introduction of heat. The kinetic and thermodynamic results were satisfactory which present good correlation with a linear correlation coefficient close to unit a low standard deviation.

The role of spark plasma sintering on the improvement of hydrogen storage properties of Mg-based composites

Spark plasma sintering (SPS) is a newly developed material preparation technology and is very suitable for the multi-component and/or dissimilar materials preparation. In this paper, Mg–V 77.8Zr 7.4Ti 7.4Ni 7.4, Mg–V 38Zr 25Ti 15Ni 22 and Mg–ZrMn 2 composites were synthesized by SPS method and their hydrogen storage properties were evaluated. The results showed that with the addition of the second alloys, the hydrogen desorption temperature of pure Mg decreased apparently, with the reversible hydrogen storage capacity increased from nearly 0 of pure Mg to near 95% of its total absorption at 573 K. The hydrogen ab/desorption kinetics were also greatly improved, with the hydrogen absorption mechanism changed from surface reaction of pure Mg to three-dimension diffusion of the composite. TEM observation indicated that a thin transition zone of nanocrystalline Mg was produced at the sintering interface during SPS, which may be responsible for the improvement of hydrogen storage properties of these Mg-based composites.

Kinetics and Thermodynamic Properties of the Thermal Decomposition of Manganese Dihydrogenphosphate Dihydrate

The thermal decomposition of manganese dihydrogenphosphate dihydrate Mn(H2PO4)2·2H2O was investigated in air using differential thermal analysis-thermogravimetry. Mn(H2PO4)2·2H2O decomposes in two steps and the final decomposition product (Mn2P4O12) was studied by X-ray powder diffraction and FT-IR spectroscopy. The activation energies of the dehydration and decomposition steps of Mn(H2PO4)2·2H2O were calculated through the isoconversional methods of Ozawa and Kissinger−Akahira−Sunose and the possible conversion functions have been estimated through the Coats−Redfern method. The activation energy calculated for the dehydration and decomposition of Mn(H2PO4)2·2H2O by different methods and techniques were found to be consistent. The possible conversion functions of the dehydration and decomposition reactions for Mn(H2PO4)2·2H2O were “cylindrical symmetry” and “three-dimension diffusion”, respectively. Activated complex theory has been applied to each step of the reaction and the thermodynamic functions ΔH∗, ΔG∗ and ΔS∗ are calculated. These values for two stages showed that they are connected with the introduction of heat and are nonspontaneous processes.