Activation Energy Distribution Function Research Articles

Transport and Kinetic Property of the Butyric Acid in Water: A Simulation Study

Microbiota is defined as a class of all microorganisms which includes fungi, protozoa, bacteria and viruses. About 90 % of all microbiota in our body are found in our gut that regulates host immunity. The gut-brain axis is a bidirectional communication system that allows gut microbiota to communicate with the brain and vice versa. Studies suggest that the gut dysbiosis may enhance neurotoxic substances such as short-chain fatty-acids (SCFAs which are acetate, propionate, and butyrate) to the blood circulation and even to the brain through damaged blood brain barrier (BBB) and may cause protein aggregation which are implicated in the pathogenesis of several neurodegenerative diseases like Alzheimer’s disease (AD), Parkinson’s disease (PD), prion disease, motor neuron disease, Huntington’s disease (HD), Amyotrophic lateral sclerosis (ALS). Specifically, butyric acid are the main SCFA product that may impact on gut health. Therefore, this article aims to investigate the transport and kinetic properties such as diffusion coefficient, activation energy and radial distribution function of butyric acid in water at different temperatures through molecular dynamics simulations. The self and binary diffusion coefficient of butyric acid in water obtained from our MD simulation are found to be 0.8699×10−9m2s−1 and 0.8714×10−9m2s−1, respectively at 300 K and the activation energy for self-diffusion coefficient of water estimated from the slope of ln(D) versus 1/T is equal to 16.07 kJ/mol. Our results are in accordance with those obtained from the experimental values. This study offers an alternate approach to researching the diffusion of butyric acid in living organisms. This knowledge contributes to advancements in various fields, including nutrition, gastroenterology, microbiology, and pharmacology.

Kinetic analysis of morphologies and crystal planes of nanostructured CeO2 catalysts on soot oxidation

Soot oxidation is a triple-phase reaction system involved in solid soot, solid catalyst and gaseous oxidant, which makes its kinetic behavior difficult to be determined. Herein, we report the kinetic behavior of crystal planes on the CeO2 catalysts with various morphologies for soot oxidation. We establish a kinetic model of crystal planes of CeO2 in soot oxidation by means of the distributed activation energy model (DAEM). Through analyzing the distribution function of apparent activation energies (f (Ea)) under loose contact condition, we discover that the Ea of the exposed (1 0 0), (1 1 1) planes and non-catalytic gaseous O2 on soot oxidation distributes in the range of 60–100, 100–150, and 150–250 kJ mol−1, respectively. Our findings show that compared with other catalysts, CeO2 nanocubes exhibit the higher intrinsic activity (turnover frequency, TOF) under loose contact condition, because of the higher f (Ea) value of abundant active exposed (1 0 0) planes located at the lower Ea range. Our work develops a methodology of kinetic analysis to investigate the soot oxidation reaction, which could be potentially extended to other complex oxidation systems.

Eliminación de carbonilla en gases de escape con catalizadores DeNOx. Determinación de parámetros cinéticos

Los catalizadores DeNOx se emplean en la eliminación de los óxidos de nitrógeno en vehículos diésel y, también, puede que entren en contacto con carbonilla o incluso sean utilizados como sistemas de reducción de NOx y soot simultáneamente (DPNR-Diesel Particulate NOx Reduction). Por ello, es importante profundizar en el mecanismo de interacción entre el Soot y el catalizador. Se ha utilizado un Soot Printex U modelo y un catalizador Pt-K/Al2O3, con el potasio en forma de óxido e hidroxicarbonato hidratado. Se ha estudiado mediante TG-MS el proceso de eliminación en diferentes atmósferas oxidantes. Los procesos han sido desacoplados mediante el establecimiento de la función de distribución de energía de activación. En ausencia de catalizador, se produce la combustión del carbonilla con el oxígeno molecular en fase gas a temperaturas alrededor de los 1100 K. En presencia de NO, la reducción tiene lugar a menor temperatura debido a su carácter más oxidante y a las especies de óxidos de nitrógeno retenidas y en fase gas. Si la carbonilla se encuentra en contacto con el catalizador Pt-K/Al2O3, los centros Pt-OH-K son los responsables de la eliminación vía gasificación a 780 K con una energía de activación alrededor de 85 kJ mol-1

Distribution-free estimation of f(E) in the distributed activation energy model based on matrix singular value decomposition method

The distribution activation energy model (DAEM) is commonly used for characterizing pyrolysis kinetics of different types of thermally active materials such as coal, biomass, charcoal, polymer, and solid waste. In this work, a new distribution-free method for estimating the activation energy distribution function f(E) in DAEM is developed by establishing a physical and mathematical analogy between DAEM and the integral equation in adsorption. A parameter sensibility analysis of the present method and algorithms for calculating f(E) at different Gaussian distribution parameter, heating rates and pre-exponential factors shows that the present method gives f(E) that leads to predictions of conversion in good agreement with the test data, and applicable to pyrolysis analysis of thermally active solid materials.

Activation Energy Distribution of Dynamical Structural Defects in RuO2 Films

Ruthenium dioxide (RuO$_2$) is an important metal widely used in nanoelectronic devices. It plays indispensable roles in the applications as catalyst and supercapacitors. A good understanding of the origin of the flicker or 1/$f$ noise in RuO$_2$ will advance the design and efficiency of these applications. We demonstrate in a series of sputtered RuO$_2$ polycrystalline films that the 1/$f$ noise originates from fluctuating oxygen vacancies which act as dynamical structural defects, i.e., moving scattering centers. Reducing the number of oxygen vacancies by adjusting thermal annealing conditions significantly reduces the noise magnitude $\gamma$, the Hooge parameter. We quantify the activation energy distribution function, $g(E)$, and calculate the oxygen vacancy density, $n_{TLS}$, from the measured $\gamma$ value. We show that $g(E)$ can be explicitly expressed in terms of $\gamma(T)$ and the electronic parameters of the metal, where $T$ denotes temperature. The inferred $n_{TLS}$ value is in line with the oxygen content determined from the x-ray photoelectron spectroscopy studies.

Application of Archimedean copula in the non-isothermal nth order distributed activation energy model

ABSTRACTThe aim of this paper is to implement one of the Archimedean copulas, Gumbel–Hougaard, to determine the influence of some of the important parameters of biomass pyrolysis on the numerical solution of the nth order distributed activation energy model. The initial distribution function of activation energy is replaced by the bivariate distribution function. In this manner, the cumulative effect of different univariate functions on modelling of biomass pyrolysis can be studied. The single marginal distribution function does not exhibit flexibility in its pattern, therefore the concept of copula is introduced to analysis the pyrolysis problem qualitatively. Activation energies E1 and E2 are assumed to initiate the primary and the secondary pyrolysis reactions respectively. Temperature distribution is considered to vary linearly with time. Thermo-analytical data is experimentally retrieved with the help of thermogravimetry and differential thermogravimetry (TG/DTG).

Studies on thermokinetic of Chlorella pyrenoidosa devolatilization via different models

The thermokinetics of Chlorella pyrenoidosa (CP) devolatilization were investigated based on iso-conversional model and different distributed activation energy models (DAEM). Iso-conversional process result showed that CP devolatilization roughly followed a single-step with mechanism function of f(α)=(1−α)3, and kinetic parameters pair of E0=180.5kJ/mol and A0=1.5E+13s−1. Logistic distribution was the most suitable activation energy distribution function for CP devolatilization. Although reaction order n=3.3 was in accordance with iso-conversional process, Logistic DAEM could not detail the weight loss features since it presented as single-step reaction. The un-uniform feature of activation energy distribution in Miura-Maki DAEM, and weight fraction distribution in discrete DAEM reflected weight loss features. Due to the un-uniform distribution of activation and weight fraction, Miura-Maki DAEM and discreted DAEM could describe weight loss features.

Pyrolysis mechanism and kinetic model of Mudanjiang oil shale in the Songliao Basin, China

In recent years, a lot of work on the development of oil shale has been done with regard to the Chinese oil shales. However, the research is mainly with respect to the processing aspects of oil shale. The pyrolysis mechanism of oil shale has been limited, to some extent, by instrumentation and analytical techniques. In this paper, pyrolysis kinetics characteristics of oil shale samples obtained from Mudanjiang were investigated by Rock-Eval analysis. The weight loss data, pyrolysis mechanism, and properties of oil shale were analyzed at different heating rates (10, 15, 20, 25, 30℃/min) in the temperature range from 200 to 600℃. In this paper, a distribution function of apparent activation energy and a relationship equation of apparent energy with frequency factor have been obtained. A special kinetic model was developed, fully suitable for the pyrolysis characteristics of oil shale. This model was also verified by experiment. Throughout the analysis of pyrolysis kinetics, it was observed that the pyrolysis reaction mechanism at different temperatures could be explained. The results may provide the theoretical basis for further effective and economical exploitation of oil shale.

Kinetic analysis of non-isothermal dehydration of poly(acrylic acid)-g-gelatin hydrogel using distributed activation energy model

The applicability of distributed activation energy model (DAEM) for describing non-isothermal dehydration kinetics of poly(acrylic acid)-g-gelatin (PAG) hydrogel has been examined. Thermogravimetric curves were recorded at different heating rates from 5 to 20 K min−1. The activation energy dependence on dehydration degree was determined by Kissinger–Akahira–Sunose and Vyazovkin’s methods. The possibility of applying thermodynamically inhibited nucleation and growth reaction model on investigating process has been examined. Miura–Maki method was used to establish the shape of activation energy distribution function and the dependence of pre-exponential factor on dehydration degree. Non-isothermal dehydration kinetics of PAG hydrogel can be successfully described by the DAEM. Here we defined the procedure by which DAEM can be successfully connected with kinetic models commonly used for reactions in solid state. The dependences of specific rate (i.e., rate constant) and reaction model function on dehydration degree were established for all of the investigated heating rates. It has been concluded that the specific rate changes with dehydration degree and that this is the one of the reasons why non-isothermal dehydration kinetics of PAG hydrogel is complex.

Intrinsic reactivity analysis of soot removal in LNT-catalysts

The soot removal process in presence of a series of LNT-catalysts, and different reaction atmospheres, has been studied, using thermogravimetric analysis coupled to mass spectrometry (TG-MS) time-resolved experiments. Kinetic parameters have been estimated, using a distribution function of activation energy: where the frequency factor was correlated approximately with the activation energies which enable the decoupling of the processes involved in the regeneration by soot removal over those synthesized catalysts. It was found that soot removal is a sequential process that is strongly dependent on the formulation and surface structure of the catalyst and atmosphere of reaction. K-containing LNT catalysts showed a high activity in the soot removal process by gasification (Ea≈70–90kJmol−1), promoted by surface hydroxylated centers, decreasing the ignition temperature in oxygen atmosphere. NO+O2 atmosphere, more oxidizing than O2, provokes in addition a reduction in the soot removal temperature due to a direct reaction between soot and NO2 (gas) and/or the adsorbed NOx onto the catalyst surface.

Method for Determining the Activation Energy Distribution Function of Complex Reactions by Sieving and Thermogravimetric Measurements.

A method for studying the kinetics of thermal degradation of complex compounds is suggested. Although the method is applicable to any matrix whose grain size can be measured, herein we focus our investigation on thermogravimetric analysis, under a nitrogen atmosphere, of ground soft wheat and ground maize. The thermogravimetric curves reveal that there are two well-distinct jumps of mass loss. They correspond to volatilization, which is in the temperature range 298-433 K, and decomposition regions go from 450 to 1073 K. Thermal degradation is schematized as a reaction in the solid state whose kinetics is analyzed separately in each of the two regions. By means of a sieving analysis different size fractions of the material are separated and studied. A quasi-Newton fitting algorithm is used to obtain the grain size distribution as best fit to experimental data. The individual fractions are thermogravimetrically analyzed for deriving the functional relationship between activation energy of the degradation reactions and the particle size. Such functional relationship turns out to be crucial to evaluate the moments of the activation energy distribution, which is unknown in terms of the distribution calculated by sieve analysis. From the knowledge of moments one can reconstruct the reaction conversion. The method is applied first to the volatilization region, then to the decomposition region. The comparison with the experimental data reveals that the method reproduces the experimental conversion with an accuracy of 5-10% in the volatilization region and of 3-5% in the decomposition region.

A comparison study on thermal decomposition behavior of poly(l-lactide) with different kinetic models

A thermal study of poly(l-lactide) under nitrogen atmosphere has been carried out through thermogravimetric (TG) analysis and differential thermal analysis (DTA) measurements. The experimental data were collected with the heating rates of 2.5 to 30 K min−1 and from ambient temperature up to 750 K. The thermal features were obtained from resultant TG and DTA curves. The results show that the thermal decomposition was mainly in the temperature range of 550–660 K. Kinetic analyses of the mass loss versus temperature data have been performed with four different temperature integral models, including the distributed activation energy model (DAEM), Flynn–Wall–Ozawa, Coats–Redfern, and Tang models. Through the DAEM model, the activation energy distribution function and the relationship between activation energy and pre-exponential factor have been obtained. The activation energy thus obtained at different conversion levels ranges from 91.34 to 107.44 kJ mol−1, and similar results have been produced using the other three models. With these kinetic parameters, the TG curves have been simulated with the above four models by assuming the first-order reaction mechanism, resulting in satisfactory simulation results.

Temperature programmed desorption studies of water interactions with Apollo lunar samples 12001 and 72501

The desorption activation energies for water molecules chemisorbed on Apollo lunar samples 72501 (highlands soil) and 12001 (mare soil) were determined by temperature programmed desorption experiments in ultra-high vacuum. A significant difference in both the energies and abundance of chemisorption sites was observed, with 72501 retaining up to 40 times more water (by mass) and with much stronger adsorption interactions, possibly approaching 1.5eV. The dramatic difference between the samples may be due to differences in mineralogy and surface exposure age. The distribution function of water desorption activation energies for sample 72501 was used as an initial condition to simulate water persistence through a temperature profile matching the lunar day.

Study on the Kinetics of Plant Oil Asphalt Pyrolysis Using Thermogravimetry and the Distributed Activation Energy Model

Plant oil asphalt (POA) is a new concerned lipid-based residue biomass generated from the oleochemical industry. In this work, the pyrolysis kinetics of POA was studied by thermogravimetric analysis at heating rates of 7, 10, 20, and 30 K min–1 under a nitrogen atmosphere using the distributed activation energy model (DAEM). The kinetic parameters, including the activation energy E, distribution function of activation energy f(E), and pre-exponential factor k0, were obtained. The activation energy E ranged from 75 to 300 kJ mol–1, and the f(E) curve showed a broad peak around 155–200 kJ mol–1. The linear relationship between ln k0 and activation energy E indicated that there existed a kinetic compensation effect in pyrolysis of POA. A double-Gaussian DAEM was employed for simulation of POA pyrolysis by assuming POA as a mixture of two pseudo-components. In comparison to the single-Gaussian DAEM, the double-Gaussian DAEM was better to predict the pyrolysis behavior of POA. This work validated the applicability of the double-Gaussian DAEM to the lipid-based material POA.

Evaluations of the apparent activation energy distribution function for the nonisothermal reduction of nickel oxide nano-powders

The differential conversion curves of the non-isothermal NiO reduction process by hydrogen are fitted by the Weibull (non-isothermal) probability density function (Wpdf), in a wide range of the degree of conversion (α = 0.06 - 0.96). It was established that the Weibull distribution parameters (β and η) show the different dependences on the heating rate of the system (vh) (shape parameter (β) - linear form and scale parameter (η) - exponential form). Model independent values of the apparent activation energy were calculated using the Friedman's isoconversional method. It was found that the calculated apparent activation energy depends on the degree of conversion, α, and it shows a constant value in the range of the degree of conversion 0.20 ≤ α ≤ 0.60 (Ea = 90.8 kJ mol- 1). Knowing the Weibull distribution function of reaction times, it is possible to determine the density distribution function of apparent activation energies at different heating rates. It was established that the changes of the symmetry of density distribution functions may be an indication for deviations from the simple crystallization kinetics as expressed by the Johnson-Mehl-Avrami (JMA) model, and this behaviour is probably due to a more complex transformation process such as a process described by the two-parameter autocatalytic Šesták-Berggren model.

Thermal characterization and kinetic analysis of non-isothermal decomposition process of Bauxite red mud. Estimation of density distribution function of the apparent activation energy

Thermal characterization and kinetic analysis of non-isothermal decomposition process of Bauxite red mud were carried out using thermogravimetry (TG), derivative thermogravimetry (DTG), differential scanning calorimetry (DSC), differential thermal analysis (DTA) and Fourier transform infrared spectroscopy (FTIR). It was found that the investigated decomposition was a complex heterogeneous process, which included two main decomposition stages and one sub-stage. The overall decomposition process consisted of the series of parallel and competitive reactions, which originated from the decomposition of various chemical species and solid-state transformations. This behavior was confirmed by the appearance of different forms of density distribution functions of apparent activation energy values. Furthermore, the conversion range of 0.10≤α≤0.30, with a constant value of the apparent activation energy (146.4kJmol−1) for the second stage of the overall process, belongs to calcite decomposition, which takes place through a two-dimensional diffusion mechanism.

Water interactions with micronized lunar surrogates JSC‐1A and albite under ultra‐high vacuum with application to lunar observations

Interactions of molecular water with two lunar regolith surrogates (micronized JSC‐1A and albite) were examined using temperature program desorption (TPD) and diffuse reflectance infrared Fourier transform spectroscopy. TPD revealed water desorption during initial heating to 750 K under ultrahigh vacuum and diffuse reflectance infrared Fourier transform spectroscopy indicated possible water formation via recombinative desorption of native hydroxyls above 425 ± 25 K. Dissociative chemisorption of water (i.e., formation of surface hydroxyl sites) was not observed on laboratory time scales after controlled dosing of samples (initially heated above 750 K) with 0.2–500 L exposures of water. However, preheated samples of both types of surrogates were found to have a distribution of molecular water chemisorption sites, with albite having at least twice as many as the JSC‐1A samples by mass. A fit to the TPD data yields a distribution function of desorption activation energies ranging from ~ 0.45 to 1.2 eV. Using the fitted distribution function as an initial condition, the TPD process was simulated on the time scale of a lunation.

The kinetic analysis of isothermal curing reaction of an unsaturated polyester resin: Estimation of the density distribution function of the apparent activation energy

The kinetic process of isothermal curing of an unsaturated polyester resin samples has been studied. The differential isoconversional method is used to yield dependency of the apparent activation energy, E a , on the degree of cure. It was found that the dependence of E a on α is complex, but in the conversion range α = 0.10–0.50, E a is practically constant. It was found that the gelling stage of curing process is mainly controlled chemically which can be best described by two-parameter autocatalytic model. At higher values of α, when vitrification point is reached, the change in rate-limiting step was observed. As the consequence of shifting effect from the kinetics to diffusion control, the kinetic law equation is modified with additional diffusion term. It was found that the experimentally obtained density distribution function of the apparent activation energy can be approximate by unbalanced modified Gaussian distribution function with quite satisfactory precision.

Seismic Damping and Creep in the Mantle

A unified theory of viscosity and viscoelasticity of the molecular-rearrangement type is given in which the two phenomena appear as special cases. The Becker theorem is reviewed; with the Becker distribution of relaxances, the distribution function of activation energies is a constant, viscoelastic creep is logarithmic and the specific damping 1/Q is frequency insensitive in wide ranges of time and frequency. The vibrating-string theories of dislocation damping in general are not feasible because the mean thermal kinetic energy of the basic mode is smaller by an order of magnitude than the Peierls—Nabarro dissipation for amplitudes equal to the Burgers vector of most materials. Low-amplitude damping is treated as a consequence of the perturbation of the activation energies of thermally activated jumps of dislocation segments by the applied stress; since the distribution function of the activation energies is probably close to the Becker distribution, the resulting damping is insensitive to frequency and amplitude and increases steeply with the temperature. The Amontons law of solid friction breaks down at very small amplitudes of displacement, such as those between the walls of small cracks in rocks. The simplest generalization of the Amontons law to include small amplitudes leads to an amplitude- and frequency-independent damping. The effect of pressure on the viscosity, if regarded as given approximately by an increase of the activation energy by the product of the pressure and the volume expansion accompanying a molecular rearrangement, seems relatively small: with an expansion of 10 cubic Ångströms and a pressure of 1 megabar (2200 km depth), the increase is about 6eV corresponding to about 0·6eV at room temperature; with 4 cubic Ångströms, about 0·24eV. The grain boundary viscosity, therefore, should be relatively low. On the other hand, the crystal grains should be very hard in the deep mantle because the shear modulus is close to that of diamond at the core boundary. These factors seem to account for the creep and damping properties of the middle and deep mantle. The high damping and low viscosity in the Gutenberg low-velocity layer seems to be due to a phase transition, possibly including some eutectic grain boundary melting. While there is no general physical relationship between damping and creep, the parallelism expressed by Anderson's empirical formula seems to express the drastic decrease of both Q and η in the presence of a phase transition.

Application of the Weibull distribution function for modeling the kinetics of isothermal dehydration of equilibrium swollen poly (acrylic acid) hydrogel

A theoretical procedure for evaluating the density distribution function ( p( E a )) of apparent activation energies ( E a ), based on modeling of the experimental isothermal conversion curves by Weibull probability function of reacting times was established. This procedure was applied on isothermal dehydration of poly (acrylic acid) hydrogel (PAAH) at four different operating temperatures (306, 324, 345 and 361 K). It was established that: (a) the experimental conversion curves at all temperatures can be described by the Weibull probability distribution function of reacting times in a wide range of the degree of conversion (0.14 ⩽ α ⩽ 0.95); (b) the Weibull distribution parameters ( β and η) show functional dependences on the operating temperature, and (c) the apparent activation energy ( E a ) varies with the degree of conversion ( α). It was shown that the density distribution function of activation energies is independent on the temperature, and because of this fact, the considered function is an Eigen characteristic of the dehydration studied. The calculated p( E a ) function is in good agreement with the experimental p( E a ) function ( p( E a ) exp), obtained by the Miura procedure.