Analytical solution for the Kissinger equation

2009 ◽  
Vol 24 (10) ◽  
pp. 3095-3098 ◽  
Author(s):  
Pere Roura ◽  
Jordi Farjas
Keyword(s):  
Activation Energy ◽  
Analytical Solution ◽  
Kinetic Analysis ◽  
Relative Error ◽  
Structural Relaxation ◽  
Amorphous Materials ◽  
Reaction Rate ◽  
Large Range ◽  
Peak Temperature ◽  
Kissinger Equation

An analytical solution for the Kissinger equation relating the activation energy, E, with the peak temperature of the reaction rate, Tm, has been found. It is accurate (relative error below 2%) for a large range of E/RTm values (from 15 to above 60) that cover most experimental situations. The possibilities opened by this solution are outlined by applying it to the analysis of some particular problems encountered in structural relaxation of amorphous materials and in kinetic analysis.

Structural Relaxation Process in CuHfTi Amorphous Alloys

2009 ◽  
Vol 283-286 ◽  
pp. 533-538 ◽  
Author(s):  
Kazumasa Yamada ◽  
N. Shinagawa ◽  
M. Sogame ◽  
I.A. Figueroa ◽  
Hywel A. Davies ◽  
...  
Keyword(s):  
Activation Energy ◽  
Relaxation Process ◽  
Structural Relaxation ◽  
Amorphous Alloys ◽  
Melt Spinning ◽  
Amorphous Materials ◽  
Ternary Alloys ◽  
Relaxation Processes ◽  
Scanning Calorimetry ◽  
Structure Relaxation

The aim of this research is to clarify a quantitative evaluation in the structural relaxation processes focusing on the activation energy in Cu based amorphous alloys. The activation energy for structural relaxation process in a metal type amorphous CuHfTi ternary alloys, with cross sections of typically 0.03 mm x 2.0 mm, prepared by chill-block melt spinning has been investigated by Differential Scanning Calorimetry (DSC) with a cyclically heating technique. Activation energies for structural relaxation with a spatial quantity in amorphous materials have been discussed by use of a relaxed ratio function that depends on annealing temperature and time. In the present work, the distributions for the Activation Energy Spectrum (AES) were observed almost 152 kJmol-1 (1.58 eV). Another result has been also established that the “reversible” AES model energy distribution though the cyclically structure relaxation occurs even in amorphous Cu60Hf20Ti20 alloy.

scholarly journals Kinetic Processes in Amorphous Materials Revealed by Thermal Analysis: Application to Glassy Selenium

Molecules ◽  
2019 ◽  
Vol 24 (15) ◽  
pp. 2725 ◽  
Author(s):  
Málek ◽  
Svoboda
Keyword(s):  
Activation Energy ◽  
Crystal Growth ◽  
Viscous Flow ◽  
Structural Relaxation ◽  
Amorphous Materials ◽  
Supercooled Liquid ◽  
Thermomechanical Analysis ◽  
Growth Data ◽  
Scanning Calorimetry ◽  
Kinetic Processes

It is expected that viscous flow is affecting the kinetic processes in a supercooled liquid, such as the structural relaxation and the crystallization kinetics. These processes significantly influence the behavior of glass being prepared by quenching. In this paper, the activation energy of viscous flow is discussed with respect to the activation energy of crystal growth and the structural relaxation of glassy selenium. Differential scanning calorimetry (DSC), thermomechanical analysis (TMA) and hot-stage infrared microscopy were used. It is shown that the activation energy of structural relaxation corresponds to that of the viscous flow at the lowest value of the glass transition temperature obtained within the commonly achievable time scale. The temperature-dependent activation energy of crystal growth, data obtained by isothermal and non-isothermal DSC and TMA experiments, as well as direct microscopic measurements, follows nearly the same dependence as the activation energy of viscous flow, taking into account viscosity and crystal growth rate decoupling due to the departure from Stokes–Einstein behavior.

Effect of Co-precursor Maliec Anhydride on the Thermal Decomposition of Acetyl Ferrocene: A Reaction Kinetic Analysis

2019 ◽  
Vol 9 (1) ◽  
pp. 22-35
Author(s):  
Bratati Das ◽  
Ashis Bhattacharjee
Keyword(s):  
Activation Energy ◽  
Thermal Decomposition ◽  
Reaction Mechanism ◽  
Kinetic Analysis ◽  
Reaction Rate ◽  
Reaction Kinetic ◽  
Step Process ◽  
Probable Reaction Mechanism ◽  
Probable Reaction ◽  
Reaction Atmosphere

Background: Thermal decomposition of iron-bearing organometallic complex acetyl ferrocene, (C5H4COCH3)Fe(C5H5), leads to hematite (α-Fe2O3) nanoparticles. Presence of maliec anhydride, C4H2O3 as co-precursor during thermal decomposition modifies the size of the particles as well as the quantity of the reaction product significantly. Objective: Kinetic analysis of the solid-state thermal reaction of acetyl ferrocene in the presence of varying amount of co-precursor maliec anhydride under inert reaction atmosphere has been studied in order to understand the reaction mechanism involved behind the formation of hematite and the role of co-precursor in the reaction process. For this purpose, reaction kinetic analysis of three mixtures of acetyl ferrocene and maliec anhydride has been carried out. Methods: Thermogravimetry under non-isothermal protocol with multiple heating rates has been employed. The data are analyzed using model-free iso-conversional kinetic techniques to estimate the activation energy of reaction and reaction rate. The most-probable reaction mechanism has been identified by master plot method. The kinetic triplets (activation energy, reaction rate, most probable reaction mechanism function) have been employed to estimate the thermodynamic triplets (ΔS, ΔH and ΔG). Observations: Acetyl Ferrocene (AFc) undergoes thermal decomposition in a four-step process leaving certain residual mass whereas maliec anhydride (MA) undergoes complete mass loss owing to melting followed by evaporation. In contrast, the (AFc1-x-MAx) mixtures undergo thermal decomposition through a two-step process, and the decompositions are completed at much lower temperatures than that in AFc. The estimated activation energy and reaction rate values are found strongly dependent on the extent of conversion as well as on the extent of mixing. Introduction of MA in the solid reaction atmosphere of AFc in one hand reduces the activation energy required by AFc to undergo thermal decomposition and the reaction rate, while on the other hand varies the nature of reaction mechanism involved. Results: The range of reaction rate values estimated for the mixtures indicate that the activated complexes during Step-I of thermal decomposition may be treated as ‘loose’ complex whereas ‘tight’ complex for the Step-II. From the estimated entropy values, thermal process of (AFc1-x-MAx) mixture for Steps I and II may be interpreted as ‘‘slow’’ stage. Conclusion: Variation of Gibb’s free energy with the fraction of maliec anhydride in the mixtures for Step-I and II indicate that the thermal processes of changing the corresponding activated complexes are non-spontaneous at room temperature.

Structural Relaxation Process by Addition of B in CuHfTi Amorphous Alloys

2010 ◽  
Vol 297-301 ◽  
pp. 702-707
Author(s):  
Kazumasa Yamada ◽  
N. Miura ◽  
A. Yamamoto ◽  
I.A. Figueroa ◽  
Hywel A. Davies ◽  
...  
Keyword(s):  
Activation Energy ◽  
Relaxation Process ◽  
Structural Relaxation ◽  
Amorphous Alloys ◽  
Melt Spinning ◽  
Amorphous Materials ◽  
Relaxation Processes ◽  
Quaternary Alloys ◽  
Scanning Calorimetry ◽  
Structure Relaxation

The aim of this research is to clarify a quantitative evaluation in the structural relaxation processes focusing on the activation energy on the addition of B to Cu-based amorphous alloys. The activation energy for structural relaxation process in a metal type amorphous CuHfTi ternary and CuHfTiB quaternary alloys, with cross sections of typically 0.03 mm x 2.0 mm, prepared by chill-block melt spinning has been investigated by Differential Scanning Calorimetry (DSC) with a cyclically heating technique. Activation energies for structural relaxation with a spatial quantity in amorphous materials have been discussed by use of a total relaxed ratio function that depends on annealing temperature and time. In the present work on CuHfTi ternary and CuHfTiB quaternary alloys, the distributions for the Activation Energy Spectrum (AES) by calculation with derivative-type relaxed ratio function were observed almost 160 kJmol-1, whereas in difference for shape only in the CuHfTi-B3% quaternary alloy. Another result has been also established that the ‘reversible’ AES model energy distribution though the cyclically structure relaxation occurs even in amorphous CuHfTiB alloy system.

Kinetic Analysis of the Decomposition of Calcium Carbonate Using Danyang Limestone

2006 ◽  
Vol 510-511 ◽  
pp. 502-505 ◽  
Author(s):  
Sang Hwan Cho ◽  
Sung Min Joo ◽  
Jin Sang Cho ◽  
Young Hwan Yu ◽  
Ji Whan Ahn ◽  
...  
Keyword(s):  
Activation Energy ◽  
Calcium Carbonate ◽  
Kinetic Parameter ◽  
Kinetic Analysis ◽  
Heating Rate ◽  
Reaction Rate ◽  
Decomposition Temperature ◽  
Final Point ◽  
Maximum Reaction

Non-isothermal behaviors of calcium carbonate using Danyang limestone were investigated. It was attempted to provide non-isothermal data with a precision sufficient for the determination of reliable decomposition behaviors and for the estimation of accurate kinetic parameter. The decomposition temperature of calcium carbonate on the onset, peak and final point were measured. Reaction rate was decreased and maximum reaction temperature was increased with increasing heating rate. Activation energy of Danyang limestone was 45.14㎉/㏖ and 50.80㎉/ ㏖ by Kissinger method and Freeman method, respectively.

Kinetic Analysis of Alkaline Extraction on Sweet-Bamboo Leaves

2011 ◽  
Vol 332-334 ◽  
pp. 467-470
Author(s):  
Porntip Sae Be ◽  
Suesat Jantip ◽  
Sirisin Chum Rum
Keyword(s):  
Activation Energy ◽  
Kinetic Analysis ◽  
Rate Constant ◽  
Reaction Rate ◽  
Reaction Rate Constant ◽  
Extraction Temperature ◽  
Alkaline Extraction ◽  
K Value ◽  
Bamboo Leaves ◽  
Kinetics Of

This study aimed to investigate the influence of NaOH concentration and temperature used for cellulose extraction from sweet-bamboo leaves on the kinetics of the extraction reaction. The NaOH concentration and the temperature used for the extraction were varied and their effect was examined. It was found that the extraction rate was accelerated by either the increase of NaOH concentration or extraction temperature. The NaOH concentration affected the reaction rate constant, k, and the activation energy, E and the order of the reaction, n. Increase of NaOH concentration enhanced the reaction to move forwards, thus reducing the k and E values of the reaction and the order of the reaction, n, was changed. The correlation of the temperature and the NaOH concentration with the k value showed that at the lower NaOH concentration, the temperature influenced on the k value more significantly. The influence of the NaOH concentration on the k value was lessened with increase of the extraction temperature.

scholarly journals Mechanistic Study on the Reaction of pinB-BMes2 with Alkynes Based on Experimental Investigation and DFT Calculations: Gradual Change of Mechanism Depending on the Substituent

2021 ◽  
Author(s):  
Linlin Wu ◽  
Chiemi Kojima ◽  
Ka Ho Lee ◽  
Shogo Morisako ◽  
Zhenyang Lin ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Transition Metal ◽  
Dft Calculations ◽  
Kinetic Analysis ◽  
Reaction Rate ◽  
Mechanistic Study ◽  
Isomer Ratio ◽  
Gradual Change ◽  
Isomeric Mixture ◽  
Metal Free

Transition-metal free direct and base-catalyzed 1,2-diborations of arylacetylenes using pinB-BMes2 provided syn/anti-isomeric mixture of diborylalkenes. The kinetic analysis showed that the reaction rate and isomer ratio were affected by reaction...

Activation energy spectra and relaxation in amorphous materials

1983 ◽  
Vol 18 (1) ◽  
pp. 278-288 ◽  
Author(s):  
M. R. J. Gibbs ◽  
J. E. Evetts ◽  
J. A. Leake
Keyword(s):  
Activation Energy ◽  
Amorphous Materials ◽  
Energy Spectra

Kinetic analysis of biomass pyrolysis using a double distributed activation energy model

2015 ◽  
Vol 121 (3) ◽  
pp. 1403-1410 ◽  
Author(s):  
Benedetta de Caprariis ◽  
Maria Laura Santarelli ◽  
Marco Scarsella ◽  
Carlos Herce ◽  
Nicola Verdone ◽  
...  
Keyword(s):  
Activation Energy ◽  
Kinetic Analysis ◽  
Energy Model ◽  
Biomass Pyrolysis ◽  
Distributed Activation Energy Model
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