Non-isothermal kinetics: best-fitting empirical models instead of model-free methods

AbstractThe isoconversional (or model-free) methods cannot provide meaningful kinetic description for most samples in thermal analysis. Nevertheless, they can serve as empirical models. A usable empirical model should describe well the observed data and should be suitable for predictions, too. For this purpose, the functions in the isoconversional kinetic equation were parametrized, and the parameters were determined by the method of least squares. This procedure ensures that the data calculated from the model would be close to the experimental data. The present work supplemented a preceding work of Várhegyi (Energy and Fuels 33:2348–2358, 2019) by further considerations and by various evaluations on the TGA curves of a wood sample. The prediction capabilities of the models were also tested. It was found that an evaluation based on three experiments with constant heating rates could predict well two further experiments with stepwise temperature programs. Furthermore, a modification of the model was proposed and examined. The aim of this modification was to improve the fit quality without increasing the number of parameters in the least-squares procedure.

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SOĞUK HADDELENMİŞ AA3105 VE AA5005 LEVHALARIN DSC ANALİZİ İLE YENİDEN KRİSTALLENME KİNETİĞİ

Euroasia Journal of Mathematics, Engineering, Natural and Medical Sciences ◽

10.38065/euroasiaorg.621 ◽

2021 ◽

Vol 8 (17) ◽

pp. 80-85

Author(s):

Atae RAOUGUI ◽

Ion GRECU ◽

Volkan Murat YILMAZ ◽

Kenan YILDIZ

Keyword(s):

Differential Scanning Calorimetry ◽

Aluminum Alloy ◽

Activation Energies ◽

Isothermal Kinetics ◽

Heating Rates ◽

Scanning Calorimetry ◽

Recrystallization Kinetics ◽

Model Free ◽

Cold Rolled ◽

Kinetics Of

In this study, the non-isothermal recrystallization kinetics of cold rolled AA3105 and AA5005 aluminum alloy sheets obtained from ASAŞ Aluminum located in Akyazı-Sakarya was studied by using differential scanning calorimetry (DSC). The non – isothermal kinetics was performed by using Kissenger, Boswell, Ozawa and Starink methods known as model – free methods. The recrystallization temperatures on DSC graphics at different heating rates (β) were deduced and the activation energies were calculated from the slopes from Y – 1/T diagrams. Y is ln(β/T2) for Kissenger, ln(β/T) for Boswell, ln(β) for Ozawa and ln(β/T1.92) for Starink. The results showed that the activation energies of recrystallization are in the range of 194 – 206 kJ/mol for cold rolled AA5005 sheet and in the range of 235 – 257 kJ/mol for cold rolled AA3105 sheet, according to four non-isothermal kinetics model.

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Characterization of PVC/MWCNTs Nanocomposite: Solvent Blend

Science and Engineering of Composite Materials ◽

10.1515/secm-2020-0003 ◽

2020 ◽

Vol 27 (1) ◽

pp. 55-64 ◽

Cited By ~ 1

Author(s):

Abdullah F. Al Naim ◽

Huda AlFannakh ◽

Samia Arafat ◽

S. S. Ibrahim

Keyword(s):

Thermal Properties ◽

Kinetic Method ◽

Multiwall Carbon Nanotubes ◽

Isothermal Kinetics ◽

Hysteresis Curve ◽

Heating Rates ◽

Model Free ◽

Main Decomposition ◽

Apparent Activation Energies ◽

The Stability

AbstractPolyvinyl Vinyl Chloride (PVC) multiwall carbon nanotubes (MWCNTs) nanocomposite flexible films were prepared using the solvent blend technique. Chloroform (CHCl3) and tetrahydrofuran ((CH2)4O) were used as solvents for MWCNTs and PVC, respectively. The effect of the solvents’ blend on electrical, optical and thermal properties of PVC/MWCNTs were investigated. The results of the Raman spectrum showed that all the characteristic bands of PVC polymer have a slight shift due to addition of MWCNTs. Electrical results showed that the nanocomposite samples with chloroform volume ratios of 10% and 25% had nearly the same conductivity. This is attributed to the formation of the MWCNTs network, which assisted in electrical conductivity. The I-V hysteresis curve decreases as the temperature increases and as it approaches the glass transition temperature. The non-isothermal kinetics analysis for PVC and PVC/MWCNTs were investigated by Thermogravimetry Analysis (TGA) using the model-free kinetic method. The non-isothermal measurements were carried out at five heating rates of 5 to 40∘C/min. The results show that the main decomposition process has constant apparent activation energies for all samples. The use of the bi-solvent method has improved the dispersion of untreated MWCNTs, and this has been reflected on the stability of both electrical and thermal properties.

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A Procedure for Finding the Coefficients of the Best Fitting Second and Third Degree Polynomials by Application of the Method of Least Squares

Mathematics of Computation ◽

10.2307/2003276 ◽

1967 ◽

Vol 21 (99) ◽

pp. 514

Author(s):

Roy H. Wampler ◽

Asko Visapaa

Keyword(s):

Least Squares ◽

Method Of Least Squares ◽

Best Fitting

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The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.1.05 ◽

2020 ◽

pp. 60-73

Author(s):

Yu V Nemirovskii ◽

S V Tikhonov

Keyword(s):

General Solution ◽

Least Squares ◽

Nonlinear Differential Equations ◽

Limit State ◽

Algebraic Equations ◽

Method Of Least Squares ◽

Elasticity Limit ◽

Limit Values ◽

Symbolic Calculations ◽

Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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Some Aspects of Discrete Relaxation Time Spectra as Obtained from Dynamic Moduli Data

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19951815 ◽

1995 ◽

Vol 60 (11) ◽

pp. 1815-1829 ◽

Cited By ~ 1

Author(s):

Jaromír Jakeš

Keyword(s):

Relaxation Time ◽

Least Squares ◽

Discrete Spectrum ◽

Integral Transform ◽

Time Spectrum ◽

Relaxation Time Spectrum ◽

Dynamic Moduli ◽

Best Fitting ◽

Discrete Spectra ◽

Well Posed

The problem of finding a relaxation time spectrum best fitting dynamic moduli data in the least-squares sense is shown to be well-posed and to yield a discrete spectrum, provided the data cannot be fitted exactly, i.e., without any deviation of data and calculated values. Properties of the resulting spectrum are discussed. Examples of discrete spectra obtained from simulated literature data and experimental literature data on polymers are given. The problem of smoothing discrete spectra when continuous ones are expected is discussed. A detailed study of an integral transform inversion under the non-negativity constraint is given in Appendix.

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Functional ratings in sports

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2020-0001 ◽

2020 ◽

Vol 16 (3) ◽

pp. 183-191

Author(s):

Brad Lowery ◽

Abigail Slater ◽

Kaison Thies

Keyword(s):

Least Squares ◽

Method Of Least Squares ◽

Sports Teams ◽

New Model ◽

College Basketball ◽

Division 1

AbstractIn this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a team average point differential adjusted for strength of schedule. Using two team’s functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018–2019 NCAA Division 1 men’s college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.

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On the Appropriate Measure to Estimate Hyperbolic Discounting Rate (K) using the Method of Least Squares

Perspectives on Behavior Science ◽

10.1007/s40614-021-00306-x ◽

2021 ◽

Author(s):

Harli R. Berk ◽

Tanya A. Gupta ◽

Federico Sanabria

Keyword(s):

Least Squares ◽

Hyperbolic Discounting ◽

Method Of Least Squares

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Thermo-catalytic decomposition of polystyrene waste: Comparative analysis using different kinetic models

Waste Management & Research ◽

10.1177/0734242x19865339 ◽

2019 ◽

Vol 38 (2) ◽

pp. 202-212 ◽

Cited By ~ 14

Author(s):

Ghulam Ali ◽

Jan Nisar ◽

Munawar Iqbal ◽

Afzal Shah ◽

Mazhar Abbas ◽

...

Keyword(s):

Activation Energy ◽

Copper Oxide ◽

Solid Waste ◽

Thermodynamic Parameters ◽

Model Fitting ◽

Catalytic Decomposition ◽

Decomposition Reaction ◽

Inert Atmosphere ◽

Heating Rates ◽

Model Free

Due to a huge increase in polymer production, a tremendous increase in municipal solid waste is observed. Every year the existing landfills for disposal of waste polymers decrease and the effective recycling techniques for waste polymers are getting more and more important. In this work pyrolysis of waste polystyrene was performed in the presence of a laboratory synthesized copper oxide. The samples were pyrolyzed at different heating rates that is, 5°Cmin−1, 10°Cmin−1, 15°Cmin−1 and 20°Cmin−1 in a thermogravimetric analyzer in inert atmosphere using nitrogen. Thermogravimetric data were interpreted using various model fitting (Coats–Redfern) and model free methods (Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose and Friedman). Thermodynamic parameters for the reaction were also determined. The activation energy calculated applying Coats–Redfern, Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose and Friedman models were found in the ranges 105–148.48 kJmol−1, 99.41–140.52 kJmol−1, 103.67–149.15 kJmol−1 and 99.93–141.25 kJmol−1, respectively. The lowest activation energy for polystyrene degradation in the presence of copper oxide indicates the suitability of catalyst for the decomposition reaction to take place at lower temperature. Moreover, the obtained kinetics and thermodynamic parameters would be very helpful in determining the reaction mechanism of the solid waste in a real system.

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