Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

Deng, Chao; Cai, Junmeng

doi:10.1016/j.solidstatesciences.2009.04.009

Cited by 40 publications

(19 citation statements)

References 43 publications

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“…The integral on the right-hand side of Eqn (8) is called the temperature integral (or Arrhenius integral). 50,51 This has no analytical solution. However, it can be approximated as follows.…”

Section: General Linear Isoconversional Methodsmentioning

confidence: 99%

“…Both the above forms have been comprehensively tabulated in the literature. 50,51 Combining Eqns (9) and (11), we can write the following general linear model-free isoconversional thermo-analytical equation:…”

Section: General Linear Isoconversional Methodsmentioning

confidence: 99%

“…One is an exponential form and the other is a rational fractional form. The exponential form can be written as

p_{\exp} (u) = \frac{\exp (- au + b)}{u^{c}}

\ln (p_{\exp} (u)) = b - c \ln (u) - au

…”

Section: Mathematical Treatmentmentioning

confidence: 99%

“…where Q ( u ) represents rational fractions of u , usually ratios between polynomial functions, derived from different series expansions or approximate fitting procedures relative to the values calculated from numerical integration in a certain range of u . Both the above forms have been comprehensively tabulated in the literature …”

Section: Mathematical Treatmentmentioning

confidence: 99%

See 3 more Smart Citations

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling ratesversusmathematical artefact

Atiqullah

Hossain

Adamu

et al. 2014

Polymer International

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show abstract

Section: General Linear Isoconversional Methodsmentioning

confidence: 99%

Section: General Linear Isoconversional Methodsmentioning

confidence: 99%

“…One is an exponential form and the other is a rational fractional form. The exponential form can be written as

p_{\exp} (u) = \frac{\exp (- au + b)}{u^{c}}

\ln (p_{\exp} (u)) = b - c \ln (u) - au

…”

Section: Mathematical Treatmentmentioning

confidence: 99%

Section: Mathematical Treatmentmentioning

confidence: 99%

See 2 more Smart Citations

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling ratesversusmathematical artefact

Atiqullah

Hossain

Adamu

et al. 2014

Polymer International

View full text Add to dashboard Cite

show abstract

“…This issue is still very much discussed in the literature. In several articles, the existence of these different kinetic triplets [ E, A , and g (α)], especially the values of A , from various kinetic equations of the same class are explained by the different approximations used in the methods 23–26…”

Section: Resultsmentioning

confidence: 99%

Thermal decomposition studies of Schiff‐base‐substitute polyphenol–metal complexes

Doğan

Kaya

2012

J of Applied Polymer Sci

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The thermal behaviors of 2,3‐bis[(2‐hydroxyphenyl)methylene] diaminopyridine, oligo‐2,3‐bis[(2‐hydroxyphenyl)methylene] diaminopyridine, and some oligo‐2,3‐bis[(2‐hydroxyphenyl) methylene] diaminopyridine–metal complexes were studied in a nitrogen atmosphere with thermogravimetric analysis, derivative thermogravimetric analysis, and differential thermal analysis techniques. The decompositions of oligo‐2,3‐bis[(2‐hydroxyphenyl) methylene] diamino pyridine–metal complexes occurred in multiple steps. The values of the activation energy (E) and reaction order of the thermal decomposition were calculated by means of several methods, including Coats–Redfern, Horowitz–Metzger, Madhusudanan–Krishnan–Ninan, van Krevelen, Wanjun–Yuwen–Hen–Cunxin, and MacCallum–Tanner on the basis of a single heating rate. The most appropriate method was determined for each decomposition step according to a least‐squares linear regression. The E values obtained by each method were in good agreement with each other. It was found that the E values of the complexes for the first decomposition stage followed the order EOHPMDAP–Ni > EOHPMDAP–Cd > EOHPMDAP–Cu > EOHPMDAP–Fe > EOHPMDAP–Zn > EOHPMDAP–Co > EOHPMDAP–Cr > EHPMDAP > EOHPMDAP. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

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Crystallization kinetics of PE‐b‐isotacticPMMA diblock copolymer synthesized using SiMe₂(Ind)₂ZrMe₂ and MAO cocatalyst

et al. 2012

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Polyethylene‐b‐poly(methyl methacrylate) (PE‐b‐PMMA) diblock copolymer has important interfacial applications. Hence, a PE‐b‐isotactic PMMA diblock copolymer was synthesized using SiMe2(Ind)2ZrMe2 and MAO cocatalyst. The polymerization mechanism and the origin of PMMA isotacticity were duly explained. An appropriate nonisothermal Avrami‐Erofeev crystallization model was developed to compare the crystallization kinetics of the above copolymer with that of a PE homopolymer. For both polymers, the model well matched the entire differential scanning calorimeter crystallinity profile, notably for a single Avrami‐Erofeev index, and predicted cylindrical crystal growth. This model particularly overcomes the limitations of the published nonisothermal crystallization models, and provides interesting insight into PE crystallization. The PMMA block significantly decreased the heats of crystallization and fusion, % crystallinity, and the relative crystallization function; increased the nonisothermal crystallization rate constant; and introduced minimal dilution effect whereas the PE block formed a continuous or percolated phase. This study correlates catalyst structure, copolymer block tacticity, and PE nonisothermal crystallization and melting behavior. © 2012 American Institute of Chemical Engineers AIChE J, 59: 200–214, 2013

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Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

Cited by 40 publications

References 43 publications

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling ratesversusmathematical artefact

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling ratesversusmathematical artefact

Thermal decomposition studies of Schiff‐base‐substitute polyphenol–metal complexes

Crystallization kinetics of PE‐b‐isotacticPMMA diblock copolymer synthesized using SiMe₂(Ind)₂ZrMe₂ and MAO cocatalyst

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Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

Cited by 40 publications

References 43 publications

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling ratesversusmathematical artefact

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling ratesversusmathematical artefact

Thermal decomposition studies of Schiff‐base‐substitute polyphenol–metal complexes

Crystallization kinetics of PE‐b‐isotacticPMMA diblock copolymer synthesized using SiMe2(Ind)2ZrMe2 and MAO cocatalyst

Contact Info

Product

Resources

About

Crystallization kinetics of PE‐b‐isotacticPMMA diblock copolymer synthesized using SiMe₂(Ind)₂ZrMe₂ and MAO cocatalyst