Multiple reaction scheme modelling

Elder, John P.

doi:10.1007/bf01914371

Cited by 9 publications

(19 citation statements)

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“…As in previous work [4,5], the parameters E 1 = 220 kJ-mol -~ and A1 = 1.250.10 ~2 K -l.min -1 are used for the master reaction throughout this analysis. Figure 1 shows the complement, 1-ct, and the rate, ~, of reaction as a …”

Section: Analytical Resultsmentioning

confidence: 99%

“…Since the indicated separation between contiguous extent of reaction--temperature curves occurs only at Tma x of the master reaction, these A Tmax values are only demonstrative of the changing separation. As previously indicated [5], for multi-heating rate calculations, the individual member Ei, A i values are generated by program PARCAL at the upper heating rate to be used in the Kissinger "rod Friedman analyses in program KINMOD. As can be seen, there is a slight increase with increase in the value of the order of the individual member reactions.…”

Section: Analytical Resultsmentioning

confidence: 99%

“…Details of the basic reaction kinetics modelling program, K|NMOD, and the multiple set individual member parameter selection program, PARCAL, both written in Fortran 77, are given in the first two papers of this series [4,5]. Utilizing the individual Ei, Ai values, generated by PARCAL, KINMOD enables: (a) the generation of each singular reaction, and the normalized effective reaction, extents and rates of reaction as functions of temperature over the range, ~, = 0.001 to 0.999;…”

Section: Theoreucal I~as~smentioning

confidence: 99%

“…Elder [4,5] has considered such multiple set models, consisting of a large number of mutually independent, first order reactions with close-valued reaction kinetics parameters. It has been shown [5] that the order of the effective reaction, generated under constant heating rate conditions from these singular reactions, can vary from as low as 0.6 to as high as 3.0.…”

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confidence: 99%

“…The procedure for parameter selection of the individual members of a mutually independent multiple set, discussed in the second paper of this series [5], has been extended to cover singular reactions obeying other kinetics laws, e.g. those in which diffusion, or random nucleation or phase boundary movement are rate-controlling.…”

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Multiple reaction scheme modelling

Elder

1989

Journal of Thermal Analysis

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Analyses of the kinetics of the effective reactions, resulting from linear combinations of a wide range ofn tn order single reactions in a multiple set with variously chosen energies of activation and pre-exponential factors, generated under simulated non-isothermal conditions, have been carried out. The global kinetic] parameters of the several mode~ were obtained by subjecting extent and rate of reaction data, generated at a number of different linear heating rates, to Arrhenius, Kissinger and Friedman isoconversional analyses. Multiple sets, comprising from five to fifty individual members, with order varying from 0.25 to 5 have been considered. The effects of model design on the overall reaction kinetics parameters are discussed. Criteria applicable to experimental thermoanalytical data for recognition of multiple reactions are presented.An analysis has been performed of the characteristics of the kinetics of the effective reaction resulting from a mutually independent, equal weight combination of individual n th order reactions in a multiple set, under non-isothermal, constant heating rate conditions. Sets comprising five, ten, twenty-five and fifty members have been considered, with the individual member reaction orders varying from 0.25 to 5. With regard to the separation of the extent of reaction--temperature curves for tl~e single members at one defined temperature, namely, that of the maximum rate of the first member of the set, three model classes have been examined. The spacing either decreases (D) or increases (I) by a set fraction of the total separation between the first and last members, or remains equal (E). The activation energies and pre-exponential factors for the individual set members obey the Compensation Law relationship. The variation of the effective reaction order with model class, and number and order of members in the set has been examined. Data generated at several heating rates has been subjected to Kissinger and Friedman-isoconversional analyses. For models with n< 1, the effective reaction order is highly dependent upon the model spacing, and more importantly, the number of members in the set. For a 0.75 reaction order, the effective reaction order

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Section: Analytical Resultsmentioning

confidence: 99%

Section: Analytical Resultsmentioning

confidence: 99%

Section: Theoreucal I~as~smentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Multiple reaction scheme modelling

Elder

1989

Journal of Thermal Analysis

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Multiple reaction scheme modelling

Elder

1990

Journal of Thermal Analysis

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An analysis has been performed of the characteristics of the effective reactions, generated under non-isothermal conditions at constant heating rates, resulting from various equal weight combinations of sets of mutually independent, individual reactions obeying the Avrami-Erofeev kinetics laws in which two and three dimensional random nucleation phenomena are the rate-controlling mechanisms. As in previous analyses, dealing with multiple sets of first and n th order singular reactions, with regard to the separation of the individual extent and rate of reaction -temperature curves, three model classes have been considered. The relative spacing at one defined temperature either decreases/increases by a set increment or remains constant. Sets comprising from five to fifty members have been examined.The effective reaction data at each heating rate has been subjected to Arrhenius analysis, and data, generated over a range of heating rates, has been analyzed using the generalized Kissinger and Friedman iso-conversional approach. The effective reaction may be analyzed assuming it obeys the Avrami-Erofeev law or as an n th order reaction. The several features resulting from the various analyses will be discussed.In solid state thermophysical and thermochemical reactions, it is highly probable that the occurrence of multiple processes is more the rule than the exception. In such cases, it is the extent and rate of the effective reaction which is measured by, for example, thermoanalytical means. How useful then is such data? Further questions must be posed before this can be answered. Are there any patterns in the variation of calculated reaction kinetics parameters with the extent of the overall reaction? Which thermoanalytical approach is most useful, isothermal or non-isothermal?Are there any criteria by which to test for the occurrence of multiple reactions? What model reactions should be employed to attempt to establish such criteria?In extending the work of Ozawa [1] and Flynn [2] the author [3] first concerned himself with studying simple models, namely, sets of mutually independent, first order reactions with close-valued reaction kinetics parameter E, A values. Realizing the limitations of the early work, a more rational approach to the construction of the model has been presented [4]. This analysis enabled the development of the first criterion of the occurrence of multiple reactions, namely, a characteristic variation in the Friedman [5] reaction kinetics parameters with extent of reaction. Such analyses necessitate the non-isothermal approach. A further result of this analysis is that a set of first order reactions yield an overall n th order reaction, where the order can vary from 0.6 to 3.0.More recently, this multiple reaction scheme analysis has been extended to cover multiple sets of the n th order reactions [6]. This treatment confirmed the first criterion, and enabled the development of a second. Two equations relating the maximum rate parameters, the Arrhenius activation energy, the order of reaction an...

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A comment on mathematical expressions used in solid state reaction kinetics studies by thermal analysis

Elder

1990

Thermochimica Acta

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Multiple reaction scheme modelling

Cited by 9 publications

References 10 publications

Multiple reaction scheme modelling

Multiple reaction scheme modelling

Multiple reaction scheme modelling

A comment on mathematical expressions used in solid state reaction kinetics studies by thermal analysis

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