The document discusses the appropriateness of using the Arrhenius equation for kinetic analysis of solid state reactions from thermal analysis data. While the Arrhenius equation can be justified for homogeneous reactions, its application to heterogeneous solid state reactions is more complex due to factors like immobilized species, possible multi-step mechanisms, and variations in activation energy with reaction progress. The values of activation energy and pre-exponential factor derived also often lack clear physical meaning for solid state reactions.
1. Study of speed with which a chemical reaction occurs and the factors affecting that speed
2. Provides information about the feasibility of a chemical reaction
Provides information about the time it takes for a chemical reaction to occur
3. Provides information about the series of elementary steps which lead to the formation of product
This is a lecture is a series on combustion chemical kinetics for engineers. The course topics are selections from thermodynamics and kinetics especially geared to the interests of engineers involved in combusition
1. Study of speed with which a chemical reaction occurs and the factors affecting that speed
2. Provides information about the feasibility of a chemical reaction
Provides information about the time it takes for a chemical reaction to occur
3. Provides information about the series of elementary steps which lead to the formation of product
This is a lecture is a series on combustion chemical kinetics for engineers. The course topics are selections from thermodynamics and kinetics especially geared to the interests of engineers involved in combusition
Definition of reaction kinetics, law of mass action, rates of reaction- zero, first, second, pseudo zero & pseudo first order reaction, molecularity of reaction, determination of reaction order- graphic method, substitution method, half life method.
This slide completely describes you about the stuff include in it and also everything about chemical engineering. Fluid Mechanics. Thermodynamics. Mass Transfer Chemical Engineering. Energy Engineering, Mass Transfer 2, Heat Transfer,
A complete introduction to all things chemical kinetics designed specifically for non-chemists to understand. Fair warning: The presentation is very rigorous in its mathematical treatment, which is makes it a useful reference for looking up equations, but this can unfortunately make it less polished and flowing then a typical presentation. I tried my best to spell everything out clearly, but despite my best efforts it's still pretty dense.
My notes for A2 Chemistry Unit 4, typed by me and compiled from various sources. I cannot trace back where everything came from but again shall any intellectual property rights be violated, please comment /contact me and I will try my best to rectify them as soon as possible.
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with thermodynamics, which deals with the direction in which a process occurs but in itself tells nothing about its rate
Definition of reaction kinetics, law of mass action, rates of reaction- zero, first, second, pseudo zero & pseudo first order reaction, molecularity of reaction, determination of reaction order- graphic method, substitution method, half life method.
This slide completely describes you about the stuff include in it and also everything about chemical engineering. Fluid Mechanics. Thermodynamics. Mass Transfer Chemical Engineering. Energy Engineering, Mass Transfer 2, Heat Transfer,
A complete introduction to all things chemical kinetics designed specifically for non-chemists to understand. Fair warning: The presentation is very rigorous in its mathematical treatment, which is makes it a useful reference for looking up equations, but this can unfortunately make it less polished and flowing then a typical presentation. I tried my best to spell everything out clearly, but despite my best efforts it's still pretty dense.
My notes for A2 Chemistry Unit 4, typed by me and compiled from various sources. I cannot trace back where everything came from but again shall any intellectual property rights be violated, please comment /contact me and I will try my best to rectify them as soon as possible.
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with thermodynamics, which deals with the direction in which a process occurs but in itself tells nothing about its rate
Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
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The Addition of Aluminum Nanoparticles to Polypropylene Increases Its Thermal...IJERA Editor
This work reports the thermal degradation kinetics of isotactic polypropylene (iPP) and iPP with incorporated Al nanoparticles. The Friedman, Flynn-Wall–Ozawa (FWO), ASTM E698 and Coats-Redfern methods were used to calculate the activation energy of the samples from thermogravimetric data. The thermal stability of the iPP was improved by the introduction of the nanoparticles: the maximum decomposition temperature of the nanocomposite increased from 453 ºC to 457 ºC and the activation energy from 226 kJ/mol to 244 kJ/mol. The thermal degradation models of iPP can be described by “Contracting Sphere” model, whereas that to nanocomposite by Rn (n= 4.8) model (phase boundary reaction).
Understanding Intrinsic Properties ofBiological Molecules in Absence of Sol...jennypswong
The dissociation kinetics of a small biological molecule, leucine enkephalin (LE), are examined using a Quadruple Ion Trap Mass Spectrometer in order to determine the effect of activation waveform on ion effective temperature (Teff). The effective temperature is found to have a linear relationship with the applied activation amplitude. The dissociation kinetics of LE are found to be greatly affected by pressure in the mass spectrometer, showing faster dissociation at lower pressures. The effects of other experimental parameters, including the temperature of the inlet capillary and sensitivity to the frequency of the activation waveform, are also explored. Calibration of Teff as a function of activation waveform will provide a way to obtain Arrhenius activation parameters (activation energy and frequency factor) for other biological
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Incorporation of Linear Scaling Relations into Automatic Mechanism Generation...Richard West
Presented at the 2017 AIChE Annual Meeting on October 31, 2017, by Richard H. West and C. Franklin Goldsmith.
https://www.aiche.org/conferences/aiche-annual-meeting/2017/proceeding/paper/304c-incorporation-linear-scaling-relations-automatic-mechanism-generation-heterogeneous-catalysis
Abstract:
To predict the selectivity and reactivity of novel catalysts at industrially relevant conditions requires a detailed microkinetic mechanism, comprising many elementary reactions. Recent advances such as such as the work of Ulissi et al [5] use a combination of scaling relations, machine learning, and DFT calculations, to gradually refine a microkinetic model until the rate limiting steps have been calculated with sufficient accuracy to be confident that they are correctly identified. However, such a system requires as input a comprehensive kinetic model containing all the possible pathways. Our recently developed Reaction Mechanism Generator for Heterogeneous Catalysis (RMG-Cat) [3], built upon the open-source RMG software primarily used for gas-phase pyrolysis and combustion [1,2], can provide such mechanisms ab inito: the user supplies just the initial conditions (eg. reactant composition, temperature, pressure) and the software predicts all the possible reactions, estimates the thermochemical and kinetic parameters, solves the governing equations, and decides which reaction pathways to include and explore further. RMG-Cat makes its decisions regarding which pathways to explore and which to ignore, using the estimated parameters, so it is important that the estimates are reasonable, even if the important parameters will be refined with more accurate calculations later in the model development process.
Linear Scaling Relations (LSRs) can provide reasonable estimates of adsorption energies in a very computationally efficient manner [4-6]. We have now implemented linear scaling relationships for the estimation of adsorption energies in the RMG-Cat software. Our database of parameters is organized in a hierarchical tree structure, enabling detailed functional group descriptions to be used when data are available and more general descriptions to be used when necessary. We include parameters to describe many adsorbates on a range of metal surfaces, and a framework to re-train the parameters whenever new data are available.
[1] Gao, C.W. et al., Comput. Phys. Commun., 203, 212-225, (2016) http://doi.org/10.1016/j.cpc.2016.02.013
[2] RMG - Reaction Mechanism Generator, open-source software, RMG-Py. http://reactionmechanismgenerator.github.io
[3] Goldsmith, C. F., West, R. H., J. Phys. Chem. C., 121 (18), 9970–9981 http://doi.org/10.1021/acs.jpcc.7b02133
[4] Medford, A. J. et al., Topics in Catalysis (2013) 57, 135-142
[5] Ulissi, Z. W. et al., Nature Comm. (2017) 8, 14621-14627
[6] Hummelshøj, J.S. et al., Angewandte Chemie International Edition (2011) 51, 272-274
This slide completely describes you about the stuff include in it and also everything about chemical engineering. Fluid Mechanics. Thermodynamics. Mass Transfer Chemical Engineering. Energy Engineering, Mass Transfer 2, Heat Transfer,
Neutron evaporation spectra alongwith γ-multiplicity has been measured from the 185Re* compound nucleus at the excitation energies ~27 and 37 MeV. Statistical model analysis of the experimental data has been carried out to extract the value of the inverse level density parameter k at different angular momentum regions (J) corresponding to different γ-multiplicity. It is observed that, for the present system the value of k remains almost constant for different J. The present results on the angular momentum dependence of the nuclear level density (NLD) parameter ã (=A/k), for nuclei with A ~180 is quite different from our earlier measurements in case of light and medium mass systems. The present analysis provides useful information to understand the angular momentum dependence of NLD at different nuclear mass regions.
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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1. APPROPRIATENESS OF ARRHENIUS EQUATION FOR KINETIC ANALYSIS OF SOLID STATE REACTIONS B. Viswanathan National Centre for Catalysis Research Indian Institute of Technology, Madras, Chennai 600 036 [Presentation on 5 th February, 2008 at IGCAR]
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3. Thermal methods are employed for the study Decomposition oxidation reduction solid state reactions and so on for Materials of quality Thermal stability and Chemical processes /transformations .
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6. It is appropriate to quote Flynn at this stage. He said “ the unfortunate fact is that, since in thermal analysis, properties of the system are measured as a function of (both) time and temperature, all thermo-analytical results are potentially kinetic data, and many people ill grounded on kinetics ( like the present author) feel obliged to perform a kinetic analysis of them ”
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9. Table 2. Types of information obtainable from TPx techniques. TPD, Temperature-programmed desorption · Characterization of adsorptive properties of materials · Characterization of surface acidity · Temperature range of adsorbate release, temperatures of rate maxima · Total desorbed amount, adsorption capacity, metal surface area and dispersion · Surface energetic heterogeneity, binding states and energies of adsorbed molecules · Mechanism and kinetics of adsorption and desorption TPR, Temperature-programmed reduction · Characterization of redox properties of materials, .fingerprint. of sample · Temperature range of consumption of reducing agent, temperatures of rate maxima · Total consumption of reducing agent, valence states of metal atoms in zeolites and metal oxides · Interaction between metal oxide and support · Indication of alloy formation in bimetallic catalysts · Mechanism and kinetics of reduction TPO, Temperature-programmed oxidation · Characterization of redox properties of metaand metal oxides · Characterization of coke species in deactivated catalysts · Total coke content in deactivated catalysts · Mechanism and kinetics of oxidation reactions
10. Kinetic analysis of data generated by thermal methods Various options (i) Model based (ii) parameter based (iii) geometry based (iv) experimental variables based and so on………..
11. Why do we question the kinetic analysis of thermal methods? In contrast to the conventional homogeneous kinetics, there is no conception of a simple reaction in the solid-state reaction kinetics. The geometric-probabilistic phenomenology currently in use is not adequate for describing the interplay between the chemical mechanism and the observed kinetic behaviour. Hence it is necessary to question the use of the mode and formulations employed for homogeneous reactions when they are applied to solid state reactions.
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13. The applicability of Arrhenius equation for homogeneous molecular level reactions is well known and has been established beyond doubt since these systems obey the Maxwell-Boltzmann distribution. However the energy distributions in solids are not the same
14. However alternate functions like relating ln k with T or relating ln k with ln T in addition to ln k versus 1/T have been proposed but these equations are “theoretically sterile” since the constants of the se proposed equations do not lead to any deeper understanding of the steps of chemical reaction .
15. The kinetic reaction mechanism can be determined from the Arrhenius equation K = A exp ( - Ea/RT) Ea is the activation energy and R is the universal gas constant, A is the pre-exponential factor; T is the absolute temperature and k is the reaction rate constant. The above equation upon log transformation can be rewritten as Ln k = ln A - Ea/RT The activation energy can be determined from the slope of the plot of ln k verses 1/T. and the intercept would yield the value of pre-exponential factor.
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17. In the terminology of homogeneous kinetics, the activation energy Ea is usually identified as the energy barrier ( or threshold) that must be surmounted to enable the occurrence of the bond redistribution steps required to convert the reactants into products. The pre-exponential term A provides a measure of the frequency of occurrence of the reaction situation usually envisaged as incorporating the vibration frequency in the reaction coordinate.
18. This normally implies that the fractional reaction g (α) = kt is linear. Polanyi-Wigner model probably assumes such a relationship for solid state decompositions as well The equation (dx/dt) = (2νE/RT)x0 exp (-E/RT) This equation is based on for linear rate of advance of the interface. This has been modified for geometry in deriving rate equations. The vibration frequency ν is expected to be or the order of 10 13 s-1 Experimental or derived values of A have been compared with this expected value. Reactions are normal when A is one or two orders less than 10 13 and E is in the range of enthalpy of dissociation. Reactions are abnormal when both A and E are different from the critical values.
19. The thermodynamics of the activation process ((ΔS ± and ΔH±) for an irreversible reaction is given by Eyring type of equation The equation ( dx/dt) = (k B T/h) xo exp (ΔS ± / R) exp (-ΔH±/RT) The so called normal values of ν is calculated on the assumption that the entropy of activation (ΔS± ) is zero. For abnormal reactions the value of (ΔS± ) is of the order or 200 to 500 JK -1 mol -1 . It is possible to derive the transition state terminology using the concept of partition functions Q ± and Q. Values of Q ±/Q can be less than or equal to or greater than 1. However mechanistic differences are only postulates. The introduction of T dependence on A also has not improved the situation. Concept of discrete activated state itself is not clear. Immobility of species in solid state different from homogeneous reactions. Multi-step process electronic or phonon activation, thermal gradient and other parameters.
21. Fig The frequency of occurrence of Arrhenius pre-exponential values, expressed as lgA/s-1) in steps of equal increment. Note that there is no preference towards the normal expected value of A = Approx 10 13 s-1 Data from A.K.Galwey, Thermochimica Acta, 242 (1994) 259-264
22. Table 2. Kinetic parameters of thermal decomposition for explosives. The relevant equation is ln ( β /T p 2) = ln (AR/T) –E a /RT p pentaerythritol tetranitrate (PETN), RDX, hexanitrostilbene or 2,2′,4,4′,6,6′-hexanitrostilbene (HNS) and HMX are investigated
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25. Table experimental data of alpha –temperature curves for the decomposition of calcium carbonate in vaccum at different heating rates, 18,2,5,3,5,5,0,6.2,10.0 K min - 1 [Data reproduced from Thermochimical Acta 355(2000)125-143
26. Table experimental data of alpha –time isothermal data for the decomposition of calcium carbonate in vacuum at different temperatures, 550,540,530,520,515) [Data reproduced from Thermochimical Acta 355(2000)125-143
27. Table experimental data of alpha –temperature curves for the decomposition of calcium carbonate in vaccum at different heating rates, 18,2,5,3,5,5,0,6.2,10.0 K min-1 [Data reproduced from Thermochimical Acta 355(2000)125-143
28. Table experimental data of alpha –time isothermal data for the decomposition of calcium carbonate in nitrogen at different temperatures, 773,750,740,732,719,710 and 700 0 C) [Data reproduced from Thermochimical Acta 355(2000)125-143
29. Graphical presentation of the Arrhenius parameters for the decomposition of CaCO3 in nitrogen [data from Thermochimica Acta 355(2000) 145-154.]
30. Graphical presentation of the Arrhenius parameters for the decomposition of CaCO3 in vaccum [data from thermochimica Acta 355(2000) 145-154.]
31. Multi step nature of solid State Reactions Interface advance or proportional to surface area – deviation due to local reactivity local decrease of E or strain or formation of defect the interface R/P or R/inert gas or vacuum or topo-tactic reactions or R/I/P intervening phase of melt or R/R (mod)/I/P In this context it is possible that Polanyi-Wigner treatment is applicable averaging effect Energy in te form phonons ( vibrations internal or other wise) may be similar to the homogeneous phase reactions.
32. Fig. Suggested Band structure across the reaction zone (Reproduced from A.K.Galwey abd B.E.Brown Thermochimical Acta 386(2002)91-98. Azide excitation and activation energy arecomparable
33. Energy Distributions Fermi Dirac distribution when E e is far exceeds E f then it reduces to a Maxwell-Boltzmann distribution. If phonon energy obeys Bose Einstein statistics even then at higher energies that is h ω »2 π k B T then the expression is similar to M –B distribution fucntion.
34. Distribution of Activation Energies 1.Compensation between ln(A) being linear function of E 2. A single common value of A and a continuous distribution of activation energies 3.A single value of E and a continuous distribution of Pre-exponential factors .
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37. The mechanism of reaction in solid state may be different from that occurring in homogeneous systems, where movement and collision are envisaged as initiating steps of the reaction. In solids, the species are immobilized and hence this type of collisions may not be the initiator of the reaction. The reactions ( at least some of the reactions in solid state) may be due to bond activation through electronic energy or through phonon activation.
38. If softening and melting were to precede the solid state reaction, then one can visualize the reaction sequence as in homogeneous medium. The variation of E with α the extent of reaction, (smooth or abrupt) denotes the nature of consecutive steps involved in solid state reactions. If the solid state reaction proceeds by the development and growth of a reaction interface, then the local strain, imperfections, the crystalline phases of the reactants and products all will contribute to the acceleration or deceleration of reaction rates as well as for the change of Ea with α. It is not yet clear how the various forms of the intervening phase, like a molten product, a defect crystalline phase or reorganizations in react ( like removal of water) could provide a chemical environment where the conventional Polanyi-Wigner treatment will be as much applicable as in homogeneous phase .
39. In terms of energy transfer, the species in the interracial zone is more ordered in homogeneous liquid medium, but less ordered as compared to the fully crystalline phase. The in-between crystalline phases (interface region) may provide additional allowed energy levein the forbidden regions of energy bands in the solid. The electronic energy levethough normally follow Fermi-Dirac statistics, can approximate to Maxwell-Boltzmann distribution under the temperature conditions employed for the solid state reaction. If this situation prevaithen one can justify the use of Arrhenius equation for evaluating Ea and pre-exponential factor. If on the other hand phonons are the mode of activation, then one can expect the Bose-Einstein statistics will approximate to Maxwell-Boltzmann distribution for the conditions prevailing under reaction conditions and hence the use of Arrhenius equation can still be justified. Though the summary of the arguments given justify the use of Arrhenius type of relationship to evaluate the kinetic parameters ( Ea and ln A) it has not provided any explanation for the variation of Ea and ln A. These variations are considered in terms of compensation between Ea and ln A, or by the variation of one ( Ea o
40. The linear relationship between Ea and ln A is termed as compensation effect in the literature. The observance of this effect is usually identified by the inherent ‘heterogeneity’ of the surface and hence the changes in reactivity of these sites. However, a simple linear variation between Ea and ln A for sites of varying reactivity is not expected unless one has to invoke additional internal reorganizations which can give rise to smooth variation in both Ea and ln A. It must be remarked that these solid state reactions were to involve an intermediate vapourization and condensation steps, then it is probable that one can still invoke Arrhenius type of equation for evaluating Ea and ln A. However not all solid state reactions do proceed by evaporation of reactant and condensation of the product.
41. It is appropriate to re-quote Flynn at this stage. He said “ the unfortunate fact is that, since in thermal analysis, properties of the system are measured as a function of (both) time and temperature, all thermo-analytical results are potentially kinetic data, and many people ill grounded on kinetics ( like the present author) feel obliged to perform a kinetic analysis of them”
42. Even if one were to admit inexperience in treating kinetic data from thermal analysis, the physical significance of the kinetic parameters derived from the analysis is not clear yet. Secondly, it is yet to resolved, why the same experimental data can be fitted to various mode simultaneously? Do they reflect on the closeness of the models, or the inadequacy of the treatment of data based on the mode chosen. The widely practiced method of extracting Arrhenius parameters from thermal analysis experiments involves ‘force fitting’ of experimental data to simple reaction order kinetic models. The ‘force fit’ may not be suitable for the analysis of data of thermal analysis, outside the applicable range of variables and hence can be of limited utility for drawing mechanistic detail of the reaction. It should be remarked that the concept of kinetic order of the reaction has to assume a new significance in the case of solid state reactions. Even for simple decomposition reactions, the available mode cannot appropriately take into account like sintering before decomposition, simultaneous existence of polymorphic transition. It should be recognized that the mode so far proposed, are oversimplified and envisages one nucleation site per particle. There can be multiple and different types of nucleation simultaneously and their growth may be a complex function which cannot be treated in terms of simple geometrical considerations. The direct observation of the texture and morphology of the substances have to be coupled with the kinetic fit of the data for developing a model and draw meaningful deductions regarding nucleation and growth.
43. The values of the activation energy for solid state reactions can be rationalized only in some simple restricted conditions. For example for two systems if g(α) and A were to be equal then, the magnitude of Ea can be used to postulate on the reaction kinetics. However, even in these cases , if Ea were to vary with α , the fraction of the reaction, then it denotes changes in reactivity as a result of extent of reaction and the complex nature of the reaction. There is overwhelming tendency to compare Ea values obtained for isothermal and non-isothermal experimental conditions. Even though time and temperature are mathematically related by the heating rate (β = dT/dt), it is not clear how the species of the system will respond to the bimodal variation. Whether the changes observed will be an arithmetic sum or product of the variations observed with each of these variables. It appears that it is neither of these two mathematical functions. In conclusion, one can state that if carefully used and complemented with other techniques, the analysis of solid state kinetics can provide indications on the reaction mechanism and may yield information on reactivity which can be exploited for synthetic strategies.
44. In essence, even though the thermal data is normally kinetic in nature, the interpretation of the data within the premises of kinetics requires caution. Discussing reactions on the basis of one of the kinetic triplet is not advisable. Even when the kinetic triplet is employed it is necessary to define them in the context of the experimentation .