A time to search: finding the meaning of variable activation energy

Abstract

This review deals with the phenomenon of variable activation energy frequently observed when studying the kinetics in the liquid or solid phase. This phenomenon commonly manifests itself through nonlinear Arrhenius plots or dependencies of the activation energy on conversion computed by isoconversional methods. Variable activation energy signifies a multi-step process and has a meaning of a collective parameter linked to the activation energies of individual steps. It is demonstrated that by using appropriate models of the processes, the link can be established in algebraic form. This allows one to analyze experimentally observed dependencies of the activation energy in a quantitative fashion and, as a result, to obtain activation energies of individual steps, to evaluate and predict other important parameters of the process, and generally to gain deeper kinetic and mechanistic insights. This review provides multiple examples of such analysis as applied to the processes of crosslinking polymerization, crystallization and melting of polymers, gelation, and solid-solid morphological and glass transitions. The use of appropriate computational techniques is discussed as well.

Nanosize effects of NiO nanosorbcats on adsorption and catalytic thermo‐oxidative decomposition of vacuum residue asphaltenes

“…For optimizing the best catalytic activity, we know that when we deal with the effective activation energy profiles, the activation energy at a given point is more an estimate of how sensitive the rate of reaction is to small temperature changes rather than the value of the rate. Therefore, taken together, the kinetic triplets can give more meaningful kinetic prediction . Additionally, this should line up with the results obtained by the TGA‐MS.…”

“…Therefore, taken together, the kinetic triplets can give more meaningful kinetic prediction. [59,60] Additionally, this should line up with the results obtained by the TGA-MS. At the moment, we can see that the results of the mass loss rate go inline with the MS-EGA profiles, the lower the size of NiO nanosorbcats the better the catalytic behaviour and vice versa. Moreover, the kinetic triplets were all taken together to estimate the rate of the thermo-oxidative reaction da dt À Á of VR n-C 5 asphaltenes.…”

“…The resulting effective activation energy shown in Figure 4a for original VR n-C 5 asphaltenes demonstrated different trends, implying a change in the limiting control step during multistep oxidation pathways. [59,60] Those multistep reactions might go through these major steps: (i) initiation, where sample gets saturated with oxygen, then (ii) propagation and branching, in which a sigmoidal or an autocatalytic stage coupled with an exponential growth of the peroxy groups, and finally (iii) termination, in which after the saturation stage with oxygen, the oxidation reaction gets terminated and the peroxy groups get depleted. [53] It is seen that the effective activation energy trend of original VR n-C 5 asphaltenes ranged between 120 and 175 kJ/mol.…”

Cross‐Linkable Liquid‐Crystalline Biopolyesteramide as a Multifunctional Polymeric Platform Designed from Corn Oil Side‐Stream Product of Bioethanol Industry

“…The computation of these conversion curves using the nonlinear isoconversional (NLN) method permits the apparent activation energy (E a ) evaluation through the crosslinking for an average speed of 8 °C min −1 (the details associated with NLN method can be found below in Supporting Information). [25] Figure 3B exhibits the superimposition of these computed results with the rheological measurement of this same crosslinking recorded at the same rate. At the begin ning of the reaction, in between 150 and 162 °C, E a is constant with a value of around 60 kJ mol −1 .…”

“…The Figure A thermogram shows the exothermic event associated with the cross‐linking of PCnO, as well as the conversion curves obtained from the peak integration for the three reported heating rates. The computation of these conversion curves using the non‐linear isoconversional (NLN) method permits the apparent activation energy ( E a ) evaluation through the cross‐linking for an average speed of 8 °C min −1 (the details associated with NLN method can be found below in Supporting Information) . Figure B exhibits the superimposition of these computed results with the rheological measurement of this same cross‐linking recorded at the same rate.…”