Solid-State Kinetic Models:  Basics and Mathematical Fundamentals

Khawam, Ammar; Flanagan, Douglas R.

doi:10.1021/jp062746a

Cited by 1,602 publications

(1,123 citation statements)

References 62 publications

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“…This interpretation is in line with a switch to a diffusion limited D-H exchange reaction of various oxides in supported rhodium catalysts at temperatures above 353 K [68]. The reaction front should progress radially from the silver center and the rate law of two-dimensional diffusion, with the rate being proportional to -1/(ln (1 -Θ)), should be applicable [69]. However, for very small values of Θ (< 0.05) these two rate laws are not distinguishable because the radial spread is insignificant as long as the reaction front is close to the metal particle.…”

Section: Activation Of Dihydrogensupporting

confidence: 63%

Activation of dihydrogen on supported and unsupported silver catalysts

Hohmeyer

Kondratenko

Bron

et al. 2010

Journal of Catalysis

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The activation of dihydrogen on silica, silver, and silica-supported silver (9 wt% Ag) was investigated. Both, silica and silver are individually able to dissociate dihydrogen. Silanol groups on silica undergo H→D exchange at 393 K in D2 as detected by IR spectroscopy. HD is observed in temporal analysis of products (TAP) experiments when H2 and D2 are sequentially pulsed on silver at 673 K; even when the time delay between the isotopes is 4 s, HD is formed, indicating that long-lived surface hydrogen species are present. Differential scanning calorimetry (DSC) shows that the activation of dihydrogen is an activated process: heat signals evoked through H2 pulses on Ag/SiO2 grow with increasing temperature (373523 K). Nonetheless, the presence of silver on the silica surface accelerates the Si-OH→Si-OD exchange. Investigation of the exchange kinetics on Ag/SiO2 shows that diffusion processes of activated hydrogen species are rate-determining at higher temperatures ( 373 K), when activation of D2 on silver becomes facile. Indications of diffusion limitation are observed already at 313 K on Pt/SiO2. TAP and DSC measurements show that H2 is more readily activated on silver that has been treated in O2 at 673 K followed by reduction in H2 at 673 K. Morphological changes induced to the silver surfaces or (sub)surface oxygen species are presumed responsible for this effect

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Section: Activation Of Dihydrogensupporting

confidence: 63%

Activation of dihydrogen on supported and unsupported silver catalysts

Hohmeyer

Kondratenko

Bron

et al. 2010

Journal of Catalysis

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“…Such a behaviour is encountered in solid-state processes with nucleation mechanisms undergoing restrictions on the growth of the number of nuclei. 42 These restrictions -typical of solid-state decomposition and mainly related to coalescence between nucleation sites during the process -eventually cause a change of sign in the rate dN/dt of the nuclei number, corresponding to the inflection point of the sigmoid in the kinetics of transformation. As a matter of fact, the data can be fitted by an Avrami-Erofeyev equation for a 3-dimensional single-step nucleation process, 42 [Àln Fig.…”

Section: Isothermal Heating and Reaction Kineticsmentioning

confidence: 99%

“…42 These restrictions -typical of solid-state decomposition and mainly related to coalescence between nucleation sites during the process -eventually cause a change of sign in the rate dN/dt of the nuclei number, corresponding to the inflection point of the sigmoid in the kinetics of transformation. As a matter of fact, the data can be fitted by an Avrami-Erofeyev equation for a 3-dimensional single-step nucleation process, 42 [Àln Fig. 4) well below the temperature of the endothermic peak registered in DSC measurements that is related to the formation of b-Ga 2 O 3 .…”

Section: Isothermal Heating and Reaction Kineticsmentioning

confidence: 99%

Diffusion-driven and size-dependent phase changes of gallium oxide nanocrystals in a glassy host

Golubev

Ignat’eva

Сигаев

et al. 2015

Phys. Chem. Chem. Phys.

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Phase transformations at the nanoscale represent a challenging field of research, mainly in the case of nanocrystals (NCs) in a solid host, with size-effects and interactions with the matrix. Here we report the study of the structural evolution of g-Ga 2 O 3 NCs in alkali-germanosilicate glass -a technologically relevant system for its light emission and UV-to-visible conversion -showing an evolution drastically different from the expected transformation of g-Ga 2 O 3 into b-Ga 2 O 3 . Differential scanning calorimetry registers an irreversible endothermic process at B1300 K, well above the exothermic peak of g-Ga 2 O 3 nano-crystallization (B960 K) and below the melting temperature (B1620 K). Transmission electron microscopy and X-ray diffraction data clarify that glass-embedded g-Ga 2 O 3 NCs transform into LiGa 5 O 8 via diffusion-driven kinetics of Li incorporation into NCs. At the endothermic peak, b-Ga 2 O 3 forms from LiGa 5 O 8 dissociation, following a nucleation-limited kinetics promoted by size-dependent order-disorder change between LiGa 5 O 8 polymorphs. As a result of the changes, modifications of UV-excited NC light emission are registered, with potential interest for applications.

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“…18,19 Kinetics are basically related to the decomposition mechanisms and used as a starting tool to suggest mechanisms for the thermal dehydration and decomposition; therefore it is strongly recommended that the selection of correct model is a critical point in kinetic analysis to justify experimental data. 19 Consequently, a number of methods have been developed for scientific and practical reasons to analyze solid-state kinetic data since they provide reliable information on the thermal behavior and character of solids transformation during the isothermal or non-isothermal heating. Among which, mathematical approaches were employed that can be classified into model-fitting and model-free (isoconversional) methods.…”

Section: Kinetics Of Dehydration Of Bi-metallic Zeolitesmentioning

confidence: 99%

Influence of alternative cations distribution in AgxLi96-x-LSX on dehydration kinetics and its selective adsorption performance for N2 and O2

2016

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Adsorption characteristics of pure gases N2 and O2 on various silver exchanged low silica X-type (AgxLi96-x-LSX) zeolites were investigated. The equilibrium adsorption isotherms of N2 and O2 were measured at 273 and 298 K. Textual and structural properties of parent and resultant AgxLi96-x-LSX were characterized by XRD, BET surface area, and SEM techniques. Kinetics of their thermal dehydration were studied by exploiting thermogravimetric and differential data (TG-DTG) obtained at three heating rates (5, 10 and 15 K) using two model-free (Kissinger and Flynn-Wall-Ozawa) and one model fitting (Coats-Redfern) methods. Forty one mechanism functions were used to evaluate kinetic triplet (activation energy, frequency factor, and most probable mechanism/model) for different stages of dehydration. Results revealed that the impact of very small content of silver on the adsorption of N2 is pronounced and attributed to weak chemical bonds formed between N2 and Ag+ clusters due to strong adsorption of N2 at low pressure, whereas O2 adsorption is affected to a negligible extent. In addition, the N2/O2 adsorption selectivity shows unexpected low values for Ag87.08Li7.94Na0.98-LSX with higher Ag+ content (91.00 %), which might be due to low crystalline water content as well as Ag+ clusters located at SIII sites. N2 adsorption strongly depends on temperature as higher adsorption occurs at low temperature 273 K as compared to 298 K.

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Solid-State Kinetic Models: Basics and Mathematical Fundamentals

Cited by 1,602 publications

References 62 publications

Activation of dihydrogen on supported and unsupported silver catalysts

Activation of dihydrogen on supported and unsupported silver catalysts

Diffusion-driven and size-dependent phase changes of gallium oxide nanocrystals in a glassy host

Influence of alternative cations distribution in AgxLi96-x-LSX on dehydration kinetics and its selective adsorption performance for N2 and O2

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