Diffusion and surface reaction in porous cubical catalyst: A mathematical approach

Background: Catalysts are the most vital part of any chemical industry. Catalyst is a substance that affects the rate of reaction, but the catalyst itself does not take part in the reaction. Catalysts offer different pathways of reaction by diffusing the reactant inside it to provide a large surface area within a small volume, thus, lowering the activation energy of molecules for reaction. Most of the catalytic reactions take place in liquid-solid or gas-solid interface where catalysts are mostly porous in nature. Spherical and cubic-shaped catalyst particles are commonly used in different industries. Methods: In the first phase of the present study, the physics behind the diffusion inside the catalyst pellet has been discussed. In the second part, governing differential equations have been established at a steady-state condition. For solving the differential equation, the equation is made dimensionless. Physical boundary conditions were used to solve the diffusion equation. The assumption of writing the differential equation of the reaction is elementary. Then the Thiele modulus is derived in terms of the reaction and geometrical parameter (Length) Results and Conclusion: In the third part, the differential equation is solved for first-order reaction with some constant values of the Thiele modulus and three-dimensional plots are obtained using numerical analysis. After that, the obtained Thiele modulus and effectiveness factor plot are compared to draw the conclusion of reaction rate limited and internal diffusion limited.

Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods

A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations.

Electrochemical implications of modulating the solvation shell around redox active organic species in aqueous organic redox flow batteries

Organic and organometallic reactants in aqueous electrolytes, being composed of earth-abundant elements, are promising redox active candidates for cost-effective organic redox flow batteries (ORFBs). Various compounds of ferrocene and methyl viologen have been examined as promising redox actives for this application. Herein, we examined the influence of the electrolyte pH and the salt anion on model redox active organic cations, bis((3-trimethylammonio) propyl)- ferrocene dichloride (BTMAP-Fc) and bis(3-trimethylammonio) propyl viologen tetrachloride (BTMAP-Vi), which have exhibited excellent cycling stability and capacity retention at ≥1.00 M concentration [E. S. Beh, et al. ACS Energy Lett. 2, 639–644 (2017)]. We examined the solvation shell around BTMAP-Fc and BTMAP-Vi at acidic and neutral pH with SO42-, Cl−, and CH3SO3− counterions and elucidated their impact on cation diffusion coefficient, first electron transfer rate constant, and thereby the electrochemical Thiele modulus. The electrochemical Thiele modulus was found to be exponentially correlated with the solvent reorganizational energy (λ) in both neutral and acidic pH. Thus, λ is proposed as a universal descriptor and selection criteria for organic redox flow battery electrolyte compositions. In the specific case of the BTMAP-Fc/BTMAP-Vi ORFB, low pH electrolytes with methanesulfonate or chloride counterions were identified as offering the best balance of transport and kinetic requirements.

A Potential–dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts

<p>Electrochemical reactors often employ high surface area electrocatalysts to accelerate volumetric reaction rates and increase productivity. While electrocatalysts can alleviate kinetic overpotentials, diffusional resistances at the pore-scale often prevent full catalyst utilization. The effect of intraparticle diffusion on the overall reaction rate can be quantified through an effectiveness factor expression governed by the Thiele modulus parameter. This analytical approach is integral to the development of catalytic structures for thermochemical processes and can be extended to electrochemical processes provided the relationship between reaction kinetics and electrode overpotential is incorporated. Here, we derive a potential-dependent Thiele modulus to quantify the effectiveness factor for porous electrocatalytic structures. We apply this mathematical framework to spherical microparticles as a function of applied overpotential across catalyst properties and reactant characteristics. The relative effects of kinetics and mass transport are related to overall reaction rates, revealing markedly lower catalyst utilization at increasing overpotential. Subsequently, we generalize the analysis to alternative catalyst shapes and provide guidance on the design of porous catalytic materials for use in electrochemical reactors.</p>

A Potential–dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts

<p>Electrochemical reactors often employ high surface area electrocatalysts to accelerate volumetric reaction rates and increase productivity. While electrocatalysts can alleviate kinetic overpotentials, diffusional resistances at the pore-scale often prevent full catalyst utilization. The effect of intraparticle diffusion on the overall reaction rate can be quantified through an effectiveness factor expression governed by the Thiele modulus parameter. This analytical approach is integral to the development of catalytic structures for thermochemical processes and can be extended to electrochemical processes provided the relationship between reaction kinetics and electrode overpotential is incorporated. Here, we derive a potential-dependent Thiele modulus to quantify the effectiveness factor for porous electrocatalytic structures. We apply this mathematical framework to spherical microparticles as a function of applied overpotential across catalyst properties and reactant characteristics. The relative effects of kinetics and mass transport are related to overall reaction rates, revealing markedly lower catalyst utilization at increasing overpotential. Subsequently, we generalize the analysis to alternative catalyst shapes and provide guidance on the design of porous catalytic materials for use in electrochemical reactors.</p>

KINETICS OFPYRROLE FORM TICS OFPYRROLE FORMATIONFROM A TIONFROM ACETYLENE, AMMONIA AND AMINES

The research findings of the pyrrole formation from acetylene, ammonia and amines varying catalysts and reaction conditions have been studied in the work. The cadmium catalysts developed by us selectively lead to pyrroleformation using aluminum fluoride as a promoter. The change in the rate of acetylene consumption depending on the weight of the catalyst according to the Boreskov criterion shows that external diffusion does not influence under the conditions of T-573K and P_ (C_2 H_2) = 0.1 atm. The values of the rate of acetylene consumption of at 4, 2, 1, 0.5 mm sizes of catalyst grains with similar conditions, internal diffusion does not influence on the observed rate of acetylene consumption. Calculation on the Thiele modulus shows that the reaction of acetylene consumption does not experience intradiffusion inhibition. The presence of a noticeable amount of macropores in the porous catalyst grain eliminates the appearance of a temperature gradient and causes a high kinetic ability of the reaction