scholarly journals Reaction Model Taking into Account the Catalyst Morphology and Its Active Specific Surface in the Process of Catalytic Ammonia Decomposition

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7229
Author(s):  
Walerian Arabczyk ◽  
Rafał Pelka ◽  
Izabella Jasińska ◽  
Zofia Lendzion-Bieluń
Keyword(s):  
Specific Surface ◽  
Chemical Potential ◽  
Critical Concentration ◽  
Catalytic Decomposition ◽  
Active Surface ◽  
Reaction Model ◽  
Distribution Functions ◽  
Recrystallization Temperature ◽  
Nitrogen Diffusion ◽  
Entire Volume

Iron catalysts for ammonia synthesis/nanocrystalline iron promoted with oxides of potassium, aluminum and calcium were characterized by studying the nitriding process with ammonia in kinetic area of the reaction at temperature of 475 °C. Using the equations proposed by Crank, it was found that the process rate is limited by diffusion through the interface, and the estimated value of the nitrogen diffusion coefficient through the boundary layer is 0.1 nm2/s. The reaction rate can be described by Fick’s first equation. It was confirmed that nanocrystallites undergo a phase transformation in their entire volume after reaching the critical concentration, depending on the active specific surface of the nanocrystallite. Nanocrystallites transform from the α-Fe(N) phase to γ’-Fe4N when the total chemical potential of nitrogen compensates for the transformation potential of the iron crystal lattice from α to γ; thus, the nanocrystallites are transformed from the smallest to the largest in reverse order to their active specific surface area. Based on the results of measurements of the nitriding rate obtained for the samples after overheating in hydrogen in the temperature range of 500–700 °C, the probabilities of the density of distributions of the specific active surfaces of iron nanocrystallites of the tested samples were determined. The determined distributions are bimodal and can be described by the sum of two Gaussian distribution functions, where the largest nanocrystallite does not change in the overheating process, and the size of the smallest nanocrystallites increases with increasing recrystallization temperature. Parallel to the nitriding reaction, catalytic decomposition of ammonia takes place in direct proportion to the active surface of the iron nanocrystallite. Based on the ratio of the active iron surface to the specific surface, the degree of coverage of the catalyst surface with the promoters was determined.

scholarly journals Catalytic Decomposition of H2O2 over Pure and Li2O-Doped Co3O4 Solids

1998 ◽  
Vol 16 (9) ◽  
pp. 733-746 ◽  
Author(s):  
Gamil A. El-Shobaky ◽  
Nagi R.E. Radwan ◽  
Farouk M. Radwan
Keyword(s):  
Heat Treatment ◽  
Specific Surface ◽  
Catalytic Decomposition ◽  
Nitrogen Adsorption ◽  
Progressive Increase ◽  
Lithium Oxide ◽  
Lithium Nitrate ◽  
Surface Areas ◽  
Catalytically Active ◽  
Cobaltic Oxide

Pure and doped Co3O4 samples were prepared by the thermal decomposition at 500–900°C of pure and lithium nitrate-treated basic cobalt carbonate. The amounts of dopant added were varied in the range 0.75–6 mol% Li2O. The effects of this treatment on the surface and catalytic properties of cobaltic oxide solid were investigated using nitrogen adsorption at −196°C and studies of the decomposition of H2O2 at 30–50°C. The results obtained revealed that Li2O doping of Co3O4 followed by heat treatment at 500°C and 600°C resulted in a progressive increase in the value of the specific surface area, SBET, to an extent proportional to the amount of dopant present. However, the increase was more pronounced in the case of solid samples calcined at 500°C. This increase in the specific surface areas has been attributed to the fixation of a portion of the dopant ions on the uppermost surface layers of the solid leading to outward growth of the surface lattice. The observed increase in SBET due to Li2O doping at 500°C might also result from a narrowing of the pores in the treated solid as a result of the doping process. Lithium oxide doping of cobaltic oxide followed by heat treatment at 700–900°C resulted in a significant decrease in the SBET, Vp and r̄ values. Pure and doped solids precalcined at 500°C and 600°C exhibited extremely high catalytic activities which were not much affected by doping with Li2O. On the other hand, doping followed by calcination at 700–900°C brought about a considerable and progressive increase in the catalytic activity of the treated solids. This treatment did not modify the activation energy of the catalysed reaction, i.e. doping of Co3O4 solid followed by heating at 700°C and 900°C did not alter the mechanism of the catalytic reaction but increased the concentration of catalytically active constituents taking part in the catalytic process without altering their energetic nature.

A method for predicting the variation with temperature of the solubilities of gases in non-polar liquids

1971 ◽  
Vol 323 (1554) ◽  
pp. 361-375 ◽  
Keyword(s):  
Chemical Potential ◽  
Force Fields ◽  
Coefficient Of Thermal Expansion ◽  
Coupling Parameter ◽  
Distribution Functions ◽  
Lennard Jones ◽  
Pure Solvent ◽  
Simplifying Assumptions ◽  
Simple Systems ◽  
Solvent Solvent

An expression for the chemical potential due to Kirkwood & Boggs is adapted to give rigorous expressions for Henry’s coefficient ( H ) for the solubility of a gas in a liquid and for the temperature dependence of this coefficient, in terms of radial distribution functions ( g ) and a molecular coupling parameter. If the solute-solvent and solvent-solvent molecular interactions are similar in strength the expression for T dln H /d T reduces to T dln H / d T = L / RT + (1+ αT ) In P ° / H (i) where L, a and p ° are the molar latent heat, the coefficient of thermal expansion and the vapour pressure of the pure solvent. Equation (i) is closely obeyed by the simple systems Ar-CH 4 , Ar-O 2 and Ar—N 2 , though it becomes markedly less accurate when applied to the solubilities of common gases in liquids. This is to be expected since the solute-solvent and solvent—solvent intermolecular force fields are then very different. By assuming these force fields to be of the Lennard-Jones type and making simplifying assumptions relating g for the solute in the solvent to g for the pure solvent, the equation T dln H / d T = L / RT + (1 + αT ) In P ° / H - Q 0 (1 - ε ° αβ σ 3 αβ / ε ° ββ σ 3 ββ (ii) is then obtained in which Q 0 = L / RT - 1 + αT (1 + αT ) In P ° V β / RT , where V β is the molar volume of the solvent, ε ° ββ , σ ββ , ε ° αβ and σ αβ are the Lennard-Jones force constants for the solvent-solvent and solute—solvent interactions respectively. This equation is found to predict T dln H / d T for gases dissolved in common liquids with sufficient accuracy to be of practical value The equation T dln H / d T = 2- αT + (1 + αT ) In RT / V β H , valid at solvent reduced temperatures between about 0.5 and 0.65, is found in practice to provide a useful approximation to (ii) both for simple systems and for the permanent gases dissolved in common solvents. Expression (i) is shown to be related to an expression previously developed by Longuet-Higgins.

Bound Rubber and Elastomer-Filler Interaction

1995 ◽  
Vol 68 (2) ◽  
pp. 297-310 ◽  
Author(s):  
B. Meissner
Keyword(s):  
Specific Surface ◽  
Surface Area ◽  
Active Sites ◽  
Quantitative Description ◽  
Interfacial Area ◽  
Active Surface ◽  
Unit Surface Area ◽  
Bound Rubber ◽  
The Difference ◽  
High Structure

Abstract The statistical theory of bound rubber and the polymer-filler gel formation theory are shown to offer a satisfactory quantitative description of a set of experimental bound-rubber data recently obtained by Wolff, Wang, Tan (Rubber Chem. Technol. 66, 163 (1993)) on SBR compounds filled with 17 furnace blacks covering the whole range of rubber grades. The observed decrease of bound-rubber content per unit of interfacial area with increasing loading and/or specific surface area of carbon black is explained by the theory as being due to the statistical nature of the adsorption process. A correlation was found to exist between specific surface activity of filler D (adjustable parameter of the theory, number of active sites per unit surface area) and filler structure, the latter being characterized by the difference between DBP absorption and crushed DBP absorption. Also, D was found to increase with loading of a high-structure black. The two effects are ascribed to filler aggregates breakdown during mixing, which leads to a new active surface formation for polymer bonding.

scholarly journals APPLICABILITY OF THE LANGMUIR-HINSHELWOOD MODEL TO HYDROGENATION OF MONO - AND DISACCHARIDES ON THE Ru/HPS MN 100 CATALYST

2020 ◽  
pp. 29-40
Author(s):  
Максим Евгеньевич Григорьев ◽  
Олег Викторович Манаенков ◽  
Валентина Геннадьевна Матвеева ◽  
Роман Викторович Бровко
Keyword(s):  
Low Temperature ◽  
Specific Surface ◽  
Photoelectron Spectroscopy ◽  
Kinetic Studies ◽  
Nitrogen Adsorption ◽  
Chemical Study ◽  
Hydrogenation Reaction ◽  
Hydrogen Chemisorption ◽  
Entire Volume ◽  
Physical And Chemical

В данной статье представлены данные по физико-химическому исследованию гетерогенного рутений содержащего катализатора Ru/СПС MN 100. Представлена важность таких исследование для изучения каталитических реакций, для установления возможного механизма реакции гидрирования, а так же как дополнения при кинетических исследованиях. В статье катализатор исследован методом низкотемпературной адсорбции азота, хемосорбции водорода, просвечивающей электронной микроскопии (ПЭМ) и рентгенофотоэлектронной спектроскопии (РФЭС). Метод низкотемпературной адсорбции азота позволил установить, что катализатор характеризуется развитой внутренней удельной поверхностью (726 м/г по модели БЭТ) и характеризуется значительной мезопористостью, при этом наибольший диаметр пор составляет около 3.6 нм. Удельная площадь поверхности активного металла - Ru, по данным метода хемосорбции водорода, составляет 1 м/г. Рутений содержащие частицы распределены по всему объему носителя, при этом они способны образовывать небольшие агрегаты и характеризуются различной степенью кристалличности. Установлен элементный состав поверхности катализатора; Ru имеет различные степени окисления. На основании полученной ранее математическая модель процесса и проведенных физико-химических исследований катализатора предположена модель Ленгмюра-Хиншельвуда для описания механизма реакции жидкофазного каталитического гидрирования моно- и дисахаридов. This article presents data on the physical and chemical study of heterogeneous ruthenium-containing catalyst Ru/SPS MN 100. The importance of such studies for the study of catalytic reactions, for establishing the possible mechanism of the hydrogenation reaction, as well as additions in kinetic studies is presented. In this paper, the catalyst was studied by low-temperature nitrogen adsorption, hydrogen chemisorption, transmission electron microscopy (TEM), and x-ray photoelectron spectroscopy (XPS). The method of low-temperature nitrogen adsorption allowed us to establish that the catalyst is characterized by a developed internal specific surface (726 m/g according to the BET model) and is characterized by significant mesoporicity, with the largest pore diameter of about 3.6 nm. The specific surface area of the active metal - Ru, according to the method of hydrogen chemisorption, is 1 m/g. Ruthenium containing particles are distributed over the entire volume of the carrier, while they are able to form small aggregates and are characterized by different degrees of crystallinity. The elemental composition of the catalyst surface has been determined; Ru has different oxidation States. Based on the previously obtained mathematical model of the process and physical and chemical studies of the catalyst, the Langmuir-Hinshelwood model is proposed to describe the reaction mechanism of liquid-phase catalytic hydrogenation of mono - and disaccharides.

scholarly journals Influence mechanism of excipients on drug crystallization: experimental investigation and model analysis and prediction

2022 ◽  
Author(s):  
Qiao Chen ◽  
Jingyun Weng ◽  
Gabriele Sadowski ◽  
Yuanhui Ji
Keyword(s):  
Crystal Growth ◽  
Growth Kinetics ◽  
Surface Reaction ◽  
Chemical Potential ◽  
Potential Gradient ◽  
Reaction Model ◽  
Reaction Rate Constant ◽  
Crystal Growth Kinetics ◽  
Kinetics Of ◽  
And Diffusion

The influence of temperature, stirring speed, and excipients on crystal growth kinetics of mesalazine and allopurinol was investigated through experiment and chemical potential gradient model. The results indicated that the Diffusion-Surface Reaction model (DSR (1,2)) showed good performance in modeling API crystal growth kinetics within the ARDs of 4%. Excipients played a crucial role in inhibiting crystal growth in all the systems. It can not only improve the API solubility, but also reduce the crystal growth rate. By comparing diffusion rate and surface-reaction rate constant within the DSR (1,2) model, it was found that the controlling step of mesalazine crystallization was surface-reaction. Allopurinol crystallization was dominated by both surface-reaction and diffusion. Meanwhile, the crystal growth kinetics of mesalazine and allopurinol were predicted successfully with the ARDs of 2.53% and 4.78%. This work provided a mechanistic understanding of polymer influence on the inhibition of API crystal growth.

Quantum Mechanical Ensemble Averages and Statistical Thermodynamics

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Free Energy ◽  
Thermal Energy ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Quantum Statistical Mechanics ◽  
Bose Condensation ◽  
Distribution Functions ◽  
Ensemble Average ◽  
Statistical Thermodynamic ◽  
Quantum Mechanical

Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.

scholarly journals Computing Neutron Capture Rates in Neutron-Degenerate Matter

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 36
Author(s):  
Bryn Knight ◽  
Liliana Caballero
Keyword(s):  
Cross Section ◽  
Power Law ◽  
Cross Sections ◽  
Neutron Capture ◽  
Chemical Potential ◽  
Distribution Functions ◽  
Analytical Integration ◽  
Thermodynamic Conditions ◽  
The Cross ◽  
Capture Rates

Neutron captures are likely to occur in the crust of accreting neutron stars (NSs). Their rate depends on the thermodynamic state of neutrons in the crust. At high densities, neutrons are degenerate. We find degeneracy corrections to neutron capture rates off nuclei, using cross sections evaluated with the reaction code TALYS. We numerically integrate the relevant cross sections over the statistical distribution functions of neutrons at thermodynamic conditions present in the NS crust. We compare our results to analytical calculations of these corrections based on a power-law behavior of the cross section. We find that although an analytical integration can simplify the calculation and incorporation of the results for nucleosynthesis networks, there are uncertainties caused by departures of the cross section from the power-law approach at energies close to the neutron chemical potential. These deviations produce non-negligible corrections that can be important in the NS crust.

Study of adhesion-active surface structures in P6M5 high-speed steel

2018 ◽  
Vol 84 (12) ◽  
pp. 40-44 ◽  
Author(s):  
V. A. Kim ◽  
Ch. F. Yakubov ◽  
E. V. Shchelkunov ◽  
E. V. Samar
Keyword(s):  
Free Energy ◽  
Surface Energy ◽  
Metal Cutting ◽  
Chemical Potential ◽  
High Surface ◽  
Active Surface ◽  
Surface Structures ◽  
Active Centers ◽  
Structural Formation ◽  
High Surface Energy

Adhesive processes are the main reason for wear of the metal-cutting tool. Adhesion-active surface structures (micro and meso-scale zones with increased density of defects having a crystal structure and high surface energy) can be identified by treating the surface with reactants by analogy with etching of a metalgraphic shlif. The level of free energy of the structural formation was estimated by the degree of darkening (dark gray color intensity) of the microstructure revealed by etching. The degree of darkening can be described and rankes quantitatively using color segmentation. Most specialized programs for metallographic image processing contain similar algorithm. The images were studied using the following indices of the structural arrangement of adhesion-active centers: the density of microstructural objects with a high value of the free energy, their relative surface area and dark gray color coefficient. A high value of the coefficient corresponds to the larger chemical potential. A comparative analysis of the character of distribution of adhesion-active zones in the surface structures of the crude and tempered P6M5 highspeed steel revealed that tempered structure contains more structural elements with high free energy (or chemical potential). Their distribution on the surface forms local zones of increased hardness, possessing high surface energy, as well as adhesion-active centers acting as potential foci for the formation of strong islet growths or zones of formation of stable adsorption films.

DUALITY OF DYNAMICAL AND THERMAL DESCRIPTIONS IN PARTON DISTRIBUTION FUNCTIONS

2011 ◽  
Vol 26 (14) ◽  
pp. 1009-1016 ◽  
Author(s):  
J. CLEYMANS ◽  
G. I. LYKASOV ◽  
A. S. SORIN ◽  
O. V. TERYAEV
Keyword(s):  
Chemical Potential ◽  
Heavy Ion ◽  
Distribution Functions ◽  
Effective Width ◽  
Statistical Distributions ◽  
Free Nucleon ◽  
Parton Distribution Functions ◽  
Ion Collisions ◽  
Temperature Parameter ◽  
Statistical Form

We suggest a duality between the standard (dynamical) and statistical distributions of partons in the nucleons. The temperature parameter entering into the statistical form for the quark distributions is estimated. It is shown that the freeze-out temperature in central heavy-ion collisions at zero chemical potential or the effective width of the energy distribution of pions has a similar value which was estimated in this paper for the valence massless quarks in a free nucleon.

scholarly journals Performance of a simple energetic-converting reaction model using Linear Irreversible Thermodynamics

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1030 ◽  
Author(s):  
J. Chimal-Eguia ◽  
R. Paez-Hernandez ◽  
Delfino Ladino-Luna ◽  
Juan Velázquez-Arcos
Keyword(s):  
Energy Exchange ◽  
Chemical Potential ◽  
Biological Process ◽  
Enzymatic Reaction ◽  
Reaction Model ◽  
Irreversible Thermodynamics ◽  
Efficient Power ◽  
Degree Of Coupling ◽  
Linear Irreversible Thermodynamics ◽  
Operating Regimes

In this paper, the methodology of the so-called Linear Irreversible Thermodynamics (LIT) is applied to analyze the properties of an energetic-converting biological process using simple model for an enzymatic reaction that couples one exothermic and one endothermic reaction in the same fashion as Diaz-Hernandez et al. (Physica A, 2010, 389, 3476–3483). We extend the former analysis to consider three different operating regimes; namely, Maximum Power Output (MPO), Maximum Ecological Function (MEF) and Maximum Efficient Power Function (MEPF), respectively. Based on the later, it is possible to generalize the obtained results. Additionally, results show analogies in the optimal performance between the different optimization criteria where all thermodynamic features are determined by three parameters (the chemical potential gap Δ = μ 1 − μ 4 R T , the degree of coupling q and the efficiency η ). This depends on the election that leads to more or less efficient energy exchange.

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