Eyring Equation Research Articles

Catalytic influence of 16-s-16 gemini surfactants on the rate constant of histidine and ninhydrin.

The present paper reports the catalytic influence of 16-s-16 (spacer (s) = 4, 5, 6) gemini surfactants on the rate constant of histidine and ninhydrin at 343 K and pH 5.0 using the spectrophotometric technique. The effect of varying amounts of geminis was made on the rate constant of histidine and ninhydrin keeping other constituents constant. Characteristics of the rate constant (kψ) versus [gemini] depict the effect of surfactants on the rate constant. A systematic explanation about the effect of surfactants is revealed and discussed in the text. The influence of different parameters that includes [reactants], temperature and pH has also been performed on the study. In order to determine the critical micelle concentration (cmc) of pure surfactants and their solution mixtures, conductivity measurement was employed. By using the Eyring equation, activation parameters at different temperatures have been obtained. The resultant data of kψ versus [gemini] plot were rationalized with the pseudo-phase model of micelles.

Analysis of Thermochemical Properties of three typical Manganese based thermite

In order to investigate the thermochemical and reactive properties of thermite composed of typical manganese oxides, three common manganese oxides meaning MnO2, Mn2O3 and Mn3O4, are selected in this paper to form aluminothermic agent with Al powder, respectively. According to the chemical thermodynamics, the difference of Gibbs free energy among different components is calculated, and the reaction rate k is calculated according to Eyring equation, then the Gibbs free energy values of three thermite at different ambient temperatures are drawn. Furthermore, according to the theory of chemical reaction calorific value calculation, the reaction calorific values of three thermite at different temperatures are calculated. The results show that the Gibbs free energy of Al/MnO2 system is the smallest at different temperatures, the reaction rate and the enthalpy of reaction of Al/MnO2 are the fastest and the smallest at different temperatures and the heat release is the largest. The results of calculation provide theoretical guidance for experimental design and practice. Under the condition of the same mass of reactants, the discharge heat of MnO2 is the largest, and the heat value of the MnO2 is the highest.

The vanadium-substituted heteropolytungstate catalyzed oxidation of the organic dye by H2O2 in an aqueous solution

The main objective of this work is to study the oxidation of the acid orange 7 (AO7) in an aqueous solution by using the hydrogen peroxide in the presence of vanadium substituted heteropolytungstate (α1P2W17VO62)6− as a catalyst. The effects of various experimental parameters on the oxidation reaction of the dye were investigated. And they are as follow: The H2O2 concentration, the mass of the catalyst, and the dye concentration. The optimum conditions were determined. In addition, it was found that the efficiency of the degradation is obtained after 80 min of reaction, and it was about 100%. The optimal parameters were: initial pH = 4; [H2O2]0 = 1 mM; catalyst mass = 0.05 g; for a concentration of the dye [AO7]0 = 2 mg/L. The kinetic oxidation of the AO7 by this catalytic system was also elucidated and based on experimental data. The oxidation of the AO7 follows a pseudo second-order Kinetic model. The activation energy, as well as the activation enthalpy and the entropy were calculated by using respectively the Arrhenius and the Eyring equations. The oxidation of the AO7 by the H2O2 and the (α1P2W17VO62)6− requires a small amount of energy and has an endothermic nature.

A kinetic and mechanistic study of the osmium(VIII)-catalysed oxidation of crotyl alcohol by hexacyanoferrate(III) in aqueous Alkaline medium

The kinetics and mechanism of the osmium(VIII)-catalysed oxidation of crotyl alcohol by hexacyanoferrate(III) in aqueous alkaline medium is studied. The role of the osmium(VIII) catalyst is delineated to account for the experimental observations. A plausible reaction mechanism is suggested. Activation parameters such as the energy and entropy of activation are evaluated by employing the Eyring equation and are found to be 36.833 kJ mol−1 and −141.518 J K−1 mol−1, respectively.

A dielectric model of thawed and frozen Arctic soils considering frequency, temperature, texture and dry density

ABSTRACTA dielectric model was developed for thawed and frozen mineral soils, based on the refractive mixing dielectric formula and the dielectric measurement data for three soils collected in the Arctic tundra of the Yamal Peninsula. The refractive mixing dielectric model was used in conjunction with the Debye multi relaxation equations as a theoretical model to fit the measured complex relative permittivity spectra as a function of soil moisture and temperature. As a result, the dielectric spectroscopic parameters for the various components of water in the soil, such as the low- and high-frequency limits of the complex relative permittivity, the times of the corresponding relaxations, and the specific conductivity, were simultaneously determined for soils with different clay contents for all measured temperatures. As the theoretical temperature dependences of these parameters, the Clausius–Mossotti, Eyring, and linear equations for the conductivity were used. By using approximations of the measured data with these formulas, the parameters of the temperature-dependent model were derived, such as the coefficient of volume expansion, energy and entropy of activation, and coefficient of thermal conductivity. A set of the parameters discussed above in conjunction with the refractive mixing formula is a temperature- and mineralogically dependent multi-relaxation spectroscopic dielectric model, which enables estimation of the permittivity of moist soils as a function of dry soil density, moisture, frequency, temperature, and texture. The statistical error of the proposed dielectric model was estimated in terms of the normalized root-mean-square error (nRMSE), which was equal to 5% and 25% for the dielectric constant and dielectric loss factor, respectively.

FeII(EDTA)–NO Reduction by Mn Powder in Wet Flue Gas Denitrification Technology Coupled with Mn2+ Recycling: Performance, Kinetics, and Mechanism

FeII(EDTA) solution has been considered an efficient option in wet flue gas denitrification, whereas the generated FeII(EDTA)–NO restricts its wide application, suggesting that FeII(EDTA)–NO reduction is the key to this process. This work investigated the performance, kinetics, and mechanism of FeII(EDTA)–NO reduction by Mn powder coupled with manganese ion (Mn2+) recovery. We initially studied the performance of FeII(EDTA)–NO reduction with respect to the major influencing factors (i.e., the particle size of Mn powder, initial FeII(EDTA)–NO concentration, Mn powder concentration, stirring speed, and temperature). Shrinking core model and Arrhenius law were applied to illustrate the kinetics and mechanism between FeII(EDTA)–NO solution and Mn powder, suggesting that the solid–liquid reaction was fitted on chemical reaction control, and the activation energy was calculated as 43.0 kJ mol–1. The effects of main operating parameters, such as precipitant concentration, pH value, and temperature, were studied on Mn2+ recovery. Results indicated that the pseudo-second-order model could precisely describe the kinetics of Mn2+ recovery. Finally, according to Arrhenius and Eyring–Polanyi equations, the reaction activation energy, enthalpy of activation, and entropy of activation for Mn2+ recovery were calculated as 17.25 kJ mol–1, 14.55 kJ mol–1, and 252.07 J (k mol)−1, respectively.

A Novel Viscosity-Temperature Model of Glass-Forming Liquids by Modifying the Eyring Viscosity Equation

Many models have been created and attempted to describe the temperature-dependent viscosity of glass-forming liquids, which is the foundational feature to lay out the mechanism of obtaining desired glass properties. Most viscosity models were generated along with several impact factors. The complex compositions of commercial glasses raise challenges to settle these parameters. Usually, this issue will lead to unsatisfactory predicted results when fitted to a real viscosity profile. In fact, the introduction of the reliable viscosity-temperature data to viscosity equations is an effective approach to obtain the accurate parameters. In this paper, the Eyring viscosity equation, which is widely adopted for molecular and polymer liquids, was applied in this case to calculate the viscosity of glass materials. On the basis of the linear variation of molar volume with temperature during glass cooling, a modified temperature-dependent Eyring viscosity equation was derived with a distinguished mathematical expression. By means of combining high-temperature viscosity data and the glass transition temperature (Tg), nonlinear regression analysis was employed to obtain the accurate parameters of the equation. In addition, we have demonstrated that the different regression methods exert a great effect on the final prediction results. The viscosity of a series of glasses across a wide temperature range was accurately predicted via the optimal regression method, which was further used to verify the reliability of the modified Eyring equation.

Kinetics and Gibbs Function Studies on Lipase-Catalyzed Production of Non-Phthalate Plasticizer.

Petroleum based phthalate plasticizers encounter enormous claims to prohibit their production due to their harmful health impacts when they are mixed with plastics. That is why efforts are being done to find safer natural alternatives. We have investigated the reaction kinetics of the esterification epoxidation of oleic acid and 2-ethylhexanol in the presence of hydrogen peroxide catalyzed using Candida antarctica lipase (Novozym 435, Novozymes, Kobenhavn, Denmark). The product of this reaction is epoxidized 2-ethylhexyl oleate, a non-phthalate green plasticizer. The kinetic model for this reaction follows a multi-substrate PingPong Bi-Bi mechanism with competitive inhibition by the alcohol. The reaction's kinetic parameters were found to be 0.76 M, 0.37 M, 0.08 M, and 37.20 mM/min for Michalis-Menten constant for oleic acid (Kmo), Michalis-Menten constant for alcohol (Kma), alcohol inhibition constant (Kia), and maximum reaction velocity (Vmax), respectively. Then the Gibbs function analysis of the transition state based on the Arrhenius and Eyring equations was carried out. The internal diffusional limitations were found to be negligible as the effectiveness factor took the value of almost unity. While the external mass transfer resistance had no effect on the reaction due to operating at relatively high agitation speed and high temperature. This investigation confirms that this reaction was only kinetically controlled.

Microwave-Assisted Transesterification of Kusum Oil: Parametric, Kinetic and Thermodynamic Studies

Microwave-assisted transesterification of non-edible oil to produce biodiesel is gaining attention due to lower heat loss as well as rapid conversion. In this study, esterified kusum oil as a feedstock was transesterified in the presence of Ba(OH)2. At 800 W microwave power and constant magnetic stirring the effect of important process parameters such as solvent methanol molar ratio, Ba(OH)2, temperature, and time on biodiesel yield were evaluated. The parametric study suggested that 9:1 M methanol, 65 ºC reaction temperature, 2.5 wt% Ba(OH)2 catalyst and 3.5 min of transesterification time gave close to 96% biodiesel yield. At the above conditions of methanol and catalyst, the reaction kinetics and thermodynamic study were performed using different time intervals. The microwave-assisted transesterification followed pseudo-first-order reaction rate with 34.57 kJ/mol K activation energy and 205664 min-1 frequency factor. The reduction in activation energy and increase in the frequency factor reveal the non-thermal effect associated with microwave heating. The thermodynamic properties evaluated using the Eyring equation suggests non-spontaneity and endothermic nature of transesterification.

Photochromic properties of some azomaleimide derivatives and DFT quantum chemical study of thermal cis-trans isomerization pathways

A systematic study on the dynamics of trans-cis, thermal cis-trans backward and light induced cis-trans isomerization of some azobismaleimide derivatives was performed. Systems under study were N-[4-(carbonylaminoazobenzene)-phenyl]-maleimide (AAzM) and a styrene-maleimide copolymer containing azo units in the side chain (AAzMC). The isomerization reactions were followed by electronic absorption spectra. The kinetics of trans-cis photoisomerization was investigated in six solvents with different polarities. Results revealed that the content of the photostationary state depended on the solvent nature. In turn, the chemical environment had a minor influence on the photoisomerization rate constants. The kinetic and thermodynamic activation parameters were evaluated according to Arrhenius and Eyring equations. The theoretical calculations based on density functional theory (DFT) were employed to identify the mechanism of the thermal isomerization in AAzM. In our results, the thermal cis-trans isomerization of azobismaleimide AAzM followed an inversion assisted by rotation pathway in the S0 state.

Structure elucidation and formation mechanistic study of a methylene-bridged pregabalin dimeric degradant in pregabalin extended-release tablets.

During the pharmaceutical development of pregabalin extended-release tablets, an unknown degradant at a relative retention time (RRT) of 11.7 was observed and its nominal amount exceeded the ICH identification threshold in an accelerated stability study. The aim of this study is to identify the structure and investigate the formation mechanism of this impurity for the purpose of developing a chemically stable pharmaceutical product. By utilizing multi-stage LC-MS analysis in conjunction with mechanism-based stress study, the structure of the RRT 11.7 impurity was rapidly identified as a dimeric degradant that is caused by dimerization of two pregabalin molecules with a methylene bridging the two pregabalin moieties. The structure of the dimer was confirmed by 1D and 2D NMR measurement. The formation pathway of the dimeric degradant was also inferred from the mechanism-based stress study, which implicated that the bridging methylene could originate from formaldehyde which might be the culprit that triggers the dimerization in the first place. The subsequent API-excipients compatibility study indicated that the degradant was indeed formed in the compatibility experiments between pregabalin API and two polymeric excipients (PEO and PVPP) that are known to contain residual formaldehyde, but only in the co-presence of another excipient, colloidal silicon dioxide (SiO2). The kinetic behavior of the degradant formation was also investigated and two kinetic models were utilized based on the Arrhenius and Eyring equations, respectively, to calculate the activation energy (Ea) as well as the enthalpy of activation (△H‡), entropy of activation (△S‡), and Gibbs free energy (△G‡) of the degradation reaction. The results of this study would be useful for the understanding of similar dimeric degradant formation in finished products of drug substances containing primary or secondary amine moieties.

Reduction of FeII(EDTA)-NO by Mn powder in wet flue gas denitrification technology: stoichiometry, kinetics, and thermodynamics.

Conversion of FeII(EDTA)-NO or FeIII(EDTA) into FeII(EDTA) is a key process in a wet flue gas denitrification technology with FeII(EDTA) solution. In this work, the stoichiometry, kinetics, and thermodynamics of FeII(EDTA)-NO reduction by Mn powder were investigated. We first studied the FeII(EDTA)-NO reduction and product distribution to speculate a possible stoichiometry of FeII(EDTA)-NO reduction by Mn powder. Then, the effects of major influencing factors, such as pH value, temperature, and Mn concentration, were studied. The pseudo-second-order model was established to describe the FeII(EDTA)-NO reduction. Simultaneously, according to Arrhenius and Eyring-Polanyi equations, the reaction activation energy (Ea), enthalpy of activation (∆H‡), and entropy of activation (∆S‡) were calculated as 23.68 kJ/mol, 21.148 kJ/mol, and - 149.728 J/(k mol), respectively. Additionally, simultaneous reduction of FeIII(EDTA) and FeII(EDTA)-NO was investigated to better study the mechanism of FeII(EDTA) regeneration, suggesting that there was a competition between the two reduction processes. Finally, a simple schematic mechanism of NO absorption by FeII(EDTA) combined with regeneration of manganese ion and ammonium was proposed. These fundamental researches could offer a valuable guidance for wet flue gas denitrification technology with FeII(EDTA) solution.

On the free-volume model of multi-shape memory effect in amorphous polymer

Free volume theory, which is a popular approach to solve the problems associated with glass transition in polymers, is applied to investigate multi-shape memory effect (multi-SME) of amorphous shape memory polymers (SMPs) as well. To understand the phenomena of multiple shape recovery behaviors, theories about the SME and multi-SME in amorphous SMPs are firstly developed. The thermodynamics in the SMPs with dual- and triple-SME is then investigated in the frameworks of the free volume model and Eyring equation, taking account of the dependencies of free volume and activation energy on relaxation time. Finally, the proposed free volume model is evaluated and compared with results from the amorphous SMPs with dual- and triple-SMEs. Results from our newly proposed model show a good agreement with experimental results obtained at different temperatures.

Effect of Different Amino Acids and Heating Conditions on the Formation of 2-Amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) and Its Kinetics Formation Using Chemical Model System.

The formation of 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) was investigated using a kinetic study approach as described by first-order, Arrhenius, and Eyring equations. Chemical model systems with different amino acid precursors (proline, phenylalanine, and glycine) were examined at different times (4, 8, 12, and 16 min) and temperatures (150, 180, 210, 240, and 270 °C). PhIP was detected using high-performance liquid chromatography equipped with fluorescence detector (HPLC-FLD). The good fit in first-order suggested that PhIP formation was influenced by the types of amino acids and PhIP concentration significantly increased with time and temperature (up to 240 °C). PhIP was detected in proline and phenylalanine model systems but not in the glycine model system. The phenylalanine model system demonstrated low activation energy (Ea) of 95.36 kJ/mol that resulted in a high rate of PhIP formation (great amount of PhIP formed). Based on the ∆S‡ values both proline and phenylalanine demonstrated bimolecular rate-limiting steps for PhIP formation. Altogether these kinetic results could provide valuable information in predicting the PhIP formation pathway.

Influence of binary, ternary and quaternary mixtures on oxidative stability and study of kinetics and thermodynamic parameters of the degradation process of soybean biodiesel

Currently, studies show that plant extracts may exert antioxidant action and have aroused great interest because they have the property of preventing or minimizing the oxidative stress caused by free radicals. This study concerning to the binary, ternary and quaternary mixtures of plant extracts and the natural antioxidant quercetin with soybean biodiesel in concentrations ranging from (500 to 3000 ppm), using the acceletated oxidation techniques (Rancimat and PetroOXY), where the temperatures varied from 90 °C to 140 °C. The stabilizing factor was studied and indicated the existence of an antioxidant effect and not an antagonistic effect. Among the extracts the highest quantitative levels of flavonoids and total carotenoids were obtained in the following decreasing sequence: oregano extract (OE) > basil extract (BAE) > bilberry extract (BE), while for antioxidant activity front the DPPH radical the decreasing sequence was: oregano extract (OE) > bilberry extract (BE) > basil extract (BAE). The activation energies of the antioxidant mixtures were obtained by the Arrhenius equation and followed the ascending order: OEQC (62.69 kJ/mol) < BOBE (65.01 kJ /mol) < BAEQC (77.15 kJ/mol) < BEQC (77.73 kJ/mol) < BOBEQC (81.73 kJ /mol) by the technique Rancimat and BEQC (40.90 kJ/mol) < OEQC (41.82 kJ/mol) < BAEQC (42.32 kJ/mol) < BOBEQC (44.48 kJ/mol) < BOBE (45.31 kJ/mol) by the technique PetroOXY. The thermodynamic parameters ΔH* and ΔS*, were obtained by the Eyring equation and the ΔG* by the fundamental equation of thermodynamics, being evident, by the results shown, the existence of an endothermic and non-spontaneous process. The shelf life of antioxidant mixtures with biodiesel followed the descending order: BAEQC > BEQC > OEQC > BOBEQC > BOBE and OEQC > BAEQC > BEQC > BOBEQC > BOBE in the Rancimat and PetroOXY method, respectively. Therefore, the use of mixtures of these natural antioxidants was very promising and of fundamental importance in the control of the oxidative process of soybean biodiesel.

Influence of drying methods on the thermodynamic parameters, effective moisture diffusion and drying rate of wastewater sewage sludge

In this study, thin layer drying experiments of direct and indirect natural convection solar drying of wastewater sewage sludge in Algeria were conducted. The purpose of these was to analyze the effect of two methods of drying on different parameters, namely: drying rate, efficient diffusion of moisture, and thermodynamic parameters. Three new universal drying kinetic models were proposed and compared with four other models existing in the literature to model the drying process. The effective diffusivity of moisture of sludge (Deff) changed from 1.91 10−8 to 9.12 10−8 m2 s−1. It was obtained by using Fick's second law, based on the resolution by Laplace's transformation method and the Fourier series. Thermodynamic parameters, to know, activation energy, free energy change, enthalpy and entropy change, were also determined using a new methodology build on the evolution of effective diffusion coefficient in terms of temperature by adopting the Eyring equation.

Kinetics of the anionic homopolymerizations of ß–myrcene and 4–methylstyrene in cyclohexane initiated by n–butyllithium

ABSTRACTThe kinetics of isothermal anionic homopolymerization of ß–myrcene (MYR) and 4–methylstyrene (4MS) in cyclohexane, initiated by n–butyllithium was studied at different temperatures (55, 63, and 71 ° C). The kinetic information obtained from the homopolymerizations was used to estimate the parameters of the Eyring equation, ΔH‡= 84080 J/mol and ΔS‡= −21.9 J/mol·K for the MYR, and ΔH‡= 51250 J/mol and ΔS‡= −116.8 J/mol·K for the 4MS, to calculate the apparent propagation coefficients as a function of temperature. Finally, the parameters obtained for the Eyring equation were validated by applying them in a mathematical model representing the kinetics of nonisothermal (quasi‐adiabatic) polymerization experiments of MYR and 4MS. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 2157–2165

On the use of aqueous solutions of polyvinyl methyl ether for the embolization of blood vessels

Aqueous solutions of polyvinyl methyl ether were investigated in order to test whether it is possible to utilize them as bases for embolic agents used to deliberately block blood vessels. This may be necessary in the course of treatment of vascular abnormalities, tumors, as well as during the preparation of patients for surgery. The right branch of the binodal curve for the binary system “polyvinyl methyl ether–water” was drawn using the cloud point method and the lower critical mixing temperature (35.5 °C) was calculated. Furthermore, the exact concentration of polyvinyl methyl ether in aqueous solutions at which phase transition occurs (given the temperature of 35.5 °C) was found to be 30 wt %. The viscosity–velocity curves for the 30% solution of polyvinyl methyl ether, obtained by rheoviscometry in the temperature range of 5 to 36 °C, indicate that this aqueous solution has a low viscosity and behaves like a Newtonian fluid. However, at the temperature of 35 °C and higher, close to the phase transition, a significant deviation from its Newtonian behavior is observed due to precipitation of polyvinyl methyl ether as it forms a solid white mass. Through the use of the Arrhenius–Frenkel–Eyring equation, the activation energy of the viscous flow for polyvinyl methyl ether solutions was found to be 31 kJ/mol. Based on refractometry data, it was demonstrated that phase transition in aqueous solutions of polyvinyl methyl ether is reversible. This feature can facilitate medical equipment cleaning before introducing the embolic agent into a patient’s bloodstream. Finally, the investigation determined some parameters, in which the formation of embolic agents from a 30% polyvinyl methyl ether aqueous solution occurs (in situ in a blood vessel at a temperature of 35.5 °C).

Modeling the effect of thermal combined with high‐pressure treatment on intramuscular lipid oxidation in pork

AbstractThe kinetics of lipid oxidation in pork during high‐pressure combined with thermal (HP‐T) treatment were studied within the condition range of 300–600 MPa and 20–60°C. Results showed that the lipid oxidation rate constants (k values) increased with increasing pressure or temperature. Lipid primary oxidation exhibited higher k values than secondary oxidation at each investigated pressure–temperature. At the studied pressure range, the temperature dependence (activation energy) of both primary lipid oxidation and secondary lipid oxidation rate constants decreased with increasing pressure; while the highest sensitivity of lipid oxidation rate constants to pressure (activation volume) was observed at 30°C for primary oxidation, and 40°C for secondary oxidation. Four kinetic models for lipid oxidation basing on Arrhenius and Eyring equation were established successfully.Practical ApplicationsHigh pressure processing plays a more and more important role in food industry, however, the application of this technology in animal products is limited because of increased lipid oxidation due to high pressure treatment, the reason for which reported by different authors is inconsistent. To better understand the real causes of lipid oxidation induced by high pressure and control it purposefully, the kinetic models for lipid primary and secondary oxidation basing on Arrhenius and Eyring equation were established successfully in this article. In practice, the predetermined combinations of temperature and pressure during HP‐T treatment of pork could be evaluated by predicting the effect of these conditions on lipid oxidation using the models established in this study, and thereafter modifying and selecting the optimal treatment conditions. The models should be validated or modified when applied to other types of meat basing on a larger number of experiments.

Influencing the Artificial UV-A light on decolorization of Chlorazol black BH Dye via using bulk ZnO Suspensions

This manuscript is interested with the using Chlorazol black BH dye as a model compound. This photo reaction was obeyed first-order kinetics with low activation energy equal to 27.135 kJ/mol. Moreover, the thermodynamic parameters were calculated using the Arrhenius equation, the Eyring-Polanyi equation and the Gibbs equation, then proved this photo reaction is exothermic, with less random and spontaneous reaction. The best conditions were controlled with the using the artificial UV-A and found to be 100 mg/L (dye concentration), 200 mg (bulk ZnO), 7.63 as initial pH and 15°C, from the other side, the photo-decolorization efficiency at these best conditions, was reached to 99.072% At final, the suitable mechanism for decolorization and degradation of Chlorazol black BH Dye was suggested.