Conventional Kinetic Analysis Research Articles

Competitive SPR chaser assay to study biomolecular interactions with very slow binding dissociation rate constant

Binding kinetics of drug and its target protein is crucial for the efficacy and safety of the drug. Using surface plasmon resonance (SPR) technology, we performed a competitive SPR chaser assay, a method to study biomolecular interactions with very slow dissociation rate constants (kd < 1E-4 s−1). This report described the principle and the experimental setup of the chaser assay, which involves using a competitive probe (chaser) to detect changes in target occupancy by a test molecule over time. We demonstrated the applicability of the chaser assay for both small and large molecules and compared the results with conventional SPR kinetic analysis and other methods. We suggest that the chaser assay is a useful and robust technique to characterize very tight biomolecular interactions, and that it can also be used to study cooperativity in ternary complex formation.

Kinetics of combustion of lignocellulosic biomass: recent research and critical issues

Predicting biomass combustion at temperatures of practical interest requires kinetic expression robust and reliable over a large temperature range.The present work examines experimental works on combustion kinetics of lignocellulosic biomass published since 2015 and reports the experimental methods used and the kinetic parameters obtained therein. The most common experimental strategy, used in 39 referenced works, was non-isothermal thermogravimetric analysis, yet the kinetic parameters obtained varied by order of magnitude.The large variability of the kinetic parameters found in literature cannot be only explained by the feedstock heterogeneity or the different data analysis methods. One possible and apparently neglected source of error lies in the fact lignocellulosic biomasses are complex materials, constituted by different components, thus thermogravimetric curves are the resultant of multiple and partly overlapping stages of mass loss. Kinetic analysis in this case easily generates errors. Another criticality that the work wants to emphasize is the fact that biomass pyrolyses, burns and even thermally anneals throughout a TGA experiment. These progressive structural changes are a further problem for application of conventional kinetic analysis methods.Altogether, it can be concluded that it is difficult to obtain from conventional TGA analysis reliable kinetic expressions of biomass combustion to be used for boilers modelling. For complex materials like biomass, it is recommended to adopt expert-case sensitive approaches. As an example, the case of walnut shells combustion is presented. For this material, four components with different combustion reactivity have been identified and simplified single rate kinetics are proposed according to the temperature interval of interest.

Study on the thermal decomposition mechanism of Mg(NO3)2·6H2O from the perspective of resource utilization of magnesium slag

ABSTRACT The magnesium slag (magnesium nitrate hydrate Mg(NO3)2·6H2O) produced in the nitric acid leaching process of laterite nickel ore can be effectively recycled by thermal decomposition. To this end, this study placed great emphasis on disclosing the thermal decomposition mechanism of Mg(NO3)2·6H2O. Firstly, thermal decomposition paths of Mg(NO3)2·6H2O were revealed through Thermogravimetry-Mass Spectrometry, Differential Scanning Calorimetry and powder X-ray diffraction. It was found that the thermal decomposition of Mg(NO3)2·6H2O was a multistep endothermic reaction involving two dehydration stages and one denitration stage. The two dehydration stages were characterized by the evolution of H2O, with the formation of magnesium nitrate dihydrate and anhydrous magnesium nitrate. The denitration stage was characterized by the simultaneous evolution of O2 and NO2, with the formation of MgO. The conventional kinetic analysis was not suitable for describing such complex multistep reaction behaviour. Thus, the kinetic rate data (dα/dt-T) for the overall reaction were separated into those for three contributing stages by mathematical peak deconvolution. Then, the complete kinetic interpretations of the separated reaction stages for Mg(NO3)2·6H2O pyrolysis were achieved by the Friedman method and the master plots method. Finally, the original experimental α-T curves were successfully simulated using the resulting kinetic triplets.

Synthesis and characterization of novel sulfonamide functionalized maleimide polymers: Conventional kinetic analysis, antimicrobial activity and dielectric properties

In this study, novel maleimide monomers, N-sulfamethoxazole maleimide(SMM), and N-sulfanilamide maleimide(SAM) were synthesized. Homopolymers of SMM and SAM were obtained by free radical polymerization method in 1,4-dioxane solvent at 65 °C. The structural characterizations of monomers and their homopolymers were carried out via FTIR, 1H- and 13C-NMR techniques. The glass transition temperature (Tg) of the polymers was determined using differential scanning calorimetry (DSC). Using the thermogravimetric analysis (TGA) method determined the thermal stability of the polymers. The thermal degradation activation energies (Ea) of the polymers were calculated by Kissinger, Flynn Wall Ozawa (FWO), and Kissinger-Akahira-Sunose (KAS) methods. The biological activities of compounds have been also studied on various bacteria and fungi. The weight average (Mw) and number average (Mn) molecular weights of the polymers were determined by gel permeation chromatography (GPC). Photochemical properties of polymers were investigated with ultraviolet (UV) and fourier transform infrared (FTIR) spectra. In addition, some physical constants of polymers such as density, solubility parameter, and viscosity were determined. Finally, the dielectric constant, dielectric loss factor and ac conductivity values ​​of the polymers were estimated in the frequency range of 100 Hz–20 kHz.

Electrical investigation on Eu+3- doped copolymer composite system and conventional kinetic analysis

Poly(maleic anhydride-co-benzyl methacrylate) copolymer was prepared by using free radical polymerization (FRP) method at 70 °C. The structural characterization of the polymer was accomplished FT-IR, 1H and 13C NMR spectroscopic techniques. P(MA-co-BMA)/ EuCl3 composites were prepared rate of 2%, 5% and 10% (wt/wt). The thermal behavior of pure copolymer was investigated by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Thermal decomposition kinetics of poly(MA-co-BMA) carried out from Flynn–Wall–Ozawa method via TG curves for calculated apparent activation energies. According to FWO; the activation energy (Ea) was estimated as; 185.61 kJ/mol. Dielectric and electrical properties of copolymer/composite systems were investigated against frequency (range from 100 Hz to 20 kHz) at room temperature by using an impedance analyzer. The effect of EuCl3 concentration on dielectric constant, dielectric loss factors, ac conductivity, susceptance (B) and impedance (Z) was investigated. A remarkable increase was observed in dielectric and AC electrical properties were observed with the addition of Eu+3 to the polymer matrix. The B and Z parameters of poly(MA-co-BMA) and composites were investigated depending on frequency at room temperature based on the alternating current (AC).

Iron Ore Reduction by Hydrogen Using a Laboratory Scale Fluidized Bed Reactor: Kinetic Investigation\u2014Experimental Setup and Method for Determination

The reduction kinetics of hematite iron ore fines to metallic iron by hydrogen using a laboratory fluidized bed reactor were investigated in a temperature range between 873 K and 1073 K, by measuring the weight change of the sample portion during reduction. The fluidization conditions were checked regarding plausibility within the Grace diagram and the measured pressure drop across the material during experiments. The apparent activation energy of the reduction was determined against the degree of reduction and varied along an estimated two-peak curve between 11 and 55 kJ mol−1. Conventional kinetic analysis for the reduction of FeO to metallic iron, using typical models to describe gas–solid reactions, does not show results with high accuracy. Multistep kinetic analysis, using the Johnson–Mehl–Avrami model, shows that the initial stage of reduction from Fe2O3 to Fe3O4, and partly to FeO, is controlled by diffusion and chemical reaction, depending on the temperature. Further reduction can be described by a combination of nucleation and chemical reaction, whereby the influence of nucleation increases with an increasing reduction temperature. The results of the kinetical analysis were linked to the shape of the curve from apparent activation energy against the degree of reduction.

New parameters of ultrafast dynamic contrast-enhanced breast MRI using compressed sensing.

Ultrafast dynamic contrast-enhanced (UF-DCE) breast MRI is considered a promising method of accelerated breast MRI. However, the value of new kinetic parameters derived from UF-DCE need clinical evaluation. To evaluate the diagnostic performance of the maximum slope (MS), time to enhancement (TTE), and time interval between arterial and venous visualization (AVI) derived from UF-DCE MRI using compressed sensing (CS). Retrospective. Seventy-five patients with histologically proven breast lesions. The total number of analyzed lesions was 90 (61 malignant and 29 benign). 3T MRI with UF-DCE MRI based on the 3D gradient-echo volumetric interpolated breath-hold examination (VIBE) sequence using incoherent k-space sampling combined with a CS reconstruction followed by conventional DCE MRI. The diagnostic performance of the MS, TTE, AVI, and conventional kinetic analysis was analyzed and compared with histology. Wilcoxon rank sum test, receiver operating characteristic analysis. The MS was larger and the TTE and AVI were smaller for malignant lesions compared with benign lesions: MS: 29.3%/s and 18.4%/s (P < 0.001), TTE: 7.0 and 12.0 seconds (P < 0.001), AVI: 2.7 and 4.4 frames (P = 0.006) for malignant and benign lesions. The discriminating power of the MS (area under the curve [AUC], 0.76) was slightly better than that of conventional kinetic analysis (AUC, 0.69) and comparable to that of the TTE and AVI (AUC, 0.78 and 0.76 for TTE and AVI, respectively). Invasive lobular carcinoma had smaller MS (21.8%/s) among malignant lesions (29.3%/s). The MS, TTE, and AVI can be used to evaluate breast lesions with clinical performance equivalent to that of conventional kinetic analysis. These parameters vary among histologies. 3 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2020;51:164-174.

Snapshot transient absorption spectroscopy: toward in vivo investigations of nonphotochemical quenching mechanisms

Although the importance of nonphotochemical quenching (NPQ) on photosynthetic biomass production and crop yields is well established, the in vivo operation of the individual mechanisms contributing to overall NPQ is still a matter of controversy. In order to investigate the timescale and activation dynamics of specific quenching mechanisms, we have developed a technique called snapshot transient absorption (TA) spectroscopy, which can monitor molecular species involved in the quenching response with a time resolution of 30s. Using intact thylakoid membrane samples, we show how conventional TA kinetic and spectral analyses enable the determination of the appropriate wavelength and time delay for snapshot TA experiments. As an example, we show how the chlorophyll-carotenoid charge transfer and excitation energy transfer mechanisms can be monitored based on signals corresponding to the carotenoid (Car) radical cation and Car S1 excited state absorption, respectively. The use of snapshot TA spectroscopy together with the previously reported fluorescence lifetime snapshot technique (Sylak-Glassman et al. in Photosynth Res 127:69-76, 2016) provides valuable information such as the concurrent appearance of specific quenching species and overall quenching of excited Chl. Furthermore, we show that the snapshot TA technique can be successfully applied to completely intact photosynthetic organisms such as live cells of Nannochloropsis. This demonstrates that the snapshot TA technique is a valuable method for tracking the dynamics of intact samples that evolve over time, such as the photosynthetic system in response to high-light exposure.

Topological Dissection of the Membrane Transport Protein Mhp1 Derived from Cysteine Accessibility and Mass Spectrometry.

Cys accessibility and quantitative intact mass spectrometry (MS) analyses have been devised to study the topological transitions of Mhp1, the membrane protein for sodium-linked transport of hydantoins from Microbacterium liquefaciens. Mhp1 has been crystallized in three forms (outward-facing open, outward-facing occluded with substrate bound, and inward-facing open). We show that one natural cysteine residue, Cys327, out of three, has an enhanced solvent accessibility in the inward-facing (relative to the outward-facing) form. Reaction of the purified protein, in detergent, with the thiol-reactive N-ethylmalemide (NEM), results in modification of Cys327, suggesting that Mhp1 adopts predominantly inward-facing conformations. Addition of either sodium ions or the substrate 5-benzyl-l-hydantoin (L-BH) does not shift this conformational equilibrium, but systematic co-addition of the two results in an attenuation of labeling, indicating a shift toward outward-facing conformations that can be interpreted using conventional enzyme kinetic analyses. Such measurements can afford the Km for each ligand as well as the stoichiometry of ion–substrate-coupled conformational changes. Mutations that perturb the substrate binding site either result in the protein being unable to adopt outward-facing conformations or in a global destabilization of structure. The methodology combines covalent labeling, mass spectrometry, and kinetic analyses in a straightforward workflow applicable to a range of systems, enabling the interrogation of changes in a protein’s conformation required for function at varied concentrations of substrates, and the consequences of mutations on these conformational transitions.

Rapid extraction of quantitative kinetic information from variable-temperature reaction profiles

Analysis of variable-temperature reaction profiles, measured in an isothermal packed-bed reactor (PBR) whose temperature increases during the experiment, has the potential to yield accurate and precise kinetic parameters quickly for some heterogeneous catalysts. The method is demonstrated here for a typical supported nanoparticle catalyst, 2wt% Pd/Al2O3, in the oxidation of H2, C3H8 and CO by O2. These reactions do not exhibit major changes in activation energy as a function of conversion over the range of reaction conditions analyzed. Reliable and quantitative information about rate laws was extracted readily from the shapes and positions of the profiles, as an alternative to more laborious conventional kinetic analyses. Temperature and pressure gradients were minimized by the use of sieved catalyst particles and large amounts of inert diluent for both the catalyst and feed gas. Curve-fitting of analytical expressions with as few as two adjustable parameters results in remarkable agreement between models and data. First-order profiles are kinetically-limited, without mass and heat transfer effects, while inverse-first-order profiles deviate from kinetically-controlled behavior at intermediate-to-high conversions. The activation energy and reaction order with respect to the limiting reactant obtained from a single reaction profile (with appropriate data truncation for non-kinetic phenomena, as necessary) are at least as accurate and precise as those obtained from a conventional Arrhenius analysis conducted with data obtained under differential conditions, and can be measured in a fraction of the experimental time. Information about more elaborate rate laws can be obtained by global curve-fitting of a family of such profiles recorded with different volumetric flow rates.

Model-Free Kinetic Data Analysis Using Massive Dynamic Impedance Data Sets

Dynamic Electrochemical Impedance Spectroscopy (dEIS) enables the collection of impedance data sets continuously as a slow-sweep cyclic voltammogram is carried out. Provided that careful baseline corrections are carried before the Fourier analysis of the multisine signal and the lowest frequency is not too low for the chosen sweep rate (typically 1 Hz at 2 mV s-1), then it may be shown that the impedance data is valid, for example by the Kramers-Kronig transformation [1]. The method can measure the dynamic state of the surface, and the correlation with the voltammetric features, such as integrated charges or subtle changes in the peak shape, assists in the interpretation. The enormous amount of data produced, e.g., spectra every 1 mV over 3 V for a voltammetry cycle, is daunting in terms of data analysis (and required disk space), but this is solved to some extent by automated batch fitting to equivalent circuits. However, the large data density offers the possibility to deduce the form of the rate law in a model-free kinetic data analysis, rather than the more usual propose-mechanism—fit—reject--modify cycle of identifying reaction mechanisms. This cycle frequently fails because (1) many standard assumptions are oversimplified, and (2) the real behaviour may be outside known models. Consider the surface reaction step that is key in many small molecule oxidation mechanisms, OH(ads) + CO(ads) → CO2 + H+ + e- + 2(site) rate = kθ OH· θ CO The rate law is written as a product of coverages, θ, in the most common, but oversimplified, Langmuir (mass-action) form. An unrealistically high maximum coverage of one adsorbate per metal site is typically assumed. There is controversy over whether this proceeds by random collisions between mobile adsorbed species, or at the edge of islands of the adsorbed species (nucleation-collision-growth kinetics). This debate hinges on the surface diffusion rate, and it needs to be remembered that these are extremes. Interactions between adsorbed species are sometimes modeled by the Frumkin isotherm, which is only approximate. Adsorption of OH and mass transport of CO typically involve approximations. Anion adsorption can be significant in these types of reactions, but is usually not explicitly invoked. This type of complexity thwarts conventional kinetic analysis. We illustrate an alternative method, applied here to the simpler case of the oxide formation and reduction on polycrystalline Pt and Pd. The kinetics are characterized by seeking (i) the net rate of production of the adsorbed species as a function of both coverage and potential, r(θ,E), and (ii) the current density as a function of these variables, j(θ,E). Under the very generic assumption that these rates are some (unknown) function of coverage times some function of potential times some function of bulk concentration (mass transport being fast for this system), we can show that the experimental quantity R ct times the voltammetry current density must be the function of the potential divided by its derivative with respect to potential. Integration of this ratio with potential at constant coverage and concentration then shows (for this system) that the data obeys the Tafel relationship and enables extraction of the transfer coefficient without assuming any functional form for the coverage and concentration functions. Similar tests may be devised to determine the latter functions, and in this way, the rate law may be deduced directly from the data. [1] R.L. Sacci, F. Seland and D.A. Harrington, Dynamic Electrochemical Impedance Spectroscopy for Electrocatalytic Reactions, Electrochim. Acta., 131 (2014) 13-19. * Present address, Oak Ridge National Laboratory

Experimental study and kinetic analysis on sodium oxide–silica reaction

ABSTRACTIn a sodium-cooled fast reactor (SFR), if considering hypothetical severe accidental condition such as the steel liner failure of structural concrete caused by intensive leakage of liquid sodium (Na) coolant, the liquid sodium–concrete reaction (SCR) may take place. The major consequences of SCR are hydrogen release, energy release and concrete ablation. Thus, it is important to understand the phenomenology and kinetic behavior of SCR. As a part of a series of studies on SCR, this study focused on the reaction between sodium oxide (Na2O) and silica (SiO2), which is dealt with possible formation of Na2O as the result of sodium–water reaction in the initial stage of SCR. Through thermoanalytical and X-ray diffraction measurements, it was revealed that Na2O–SiO2 reaction to form sodium orthosilicate (Na4SiO4) occurs at significantly lower temperature in comparison with Na–SiO2 reaction. The reaction is kinetically characterized as a largely overlapping multistep reaction, which is composed of at least three reaction steps. On the basis of the observations, the impact of Na2O–SiO2 reaction in the overall SCR and the significance of the conventional kinetic analysis using the Kissinger method are discussed.

Exploiting temperature measurements for cure monitoring of FRP composites—Applications with thermocouples and infrared thermography

The curing behavior of a fiber-reinforced polymer composite part is interesting for both the industrial and scientific community, for it is related to process optimization, quality upgrade, and material characterization. The study at hand focuses on the potential of temperature measurements as a means to monitor curing; kinetic analysis which conventionally is being done for small neat resin samples in a thermally stable environment (laboratory instruments), is in this study implemented for actual scale composite samples in an environment with significant thermal gradients (manufacturing). To ensure the success of this transition, live temperature data and kinetic parameters derived from DSC of composite samples were used as input to the kinetic equations. Process monitoring with thermocouples that was compared with dielectric constant monitoring and conventional kinetic analysis confirmed the validity of the method. An application with infrared thermography determined the impact of heat insulators within the composite (e.g. delaminations) on the superficial curing degree.

Enzyme kinetics: the whole picture reveals hidden meanings.

The methodology adopted by Michaelis and Menten in 1913 is still routinely used to characterize the catalytic power and selectivity of enzymes. These kinetic measurements must be performed soon after the purified enzyme is mixed with a large excess of substrate. Other time scales and solution compositions are no less physiologically relevant, but fall outside the range of applicability of the classical formalism. Here we show that the complete picture of an enzyme's mode of function is critically obscured by the limited scope of conventional kinetic analysis, even in the simplest case of a single active site without inhibition. This picture is now unveiled in a mathematically closed form that remains valid over the reaction time for all combinations of enzyme/substrate concentrations and rate constants. Algebraic simplicity is maintained in the new formalism when stationary reaction phases are considered. By achieving this century-old objective, the otherwise hidden role of the reversible binding step is revealed and atypical kinetic profiles are explained. Most singular kinetic behaviors are identified in a critical region of conditions that coincide with typical cell conditions. Because it is not covered by the Michaelis-Menten model, the critical region has been missed until now by low- and high-throughput screenings of new drugs. New possibilities are therefore raised for novel and once-promising inhibitors to therapeutically target enzymes.

Determining the affinity and stoichiometry of interactions between unmodified proteins in solution using Biacore

We describe a general Biacore method for measuring equilibrium binding affinities and stoichiometries for interactions between unmodified proteins and their unmodified ligands free in solution. Mixtures of protein and ligand are preequilibrated at different ratios in solution and then analyzed by Biacore using a sensor chip surface that detects only unbound analyte. Performing the Biacore analysis under mass transport limited conditions allows the concentration of unbound analyte to be determined from the initial velocity of binding. Plots of initial velocity versus the concentration of the varied binding partner are fitted to a quadratic binding equation to give the affinity and stoichiometry of binding. We demonstrate the method using soluble Her2 extracellular domain binding to monovalent, bivalent, and trivalent forms of an anti-Her2 antibody. The affinity we measured agrees with that obtained from conventional Biacore kinetic analysis, and the stoichiometries for the resulting 1:1, 1:2, and 1:3 complexes were confirmed by gel filtration with in-line light scattering. The method is applicable over an affinity range of approximately 100pM to 1μM and is particularly useful when there is concern that covalently modifying one or the other binding partner might affect its binding properties or where multivalency might otherwise complicate a quantitative analysis of binding.

18 F]Fluoroethyltyrosine–Positron Emission Tomography-Based Therapy Monitoring after Stereotactic Iodine-125 Brachytherapy in Patients with Recurrent High-Grade Glioma

Therapy monitoring of glioma after stereotactic iodine-125 brachytherapy (SBT) remains challenging because posttherapeutic changes in magnetic resonance imaging can mimic tumor progression. We evaluated the prognostic value of serial [18F]fluoroethyltyrosine (FET)-positron emission tomographic (PET) scans for therapy monitoring of high-grade glioma (HGG) after SBT. Thirty-three patients with recurrent HGG were included. Serial FET-PET scans were performed prior to therapeutic intervention and at 3-month intervals during the first year after SBT. FET-PET evaluation was performed by both conventional data analysis and kinetic analysis. Prognostic factors were obtained from proportional hazard models. Median local progression-free survival (LPFS) was 11.1 months. Maximal standardized background uptake value (SUVmax/BG) and biologic tumor volume (BTV) differentiated accurately between therapeutic effects and local tumor progression at the 6-month and subsequent examinations. Increasing uptake kinetics at baseline (p < .05) and during follow-up (p < .01) were stringently associated with a longer LPFS. Early increase in FET uptake after SBT is not unequivocally associated with tumor progression; it might be induced by reactive changes and could easily lead to a misclassification of the tumor status (pseudoprogression). Six months after SBT (or later), however, increased SUVmax/BG and BTV values are associated with a worse prognosis. Multivariate analysis stresses the prognostic importance of dynamic studies.

Reactions of the simple nitroalkanes with hydroxide ion in water. Evidence for a complex mechanism

Conventional kinetic analysis of the reactions of nitromethane (NM), nitroethane (NE) and 2-nitropropane (2-NP) with hydroxide ion in water revealed that the reactions are complex and involve kinetically significant intermediates. Kinetic experiments at the isosbestic points where changes in reactant and product absorbance cancel indicate the evolution and decay of absorbance characteristic of the formation of reactive intermediates. The deviations from 1st-order kinetics were observed to increase with increasing extent of reaction and in the reactant order: NM < NE < 2-NP. The apparent deuterium kinetic isotope effects for proton/deuteron transfer approach unity near zero time and increased with time toward plateau values as the reaction kinetics reach steady state. It is proposed that the initially formed preassociation complexes are transformed to more intimate reactant complexes which can give products by two possible pathways.

The non-isothermal thermogravimetric tests of animal bones combustion. Part II. Statistical analysis: Application of the Weibull mixture model

The possibility of applying the Weibull mixture model for the fitting of the non-isothermal conversion data for the combustion process of animal bone samples has been investigated. It has been found that the conversion data at the different heating rates for the investigated samples, can be successfully described by the linear combination of few Weibull distribution functions. An optimal fitting of the conversion data has been obtained by a mixture of three Weibull distribution functions. It was established that the conversion curves calculated by the proposed model, are in good agreement with the raw conversion data of the investigated bone samples. The alterations of distribution parameters in the Weibull mixture model, indicate a probably change of the kinetic nature of the particular reaction stage. A model with a continuous distribution of the apparent activation energies ( E a ) can adequately represents the individually stages of the complex combustion process. The characterization of the estimated distribution curves, enable us to receive the additional information's about the kinetic behaviour of individual reaction stages, which does not attainable from the results of conventional kinetic analysis.

The steady-state kinetics of parallel reaction networks

The conventional kinetic analysis of an overall reaction (OR) is limited to a single sequential pathway of molecular steps at a time, based either on the general quasi-steady state (QSS) approach of Bodenstein, or on the much simpler but limited Langmuir–Hinshelwood–Hougen–Watson (LHHW) approach based on assuming a single rate-determining step (RDS), the remaining being quasi-equilibrated (QE). We recently described a new algebraic methodology for deriving the QSS rate expression for a reaction sequence, which allowed interpretation of the final result in an Ohm's law form, i.e., OR rate=OR motive force/OR resistance of an equivalent electric circuit, where the consecutive mechanistic steps represent resistors in series. Here, we propose a similar Ohm's law form of QSS rate for a reaction system involving parallel pathways, whose equivalent electrical circuit derives directly from the reaction route (RR) Graph of its mechanism, as proposed earlier by us. The results are exact for a reaction network with mechanistic steps linear in intermediates concentrations, while they are approximate, albeit accurate, for non-linear step kinetics. We further show how the LHHW methodology, combined with the concept of intermediate reaction might be utilized to obtain the step resistances involved. For illustration, we utilize the relatively simple examples of: (1) the gas-phase hydrogen–bromine non-catalytic reaction (non-linear kinetics), and (2) zeolite catalyzed N 2O decomposition reaction (linear kinetics). However, the approach is useful for more complex non-catalytic, catalytic and enzymatic reactions networks as well.

Kinetic analysis of solid state reactions without neglecting temperature integral at starting temperature: relationship between conversion degree at maximum reaction rate and reaction mechanism

In the conventional kinetic analyses of solid state reactions studied during linear heating, the temperature integral at the starting temperature is usually neglected. In this paper, an analytical equation is mathematically derived without neglecting the temperature integral at the starting temperature of the linear heating, which describes the relationship between the conversion degree at the maximum reaction rate and the reaction mechanism. This relationship can be expressed as f′(α m)g(α m)=— γ/ζm2eγ/ζm ∫ζm e–γ/ζdζ. It is shown that the conversion degree at the maximum reaction rate is dependent on the reaction mechanism and two dimensionless variables: ζ m=T m/T 0 and γ=E/RT 0.