Reaction Constants Research Articles

Kinetic Computation of Cyclization Reactions of Large Keto-Hydroperoxide Radicals in Low Temperature Combustion.

The cyclization reactions of keto-hydroperoxide (KHP) radicals leading to the formation of keto cyclic ethers and OH radicals play an important role in low temperature combustion for hydrocarbon fuels or oxygenated hydrocarbon fuels. However, due to the lack of kinetic data of cyclization reactions of KHP radicals, researchers often derive high-pressure-limit rate constants of cyclization reactions of KHP radicals from analogous cyclization reactions of hydroperoxyl alkyl radicals during construction of the combustion mechanism. This study aims to systematically investigate the kinetics of cyclization reactions of KHP radicals involving short-to-large-sized radicals. The studied reactions are divided into 7 reaction classes, according to the size of the cyclic transition state, the conjugative effect (whether KHP radicals are resonance-stabilized or not), and the position of the carbonyl group (whether the carbonyl group is inside or outside of the reaction center). The isodesmic reaction method, in conjunction with transition state theory, is utilized for each reaction class to compute the energy barriers and high-pressure-limit rate constants at the DFT level. The study revealed that energy barriers calculated at the DFT level with correction by the isodesmic reaction method are close to the results from the benchmark CCSD(T) method. To develop more accurate rate rules, these reaction classes are further divided into subclasses based on the relative site of the OOH group with the carbonyl group, the type of carbon atoms where the OOH group is located, and the type of carbon atoms where the radical site is located. For each subclass, high-pressure-limit rate rules are derived by averaging the rate constants of reactions in the subclass, and it is found that the maximum absolute deviation of the energy barrier and the ratio of the largest rate constant to the smallest rate constant among reactions in each subclass are within chemical accuracy limits, indicating acceptable use of the developed rate rules. A comparison of the rate constants for cyclization reactions of KHP radicals with the values of analogous cyclization reactions of hydroperoxyalkyl radicals as provided in reported mechanisms is made. Additionally, a comparison is drawn between our developed rate rules for subclasses of the cyclization reactions of KHP radicals and the rate rules for analogous subclasses of cyclization reactions of hydroperoxyl alkyl radicals. These comparisons demonstrate significant differences and highlight the necessity for improved rate rules for cyclization reactions of KHP radicals to enhance the automatically generated combustion mechanisms for hydrocarbon and oxygenated hydrocarbon fuels.

Enhancement of Catalytic Efficiency of Enzymatic Redox Reactions by Composing Horseradish Peroxidase-Modified Electrode with Ionic Liquids

We have kinetically estimated the enzymatic redox reaction at the horseradish peroxidase (HRP)-modified electrode combined with ionic liquids by adding N-(2-methoxythethyl)-N-methylpyrrolidinium bis(trifluoromethane sulfonyl)imide (MEMPTFSI) to HRP/carbon paste (CP)/Ketjenblack EC600JC (EC). The fluctuation of the steady-state reduction current of HRP at the HRP/CP-modified electrode progressively increased as the applied potential was lowered. The enzymatic redox reaction with hydrogen peroxide as a substrate at the HRP/CP/EC/MEMPTFSI-modified electrode and the HRP/CP-modified electrode could be correlated by the Michaelis–Menten equation. The Michaelis constant of the enzymatic redox reaction at the HRP/CP/EC/MEMPTFSI-modified electrode was the same as that at the HRP/CP-modified electrode. On the other hand, the turnover number of the enzymatic redox reaction at the HRP/CP/EC/MEMPTFSI-modified electrode was six times larger than that at the HRP/CP-modified electrode. Consequently, the specificity constant of the enzymatic redox reaction at the HRP/CP/EC/MEMPTFSI-modified electrode was much higher than that at the HRP/CP-modified electrode.

Experimental Study of the Reaction of OH Radicals with Carbonyl Sulfide between 365 and 960 K: Kinetics and Products

Reaction OH + OCS ® products (1) has been studied in a discharge–flow reactor combined with modulated molecular beam mass spectrometry. The reaction rate constant has been determined under pseudo-first-order conditions through monitoring OH decays in a high excess of OCS: k1 = (2.35 ± 0.25) × 10−12 exp(−(2144 ± 56)/T) cm3 molecule−1 s−1 at T = 365–960 K (the uncertainties represent precision at the 2σ level, the total 2σ relative uncertainty including statistical and systematic errors on the rate constant being 20% at all temperatures). The rate constant of reaction (1) was found to be similar at a total helium pressure of 1, 2, and 8 torr at around 500 K. The SH radical was identified as the primary product of the reaction, and its yield was determined to be about 100% at T = 500 and 750 K. The kinetic and mechanistic data from the present study are compared to previous experimental and theoretical work.

Effect of pH on degradation and mineralization of catechol in calcium-aid ozonation: Performance, mechanism and products analysis

Catechol, common in industrial wastewater, is very toxic and non-biodegradable, and its desirable removal is still a challenge. Catalytic ozonation as an effective advanced oxidation process, however was limited by the application of intricately fabricated catalysts. Herein, catalytic ozonation by OH– (generated by common sodium hydroxide) with the aid of calcium was developed for catechol degradation and mineralization in this study. The removal performance, mechanism and products were investigated. The results showed that ozonation at pH 12.5 could achieve complete catechol removal and excellent mineralization (maximum of 75 % COD removal efficiency) within 15 min. The adorable effect of calcium for enhanced organics removal was observed at pH 12.5, with the formation of precipitates as well. Catechol and COD removal were fitted to the pseudo-first-order kinetic model, while the reaction constant was increased by higher pH and calcium concentration. The results of quenching experiment and EPR affirmed •OH and •O2– radicals were pivotal for the enhanced organics removal. In addition, DFT calculation revealed the O atoms were reactive sites for electrophilic and radical attack via molecular electrostatic potential, highest occupied molecular orbital, lowest unoccupied molecular orbital and Fukui index. UPLC-Q-TOF-MS analysis revealed the intermediate products and verified the brilliant performance of catalytic ozonation. According to reactive sites and intermediates identification, the degradation pathway of catechol was proposed. As tawny precipitate appeared after reaction, the characteristics of insoluble product was analyzed using FTIR, XRD and XPS. The component of the precipitate was recognized as calcium oxalate and calcium carbonate, accompanied by the decreased Ca2+ concentration at high pH, which declared the enhanced removal was linked to the precipitation of Ca2+. Finally, toxicity assessment stated the lower acute toxicity, bioconcentration factor, developmental toxicity and mutagenicity of intermediates, indicating that calcium-aid ozonation catalyzed by high pH was useful for both catechol degradation and toxicity reduction. This study provides a reference for understanding the performance and mechanism of catechol degradation. More importantly, as an environmentally friendly process, catalytic ozonation possesses a great application potential for treatment of wastewater containing metal ions in terms of simultaneous removal of organics and metal ions.

Two-term Boltzmann approximation versus Monte-Carlo simulation: effect of magnetic field

In this paper, we investigate the spatial-local electron energy distribution function (eEDF) interacting with a background gas at the sub-atmospheric pressure in a wide range of applied crossed electric and magnetic fields using the Boltzmann kinetic equation. We compare solutions obtained using two numerical approaches (deterministic two-term approximation and stochastic Monte Carlo method) to identify their applicability in the context of determining drift velocity and reaction constants for electrons. For argon and helium, the upper limit of the reduced electric field applicability of the two-term approximation is discussed. It has been shown that the presence of a magnetic field can reduce this limit. Two explanations are given, one is based on the math of two-term formalism, and the other is based on velocity-space analysis. Two-term approximation fails due to it’s inability to resolve underlying cyclotron oscillation (it should result in an energy variation along the electron’s trajectory). The absence of this feature causes an incorrect estimation of momentum-transfer rate. This results an inaccuracy in the estimation of the angle between electric field and drift velocity.

Effect of irradiation intensity on the rate of photocatalysis of TiO2 coatings obtained by detonation spraying

AbstractThe influence of UV irradiation intensity on the rate constant of photocatalytic reaction of TiO2 coatings applied by detonation spraying on the hot‐rolled carbon steel and glass‐cloth‐base laminate (plastic) is studied. The effect of substrate material on the studied phenomenon is pronounced. The kinetic curves at different UV irradiation intensities and the rate constants of the photocatalytic reaction are obtained for different values of energy flux density varied from 3.0 to 8.0 mW/m2. The photocatalytic rate constant of coatings placed on plastic increases with an increase in the energy flux density from.038 to.055 1/h. Samples applied at a spray distance of 50 mm are characterized by a higher the photocatalytic rate constant than those applied at a distance of 40 mm. The value of photocatalytic rate constant does not change starting from a certain flow value for such samples and reaches the saturation value of about.054 1/h. Saturation is achieved quite quickly already at a density flux of about 5.5 mW/m2. Two new phenomenological models based on differential equation, the analytical solutions to which sufficiently describe experimental dependence of the photocatalytic rate constant on the energy flux density, are proposed.

Quantum dynamics of O(3P) + HBr → OH + Br reaction: integral cross sections and rate constants and their initial state dependence.

The integral cross sections (ICSs) and rate constants (RCs) for the title reaction are calculated by means of accurate quantum wave packet method employing the recent ab initio potential energy surface developed by Peterson and co-workers. Hundreds of partial wave contributions (up to J=150) are calculated explicitly taking Coriolis coupling into account. The ICSs are found to increase monotonically with energy and their energy dependences are smooth except in the energy range below the potential energy barrier, where several resonance peaks are observed. The temperature dependences of the RCs obey in general the Arrhenius law. These behaviors manifest the dominance of abstract mechanism. Initial rotational state (ji) excitations are found to greatly enhance the reactivity starting from ji=4, while exhibiting a complicated dependence for ji<4. From Boltzmann average of the initial state specified RCs (for ji=0-15) we obtained thermal RCs which are in reasonable agreement with available experimental results.

Construction of a screening system for lipid-derived radical inhibitors and validation of hit compounds to target retinal and cerebrovascular diseases

Recent studies have highlighted the indispensable role of oxidized lipids in inflammatory responses, cell death, and disease pathogenesis. Consequently, inhibitors targeting oxidized lipids, particularly lipid-derived radicals critical in lipid peroxidation, which are known as radical-trapping antioxidants (RTAs), have been actively pursued. We focused our investigation on nitroxide compounds that have rapid second-order reaction rate constants for reaction with lipid-derived radicals. A novel screening system was developed by employing competitive reactions between library compounds and a newly developed profluorescence nitroxide probe with lipid-derived radicals to identify RTA compounds. A PubMed search of the top hit compounds revealed their wide application as repositioned drugs. Notably, the inhibitory efficacy of methyldopa, selected from these compounds, against retinal damage and bilateral common carotid artery stenosis was confirmed in animal models. These findings underscore the efficacy of our screening system and suggest that it is an effective approach for the discovery of RTA compounds.

Efficient green synthesis of n-amyl acetate in liquid phase over metal-organic framework catalysts

This investigation describes, for the first time, the efficient and selective liquid-phase green synthesis of n-amyl acetate over UiO-66 and NH2-UiO-66 metal-organic framework catalysts. By employing UiO-66 and NH2-UiO-66 solid acid catalysts, n-amyl acetate can be produced without the corrosive impact and separation problems associated with homogeneous catalysis by mineral acids. Thermal, structural, textural, and morphological properties of the catalysts were evaluated by TG-DTA, XRD, FTIR, Raman spectroscopy, BET-surface area, SEM and HRTEM. Their surface acidities were characterized by the dehydration of isopropanol and the chemical adsorption of suitable probs. The effects of reflux time, acid: alcohol molar ratio, and catalyst load were extensively studied. Under the optimized conditions, UiO-66, and NH2-UiO-66 catalysts, respectively offered 85 and 67 % conversions, and 100 % selectivity into n-amyl acetate. Activity of catalysts was well correlated with the total number of acidic sites, SBET and the kinetic rate constants of the esterification reaction. Analysis of the pre-adsorption studies of the reactants on the catalyst surface demonstrated that the Langmuir-Hinshelwood mechanism was followed in this reaction. The UiO-66 catalyst was regenerated numerous times with nearly the same activity and 100 % selectivity.

Theoretical Study of the Decomposition Reactions of 2-Vinylfuran.

With the development of new synthetic methods, 2-vinylfuran (V2F) has become a potential renewable biofuel. In this work, the potential energy surfaces for the V2F unimolecular dissociation reaction, the H-addition reaction, and the H-abstraction reaction were constructed at the G4 level. The temperature- and pressure-dependent rate constants for the relevant reactions on the potential energy surfaces were calculated by solving the master equation based on the transition state theory and Rice-Ramsperger-Kassel-Marcus theory. The results show that the rate constant for the intramolecular H-transfer reaction of V2F with H atoms from the C(5) site to the C(4) site to form 2-vinylfuran-3(2H)-carbene, followed by the decomposition to form h145te3o, is the highest. The rate constants for the H-abstraction reaction of V2F with H atoms were the largest at C(6) on the branched chain, followed by C(7), and the rate constants for the H-abstraction reaction at C(3), C(4), and C(5) on the furan ring were not competitive. Negative temperature coefficient effects are observed for the rate constants of the addition reactions of V2F with H atoms at low pressures, with the H-addition rate constant at the C(5) site being the largest. This work not only provides the necessary rate constants for the reaction mechanism of V2F combustion but also provides theoretical guidance for the practical application of furan-based fuels.

Challenges and Breakthroughs in Enhancing Temperature Tolerance of Sodium-Ion Batteries.

Lithium-based batteries (LBBs) have been highly researched and recognized as a mature electrochemical energy storage (EES) system in recent years. However, their stability and effectiveness are primarily confined to room temperature conditions. At temperatures significantly below 0°C or above 60°C, LBBs experience substantial performance degradation. Under such challenging extreme contexts, sodium-ion batteries (SIBs) emerge as a promising complementary technology, distinguished by their fast dynamics at low-temperature regions and superior safety under elevated temperatures. Notably, developing SIBs suitable for wide-temperature usage still presents significant challenges, particularly for specific applications such as electric vehicles, renewable energy storage, and deep-space/polar explorations, which requires a thorough understanding of how SIBs perform under different temperature conditions. By reviewing the development of wide-temperature SIBs, the influence of temperature on the parameters related to battery performance, such as reaction constant, charge transfer resistance, etc., is systematically and comprehensively analyzed. The review emphasizes challenges encountered by SIBs in both low and high temperatures while exploring recent advancements in SIB materials, specifically focusing on strategies to enhance battery performance across diverse temperature ranges. Overall, insights gained from these studies will drive the development of SIBs that can handle the challenges posed by diverse and harsh climates.

Kinetic analysis of monomolecular cracking of normal Alkanes (C4[sbnd]C6) over Brønsted Acid site of Zeolitic type catalyst with energetic evaluation of transition states using Quantum-Chemical modeling

The work aims to determine the kinetic parameters of reactions for production of light olefins via catalytic cracking reactions of C4–C6 n-alkanes based on the energy characteristics of the transition state using quantum chemical calculations. Cracking reactions of C4–C6 n-alkanes proceed via protolytic mechanism on the Brønsted acid sites of zeolite-containing catalysts. For kinetic studies in this work, the thermochemical parameters of the intermediate stages, including hydrocarbon adsorption and transition state were determined, then the activation energies and rate constants were determined over the temperature range of catalytic cracking process from 773 to 903 K (500–630 °C).The results showed that DFT method in combination with B3LYP and ωB97X-D functionals, and 3–21 G basis demonstrated quite high accuracy in determining thermochemical parameters, including enthalpy, entropy and Gibbs free energy at both energetic levels of adsorption and transition state. Then, modeling continued by calculations of activation energies and rate constants of reactions. Obtained kinetic parameters made it possible to determine the reactivity of hydrocarbons with different chain length. It was obtained that the rate constants of butane cracking reactions with the formation of ethylene are 54–90 times higher than the formation of propylene. The rate constants of pentane cracking reactions with the formation of butylene are on average 5 times higher than the formation of propylene. The rate constants for hexane cracking reactions with the formation of butylene are 2.9–3.7 times higher compared to the formation of propylene.

Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations.

The rate constants of enzyme-catalyzed reactions (kcat) are often approximated from the barrier height of the reactive step. We introduce an enhanced sampling QM/MM approach that directly calculates the kinetics of enzymatic reactions, without introducing the transition-state theory assumptions, and takes into account the dynamical equilibrium between the reactive and non-reactive conformations of the enzyme/substrate complex. Our computed kcat values are in order-of-magnitude agreement with the experimental data for two representative enzymatic reactions.

Innovative application of plasma-activated water in the inactivation of Escherichia coli: Temperature-dependent chemical processes leading to the synergistic microbicidal effect

Plasma-based technologies, including plasma-activated water (PAW), offer the capability to deactivate microorganisms on fruits and vegetables, preserving their sensory and nutritional quality. Although many studies have reported a synergistic microbicidal effect between PAW and mild heating, the underlying chemical processes driving these effects remain unexplored. Our study aims to evaluate the microbicidal capacity of two PAW types, one containing NO2− (PAW-N) and the other H2O2 (PAW-H), as well as their mixture (PAW-M), at different temperatures, and to elucidate the underlying temperature-dependent chemical processes. Using E. coli DH5α as the target microorganism, we measured colony-forming units under varying exposure times for each PAW type and their mixture at 8 and 28 °C. Additionally, we determined the time-dependent concentrations of NO2−, H2O2, and NO3− in the mixture, and calculated the reaction rate constant for peroxynitrous acid generation. The kinetic study revealed a fivefold increase in the reaction constant between H2O2 and NO2− in PAW-M at 28 °C compared to 8 °C, leading to a significant rise in hydroxyl radical production. The microbicidal efficacy of PAW-M exceeded that of individual PAWs or temperatures. Moreover, this effect was significantly enhanced by mild heating, resulting in log reductions of 0.24, 0.34, 2.3 (at 8 °C) and 0.74, 2.3, 3.6 (at 28 °C) for PAW-H, PAW-N, and PAW-M, respectively, after a 10-min exposure. In conclusion, the synergistic effect between PAW and mild heating may be attributed to the accelerated reaction rate of peroxynitrous acid formation in an acidic medium, leading to heightened hydroxyl radical generation.

Deciphering heterogeneous enzymatic surface reactions on xylan using surface plasmon resonance spectroscopy

Xylans' unique properties make it attractive for a variety of industries, including paper, food, and biochemical production. While for some applications the preservation of its natural structure is crucial, for others the degradation into monosaccharides is essential. For the complete breakdown, the use of several enzymes is required, due to its structural complexity. In fact, the specificity of enzymatically-catalyzed reactions is guided by the surface, limiting or regulating accessibility and serving structurally encoded input guiding the actions of the enzymes. Here, we investigate enzymes at surfaces rich in xylan using surface plasmon resonance spectroscopy. The influence of diffusion and changes in substrate morphology is studied via enzyme surface kinetics simulations, yielding reaction rates and constants. We propose kinetic models, which can be applied to the degradation of multilayer biopolymer films. The most advanced model was verified by its successful application to the degradation of a thin film of polyhydroxybutyrate treated with a polyhydroxybutyrate-depolymerase. The herein derived models can be employed to quantify the degradation kinetics of various enzymes on biopolymers in heterogeneous environments, often prevalent in industrial processes. The identification of key factors influencing reaction rates such as inhibition will contribute to the quantification of intricate dynamics in complex systems.

Antioxidant Activity of Bilirubin in Micellar and Liposomal Systems Is pH-Dependent.

Bilirubin (BR), a product of heme catabolism, plays a critical role in biological systems. Although increased levels of BR result in hyperbilirubinemia or jaundice, there is increasing evidence that lower concentrations substantially decrease the risk of oxidative stress-mediated diseases due to antioxidant functions of BR. We studied the radical-trapping ability of BR in two model systems, micellar and liposomal, at a broad pH range. At pH < 6.0, BR behaves as a retardant; however, at pH ≥ 6.0, BR becomes strong radical trapping antioxidant, with rate constants for reaction with lipidperoxyl radicals (kinh) within the range from 1.2 × 104 M-1 s-1 to 3.5 × 104 M-1 s-1, and in liposomal system, the activity of BR is comparable to α-tocopherol. This transition is likely facilitated by the ionization of carboxyl groups, leading to a conformational shift in BR and improved solubility/localization at the water/lipid interface. This is the first experimental evidence of the role of pH on the antioxidant activity of bilirubin, and the observed pH-dependent radical-trapping ability of BR holds practical significance, particularly in jaundice treatment where light therapy targets the skin's weakly acidic surface. Minor adjustments toward neutral or alkaline pH can enhance radical-trapping action of BR, thereby mitigating oxidative stress induced with blue or violet light exposure.

Kinetic modeling and optimization of the mono- and diglycerides synthesis mediated by the lipase Lipozyme® TL 100 L immobilized on clayey support.

Mono- and diglycerides play a crucial role in the food industry as multifunctional food additives and emulsifiers. Their importance stems from their unique properties, which allow them to improve the quality, texture, and stability of various food products. Here, results of the kinetic modeling of the mono- and diglycerides synthesis mediated by the lipase Lipozyme® TL 100 L immobilized on the clayey support Spectrogel® type C are reported. The support was characterized by TEM, SEM, and FTIR. Firstly, the influence of pH and lipase load on the immobilization process was analyzed, resulting in an enzymatic activity of 93.2 ± 0.7Ug-1 under optimized conditions (170.9Ug-1 of lipase and pH of 7.1). Afterward, the effects of reaction temperature and concentration of immobilized biocatalyst in the feedstock conversion were evaluated. At optimized parameters, a triglycerides conversion of 97% was obtained at 36.5°C, 7.9 vol.% of enzyme, a glycerol to feedstock molar ratio of 2:1, and 2h. The optimized conditions were used to determine the kinetic constants of the elementary reactions involved in the glycerolysis, where a fit superior to 0.99 was achieved between experimental values and predicted data.

Response surface methodology as an approach for optimization of alpha amylase production by using bacterial consortium under submerged fermentation

The present study aims to isolate amylolytic bacteria and later the formation of a bacterial consortium for alpha-amylase production. The potent amylolytic strains in a selected consortium were identified as B. subtilis and B. licheniformis on the basis of 16S rRNA sequencing. Initially cultural conditions for alpha amylase were optimized in Plackett–Burman design, followed by the central composite design. Analysis of Variance (ANOVA) of the optimization study indicated pH 7, 0.05 %CaCl2 and 24 h incubation time were the significant variables that mainly effect the alpha amylase production. After the process of statistical optimization, the enzyme was then partially purified by means of ammonium sulfate precipitation at a 60% saturation level, resulting in a 2-fold purification with 1.4 U/mg specific activity. Enzyme kinetics studies showed that the maximum velocity of the reaction (Vmax) and Michaelis constant (Km) were 47.4 mg/ml and 13.2 mM, respectively. Current results suggest the newly isolated bacterial consortium could be considered as a promising candidate for industrial applications.

Effect of detonation spray regimes on photocatalytic activity of Ti-TiO2 coatings

The influence of the regimes of detonation spraying the Ti-TiO2 based coatings on its photocatalytic properties is studied. The spray distance and the speed of passage of the detonation gun are varied when the coatings are applied. The microstructure and phase composition are studied. It is found that proportion of rutile prevails over the other phases in all samples obtained under all spray regimes used. The kinetics of photocatalytic reaction basing on Langmuir-Hinshelwood model of heterogeneous photocatalysis is analyzed. The photocatalytic activity and the rate constant of photocatalytic reaction of the coatings decrease with an increase in the spray distance. New equation describing the dependence observed is proposed. The decrease in the rate constant occurs according to a power law. The photocatalytic activity and the rate constant of the photocatalytic reaction of coatings increase with an increase in the rutile percentage. New equation describing such dependence is proposed. The increase occurs according to an exponential law. The photocatalytic rate constant depends on the speed of passage accordingly with a parabolic law.

Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems.

Fluorescence correlation spectroscopy (FCS) applied to chemically reactive systems provides information about chemical reaction equilibrium constants and diffusion coefficients of reactants. These physical quantities are determined from the FCS-measured autocorrelation function, G(t), as a function of time, t. In most of the studied cases, the analytical form of G(t) is well-known for reactions that are much faster than the diffusion time of reactants across the focal volume probed by FCS or when they are much slower than the diffusion time. Here, we develop an analytical form of G(t) for reactions occurring at an intermediate time scale comparable to the diffusion time. G(t) depends on the reaction rates in such reactions. We focus on reversibly binding a fluorescently labeled small molecule to a macromolecule in a diluted solution in thermodynamic equilibrium. Our approach allows the analysis of FCS data over a wide range of diffusion coefficients, reaction rate constants, and brightness levels of fluorescent labels. Our G(t) is valid even when the fluorescent label changes its brightness upon binding. The easy-to-implement analytical form of the autocorrelation function greatly helps experimentalists study chemical reactions, determining the equilibrium constants of reactions and the reaction rates.