Showing papers on "Rate equation published in 2015"

Rate law analysis of water oxidation on a hematite surface

Abstract: Water oxidation is a key chemical reaction, central to both biological photosynthesis and artificial solar fuel synthesis strategies. Despite recent progress on the structure of the natural catalytic site, and on inorganic catalyst function, determining the mechanistic details of this multiredox reaction remains a significant challenge. We report herein a rate law analysis of the order of water oxidation as a function of surface hole density on a hematite photoanode employing photoinduced absorption spectroscopy. Our study reveals a transition from a slow, first order reaction at low accumulated hole density to a faster, third order mechanism once the surface hole density is sufficient to enable the oxidation of nearest neighbor metal atoms. This study thus provides direct evidence for the multihole catalysis of water oxidation by hematite, and demonstrates the hole accumulation level required to achieve this, leading to key insights both for reaction mechanism and strategies to enhance function.

Simulating Energy Transfer and Upconversion in β-NaYF4: Yb3+, Tm3+

Abstract: The design of upconversion phosphors with higher quantum yield requires a deeper understanding of the detailed energy transfer and upconversion processes between active ions inside the material. Rate equations can model those processes by describing the populations of the energy levels of the ions as a function of time. However, this model presents some drawbacks: energy migration is assumed to be infinitely fast, it does not determine the detailed interaction mechanism (multipolar or exchange), and it only provides the macroscopic averaged parameters of interaction. Hence, a rate equation model with the same parameters cannot correctly predict the time evolution of upconverted emission and power dependence under a wide range of concentrations of active ions. We present a model that combines information about the host material lattice, the concentration of active ions, and a microscopic rate equation system. The extent of energy migration is correctly taken into account because the energy transfer process...

Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er3+ doped germanate glass

Abstract: Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er 3+ doped germanate glass

Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass

Abstract: Er3+ doped oxyfluoride tellurite glasses have been prepared. Three Judd-Ofelt parameters Ωt (t = 2, 4, 6) and radiative properties are calculated for prepared glasses. Emission characteristics are analyzed and it is found that prepared glasses possess larger calculated predicted spontaneous transition probability (39.97 s−1), emission cross section σem (10.18 × 10−21 cm2) and σem × Δλeff (945.32 × 10−28 cm3), corresponding to the 2.7 μm emission of Er3+: 4I11/2→ 4I13/2 transition. The results suggest that the prepared glasses might be appropriate optical material for mid-infrared laser application. Moreover, rate equation analysis which is rarely used in bulk glass has been carried out to explain the relationship between emission intensity and Er3+ concentration. The calculation results show that with the increment of Er3+ concentration, the energy transfer up-conversion rate of 4I13/2 state increases while the rate of 4I11/2 state reduces, resulting in the change of 2.7 μm emission.

Controlling the dynamics of Förster resonance energy transfer inside a tunable sub-wavelength Fabry–Pérot-resonator

Abstract: In this study we examined the energy transfer dynamics of a FRET coupled pair of chromophores at the single molecule level embedded in a tunable sub-wavelength Fabry–Perot resonator with two silver mirrors and separations in the λ/2 region. By varying the spectral mode density in the resonator via the mirror separation we altered the radiative relaxation properties of the single chromophores and thus the FRET efficiency. We were able to achieve wavelength dependent enhancement factors of up to three for the spontaneous emission rate of the chromophores while the quenching due to the metal surfaces was nearly constant. We could show by confocal spectroscopy, time correlated single photon counting and time domain rate equation modeling that the FRET rate constant is not altered by our resonator.

Coupled rate and transport equations modeling proportionality of light yield in high-energy electron tracks: CsI at 295 K and 100 K; CsI:Tl at 295 K

Abstract: A high-energy electron in condensed matter deposits energy by creation of electron-hole pairs whose density generally increases as the electron slows, reaching the order of ${10}^{20}$ eh/${\mathrm{cm}}^{3}$ near the end of its track. The subsequent interactions of the electrons and holes include nonlinear rate terms and transport as first hot and then thermalized carriers in the nanometer-scale radial dimension of the track. Charge separation and strong radial electric fields occur in a material such as CsI with contrasting diffusion rates of self-trapped holes and hot electrons. Eventual radiative recombination has a nonlinear relation to the primary electron energy because of these interactions. This so-called intrinsic nonproportionality of electron response limits the achievable energy resolution of a given scintillation radiation detector material. We use a system of coupled transport and rate equations to describe a pure host (three equations) and one dopant (four more equations per dopant). Applying it first to the experimentally well-characterized system of CsI and CsI:Tl in this work, we use results of picosecond absorption spectroscopy, interband $Z$-scan measurements of nonlinear rate constants, and other experiments and calculations to determine most of the more than 20 rate and transport coefficients required for modeling. The model is solved in a track environment approximated as cylindrical and is compared to the proportionality curve and total light yield of undoped CsI at temperatures of 295 and 100 K, as well as thallium dopant in CsI:Tl at 295 K. With this degree of validation, the space and time distributions of carriers and excitons, both untrapped and trapped, are examined within the model to gain an understanding of the main competitions controlling the nonproportionality of response.

Partial oxidation of methane over Ni0/La2O3 bifunctional catalyst II: Global kinetics of methane total oxidation, dry reforming and partial oxidation

Abstract: The global kinetics (power rate law) of methane total oxidation (TO) over La2O3 catalyst was performed at 773, 823 and 873 K. The global kinetics of methane dry reforming (DR) at 648, 673, 698 and 723 K and partial oxidation (POM) at 993, 1013, 1023 and 1053 K were conducted over Ni0/La2O3 catalyst. The initial rate method and isolation method were used to determine initial rates, rate constants, and partial orders to reactants and establish the Arrhenius equations for TO, DR, POM. The experimental apparent activation energies were 87.8, 116.4 and 112.8 kJ mol−1 for DR, TO and POM, respectively. For TO, the reaction order to CH4 was varying with conversion whereas that to O2 was zero. For DR, the reaction order to CH4 was constant, whereas that to CO2 was dependent on the concentration of CO2. The values of rate constants revealed the following order: kDR ≫ kPOM, kTO. It was found that the rate constant of POM reaction is linked to that of methane TO: kPOM ≈ 2kTO. The catalytic cycle of methane TO is the “rate determining cycle” (rdc) of the POM process.

Model reduction for stochastic chemical systems with abundant species

Abstract: Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

Reaction kinetics and mechanism of catalyzed hydrolysis of waste PET using solid acid catalyst in supercritical CO2

Abstract: Hydrolysis of waste poly(ethylene terphthalate) (PET) using solid acid catalyst in SCCO2 is presented in this work for the first time. The mechanism of PET chains scission was proved to be a combination of chain end and random chain scission by Fourier transform - infrared spectroscopy (FT-IR) and titration analysis. A new reaction kinetics model of PET hydrolysis in SCCO2 was setup by introducing the Arrhenius equation into an ordinary reaction rate equation, the frequency factor and apparent activation energy were expressed in terms of temperature and CO2 pressure, respectively. With this reaction kinetics model, the effects of temperature, and pressure were investigated. An interesting mechanism was proposed to describe the reaction process that both water molecules and hydroniums were carried and penetrated into the amorphous regions of the swollen PET by SCCO2, subsequently hydrolysis reaction preferentially took place in the amorphous regions of both surface and bulk of PET matrix. © 2014 American Institute of Chemical Engineers AIChE J, 61: 200–214, 2015

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

Abstract: The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute to dense systems.

Efficient prediction of terahertz quantum cascade laser dynamics from steady-state simulations

Abstract: Terahertz-frequency quantum cascade lasers (THz QCLs) based on bound-to-continuum active regions are difficult to model owing to their large number of quantum states. We present a computationally efficient reduced rate equation (RE) model that reproduces the experimentally observed variation of THz power with respect to drive current and heat-sink temperature. We also present dynamic (time-domain) simulations under a range of drive currents and predict an increase in modulation bandwidth as the current approaches the peak of the light–current curve, as observed experimentally in mid-infrared QCLs. We account for temperature and bias dependence of the carrier lifetimes, gain, and injection efficiency, calculated from a full rate equation model. The temperature dependence of the simulated threshold current, emitted power, and cut-off current are thus all reproduced accurately with only one fitting parameter, the interface roughness, in the full REs. We propose that the model could therefore be used for rapid dynamical simulation of QCL designs.

Kinetic Analysis for the Multistep Profiles of Organic Reactions: Significance of the Conformational Entropy on the Rate Constants of the Claisen Rearrangement.

Abstract: The significance of kinetic analysis as a tool for understanding the reactivity and selectivity of organic reactions has recently been recognized. However, conventional simulation approaches that solve rate equations numerically are not amenable to multistep reaction profiles consisting of fast and slow elementary steps. Herein, we present an efficient and robust approach for evaluating the overall rate constants of multistep reactions via the recursive contraction of the rate equations to give the overall rate constants for the products and byproducts. This new method was applied to the Claisen rearrangement of allyl vinyl ether, as well as a substituted allyl vinyl ether. Notably, the profiles of these reactions contained 23 and 84 local minima, and 66 and 278 transition states, respectively. The overall rate constant for the Claisen rearrangement of allyl vinyl ether was consistent with the experimental value. The selectivity of the Claisen rearrangement reaction has also been assessed using a substituted allyl vinyl ether. The results of this study showed that the conformational entropy in these flexible chain molecules had a substantial impact on the overall rate constants. This new method could therefore be used to estimate the overall rate constants of various other organic reactions involving flexible molecules.

Lagergren equation: Can maximum loading of sorption replace equilibrium loading?

Abstract: In this article, a modified formulation of the well known Lagergren pseudo first order rate equation is suggested. The equation is obtained simply by substituting the mass balance equation of a single stage batch-type system into integrated first order rate equation. The suggested new formulation relies on maximum sorption (or removal) rather than equilibrium sorption, as given by Lagergren equation. The exact value of equilibrium sorption is not easy to define in many cases, and it is shown that the modified formulation provides better correlation with sorption data when the process is far from completion.

Model reduction for stochastic chemical systems with abundant species

Abstract: Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently we prove that in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

Viscosity Dependence of Some Protein and Enzyme Reaction Rates: Seventy-Five Years after Kramers.

Abstract: Kramers rate theory is a milestone in chemical reaction research, but concerns regarding the basic understanding of condensed phase reaction rates of large molecules in viscous milieu persist. Experimental studies of Kramers theory rely on scaling reaction rates with inverse solvent viscosity, which is often equated with the bulk friction coefficient based on simple hydrodynamic relations. Apart from the difficulty of abstraction of the prefactor details from experimental data, it is not clear why the linearity of rate versus inverse viscosity, k ∝ η(-1), deviates widely for many reactions studied. In most cases, the deviation simulates a power law k ∝ η(-n), where the exponent n assumes fractional values. In rate-viscosity studies presented here, results for two reactions, unfolding of cytochrome c and cysteine protease activity of human ribosomal protein S4, show an exceedingly overdamped rate over a wide viscosity range, registering n values up to 2.4. Although the origin of this extraordinary reaction friction is not known at present, the results indicate that the viscosity exponent need not be bound by the 0-1 limit as generally suggested. For the third reaction studied here, thermal dissociation of CO from nativelike cytochrome c, the rate-viscosity behavior can be explained using Grote-Hynes theory of time-dependent friction in conjunction with correlated motions intrinsic to the protein. Analysis of the glycerol viscosity-dependent rate for the CO dissociation reaction in the presence of urea as the second variable shows that the protein stabilizing effect of subdenaturing amounts of urea is not affected by the bulk viscosity. It appears that a myriad of factors as diverse as parameter uncertainty due to the difficulty of knowing the exact reaction friction and both mode and consequences of protein-solvent interaction work in a complex manner to convey as though Kramers rate equation is not absolute.

Exchange Current Density of SOFC Electrodes: Theoretical Relations and Partial Pressure Dependencies Rate-Determined by Electrochemical Reactions

Abstract: As a theoretical consideration on electrode defect chemistry, general relations of exchange current density quantitatively representing Solid Oxide Fuel Cell (SOFC) electrode performance are systematically derived as a function of gas partial pressures, equilibrium constants of adsorption and dissociation reactions on electrode surfaces, and electrochemical reaction rate constants for possible elementalreactionsatthecathodeandtheanode,inthecasethatanelectrochemicalreactionistherate-determiningelectrodereaction. Simplified expressions are also derived, under the condition that one kind of neutral or charged adsorbed species is predominant at the electrode, to derive gas partial pressure dependence of exchange current density for given rate-determining electrochemical reactions. Importance of considering elementary steps is highlighted to derive rate equations and to clarify various dependencies. Partial pressure dependencies of the exchange current density are compiled and discussed by simulating normalized exchange current density values for given partial pressures. The applicability and limitation of the Butler-Volmer type expressions of exchange current density for SOFC electrodes are carefully discussed. © The Author(s) 2014. Published by ECS. This is an open access article distributed under the terms of the Creative Commons

Mass transfer kinetics of lanthanum (III) extraction in the presence of two complexing agents by D2EHPA using a constant interfacial area cell with laminar flow

Abstract: The lanthanum (La) extraction kinetics from chloride medium containing two complexing agents lactic acid (HLac) and citric acid (H 3 cit) by D2EHPA (H 2 A 2 ) have been investigated using constant interfacial area cell with laminar flow. The stoichiometry of the complex formation reaction between La and H 2 A 2 has been evaluated. The extraction kinetics data have been analyzed in terms of pseudo-first order constants. From the effects of stirring speed, temperature and specific interfacial area on the extraction rate, it is found that the extraction process is a diffusion-controlled kinetics process with an interface reaction. The rate-determining step is made by predictions derived from interfacial reaction models, and the rate equation has been evaluated from analysis of the experimental results, also, the extraction model has been proposed.

Order and disorder in irreversible decay processes.

Abstract: Dynamical disorder motivates fluctuating rate coefficients in phenomenological, mass-action rate equations. The reaction order in these rate equations is the fixed exponent controlling the dependence of the rate on the number of species. Here, we clarify the relationship between these notions of (dis)order in irreversible decay, n A → B, n = 1, 2, 3, …, by extending a theoretical measure of fluctuations in the rate coefficient. The measure, Jn−Ln2≥0, is the magnitude of the inequality between Jn, the time-integrated square of the rate coefficient multiplied by the time interval of interest, and Ln2, the square of the time-integrated rate coefficient. Applying the inequality to empirical models for non-exponential relaxation, we demonstrate that it quantifies the cumulative deviation in a rate coefficient from a constant, and so the degree of dynamical disorder. The equality is a bound satisfied by traditional kinetics where a single rate constant is sufficient. For these models, we show how increasing the...

Mass Transfer-Reaction Kinetics Study on Absorption of NO with Dual Oxidants (H2O2/S2O82–)

Abstract: The mass transfer-reaction kinetics of NO absorption by dual oxidants (H2O2/S2O82–) was studied in a bubble column reactor. The comparison experiments in different systems showed that the combination of Na2S2O8 and H2O2 had significant synergistic effects on the rate of NO absorption. The effects of Na2S2O8 concentration, H2O2 concentration, NO concentration, pH, O2 concentration, and gas flow rate on the rate of NO absorption were investigated. The rate of NO absorption increased with the increase in Na2S2O8 concentration, H2O2 concentration, and gas flow rate. The rate of NO absorption increased slightly with the increase in O2 concentration, whereas it increased linearly with the increase in NO concentration. At pH 11, the rate of NO absorption reached 1.31 × 10–6 mol/m2·s. The NO absorption by dual oxidants (H2O2/S2O82–) was pseudo-first-order with respect to the NO concentration. Moreover, a simple rate equation of NO absorption by H2O2/S2O82– was obtained. The results of the rate equation indicate t...

Theoretical study on nonlinear properties of four level systems under nano-second illumination

Abstract: In this work, we report the theoretical results of the single beam transmittance of an absorber by employing the rate equation approach, utilizing 10 ns laser pulses. With the appropriate choice of lifetimes of the participating levels in the transition and their corresponding absorption cross-section, it is possible to control the onset of different phenomena like saturable absorption, reverse saturable absorption, and double saturable absorption. We discuss how to increase the saturable and optical limiting nature of the system by appropriate changes of spectroscopic parameters. We discuss the estimation of spectroscopic terms from their contribution in the single beam transmittance.

Laser Rate Equation-Based Filtering for Carrier Recovery in Characterization and Communication

Abstract: We formulate a semiconductor laser rate equation-based approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or unuseable rate equation coefficients) are discussed. Two potential application areas are explored: Laser characterization and carrier recovery in coherent communication. Two rate equation-based Bayesian filters, the particle filter and extended Kalman filter, are used in conjunction with a coherent receiver to measure frequency noise spectrum of a photonic crystal cavity laser with less than 20 nW of fiber-coupled output power. The extended Kalman filter is also used to recover a 28-GBd DP-16 QAM signal where a decision-directed phase-locked loop fails.

All-optical 1st- and 2nd-order differential equation solvers with large tuning ranges using Fabry-Pérot semiconductor optical amplifiers

Abstract: We experimentally demonstrate an all-optical temporal computation scheme for solving 1st- and 2nd-order linear ordinary differential equations (ODEs) with tunable constant coefficients by using Fabry-Perot semiconductor optical amplifiers (FP-SOAs). By changing the injection currents of FP-SOAs, the constant coefficients of the differential equations are practically tuned. A quite large constant coefficient tunable range from 0.0026/ps to 0.085/ps is achieved for the 1st-order differential equation. Moreover, the constant coefficient p of the 2nd-order ODE solver can be continuously tuned from 0.0216/ps to 0.158/ps, correspondingly with the constant coefficient q varying from 0.0000494/ps2 to 0.006205/ps2. Additionally, a theoretical model that combining the carrier density rate equation of the semiconductor optical amplifier (SOA) with the transfer function of the Fabry-Perot (FP) cavity is exploited to analyze the solving processes. For both 1st- and 2nd-order solvers, excellent agreements between the numerical simulations and the experimental results are obtained. The FP-SOAs based all-optical differential-equation solvers can be easily integrated with other optical components based on InP/InGaAsP materials, such as laser, modulator, photodetector and waveguide, which can motivate the realization of the complicated optical computing on a single integrated chip.

Evaporation Mechanism of Sn and SnS from Liquid Fe: Part I: Experiment and Adsorption of S on Reaction Site

Abstract: In order to evaluate feasibility of Sn-containing ferrous scrap recycling by evaporation of Sn, a number of liquid–gas experiments were carried out using an electromagnetic levitation melting technique. Rate of decrease of Sn concentration in liquid steel droplets by evaporation in Ar-H2 gas mixture was determined at 1873 K (1600 °C). Evaporation rate of the Sn under various conditions (various flow rates of the gas mixture, initial S concentration, [pct Sn]0) was examined using previously reported rate equations. Increasing flow rate increased the evaporation rate of Sn initially, but the rate became constant at higher flow rate, which indicates that the rate-controlling step is the chemical reaction at the liquid/gas interface. Increasing initial S concentration significantly increased the evaporation rate of Sn, which is in good agreement with previous understanding that Sn could be evaporated as SnS(g). It was found in the present study that neither a simple first-order reaction (rate proportional to [pct Sn]) nor a second-order reaction (rate proportional to [pct Sn] × [pct S]) could account for the Sn evaporation under a chemical-reaction-controlled regime. It is proposed in the present study that surface adsorption of S should be taken into account in order to interpret the evaporation rate of Sn in such a way that S blocks available sites for SnS evaporation on the liquid steel. The ideal Langmuir isotherm was applied in order to better represent evaporation rate constant k SnS as a function of [pct S] (0.06 < [pct S]0 < 0.29). The obtained rate constant of a reaction Sn i + S i = SnSi(g), $$ k_{\text{SnS}}^{\text{R}} $$ , is 2.57 × 10−8 m4 mol−1 s−1.

Measuring the elevated temperature dependence of up-conversion in Nd:YAG

Abstract: We present the measurement of the energy transfer upconversion coefficient temperature-dependence from the main upper laser level (4F3/2) of 1at.% doped Nd:YAG. This is achieved by a very simple method employing the z-scan technique, through monitoring the transmitted power of a probe laser tuned to the main absorption peak at 808 nm. In addition, to fully develop a simple model to support the measurements, we have accurately measured the temperature dependent absorption coefficient for this absorption band, covering the range from 300-450K. The spatially dependent two-level rate equation model is described, which simulates the relationship between the incident pump irradiance and power transmitted by the crystal, in function of its temperature. By comparing the experimental results with the model, we obtain a value for the energy transfer upconversion coefficient of 5.1±0.4 ×10-17 cm3/s, at room temperature, decreasing to 2.0 ×10-17 cm3/s at 450 K.

The Rate Equation of Decomposition for Electrolytes with LiPF6 in Li-Ion Cells at Elevated Temperatures

Abstract: Organic compounds that are unstable at high temperatures are used as electrolytes in Li-ion cells. Therefore, the heat generation by chemical reactions of these organic compounds within the cells is an important factor to be considered. The thermal stabilities of 1M LiPF6/PC and 1M LiPF6/EC+DMC (1:1 in vol.) electrolytes used in lithium cells were measured by differential scanning calorimetry (DSC) using airtight containers. Rate equations, which explain the heat generation, were studied. The salt LiPF6 is in equilibrium with LiF and PF5 in the electrolyte solutions. As a mechanism of electrolyte decomposition, Sloop et al. showed that the PF5 reacts with solvents, generating heat. Based on Sloop’s mechanism and Wang’s rate equation for thermal LiPF6 decomposition, rate equations were developed, and the rate of heat generation as a function of temperature was calculated using the rate equations at DSC scan rate of 3, 7, 10, 12, 15, 17, and 20 ◦ Cm in −1 . Unfortunately, these calculated curves did not fit the experimental data well. Therefore, an additional side reaction of PF5, which did not contribute to heat generation, was assumed. With the inclusion of this side reaction, the calculated curves showed good agreement with the experimental data. © The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any