Reaction Rate Theory Research Articles

Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites

Based on experimental examples, the strength characteristics of metal alloys and composites under tensile and compressive loads are considered to demonstrate both their similarity and difference. Under tensile loads, their behavior is essentially the same. Under compressive loads, the composite shows different properties, but similar to the behavior of a metal alloy under tension. When tensioned and compressed, it fractured as a material with a different structure. When a metal alloy is cyclically compressed, the damage accumulation process is attenuated, which reduces the alloy longevity during subsequent tension. The analysis of experimental data for various types of loading from the standpoint of the kinetic concept of fracture is carried out. Instead of a number of incompatible approaches or a formal description of experimental data, that based on the theory of reaction rates is used. Mathematical modeling of processes is carried out using rheological models of the material. Structural models of the material, called physical media, reflect the thermodynamic processes of flow, failure, and changes in the structure of the material. Parametric identification of structural models is carried out on the basis of the minimum necessary basic experiment: loading of specimens with different speeds at several temperature values and by the amplitude dependence of inelasticity. Based on results of these experiments, the scope of applicability conditions for this material and test modes necessary for parametric identification of models are selected. One fracture criterion is used, which formally corresponds to the achievement of a threshold concentration of micro-damage in any volume of the material, leading to macro-fracture. The application of mathematical models for calculating the longevity of materials depending on the temperature and force loading conditions and the nature of their changes is shown. Calculations of longevity under constant, monotonously increasing and variable loads under conditions of constant or changing temperatures are based on the relationship of plastic flow and failure processes distributed over the volume of the material. They are performed numerically by time steps depending on the ratio of the rate of change of temperature and stresses.

Analysis of transient and tertiary creep behavior of Titanium modified 14Cr-15Ni stainless steel after cold working

Characteristic of transient and tertiary creep behavior of ten, twenty, thirty, and forty percent cold worked indigenously developed Titanium modified 14Cr-15Ni stainless steel at 700 °C and various stress levels have been assessed. Small primary creep region followed by secondary creep and then substantial tertiary creep regions were exhibited by all steels. Creep parameters like transient strain and rate of exhaustion of transient creep in Garofalo equation and tertiary strain and rate of acceleration of tertiary creep in modified Dobes and Cadek equation have been extensively studied. The relationships among exhaustion rate of transient creep, acceleration rate of tertiary creep, and minimum creep rate revealed the prevailing theory of first order reaction rate during transient and tertiary creep deformation of the Titanium modified 14Cr-15Ni stainless steel. The exhaustion rate of transient creep decreased, whereas tertiary creep parameter decreased as the amount of cold work increased. Creep damage tolerance parameter indicated that necking, precipitate coarsening, and recovery of substructures are dominant creep damage mechanisms in the Titanium modified 14Cr-15Ni stainless steel.

Assembly of heteropolymers via a network of reaction coordinates.

In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate metastable states. In this paper, we use ideas from reaction rate theory and describe nonequilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows for estimating the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms, such as kinetic proofreading.

Phase field modeling precipitation of β-phase and mechanical properties change in Zr–Nb alloys under neutron irradiation

ABSTRACT We study microstructure transformation in Zr–Nb system under neutron irradiation and its mechanical properties change under mechanical loads in a form of shear deformation by using phase field methodology. The developed phase field approach takes into account defects dynamics based on reaction rate theory and elastic contribution to study mechanical properties change. A numerical modeling is provided in three stages: sample preparation, irradiation of the prepared sample and mechanical loading of the irradiated sample. A precipitation of β-Niobium particles of the size of several nanometers is discussed. Results of phase field modeling indicate that β-Niobium particles grow slowly during irradiation due to point defects rearrangement. Statistical analysis of dynamics of radiation-induced microstructure transformations is provided. Simulation results of shear deformation of pre-irradiated and post-irradiated alloys are discussed. Maps of local distribution of strain and stress and strain–stress curves are obtained. Results are verified with experimental data.

Decomposition kinetics of perfluorinated sulfonic acids

Perfluorooctanesulfonic acid (PFOS) is a widespread and persistent pollutant of concern to human health and the environment. Although incineration is often used to treat material contaminated with PFOS and related per- and polyfluoroalkyl substances (PFAS), little is known about the precise chemical mechanism for the thermal decomposition of these substances of concern. Here, we present the first study of the thermal decomposition kinetics of PFOS and related perfluorinated acids, using computational chemistry and reaction rate theory methods. We discover that the preferred channel for PFOS decomposition is via an α-sultone that spontaneously decomposes to form perfluorooctanal and SO2. At 1000 K the halflife for PFOS is predicted to be 0.2 s, decreasing sharply as temperature increases further. These results show that the acid headgroup in PFOS can be efficiently destroyed in incinerators operating at relatively modest temperatures. The new insights provided into the exact decomposition mechanism and kinetics of PFOS will help to improve remediation technologies actively under development.

Passage through a sub-diffusing geometrical bottleneck.

The usual Kramers theory of reaction rates in condensed media predict the rate to have an inverse dependence on the viscosity of the medium, η. However, experiments on ligand binding to proteins, performed long ago, showed the rate to have η-ν dependence, with ν in the range of 0.4-0.8. Zwanzig [J. Chem. Phys. 97, 3587 (1992)] suggested a model in which the ligand has to pass through a fluctuating opening to reach the binding site. This fluctuating gate model predicted the rate to be proportional to η-1/2. More recently, experiments performed by Xie et al. [Phys. Rev. Lett. 93, 180603 (2004)] showed that the distance between two groups in a protein undergoes not normal diffusion, but subdiffusion. Hence, in this paper, we suggest and solve a generalization of the Zwanzig model, viz., passage through an opening, whose size undergoes subdiffusion. Our solution shows that the rate is proportional to η-ν with ν in the range of 0.5-1, and hence, the subdiffusion model can explain the experimental observations.

Measurement and correlation of density and viscosity of binary mixtures of fatty acid (methyl esters + methylcyclohexane)

The thermodynamics properties of the mixtures of biodiesel and petroleum-based fuel are useful for the research of blending fuels. Biodiesel is mainly consisting of fatty acid alkyl esters. Densities and viscosity for the binary mixtures of three fatty acid methyl esters (methyl decanoate, methyl dodecanoate and methyl tetradecanoate) with methylcyclohexane (MCH) were measured at 7 temperatures from 293.15 to 323.15 K and at atmospheric pressure. Excess molar volumes and viscosity deviations of the three binary systems have been correlated and fitted to Redlich-Kister equation. The change of enthalpy, entropy and Gibbs energy of activation for the flow process for the binary mixtures were calculated on the basis of Eyring’s absolute reaction rate theory. The experimental data and correlated results could provide important information for the research of the blends of biodiesel and diesel oil.

Isokinetics.

The study of the rates of chemical reactions and their relationship to temperature began in the 19th century with empirical measurements of the time required to reach a particular reaction end point at a constant temperature. By the mid-20th century, the theory of reaction rates had advanced and instruments had been developed in which the temperature of the sample could be increased at a constant rate. These nonisothermal methods are now widely used to determine the kinetic parameters of reactions because of their convenience. In this paper, the mathematical relationship between measurements at constant temperature (isothermal) and constant heating rate (nonisothermal) is developed and it is shown that there is a point in the temperature history of a single-step reaction at which the isothermal and nonisothermal reaction rates are equal. This equal (iso) kinetic point occurs at a temperature early in the heating history of nonisothermal analyses at which the reaction rate begins to accelerate. The isokinetic temperature is the basis for a new method of nonisothermal kinetic analysis that provides a direct measurement of the Arrhenius frequency factor A and activation energy Ea for the elementary step of a solid-state reaction without any assumptions about the relationship between these parameters (i.e., kinetic compensation) or the reaction mechanism.

Viscosity of Cu–Ni Melts

The kinematic viscosity of Cu–Ni melts with nickel contents of 10, 20, 30, 40, 50, 60, 70, 80, and 90 at % is measured. Kinematic viscosity is measured using the damped torsional vibrations of a crucible with a melt in the mode of sample cooling. The measuring results are discussed within the theory of absolute reaction rates. The temperatures at which the viscous flow characteristics (and thus the structural state of the melt) change are determined by analyzing the temperature dependences of kinematic viscosity. The patterns of the liquid–liquid transition in metal alloys of the Cu–Ni system that form a continuous series of solid solutions during crystallization are analyzed.

Mechanisms and Beyond: Elucidation of Fluxional Dynamics by Exchange NMR Spectroscopy.

Detailed mechanistic information is crucial to our understanding of reaction pathways and selectivity. Dynamic exchange NMR techniques, in particular 2D exchange spectroscopy (EXSY) and its modifications, provide indispensable intricate information on the mechanisms of organic and inorganic reactions and other phenomena, for example, the dynamics of interfacial processes. In this Review, key results from exchange NMR studies of small molecules over the last few decades are systemised and discussed. After a brief introduction to the theory, the key types of dynamic processes are identified and fundamental examples given of intra- and intermolecular reactions, which, in turn, could involve, or not, bond-making and bond-breaking events. Following that logic, internal molecular rotation, intramolecular stereomutation and molecular recognition will first be considered because they do not typically involve bond breaking. Then, rearrangements, substitution-type reactions, cyclisations, additions and other processes affecting chemical bonds will be discussed. Finally, interfacial molecular dynamics and unexpected combinations of different types of fluxional processes will also be highlighted. How exchange NMR spectroscopy helps to identify conformational changes, coordination and molecular recognition processes as well as quantify reaction energy barriers and extract detailed mechanistic information by using reaction rate theory in conjunction with computational techniques will be shown.

100 Years of Progress in Gas-Phase Atmospheric Chemistry Research

Abstract Remarkable progress has occurred over the last 100 years in our understanding of atmospheric chemical composition, stratospheric and tropospheric chemistry, urban air pollution, acid rain, and the formation of airborne particles from gas-phase chemistry. Much of this progress was associated with the developing understanding of the formation and role of ozone and of the oxides of nitrogen, NO and NO2, in the stratosphere and troposphere. The chemistry of the stratosphere, emerging from the pioneering work of Chapman in 1931, was followed by the discovery of catalytic ozone cycles, ozone destruction by chlorofluorocarbons, and the polar ozone holes, work honored by the 1995 Nobel Prize in Chemistry awarded to Crutzen, Rowland, and Molina. Foundations for the modern understanding of tropospheric chemistry were laid in the 1950s and 1960s, stimulated by the eye-stinging smog in Los Angeles. The importance of the hydroxyl (OH) radical and its relationship to the oxides of nitrogen (NO and NO2) emerged. The chemical processes leading to acid rain were elucidated. The atmosphere contains an immense number of gas-phase organic compounds, a result of emissions from plants and animals, natural and anthropogenic combustion processes, emissions from oceans, and from the atmospheric oxidation of organics emitted into the atmosphere. Organic atmospheric particulate matter arises largely as gas-phase organic compounds undergo oxidation to yield low-volatility products that condense into the particle phase. A hundred years ago, quantitative theories of chemical reaction rates were nonexistent. Today, comprehensive computer codes are available for performing detailed calculations of chemical reaction rates and mechanisms for atmospheric reactions. Understanding the future role of atmospheric chemistry in climate change and, in turn, the impact of climate change on atmospheric chemistry, will be critical to developing effective policies to protect the planet.

Numerical simulation of fatigue failure of composite materials under compression

The process of fatigue fracture of carbon fibres reinforced plastic under compressive loads is considered from the standpoint of the theory of reaction rates. Numerical simulation is based on rheological structural models of the material, which reproduce thermodynamic processes of local plastic deformation and failure occurring in time. The prediction of longevity of composite materials under compressive loads is similar to the solution of the problem for metal alloys under tensile loads when temperature and stresses are arbitrary functions of time.

Some Remarks on Two-Step Exothermic Reactions with Arrhenius Kinetics and Reactants Consumption

Many reactions that are written as a single reaction equation in actual fact consist of a series of elementary steps. Even though a balanced chemical equation may give the ultimate result of a reaction, what actually happens in the reaction may take place in several steps. A chemical equation does not tell us how reactants become products. Knowledge about this process will become extremely important as we learn more about the theory of chemical reaction rates. This paper presents an analytical method for describing two-step exothermic reactions with Arrhenius kinetics and reactants consumption. We assume that the reaction is not stirred, that is, change depends on space variable and examines the properties of the solution of the model. We solve the equations using parameter-expanding method and eigenfunctions expansion technique. The results obtained revealed that the temperature of the medium, for a non-stirred reaction, is symmetric and monotonically increasing. Also, the temperature of the medium increases and reaches steady state as activation energies ratio increases, for a well-stirred reaction.

Some Remarks on Two-Step Exothermic Reactions with Arrhenius Kinetics and Reactants Consumption

Many reactions that are written as a single reaction equation in actual fact consist of a series of elementary steps. Even though a balanced chemical equation may give the ultimate result of a reaction, what actually happens in the reaction may take place in several steps. A chemical equation does not tell us how reactants become products. Knowledge about this process will become extremely important as we learn more about the theory of chemical reaction rates. This paper presents an analytical method for describing two-step exothermic reactions with Arrhenius kinetics and reactants consumption. We assume that the reaction is not stirred, that is, change depends on space variable and examines the properties of the solution of the model. We solve the equations using parameter-expanding method and eigenfunctions expansion technique. The results obtained revealed that the temperature of the medium, for a non-stirred reaction, is symmetric and monotonically increasing. Also, the temperature of the medium increases and reaches steady state as activation energies ratio increases, for a well-stirred reaction.

Finding Order in the Disordered Hydration Shell of Rapidly Exchanging Water Molecules around the Heaviest Alkali Cs+ and Fr.

We report the structural and dynamical characterization of the intrinsically disordered hydration shells of the heaviest alkali ions, Cs+ and Fr+, obtained in ab initio molecular dynamics simulations. The knowledge of solvation and complexation properties of short-lived Fr+ is very limited and mostly based on extrapolations from the smaller alkali metal ions. To this end, we provide a critical insight into Fr+ solvation, demonstrating an extreme example of disordered solvation with no distinction between the ion-bound and solvent-bound states of water based on the ion-water distance. However, these two states are distinguished through distance-solvent rearrangement correlation, where either coordination number or electric field is employed to treat solvent rearrangement. Utilizing reaction rate theory, we find that the water exchange time scale for Fr+ (2.1-2.3 ps) is unexpectedly slower than for Cs+ (0.5-1.2 ps), because Fr+ experiences stronger nonequilibrium solvent effects. This study provides a new perspective on weak and hydrophobic solvation.

Excess volume and surface tension of some flavoured binary alcohols at temperatures 298.15, 308.15 and 318.15 K

ABSTRACTFrom the measured work of Ching-Ta and Chein-Hsiun Tu, we have presented the theoretical results of Surface tension and excess volume for three binary systems: namely 2-Propanol+Benzyl alcohol(1), 2-Propanol+2-Phenylethnol(2) and Benzyl alcohol+2-Phenylethanol(3) at temperatures 298.15, 308.15 and 318.15 K and atmospheric pressure over the concentration range 0.05–0.95. Theoretical results were computed from Flory model, Ramaswamy and Anbananthan (RA) model and model devised by Glinski, and studied the mixing properties and interactions of these liquids. Deviations in the surface tension (∆σ) were evaluated and fitted to the Redlich–Kister polynomial equation to derive the binary coefficients and standard errors. Moreover, McAllister multi-body interaction model based on Eyring’s theory of absolute reaction rates has also been applied. For liquid mixtures, the free energy of activation is additive, based on the proportions of the different components of the mixture and interactions of like and unlike molecules. The behaviour of the liquids was studied and correlated with the molecular interactions from these liquid state models. Conclusively, these non-associated and associated models were compared and tested for different systems showing that the McAllister multi-body interaction model yields good results as compared to associated models, while Flory model shows more deviations.

A novel approach for the prediction of viscosity of water + alkanediols mixtures

The reaction rate theory for viscosity modeling has been widely applied for decades. In this study, it is demonstrated that when a function containing the reciprocal of the excess energy of flow of several aqueous solutions of alkanediol is plotted against the mole fraction of the water, there is a universal common intercept that is independent of the alkanediol and the temperature. This common intercept is found to be valid in the temperature range of (283.15 K–338.15 K). The alkanediols studied include 1,2-ethanediol, 1,3-propanediol, 1,4-butanediol, and 1,5-pentanediol. This methodology allows an accurate prediction of the viscosity of binary water-alkanediol mixtures using a single viscosity data point of the mixture at the temperature of interest. The proposed methodology was shown capable of modeling the primary data set in the temperature range of (293.15K-303.15K) with an average absolute percent deviation (AAPD) between 1.5 and 2.6 for all of the systems tested. In addition, the methodology was also shown capable of predicting the secondary data set in the expanded temperature range of (283.15K-338.15K) with an overall AAPD of 4.0.

Spin-selective electron transfer reactions of radical pairs: Beyond the Haberkorn master equation

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond the second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact hierarchical equations of motion method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.

On the low-temperature limit of HACA

Rates of two mechanisms, hydrogen abstraction C2H2 (carbon) addition (HACA) and C2H2 (carbon) addition hydrogen migration (CAHM), were intercompared with each other at postflame conditions of a laminar premixed flame of ethylene. The analysis showed that HACA is substantially faster than CAHM, in contrast with the conclusions reached in a recent study of Zhang et al. [J. Phys. Chem. A 120 (2016) 683]. The difference between the two studies is largely due to dissimilar assignments of the thermodynamics of the H abstraction and of the islands of stability pulling the HACA reaction sequence. In support of this conclusion, the kinetics and thermodynamics of the key HACA reaction step were recalculated at a reliable level of quantum and reaction-rate theories. The implication of the present results is that both HACA and CAHM mechanisms can explain formation of aliphatic groups chemisorbed at edges of aromatics; however, a quantitative relationship is yet to be established with the experimental observations.

Combustion and Pyrolysis Kinetics of Chloropicrin.

Chloropicrin (CCl3NO2) is widely used in agriculture as a pesticide, weed-killer, fungicide or nematicide. It has also been used as a chemical agent during World War I. The precise understanding of its combustion chemistry for destruction processes or in the event of accidental fire of stored reserves is a major safety issue. A detailed chemical kinetic model for the combustion and pyrolysis of chloropicrin is proposed for the first time. A large number of thermo-kinetic parameters were calculated using quantum chemistry and reaction rate theory. The model was validated against experimental pyrolysis data available in the literature. It was shown that the degradation of chloropicrin is ruled by the breaking of the C-N bond followed by the oxidation of the trichloromethyl radical by NO2 through the formation of the adduct CCl3ONO, which can decompose to NO, chlorine atom, and phosgene. Phosgene is much more stable than chloropicrin and its decomposition starts at much higher temperatures. Combustion and pyrolysis simulations were also compared and demonstrated that the addition of oxygen has very little effect on the reactivity or product distribution due to the absence of hydrogen atoms in chloropicrin.