Reaction Rate Theory Research Articles

Dynamical Models of Chemical Exchange in Nuclear Magnetic Resonance Spectroscopy.

Chemical exchange line-broadening is an important phenomenon in nuclear magnetic resonance (NMR) spectroscopy, in which a nuclear spin experiences more than one magnetic environment as a result of chemical or conformational changes of a molecule. The dynamic process of chemical exchange strongly affects the sensitivity and resolution of NMR experiments, and increasingly provides a powerful probe of the inter-conversion between chemical and conformational states of proteins, nucleic acids, and other biological macromolecules. A simple and often used theoretical description of chemical exchange in NMR spectroscopy is based on an idealized two-state jump model (the random-phase or telegraph signal). However, chemical exchange can also be represented as a barrier-crossing event that can be modeled using chemical reaction rate theory. The time scale of crossing is determined by the barrier height, the temperature, and the dissipation modeled as collisional or frictional damping. This tutorial explores the connection between the NMR theory of chemical exchange line-broadening and strong-collision models for chemical kinetics in statistical mechanics. Theoretical modeling and numerical simulation are used to map the rate of barrier-crossing dynamics of a particle on a potential energy surface to the chemical exchange relaxation rate constant. By developing explicit models for the exchange dynamics, the tutorial aims to elucidate the underlying dynamical processes that give rise to the rich phenomenology of chemical exchange observed in NMR spectroscopy. Software for generating and analyzing the numerical simulations is provided in the form of Python and Fortran source codes.

New Mechanistic Pathways for the Reactions of Formaldehyde with Formic Acid Catalyzed by Sulfuric Acid and Formaldehyde with Sulfuric Acid Catalyzed by Formic Acid: Formation of Potential Secondary Organic Aerosol Precursors

Formaldehyde (HCHO) plays an important role in the formation of secondary organic aerosols. Here, we report new mechanistic pathways for the reactions of formaldehyde with formic acid catalyzed by sulfuric acid and formaldehyde with sulfuric acid catalyzed by formic acid by using quantum chemical methods and reaction rate theory. We have found that sulfuric acid and formic acid have a strong catalytic role in the HCHO···HCOOH + H2SO4 and HCHO···H2SO4 + HCOOH reactions because the calculated energy barriers of the sulfuric acid-catalyzed reaction of formaldehyde with formic acid and formic acid-catalyzed reaction of formaldehyde with sulfuric acid are decreased by 21.17 and 14.81 kcal/mol, respectively. The calculated rates show that the reaction rate of HCHO···HCOOH + H2SO4 is faster than those of HCHO···H2SO4 + HCOOH and HCHO + HCOOH···H2SO4. Moreover, the HCHO + HCOOH + H2SO4 → H2C(OH)OCOH + H2SO4 reaction readily forms the carboxylic acid ester (H2C(OH)OCOH); this is a new mechanistic pathway for the reaction of formaldehyde with formic acid, which is expected to extend to other aldehydes’ reaction with carboxylic acids. Additionally, the present findings also suggest that formic acid-catalyzed formaldehyde and sulfuric acid reaction leads to the formation of an organosulfate as the nucleation precursor. The present results not only help understand the mechanisms for the initial processes of atmospheric nucleation but also are expected to extend other aldehydes and acids in the atmosphere.

Understanding the Large Kinetic Isotope Effect of Hydrogen Tunneling in Condensed Phases by Using Double-Well Model Systems.

In recent years, many experiments have shown large kinetic isotope effects (KIEs) for hydrogen transfer reactions in condensed phases as evidence of strong quantum tunneling effects. Since accurate calculation of the tunneling dynamics in such systems still present significant challenges, previous studies have employed different types of approximations to estimate the tunneling effects and KIEs. In this work, by employing model systems consisting of a double-well coupled to a harmonic bath, we calculate the tunneling effects and KIEs using the numerically exact hierarchical equations of motion (HEOM) method. It is found that hydrogen and deuterium transfer reactions in the same system may show rather different behaviors, where hydrogen transfer is dominated by tunneling between the two lowest vibrational states and deuterium transfer is controlled by excited vibrational states close to the barrier top. The simulation results are also used to test the validity of various approximate methods. It is shown that the Wolynes theory of dissipative tunneling gives a good estimation of rate constants in the over-the-barrier regime, while the nonadiabatic reaction rate theory based on the Landau-Zener formula is more suitable for deep tunneling reactions.

Small activation entropy bestows high-stability of nanoconfined D-mannitol* *Project supported by the National Natural Science Foundation of China (Grant Nos. 52001319, 52071327, 51922102, 51771216, and 51701230), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LR18E010002), the Ningbo 2025 Science and Technology Innovation Project (Grant No. 2019B10051), and the Natural Science Foundation of Ningbo City (Grant No. 202003N4354).

It has been a long-standing puzzling problem that some glasses exhibit higher glass transition temperatures (denoting high stability) but lower activation energy for relaxations (denoting low stability). In this paper, the relaxation kinetics of the nanoconfined D-mannitol (DM) glass was studied systematically using a high-precision and high-rate nanocalorimeter. The nanoconfined DM exhibits enhanced thermal stability compared to the free DM. For example, the critical cooling rate for glass formation decreases from 200 K/s to below 1 K/s; the T g increases by about 20 K–50 K. The relaxation kinetics is analyzed based on the absolute reaction rate theory. It is found that, even though the activation energy E* decreases, the activation entropy S* decreases much more for the nanoconfined glass that yields a large activation free energy G* and higher thermal stability. These results suggest that the activation entropy may provide new insights in understanding the abnormal kinetics of nanoconfined glassy systems.

Thermal Decomposition Kinetics of the Indenyl Radical: A Theoretical Study.

Quantum chemistry and statistical reaction rate theory calculations have been performed to investigate the products and kinetics of indenyl radical decomposition. Three competitive product sets are identified, including formation of a cyclopentadienyl radical (c-C5H5) and diacetylene (C4H2), which has not been included in prior theoretical kinetics investigations. Rate coefficients for indenyl decomposition are determined from master equation simulations at 1800-2400 K and 0.01-100 atm, and temperature- and pressure-dependent rate coefficient expressions are incorporated into a detailed chemical kinetic model for indene pyrolysis. Indenyl is found to predominantly decompose to o-benzyne (o-C6H4) + propargyl (C3H3), with lesser amounts of fulvenallenyl (C7H5) + C2H2 and c-C5H5 + C4H2.

First-passage time theory of activated rate chemical processes in electronic molecular junctions.

Confined nanoscale spaces, electric fields, and tunneling currents make the molecular electronic junction an experimental device for the discovery of new out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining the Keldysh nonequilibrium Green's function treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers first-passage time calculations. The nonequilibrium Green's functions (NEGF) provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single reaction coordinate dependent molecular orbital and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces is shown to be the determining factors when considering chemical reaction rates, each of which results from highly tunable parameters within the system.

Isotope-specific reactions of acetonitrile (CH3CN) with trapped, translationally cold CCl.

The gas-phase reaction of CCl+ with acetonitrile (CH3CN) is studied using a linear Paul ion trap coupled to a time-of-flight mass spectrometer. This work builds on a previous study of the reaction of CCl+ with acetylene [K. J. Catani et al., J. Chem. Phys. 152, 234310 (2020)] and further explores the reactivity of CCl+ with organic neutral molecules. Both of the reactant species are relevant in observations and models of chemistry in the interstellar medium. Nitriles, in particular, are noted for their relevance in prebiotic chemistry and are found in the atmosphere of Titan, one of Saturn's moons. This work represents one of the first studied reactions of a halogenated carbocation with a nitrile and the first exploration of CCl+ with a nitrile. Reactant isotopologues are used to unambiguously assign ionic primary products from this reaction: HNCCl+ and C2H3 +. Branching ratios are measured, and both primary products are determined to be equally probable. Quantum chemical and statistical reaction rate theory calculations illuminate pertinent information for interpreting the reaction data, including reaction thermodynamics and a potential energy surface for the reaction, as well as rate constants and branching ratios for the observed products. In particular, the reaction products and potential energy surface stimulate questions regarding the strength and role of the nitrile functional group, which can be further explored with more reactions of this class.

Reaction rates and the noisy saddle-node bifurcation: Renormalization group for barrier crossing

Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to the temperature. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a barrier, particles slide down a sloping potential. We formulate a renormalization group description of this noisy saddle-node transition. We derive the universal scaling behavior and corrections to scaling for the mean escape time in overdamped systems with arbitrary barrier height. We also develop an accurate approximation to the full distribution of barrier escape times by approximating the eigenvalues of the Fokker-Plank operator as equally spaced. This lets us derive a family of distributions that captures the barrier crossing times for arbitrary barrier height. Our critical theory draws links between barrier crossing in chemistry, the renormalization group, and bifurcation theory.

Exact asymptotic solution of an aggregation model with a bell-shaped distribution.

We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates K(k,l)=1/k+1/l. In this case, it is possible to determine the behavior of large-size aggregates in the limit of large times in a way that allows a highly detailed analysis of the behavior of the system. This is the so-called scaling limit, in which the cluster size distribution collapses to a function of the ratio of the cluster size to a time-dependent typical size. The results confirm the far more general results of earlier work concerning a general scaling theory for so-called reaction rates of Type III, which are characterized by the property that aggregates of very different sizes react faster than comparable aggregates of similar sizes. For these, the cluster size distribution decays rapidly to zero both for sizes much larger and much smaller than the typical size, and is thus often described as being "bell-shaped". For clusters much larger than the typical size, however, an unexpected subleading correction is discovered. Finally, several results going beyond the scope of the scaling limit are obtained: in particular the behavior of concentrations for fixed cluster size in the large-time limit and the large-size behavior for clusters at a fixed time. The latter again shows subleading deviations from the expected behavior.

Numerical analysis of pattern shape deformation in UV imprint considering thermal deformation with UV shrinkage and curing

A novel numerical method for analyzing the deformation of molding patterns on UV imprint with soft molds considering thermal deformation in addition to UV shrinkage and curing is presented. In the case of UV imprint using an easily deformable mold-like PDMS, transfer error on UV resin is caused by thermal expansion/contraction arising from UV reaction heat and by UV shrinkage. Specifically, when a UV resin with high reaction heat such as cation polymerization-type UV resin is used, thermal deformation has a nonnegligible effect on pattern shape deformation. Therefore, it is necessary to consider thermal deformation caused by UV reaction heat in the numerical deformation analysis of UV imprint requiring high surface accuracy, such as optical devices. The present method newly adopts the theory of reaction rate to consider the temperature-dependent UV reaction rate and introduces an advanced idea of virtual temperature as a measure of UV reaction progress. By defining the time histories of thermal deformation and UV shrinkage as a function of virtual temperature, the effects of both are considered simultaneously. In order to apply the present method to actual imprints, temperature measurement experiments and various rheometry experiments are conducted on a target UV resin to identify its model parameters. A validation analysis of the present method is performed on an actual micromirror array imprint and shows that the simulation accuracy of transfer error can be significantly improved by considering thermal deformation.

Thermal decomposition and isomerization of furfural and 2-pyrone: a theoretical kinetic study.

We have studied the decomposition and isomerization of furfural in the gas phase using quantum chemical and statistical reaction rate theory techniques. This work uncovers a variety of new reaction channels in furfural pyrolysis that lead to formation of the experimentally observed products, including CO2, which was previously unexplained. In addition to the known mechanism for furan + CO production, furfural is shown to isomerize directly to 2-pyrone, with a barrier height of 69 kcal mol-1, from where it can decompose to vinylketene + CO (highest barrier of 65 kcal mol-1) or to CO2 + 1,3-cyclobutadiene (highest barrier of 66 kcal mol-1). Alternative pathways to vinylketene + CO and 4-pyrone are also described. An RRKM theory/master equation model is developed to describe reactions on the C5O2H4 surface and used to simulate the decomposition kinetics of furfural and 2-pyrone. For both molecules, decomposition at 1400-2100 K is dominated by the formation of furan + CO, which represents around 75% of the total products, compared to around 19% and 6% for vinylketene + CO and total CO2, respectively. The model also predicts significant formation of stabilized 2-pyrone under these conditions. Rate coefficient expressions are reported as a function of both temperature and pressure for the main decomposition and isomerization channels identified in the pyrolysis of furfural and 2-pyrone, to facilitate detailed chemical kinetic modelling of these important oxygenated hydrocarbons.

Frontier Orbitals, Combustion and Redox Transfer from a Fermionic-Bosonic Orbital Perspective

Oxygenations are highly exergonic, yet combustion of organic matter is not spontaneous in an atmosphere that is 21% O2. Electrons are fermions with a quantum spin number s of 1/2ħ. An orbital containing a single electron with s = 1/2 is fermionic. Orbitals can contain a maximum of two electrons with antiparallel spins, i.e., spin magnetic quantum numbers ms of 1/2 and -1/2. An orbital filled by an electron couple has s = 0 and bosonic character. The multiplicity of a reactant is defined as |2(S)| + 1 where S is the total spin quantum number. The Wigner spin conservation rules state that multiplicity is conserved. The transmission coefficient κ of absolute reaction rate theory also indicates the necessity for spin conservation. Burning is fermionic combustion that occurs when sufficient energy is applied to a bosonic molecule to cause homolytic bond cleavage yielding fermionic products capable of reaction with the bifermionic frontier orbitals of triplet multiplicity O2. Neutrophil leucocytes kill microorganisms by bosonic combustion and employ two mechanisms for changing the multiplicity of O2 from triplet to singlet. Microorganisms, composed of bosonic singlet multiplicity molecules, do not directly react with bifermionic O2, but are highly susceptible to electrophilic attack by bosonic electronically excited singlet molecular oxygen (1O2*). Hydride ion (H-) transfer is the common mode of cytoplasmic redox metabolism. Bosonic transfer of an orbital electron couple protects from damage by obviating fermionic reaction with bifermionic O2. Bosonic coupled electron transfer raises the consideration that quantum tunneling might be involved in facilitating such redox transfer.

Activation Entropy as a Key Factor Controlling the Memory Effect in Glasses.

As opposed to the common monotonic relaxation process of glasses, the Kovacs memory effect describes an isothermal annealing experiment, in which the enthalpy and volume of a preannealed glass first increases before finally decreasing toward equilibrium. This interesting behavior has been observed for many materials and is generally explained in terms of heterogeneous dynamics. In this Letter, the memory effect in a model Au-based metallic glass is studied using a high-precision high-rate calorimeter. The activation entropy (S^{*}) during isothermal annealing is determined according to the absolute reaction rate theory. We observe that the memory effect appears only when the second-annealing process has a large S^{*}. These results indicate that a large value of S^{*} is a key requirement for observation of the memory effect and this may provide a useful perspective for understanding the memory effect in both thermal and athermal systems.

Nanoparticles Size in Fe<sub>73.5</sub>Cu<sub>1</sub>Mo<sub>3</sub>Si<sub>13.5</sub>B<sub>9</sub> Melt

The size of the nanoparticles participating in the viscous flow and the diffusion coefficient were calculated using statistical mechanical theory of absolute reaction rates and the Arrhenius equation. As experimental data, temperature dependence of the kinematic viscosity and density of Fe73.5Cu1Mo3Si13.5B9 melt was used. At a temperature of 1600 K, after the melt is overheated above the critical temperature Tk = 1770 K, the nanoparticles size decreases from 0.92 to 0.47 nm, and the diffusion coefficient increases from 2.4·10-10 to 4.5·10-10 m2·s-1.

Pyrolysis of Triclosan and Its Chlorinated Derivatives

Triclosan (TCS) is a commonly used antimicrobial agent which persists in the environment and may undergo chlorination and/or photodegradation to produce toxic polychlorinated dibenzo-p-dioxins and polychlorinated benzenes. TCS accumulates in wastewater treatment biosolids, which may be used to fuel waste-to-energy plants, although little is known about the fate of TCS at high temperatures. Here, we have studied the thermal decomposition of TCS and chlorinated TCS derivatives in the gas phase using computational chemistry coupled with reaction rate theory calculations to predict rate coefficients and develop a chemical kinetic model to simulate TCS pyrolysis in a plug flow reactor. TCS is shown to interconvert with 4-chloro-2-(2,4-dichlorophenoxy)phenol (TCSi) with a relatively low barrier, achieving equilibrium at temperatures of around 900 K and above. Dissociation of TCS and TCSi proceeds in parallel with barriers of ca. 60-65 kcal/mol to produce dichlorodibenzo-p-dioxin chlorobenzoquinone isomers. Reactor simulations demonstrate that TCS incineration at a temperature of 1100 K or higher leads to the formation of toxic chlorinated aromatics.

Diffusible Cross-linkers Cause Superexponential Friction Forces.

The friction between cytoskeletal filaments is of central importance for the formation of cellular structures such as the mitotic spindle and the cytokinetic ring. This friction is caused by passive cross-linkers, yet the underlying mechanism and the dependence on cross-linker density are poorly understood. Here, we use theory and computer simulations to study the friction between two filaments that are cross-linked by passive proteins, which can hop between discrete binding sites while physically excluding each other. The simulations reveal that filaments move via rare discrete jumps, which are associated with free-energy barrier crossings. We identify the reaction coordinate that governs the relative microtubule movement and derive an exact analytical expression for the free-energy barrier and the friction coefficient. Our analysis not only elucidates the molecular mechanism underlying cross-linker-induced filament friction, but also predicts that the friction coefficient scales superexponentially with the density of cross-linkers.

On the origin of ground-state vacuum-field catalysis: Equilibrium consideration.

Recent experiments suggest that vibrational strong coupling (VSC) may significantly modify ground-state chemical reactions and their rates even without external pumping. The intrinsic mechanism of this "vacuum-field catalysis" remains largely unclear. Generally, modifications of thermal reactions in the ground electronic states can be caused by equilibrium or non-equilibrium effects. The former are associated with modifications of the reactant equilibrium distribution as expressed by the transition state theory of chemical reaction rates, while the latter stem from the dynamics of reaching and leaving transition state configurations. Here, we examine how VSC can affect chemical reactions rates in a cavity environment according to transition state theory. Our approach is to examine the effect of coupling to cavity mode(s) on the potential of mean force (PMF) associated with the reaction coordinate. Within the context of classical nuclei and classical photons and also assuming no charge overlap between molecules, we find that while the PMF can be affected by the cavity environment, this effect is negligible for the usual micron-length cavities used to examine VSC situations.

Mechanical versus calorimetric glass transition temperature in the diffusion of nicotinic acid from a condensed gelatin/glucose syrup system

Condensed systems of 25% (w/w) bovine gelatin (Mw = 173 kDa) or 25% (w/w) fish gelatin (Mw = 60 kDa) with 59% (w/w) glucose syrup and 1% (w/w) nicotinic acid to a total solids level of 85% (w/w) were prepared in this study. Analysis was carried out using Fourier transform infrared spectroscopy (FTIR), wide angle X-ray diffraction (WAXD), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and small deformation dynamic oscillation in-shear. Work allowed elucidation of the micromolecular and macromolecular properties focusing on the estimation of the mechanical (Tgm) and calorimetric (Tgc) glass transition temperature of these systems. A combined protocol of free volume and reaction rate theories was considered to rationalise results in the vicinity of the glass transition region. Following this, a diffusion procedure of nicotinic acid was set up over a wide temperature range (from 5 to −40 °C) using UV–vis spectroscopy and an appropriate chromogenic reaction to detect the presence of the bioactive compound. Time dependence of the mass transfer of nicotinic acid throughout the delivery vehicle of gelatin/co-solute was followed using diffusion theory. The treatise unveiled the correlation between structural relaxation of the vitrified matrix and release kinetics of the diffusant.

Kinetic modeling of oleic acid esterification with UiO-66: from intrinsic experimental data to kinetics via elementary reaction steps

This work reports the experimental conversion of oleic acid (OA) into methyl oleate via UiO-66 MOF catalyst. Strong focus is on the kinetic modeling: 67 models, based on elementary reaction steps for Eley-Rideal, Langmuir-Hinshelwood and Hattori kinetic mechanisms, are proposed. Via the application of initial reaction rate theory and nonisothermal kinetic modeling, one model adequately describes the experimental data. It is a variant on the Eley-Rideal type of model, such that the surface reaction includes the oleic acid adsorbate, methanol reacts from the liquid phase and one additional active site is considered to make the ester and water as surface reaction products, so that overall two active sites are used in the surface reaction. An activation energy of 54.9 ± 1.8 kJ mol−1 is reported and the desorption of the ester was found to be irreversible. In addition, NH3 TPD revealed at least two types of acid sites (#) on the UiO-66 MOF, from which turnover rates were calculated in the range of 2.54 ± 0.33 to 8.82 ± 0.87 mmolOA mol#−1 s−1. Since the catalyst is recyclable and no additional acids have to be used, this system can be considered as a green alternative for the well-known homogeneously catalyzed esterification reaction.

Esterification of Palm Fatty Acid Distillate for FAME Synthesis Catalyzed by Super-Acid Catalyst HClSO3–ZrO2

The current work investigates biodiesel synthesis from the cheaper source- palm fatty acid distillate (PFAD) using HClSO3–ZrO2 acid catalyst. The effect of various physicochemical parameters such as molar ratio, catalyst loading, temperature, molecular sieves addition, and agitation speed was studied. The maximum conversion of 91.5% and yield of 90.2% was achieved in 150 min under the reaction conditions of molar ratio 8:1, amount of catalyst 3.5 wt%, 60 °C, agitation speed 250 rpm, and molecular sieves 5 wt%. While comparing the catalytic activity with Amberlyst-15 in converting PFAD to FAME, it was found that HClSO3–ZrO2 gave 7.2 times more conversion as compared to Ambetlyst-15 for similar reaction conditions. Catalyst reusability was also tested and showed a negligible decrease in the conversion at least for three cycles. The kinetics and thermodynamics properties were investigated with the help of Arrhenius equation and Eyring reaction rate theory. The physicochemical properties of the purified PFAD biodiesel were compared with the petroleum diesel and also matched with American Society for Testing and Materials (ASTM) standards and found within the limit.