Temperature rule for the speed of sound in water: a chemical kinetics model

Water forms three-dimensional polymeric structures due to the influence of hydrogen bonds and is fundamentally different from other substances. One of the simplest ways to analyze the structure of water in any system, such as hydration, is to measure the degree of compressibility, which can be determined from the speed of sound, by making use of the physical laws established by Newton and later perfected by Laplace. Although the speed of sound is strongly dependent on the temperature of a liquid, Laplace's equation does not refer to temperature in any of its terms. It is necessary, therefore, to determine the degree of temperature dependency. However, only approximate expressions of a fifth-order polynomial have been reported so far in the literature. In this paper, a universal method for describing the speed of sound from the perspective of physicochemical reaction kinetics is presented. It is shown that the speed of sound U [ms(-1)] changes with temperature T [K] according to a thermodynamically-derived formula given as U= exp(-A/T-BlnT+C) and that the motion and propagation phenomena of sound energy can also be regarded as chemical reactions.     

Some problems of recombination kinetics. II

The general phenomenological theory of diffusion-controlled defect recombination, in which the identity of similar and dissimilar defects are consistently taken into account and which was presented in part I of this series, is applied here to the reactions A + B → C (Frenkel defect recombination). A + B → B (energy transfer), A + A → B (exciton annihilation). It is shown that during the reaction A + B → C at long reaction times spatial correlations of similar defects (dynamic aggregates) are produced thus leading to a deviation from the quasi-steady reaction constant well known in formal chemical kinetics. (This confirms once more our general idea about the back-coupling of similar and dissimilar reagent spatial correlations.) The validity range of Kirkwood's standard superposition approximation used to decouple three-point densities is also discussed.     

Diffusive transient recombination kinetics of interacting molecules

A simple analytical approach to diffusive geminate recombination kinetics of interacting molecules is considered. The expressions obtained describe accurately the transient time dependence and show that the kinetics is exponential at short times and follows a power law at long times. This approach is applied to some time-resolved experiments on ion-radical pair recombination.     

Copolymerization kinetics of a model siloxane system

Using ²⁹Si NMR, we monitor the copolymerization of trimethylethoxysilane and dimethyldiethoxysilane (model compounds for more complex sol-gel copolymer systems) in a batch reactor. Under the chosen conditions, the extents of self- and cross-condensation reactions are readily determined. Using a nonideal polycondensation kinetic model, we show that the copolymerization rate coefficient for a pair of sites of differing functionality is bounded by their homopolymerization rate coefficients, lying closer to the larger one. This reactivity pattern generates a heterogeneous monomer distribution in the copolymerization products. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 1293–1302, 1997     

Integral invariants in chemical kinetics

Integral invariants of classical mechanical systems are used for the mathematical treatment of equilibrium systems of chemical reaction kinetics. Some conserved quantities and Hamilton equations in chemistry are shown.

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Mean-field cooperativity in chemical kinetics

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, a cooperative behavior naturally emerges from the model; in particular, by means of various cooperative measures previously introduced, we highlight how the degree of cooperativity depends on the interaction strength among components. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of “susceptibility.” We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model p-body interactions, whose non-trivial cooperative capability is investigated too.     

Computer simulation of charge recombination in model tracks of high-energy electrons in nonpolar liquids; kinetics and escape

The evolution in time of the recombination of ions in model tracks and spurs produced by high-energy electrons was calculated by computer simulation of the diffusion and drift of the ions in each other's Coulomb field. Tracks of high-energy electrons are subdivided into tracks of secondary electrons that can be considered as independent one from another. Energy losses smaller than 50 or 100 keV are assumed to give rise to correlated groups of charges. The diffusion and recombination in the groups is directly simulated. For electrons with an initial energy in excess of 50 or 100 keV calculations are performed by summing the contributions of energy losses below this value. The nonhomogeneous kinetics of the charge recombination has been studied for both the short-time and long-time domains. The survival probability as a function of time, W(t), has been calculated for the charged species in electron tracks with different initial energy of the electron, for gaussian and exponential distributions of the initial distance between the positive and the negative species. The behaviour of W(t) and comparisons with the available short-time experimental data do not provide any clear distinction between the two distributions. The behaviour of W(t) at long times was also investigated in detail. The region of applicability of the theoretical limiting behaviour t^−0.5 was checked and found to be very small. The experimentally observed behaviour t^−0.6 was critically examined. Results are obtained for the probability of ion escape from recombination in the track as a function of the initial energy of the electron. The experimentally observed decrease of the yield of escape with decreasing energy of the electron for two liquids is adequately explained.     

Some symmetry-induced isotope effects in the kinetics of recombination reactions

Symmetry-induced isotope effects in recombination and collision-induced dissociation reactions are discussed. Progress on understanding the anomalous isotope effects in ozone is reviewed. Then, calculations are performed for the simpler reaction xNe+yNe+H<-->xNeyNe+H, where x and y label either identical or different isotopes. The atomic masses in the model are chosen so that symmetry is the only difference between the systems. Starting from a single potential energy surface, the properties of the bound, quasibound, and continuum states of the neon dimer are calculated. Then, the vibration rotation infinite order sudden approximation is used to calculate cross sections for all possible inelastic and dissociative processes. A rate constant matrix that exactly satisfies detailed balance is constructed. It allows recombination to occur both via direct three-body collisions and via tunneling into the quasibound states of the energy transfer mechanism. The eigenvalue rate coefficients are determined. Significant isotope effects are clearly found, and their behavior depends on the pressure, temperature, and mechanism of the reaction. Both spin statistics and symmetry breaking produce isotope effects. Under most conditions the breaking of symmetry enhances the rates, but a wide spectrum of effects is observed; they range from isotope effects with a normal mass dependence to huge, mass-independent isotope effects to cancellation and even to reversal of the isotope effects. This is the first calculation of symmetry-induced isotope effects in recombination rates from first principles. The relevance of the present effects to ozone recombination is discussed.     

Complex chemical kinetics in single enzyme molecules: Kramers's model with fractional Gaussian noise

A model of barrier crossing dynamics governed by fractional Gaussian noise and the generalized Langevin equation is used to study the reaction kinetics of single enzymes subject to conformational fluctuations. The direct application of Kramers's flux-over-population method to this model yields analytic expressions for the time-dependent transmission coefficient and the distribution of waiting times for barrier crossing. These expressions are found to reproduce the observed trends in recent simulations and experiments.     

Computing minimal entropy production trajectories: an approach to model reduction in chemical kinetics

Advanced experimental techniques in chemistry and physics provide increasing access to detailed deterministic mass action models for chemical reaction kinetics. Especially in complex technical or biochemical systems the huge amount of species and reaction pathways involved in a detailed modeling approach call for efficient methods of model reduction. These should be automatic and based on a firm mathematical analysis of the ordinary differential equations underlying the chemical kinetics in deterministic models. A main purpose of model reduction is to enable accurate numerical simulations of even high dimensional and spatially extended reaction systems. The latter include physical transport mechanisms and are modeled by partial differential equations. Their numerical solution for hundreds or thousands of species within a reasonable time will exceed computer capacities available now and in a foreseeable future. The central idea of model reduction is to replace the high dimensional dynamics by a low dimensional approximation with an appropriate degree of accuracy. Here I present a global approach to model reduction based on the concept of minimal entropy production and its numerical implementation. For given values of a single species concentration in a chemical system all other species concentrations are computed under the assumption that the system is as close as possible to its attractor, the thermodynamic equilibrium, in the sense that all modes of thermodynamic forces are maximally relaxed except the one, which drives the remaining system dynamics. This relaxation is expressed in terms of minimal entropy production for single reaction steps along phase space trajectories.     

Artificial neural network model for the evaluation of chemical kinetics in thermally induced solid-state reaction

The artificial intelligence technique is utilized to improve evaluation of thermally induced solid-state reaction kinetics. A general regression neural network (GRNN) model was applied to directly determine the kinetic triplets, i.e., activation energy, pre-exponential factor, and mechanism model. The effect of number of heating rate on prediction performance of the GRNN model was assessed based on the estimation indictors. The obtained kinetic triplets based on the triple heating rates were considered to be accepted. The prediction ability of the GRNN model was very robust at more than three heating rates. The relative errors for kinetic parameters derived from five heating rates were within ±?4%, and the cognition rates for mechanism models were up to 99.6%. The developed GRNN model was successfully applied in the high-temperature synthesis of Li₄Ti₅O₁₂/C composites. It is expected that the model also could be extended to estimate the kinetics of other solid-state reactions.

     

Tracking chemical kinetics in high-throughput systems

Combinatorial chemistry and high‐throughput experimentation (HTE) have revolutionized the pharmaceutical industry—but can chemists truly repeat this success in the fields of catalysis and materials science? We propose to bridge the traditional “discovery” and “optimization” stages in HTE by enabling parallel kinetic analysis of an array of chemical reactions. We present here the theoretical basis to extract concentration profiles from reaction arrays and derive the optimal criteria to follow (pseudo)first‐order reactions in time in parallel systems. We use the information vector f and introduce in this context the information gain ratio, χ_r, to quantify the amount of useful information that can be obtained by measuring the extent of a specified reaction r in the array at any given time. Our method is general and independent of the analysis technique, but it is more effective if the analysis is performed on‐line. The feasibility of this new approach is demonstrated in the fast kinetic analysis of the carbon–sulfur coupling between 3‐chlorophenylhydrazonopropane dinitrile and β‐mercaptoethanol. The theory agrees well with the results obtained from 31 repeated C? S coupling experiments.     

Effect of brownian diffusion on chemical kinetics

A new method of theoretical prediction of the kinetic rate constants of fast chemical reactions in solutions is presented. It takes into account the effect of finite diffusive displacements of the reacting molecules. The approach is based on the solution of the steady-state Fokker–Planck equation by the moments method of Grad developed in the theory of coagulation of aerosol particles. A comparison of the predicted rate constants with the experimental data provided by Schuh and Fischer for the self-reaction of tert-butyl radicals in n-alkanes shows a good correspondence.     

Stoichiometry as canonical transformation of chemical kinetics

Applying the apparatus of differential manifolds and that of classical conservative point mechanics, it is shown that stoichiometry plays the role of canonical transformations in chemical reaction kinetics.

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Understanding the kinetics of spin-forbidden chemical reactions

Many chemical reactions involve a change in spin-state and are formally forbidden. This article summarises a number of previously published applications showing that a form of Transition State Theory (TST) can account for the kinetics of these reactions. New calculations for the emblematic spin-forbidden reaction HC + N(2) are also reported. The observed reactivity is determined by two factors. The first is the critical energy required for reaction to occur, which in spin-forbidden reactions is often defined by the relative energy of the Minimum Energy Crossing Point (MECP) between potential energy surfaces corresponding to the different spin states. The second factor is the probability of hopping from one surface to the other in the vicinity of the crossing region, which is largely defined by the spin-orbit coupling matrix element between the two electronic wavefunctions. The spin-forbidden transition state theory takes both factors into account and gives good results. The shortcomings of the theory, which are largely analogous to those of standard TST, are discussed. Finally, it is shown that in cases where the surface-hopping probability is low, the kinetics of spin-forbidden reactions will be characterised by unusually unfavourable entropies of activation. As a consequence, reactions involving a spin-state change can be expected to compete poorly with spin-allowed reactions at high temperatures (or energies).     

Consequences of resonance tunnelling in chemical kinetics

The kinetic consequences of resonance tunnelling processes that may occur in chemical reactions are investigated in terms of a multi-centered unsymmetrical Eckart potential barrier. This potential function does not only simulate the possible existence of intermediate wells in the effective potential energy cut along the reaction path, but also is amenable to analytic solutions. The reaction rate as well as its dependence on temperature, reduced mass,Q-value, activation energy and barrier diffuseness are evaluated for successively increasing the number of barrier stages. Comparisons between results due to single and multi-humped potential energy barriers are made and discussed.