Mechanistic investigations and spectrokinetic parameter determination during thermoreversible photochromism with degradation: example of application to the triphenylimidazolyl dimer (TPID) system

A numerical method is proposed for the kinetic analysis of the experimental absorbance vs. time curves obtained during continuous irradiation and thermal equilibration of a thermoreversible photochromic system with degradation. The quantum yield amd molar absorption coefficients of the unstable coloured species can be determined simultaneously using a kinetic model which encompasses all details of the reaction mechanism including the degradation process. The efficacy and accuracy of this method are illustrated by an analysis of the triphenylimidazolyl dimer (TPID) system in toluene solution.     

Sensitivity analysis in chemical kinetics by the method of polynomial approximations

A new approach, the method of polynomial approximations (PAM), to the sensitivity analysis in chemical kinetics is presented. The method is based on first dividing the time domain of interest into subintervals, and then, within each subinterval, using low-degree interpolation polynomials to mimic the system temporal behavior. This procedure forces all parametric dependences of the system to reside in the expansion coefficients and transforms the differential sensitivity equations into a set of algebraic ones. The major computational effort of PAM is proportional to the number of components in the system, not to the number of parameters. In addition, higher order sensitivity coefficients in PAM can be generated quite readily once first-order ones are known. The information required to divide the time domain comes from a preliminary simulation study of the system temporal behavior, which is always available in any kind of modeling studies. Typically, for an interpolation polynomial of degree 3–4, only 10–20 subintervals are needed to attain satisfactory accuracy. The application of PAM is well suited to large-scale kinetic models, especially when an inexpensive scanning of the system sensitivity behavior is desired. The extremely high computational speed of PAM in securing sensitivity informations was demonstrated by two illustrative kinetic examples. Furthermore the problem of utilizing sensitivity information to unravel the functional dependence of a species concentration upon rate coefficients, to simplify a complex reaction model, and to elucidate mechanistic details of a reaction process was examined in detail.     

Sensitivity analysis of uncertainty in model prediction

Data Collaboration is a framework designed to make inferences from experimental observations in the context of an underlying model. In the prior studies, the methodology was applied to prediction on chemical kinetics models, consistency of a reaction system, and discrimination among competing reaction models. The present work advances Data Collaboration by developing sensitivity analysis of uncertainty in model prediction with respect to uncertainty in experimental observations and model parameters. Evaluation of sensitivity coefficients is performed alongside the solution of the general optimization ansatz of Data Collaboration. The obtained sensitivity coefficients allow one to determine which experiment/parameter uncertainty contributes the most to the uncertainty in model prediction, rank such effects, consider new or even hypothetical experiments to perform, and combine the uncertainty analysis with the cost of uncertainty reduction, thereby providing guidance in selecting an experimental/theoretical strategy for community action.     

Pentanary cross-diffusion in water-in-oil microemulsions loaded with two components of the Belousov-Zhabotinsky reaction

We measure cross-diffusion coefficients in a five-component system, an aerosol OT (AOT) water-in-oil microemulsion loaded with two constituents of the Belousov-Zhabotinsky (BZ) reaction (H(2) O/AOT/BZ1/BZ2/octane). The species BZ1 is either NaBr, an inhibitor of the BZ reaction, or ferroin, a catalyst for the reaction. As species BZ2, we choose Br(2) , an intermediate in the reaction. The cross-diffusion coefficients between BZ1 and BZ2 are found to be negative, which can be understood in terms of complexation between these species. Using a four-variable model for the BZ reaction, we find that the cross-diffusion coefficients measured here can lead to a noticeable shift in the onset of Turing instability in the BZ-AOT system.     

Combined experimental and master equation investigation of the multiwell reaction H + SO2

The temperature and pressure dependence of the rate coefficient for the reaction H + SO2 has been measured using a laser flash photolysis/laser-induced fluorescence technique, for 295 10(3) atm, the latter proceeds directly from H + SO2, via the energized states of HOSO. The derived rate coefficients rely heavily on measurements of the reverse reaction, OH + SO, which has only been determined at temperatures up to 700 K.     

Analysis of nonlinear reactions in modulated molecular beam surface experiments

An approximate method of analyzing nonlinear reaction models in modulated molecular beam surface kinetic studies is developed. The exact method for treating nonlinear surface mechanisms is tedious and almost always requires computer analysis. The proposed approximate method is a simple extension of the Fourier expansion technique valid for linear surface reactions; it quickly provides analytical expressions for the phase lag and amplitude of the reaction product for any type of nonlinear surface mechanism, which greatly facilitates comparison of theory and experiment. The approximate and exact methods are compared for a number of prototypical adsorption–desorption reactions which include coverage-dependent adsorption and desorption kinetics of order greater than unity. Except for certain extreme forms of coverage-dependent adsorption, the approximate method provides a good representation of the exact solution. The errors increase as the nonlinearities become stronger. Fortunately, when the discrepancy between the two methods is substantial, the reaction product signal is so highly demodulated that reliable experimental data usually cannot be obtained in these regions anyway.     

Mathematical treatment of concentration profiles and anodic current for amperometric enzyme electrodes

Formulae are presented for the exact solution of partial differential equations describing the transient behaviour of concentration profiles and the anodic current in amperometric enzyme electrodes. The mathematical treatment is based on a reaction/diffusion model in which the reaction rate depends linearly on the substrate concentrations. Numerical results are presented to demonstrate the feasibility of the given formulae.     

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.     

Dual control cell reaction ensemble molecular dynamics: a method for simulations of reactions and adsorption in porous materials

We present a simulation tool to study fluid mixtures that are simultaneously chemically reacting and adsorbing in a porous material. The method is a combination of the reaction ensemble Monte Carlo method and the dual control volume grand canonical molecular dynamics technique. The method, termed the dual control cell reaction ensemble molecular dynamics method, allows for the calculation of both equilibrium and nonequilibrium transport properties in porous materials such as diffusion coefficients, permeability, and mass flux. Control cells, which are in direct physical contact with the porous solid, are used to maintain the desired reaction and flow conditions for the system. The simulation setup closely mimics an actual experimental system in which the thermodynamic and flow parameters are precisely controlled. We present an application of the method to the dry reforming of methane reaction within a nanoscale reactor model in the presence of a semipermeable membrane that was modeled as a porous material similar to silicalite. We studied the effects of the membrane structure and porosity on the reaction species permeability by considering three different membrane models. We also studied the effects of an imposed pressure gradient across the membrane on the mass flux of the reaction species. Conversion of syngas (H2/CO) increased significantly in all the nanoscale membrane reactor models considered. A brief discussion of further potential applications is also presented.     

金属溶剂萃取的热力学研究(Ⅶ)——2-乙基己基膦酸单(2-乙基己基)酯-硫酸钻-硫酸铜体系

本文提出了具有相同电荷的同号离子间作用力相等的假定, 简化了Pitzer的电解质溶液活度系数计算公式, 用此公式, 计算了H_2SO_4-CoSO_4-CuSO_4水相体系各单个离子活度系数以及水的渗透系数。本文还应用由作者提出的工作参考态法, 应用改进的Scatchard-Hildebrand模型计算了EHEHPA-CoSO_4-CuSO_4萃取体系中有机相各组分的活度系数以及萃取反应热力学平衡常数.     

A new approach to response surface development for detailed gas‐phase and surface reaction kinetic model optimization

We propose a new method for constructing kinetic response surfaces used in the development and optimization of gas‐phase and surface reaction kinetic models. The method, termed as the sensitivity analysis based (SAB) method, is based on a multivariate Taylor expansion of model response with respect to model parameters, neglecting terms higher than the second order. The expansion coefficients are obtained by a first‐order local sensitivity analysis. Tests are made for gas‐phase combustion reaction models. The results show that the response surface obtained with the SAB method is as accurate as the factorial design method traditionally used in reaction model optimization. The SAB method, however, presents significant computational savings compared to factorial design. The effect of including the partial and full third order terms was also examined and discussed. The SAB method is applied to optimization of a relatively complex surface reaction mechanism where large uncertainty in rate parameters exists. The example chosen is laser‐induced fluorescence signal of OH desorption from a platinum foil in the water/oxygen reaction at low pressures. We introduce an iterative solution mapping and optimization approach for improved accuracy. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 94–106, 2004     

Mechanistic insights into the hydrolysis of a nucleoside triphosphate model in neutral and acidic solution

Nucleoside triphosphate hydrolysis is an essential component of all living systems. Despite extensive research, the exact modus and mechanism of this ubiquitous reaction still remain elusive. In this work, we examined the detailed hydrolysis mechanisms of a model nucleoside triphosphate in acidic and neutral solution by means of ab initio simulations. The timescale of the reaction was accessed through use of an accelerated sampling method, metadynamics. Both hydrolyses were found to proceed via different mechanisms; the acidic system reacted by means of concerted general acid catalysis (found to be a so-called D(N)A(N)A(H)D(xh) mechanism), whereas the neutral system reacted by way of a different mechanism (namely, D(N)*A(N)D(xh)A(H)). A neighboring water molecule took on the role of a general base in both systems, which has not been seen before but is a highly plausible reaction path, meaning that substrate-assisted catalysis was not observed in the bulk water environment.     

Locally implicit solution of a reaction-diffusion system with stiff kinetics

The Tyson-Fife reaction-diffusion equations are solved numerically using a locally implicit approach. Since the variables evolve at very different time scales, the resulting system of equations is stiff. The reaction term is responsible for the stiffness and the time step is increased by using an implicit method. The diffusion operator is evaluated explicitly and the system of implicit nonlinear equations is decoupled. The method is particularly useful for parameter values in which the equations are very stiff, such as the values obtained directly from the experimental reaction rate constants. Previous efforts modified the parameters on the equations to avoid stiffness. The equations then become a simplified model of excitable media and, for those cases, the locally implicit method gives a faster although less accurate solution. Nevertheless, since the modified equations no longer represent a particular chemical system an accurate solution is not as important. The algorithm is applied to observe the transition from simple motion to compound motion of a spiral tip.     

Bimolecular reaction rates from ring polymer molecular dynamics: application to H + CH4 → H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.     

A kinetic model for heterogeneous acetalisation of poly(vinyl alcohol)

A model for heterogeneous acetalisation of poly(vinyl alcohol) with limited solution volume is proposed based on the grain model of Sohn and Szekely. Instead of treating the heterogeneous acetalisation as purely a diffusion process, as in the Matuzawa and Ogasawara model, the present model also takes into account the chemical reaction and the physical state of the solid polymer, such as degree of swelling and porosity, and assumes segregation of the polymer phase at higher conversion into an outer fully reacted zone and an inner zone where the reaction still proceeds. The solution of the model for limited solution volume, moreover, offers a simple method of determining the kinetic parameters and diffusivity for the solid-liquid system using the easily measurable bulk solution concentration of the liquid reactant instead of conversion-distance data for the solid phase, which are considerably more difficult to obtain.     

EPDM accelerated sulfur vulcanization: a kinetic model based on a genetic algorithm

A simple closed form equation for the prediction of crosslinking of EPDM during accelerated sulfur vulcanization is presented. Such a closed form solution is derived from a second order non homogeneous differential equation, deduced from a kinetic model. The kinetic model is based on the assumption that, during vulcanization, a number of partial reactions occurs, both in series and in parallel, which determine the formation of intermediate compounds, including activated and matured polymer. Once written standard first order differential equations for each partial reaction, the differential equation system so obtained is rearranged and, after few considerations, a single second order non homogeneous differential equation with constant coefficients is derived, for which a solution may be found in closed form, provided that the non-homogeneous term is approximated with an exponential function. To estimate numerically the degree of crosslinking, kinetic model constants are evaluated through a simple data fitting, performed on experimental rheometer cure curves. The fitting procedure is a new one, and is achieved using an ad-hoc genetic algorithm, provided that a few points, strictly necessary to estimate model unknown constants with sufficient accuracy, are selected from the whole experimental cure curve. To assess the results obtained with the model proposed, a number of different compounds are analyzed, for which experimental or numerical data are available from the literature. The important cases of moderate and strong reversions are also considered, experiencing a convincing convergence of the analytical model proposed. For the single cases analyzed, partial reaction kinetic constants are also provided.     

Numerical values of individual activity coefficients of single-ion species in concentrated aqueous electrolyte solutions and the attempt of a qualitative interpretation on a model of electrostatic interaction

Individual activity coefficients of single-ion species can be achieved by the factorizing of a new concentration function for the mean activity coefficient to the required power applying a purely mathematical method. These single-ion activity coefficients, calculated in this manner, are listed for some aqueous strong electrolytes. The reasons for the magnitude and variation of the activity coefficients as a function of the concentration are, without a doubt, of complex nature. Activity coefficients have their meaning as practical values. In relation to the analytical concentration, the individual activity coefficients represent the macroscopic effectiveness of the single-ion species in solution an easy manner. However, with increasing deviations from Debye–Hückel conditions of an infinitely diluted electrolyte solution, a physically correct interpretation of the macroscopically visible activity coefficient is becoming more and more difficult, if not impossible to find. On the basis of a model of electrostatic interaction, an attempt has been made to create a qualitative interpretation of the individual ion activity coefficients in concentrated aqueous electrolyte solutions which were calculated applying the purely mathematical method by Ferse.     

Nonadiabatic quantum-classical reaction rates with quantum equilibrium structure

Time correlation function expressions for quantum reaction-rate coefficients are computed in a quantum-classical limit. This form for the correlation function retains the full quantum equilibrium structure of the system in the spectral density function but approximates the time evolution of the operator by quantum-classical Liouville dynamics. Approximate analytical expressions for the spectral density function, which incorporate quantum effects in the many-body environment and reaction coordinate, are derived. The results of numerical simulations of the reaction rate are presented for a reaction model in which a two-level system is coupled to a bistable oscillator which is, in turn, coupled to a bath of harmonic oscillators. The nonadiabatic quantum-classical dynamics is simulated in terms of an ensemble of surface-hopping trajectories and the effects of the quantum equilibrium structure on the reaction rate are discussed.