Kinetics of autocatalysis in small systems

Autocatalysis is a ubiquitous chemical process that drives a plethora of biological phenomena, including the self-propagation of prions etiological to the Creutzfeldt-Jakob disease and bovine spongiform encephalopathy. To explain the dynamics of these systems, we have solved the chemical master equation for the irreversible autocatalytic reaction A+B-->2A. This solution comprises the first closed form expression describing the probabilistic time evolution of the populations of autocatalytic and noncatalytic molecules from an arbitrary initial state. Grand probability distributions are likewise presented for autocatalysis in the equilibrium limit (A+B <==>2A), allowing for the first mechanistic comparison of this process with chemical isomerization (B<==>A) in small systems. Although the average population of autocatalytic (i.e., prion) molecules largely conforms to the predictions of the classical "rate law" approach in time and the law of mass action at equilibrium, thermodynamic differences between the entropies of isomerization and autocatalysis are revealed, suggesting a "mechanism dependence" of state variables for chemical reaction processes. These results demonstrate the importance of chemical mechanism and molecularity in the development of stochastic processes for chemical systems and the relationship between the stochastic approach to chemical kinetics and nonequilibrium thermodynamics.     

Classification of Clock Reactions

Autocatalytic systems are sometimes designated as clock reactions or reactions that exhibit clock behavior. To resolve the recent dispute over the term clock reaction, we describe a new approach to classify systems featuring clock behavior into three distinct groups: substrate‐depletive clock reactions, autocatalysis‐driven clock reactions, and systems that have pseudo clock behavior. Many of the well‐known classical and recently discovered reactions can conveniently be put into these categories. We also provide a convincing argument for classifying some autocatalytic processes as clock reactions, but it does not necessarily mean that all autocatalytic processes should be classified as autocatalysis‐driven clock reactions. This classification can be conveniently performed if the kinetic nature of the given system has been completely elucidated and understood.     

Development of a generic mechanism for the dehydrocoupling of amine-boranes: a stoichiometric, catalytic, and kinetic study of H3B·NMe2H using the [Rh(PCy3)2]+ fragment

The multistage Rh-catalyzed dehydrocoupling of the secondary amine-borane H(3)B·NMe(2)H, to give the cyclic amino-borane [H(2)BNMe(2)](2), has been explored using catalysts based upon cationic [Rh(PCy(3))(2)](+) (Cy = cyclo-C(6)H(11)). These were systematically investigated (NMR/MS), under both stoichiometric and catalytic regimes, with the resulting mechanistic proposals for parallel catalysis and autocatalysis evaluated by kinetic simulation. These studies demonstrate a rich and complex mechanistic landscape that involves dehydrogenation of H(3)B·NMe(2)H to give the amino-borane H(2)B═NMe(2), dimerization of this to give the final product, formation of the linear diborazane H(3)B·NMe(2)BH(2)·NMe(2)H as an intermediate, and its consumption by both B-N bond cleavage and dehydrocyclization. Subtleties of the system include the following: the product [H(2)BNMe(2)](2) is a modifier in catalysis and acts in an autocatalytic role; there is a parallel, neutral catalyst present in low but constant concentration, suggested to be Rh(PCy(3))(2)H(2)Cl; the dimerization of H(2)B═NMe(2) can be accelerated by MeCN; and complementary nonclassical BH···HN interactions are likely to play a role in lowering barriers to many of the processes occurring at the metal center. These observations lead to a generic mechanistic scheme that can be readily tailored for application to many of the transition-metal and main-group systems that catalyze the dehydrocoupling of H(3)B·NMe(2)H.     

Supramolecular dynamics studied using photophysics

Dynamics is an essential feature of supramolecular systems, and it's understanding will be central in achieving new chemical function. The methodology to obtain association and dissociation rate constants for fast binding of guests to host systems in real time is described. Examples are provided for binding of guests to cyclodextrins or bile salt aggregates with an emphasis on the type of information and mechanistic insight that can only be uncovered from kinetic studies and is not apparent in thermodynamic investigations.     

Mechanism-based chemical understanding of chiral symmetry breaking in the Soai reaction. A combined probabilistic and deterministic description of chemical reactions

The experimentally observed distribution of enantiomers in the Soai reaction is interpreted in this Article on the basis of a chemical mechanism using a newly developed stochastic kinetic method, accelerated Monte Carlo simulation combined with deterministic continuation and symmetrization. The method is in principle suitable for handling large mechanisms with realistic particle numbers and could be useful for any case where the kinetics of a process shows inherent random fluctuations. The mechanism shows how a slow initial reaction combined with efficient and highly enantioselective autocatalysis can give rise to chiral symmetry breaking under completely nonchiral external conditions.     

Spontaneous Emergence of Chirality in the Limited Enantioselectivity Model: Autocatalytic Cycle Driven by an External Reagent

The model of limited enantioselectivity (LES) in closed systems, and under experimental conditions able to achieve chemical equilibrium, can give rise to neither spontaneous mirror symmetry breaking (SMSB) nor kinetic chiral amplifications. However, it has been recently shown that it is able to lead to SMSB, as a stationary final state, in thermodynamic scenarios involving nonuniform temperature distributions and for compartmentalized separation between the two autocatalytic reactions. Herein, it is demonstrated how SMSB may occur in LES in a cyclic network with uniform temperature distribution if the reverse reaction of the nonenantioselective autocatalysis, which gives limited inhibition on the racemic mixture, is driven by an external reagent, that is, in conditions that keep the system out of chemical equilibrium. The exact stability analysis of the racemic and chiral final outcomes and the study of the reaction parameters leading to SMSB are resolved analytically. Numerical simulations, using chemical kinetics equations, show that SMSB may occur for chemically reasonable parameters. Numerical simulations on SMSB are also presented for speculative, but reasonable, scenarios implying reactions common in amino acid chemistry.     

Stochastic kinetic models of chiral autocatalysis: a general tool for the quantitative interpretation of total asymmetric synthesis

A continuous time discrete state stochastic kinetic approach is used to study various chiral autocatalytic models in which the possibility of total asymmetric synthesis arises. It is shown that this approach is superior to the deterministic approaches used earlier and is able to interpret many aspects of chiral autocatalysis. First-order autocatalysis, independently of further kinetic details of the system, leads to a unique final statistical distribution of enantiomers. Higher order autocatalysis, on the other hand, leads to a final state where one of the enantiomers is in overwhelming excess over the other. Criteria are postulated to differentiate between inherently stochastic phenomena in chiral autocatalytic reactions and irreproducibility because of insufficient control of external factors.     

Adiabatic decomposition kinetics by non-linear optimization

Reactions with large negative enthalpy changes are often encountered in the chemical industry. Sometimes they give rise to technical dangers and hazards, including explosions. This investigation concentrates on examination of adiabatic temperature-time-curves and gives non-linear optimization procedures for obtaining kinetic parameters of simple decompositions,e.g. o-nitrobezaldehyde, two types of autocatalysis, consecutive reactions and competitive consecutive reactions. The advantage of this computing method is that only differential kinetic equations are needed.     

Amplification of chirality as a pathway to biological homochirality

Amplification of enantiomeric enrichment is a key feature for the chemical evolution of biological homochirality from the origin of chirality. The aggregations of the enantiomers by diastereomeric interactions enable the modification of their enantiomeric excess during some chemical processes. Fluorine-containing chiral compounds possess large amplification effect via distillation, sublimation and achiral chromatography by self-disproportionation. Asymmetric amplifications in enantioselective catalysis occur by the differential formation and reactivity between homochiral and heterochiral aggregate in solution.We described the amplification of ee in asymmetric autocatalysis of 5-pyrimidyl alkanol in the reaction between diisopropylzinc and pyrimidine-5-carbaldehdye. During the reactions extremely low ee (ca. 0.00005% ee) can be amplified to achieve more than 99.5% ee. Since the proposed origins of chirality such as CPL, quartz, chiral organic crystals of achiral compounds and statistical fluctuation of ee can initiate the asymmetric autocatalysis with amplification of ee, the proposed origin of chirality can be linked with enantiopure organic compound in conjunction with amplification of ee by asymmetric autocatalysis. In addition, we described that the carbon isotopically chiral compound triggers the asymmetric autocatalysis of 5-pyrimiodyl alkanol to afford the enantioenriched product with the absolute configuration correlated with that of carbon isotope chirality, that is, isotope chirality including hydrogen isotopes can control the enantioselectivity of asymmetric addition of alkyl metal reagent to aldehyde.     

Reaction‐Diffusion Systems in Intracellular Molecular Transport and Control

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active‐transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction‐diffusion (RD) systems that control a wide range of cellular functions—from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are “wired” according to “generic” motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport‐kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction‐diffusion phenomena.     

Homogeneous redox catalysis of electrochemical reactions: Part III. Rate determining electron transfer. Kinetic characterization of follow-up chemical reactions

Electrochemical systems involving moderately fast charge transfers and very fast irreversible follow-up chemical reactions usually escape from kinetic and mechanistic characterization through the standard use of electrochemical techniques. It is shown that these difficulties can be overcome using an indirect approach which involves the homogeneous redox catalysis of the considered electrochemical reaction. A procedure for determining the rate constant of such fast follow-up reaction is presented. It is illustrated by the determination of the cleavage rate constant of the chlorobenzene anion radical in DMF which reaches a value on the order of 10⁷ s^?1.     

Kinetic aspects of non-linear effects in asymmetric synthesis,catalysis, and autocatalysis

The Kagan ML_n models developed for rationalizing non-linear effects of catalyst enantiopurity have become a valuable mechanistic tool for probing complex asymmetric catalytic reactions. This work demonstrates how these models also provide clues about reactivity that may be used for further evidence to test a mechanistic hypothesis. Special considerations for probing non-linear effects in asymmetric synthesis using stoichiometric chiral auxiliaries and in asymmetric autocatalysis are highlighted in comparison with asymmetric catalysis.     

Rheokinetic cure characterization of epoxy–anhydride polymer system with shape memory characteristics

An epoxy resin capable of exhibiting shape memory property was derived by curing diglycidyl ether of bisphenol A (DGEBA) with a blend of carboxy telechelic poly(tetramethyleneoxide) (PTAC) and pyromellitic dianhydride (PMDA). The cure kinetics of DGEBA/PTAC/PMDA blend of varying compositions was investigated using isothermal rheological analysis. The overall reaction conformed to a second-order autocatalytic model. The kinetic parameters including reaction order, kinetic constants and activation energy were determined. The results showed that increase of PTAC decreased the overall activation energy and frequency factor of the cure reaction. This effect resulted in a diminution of the overall rate of curing. The catalysis by PTAC has its origin from the activation of epoxy groups by the protons of the COOH groups. The autocatalysis was caused by the COOH groups generated by the reaction of alcohol groups with anhydride. The activation energy for the autocatalysis was more than that for the primary reaction as the COOH groups responsible for autocatalysis were generated on a sterically hindered polymer backbone. The kinetics helped generate a master equation conforming to second-order autocatalytic model that could predict the cure profile of a specified resin system at a given temperature, leading to cure optimization.     

Controlled assembly of covalent and supramolecular chemical modules: from engineering of complex structures to high-performance chromatography

A biological approach to generating complex behaviors in chemistry is described. It is suggested theoretically that the assembly of modules composed of chemical reactions or molecular structures under appropriate external constraints can lead to features typical of the biological world like autocatalysis, kinetic proofreading, or oriented molecular motion. This approach may account for the primitive steps of molecular evolution and, in addition, it can find useful applications in chemistry such as high-performance chromatography.     

Artificial-intelligence-based interpretation of feature sensitivities of the Belousov-Zhabotinsky reaction

A new approach is presented for analyzing kinetic models of relaxation-type oscillatory systems on the basis of numerical data. Feature sensitivities of the length of the two kinetic states of the Belousov-Zhabotinsky (BZ) reaction with respect to the rate constants of the model are explained by means of a logic-based inference system. The main kinetic roles of the individual reaction steps on the relaxing components are revealed, and a consistent interpretation of the kinetic states is given by this process. Both the high and the low set of rate constants were studied. According to our analysis, the bromous acid-hypobromous acid reaction is an important Br^? producing step of the model, and in the case of the low set, the bromate-bromous acid reaction is not the rate-determining step of the bromous acid autocatalysis.     

On the Autocatalysis of Methane Pyrolysis

Methane pyrolysis has been performed in a recycled flow system in the temperature range of 1103 to 1220 K to investigate the time profile of product distribution. Hydrogen, ethylene, and benzene are found to be the major products before the soot formation. Similar to the literature reports of studies in conventional flow systems, the rate of methane conversion is slow at the beginning of the decomposition and becomes fast after an incubation period. This increase in the decomposition rate after the incubation period is generally called autocatalysis. The proposed reason for this autocatalysis has been the catalytic effect of the secondary products, i.e., soots and carbon deposits. The present study showed that autocatalysis started before the accumulation of these products, and that decomposition of propylene and other minor but reactive products might be attributed to this autocatalysis effect.     

On the interpretation of the potentiometric response of the inert solid electrodes in the monitoring of the oscillatory processes involving hydrogen peroxide

Solid inert electrodes are frequently used in potentiometry. However, potentiometric responses may significantly depend on the inert electrode material, a fact which may manifest itself particularly distinctly for the dynamical chemical systems—oscillating processes. We found that for the homogeneous oscillators involving hydrogen peroxide and either thiocyanates or thiosulfates, the periodic variations of the platinum and palladium indicator electrode potential are both not in phase with the variations of the potential of the gold and glassy carbon electrodes, the latter two exhibiting in turn concordant, in-phase responses. Potentiometric responses were compared with the impedance characteristics of the electrodes during the oscillations. In spite of high mechanistic complexity of the studied homogeneous oscillatory systems, we explain different responses of inert electrodes in terms of the concept of the mixed electrode potential, i.e., determined by more than one redox couple of different kinetic characteristics (exchange current densities). In our model explanation, two coupled Ox₁/Red₁ and Ox₂/Red₂ redox systems are considered. It is suggested that for Au or glassy carbon electrodes, the mixed potential is largely determined by the Ox₁/Red₁ couple. For Pt or Pd electrodes, due to the catalytic effect of their surfaces on the Ox₂/Red₂ couple, its exchange current largely controls the measured mixed potential. Our concept is supported by numerical calculations involving the classical Brusselator as the model generator of chemical oscillations. The proper interpretation of potentiometric kinetic data is crucial for the diagnosis of the correct reaction mechanism.     

Thermal decomposition of methane: Autocatalysis

The origin of autocatalysis in the pyrolysis of methane has been investigated by kinetic modeling. A mechanism is presented that provides good agreement with experimental data at 1038 K and 433 torr into the autocatalytic region. The main causes of autocatalysis are secondary initiation by hydrocarbon products larger than C₂H₆ and chain radical methylation sequences.