Final nanoparticle size distribution under unusual parameter regimes.

We explore the large-scale behavior of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where n monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded. We delve into a previously unexplored parameter regime. Specifically, we consider a scenario where the growth rate of the first newly formed particle is of the same order of magnitude as the nucleation rate, in contrast to the classical scenario where, in the initial stage, nucleation dominates over growth. In this regime, we investigate the final size distribution as the initial number of monomers tends to infinity through extensive simulation studies utilizing state-of-the-art stochastic simulation methods with an efficient implementation and supported by high-performance computing infrastructure. We observe the emergence of a deterministic limit for the particle's final size density. To scale up the initial number of monomers to approximate the magnitudes encountered in real experiments, we introduce a novel approximation process aimed at faster simulation. Remarkably, this approximating process yields a final size distribution that becomes very close to that of the original process when the available monomers approach infinity. Simulations of the approximating process further support the conjecture of the emergence of a deterministic limit.

Minimal Reaction-Diffusion Model of Micromixing during Stopped-Flow Experiments.

The reaction-diffusion equation was used to simulate kinetic curves measured in a stopped-flow instrument in order to understand the origin of micromixing effects. The partial differential equations were solved both by numeric means and by a more analytical approach using Fourier series. A fully analytical solution was obtained for the diffusion only case (when no reaction occurs). Comparisons with the results of numerical calculations showed that very reasonable analytical approximations were obtained for the diffusion-reaction case. The simulations could readily reproduce the saturation of the pseudo-first-order rate constants with an increase in the concentration of excess reagent, a phenomenon first observed about 30 years ago. From the results, it can be concluded that further improvement of the performance of stopped-flow instruments is not possible by simply reducing the dead time; the efficiency of the mixing is the primary limiting factor.

Kinetics and Mechanism of the Autocatalytic Oxidation of Bis(terpyridine)iron(II) by Peroxomonosulfate Ion (Oxone) in Acidic Medium.

The autocatalytic oxidation of the bis(terpyridine)iron(II) complex, Fe(tpy)22+ by peroxomonosulfate ion (PMS) proceeds via the formation of the corresponding iron(III) complex (Fe(tpy)23+) as the primary oxidation product. The proton-assisted dissociation of Fe(tpy)22+ and subsequent oxidation of Fe2+ are side reactions in this system. In the initial stage of the reaction, a 1:1 adduct is formed between PMS and bis(terpyridine)iron(II), which decomposes in an intramolecular electron transfer reaction step. The autocatalytic role of Fe(tpy)23+ was also confirmed in the overall process. This effect is interpreted by considering the formation of an additional adduct between PMS and Fe(tpy)23+. The decomposition of the adduct yields two strong oxidizing intermediates, an Fe(IV) species and SO4-•, which consume the iron(II) complex in rapid reaction steps. A detailed kinetic model was postulated for the overall oxidation of Fe(tpy)22+ by PMS. The equilibrium constants for the formation of the adducts between PMS and complexes Fe(tpy)22+ and Fe(tpy)23+ were estimated as 129 ± 18 M-1 and 87 ± 10 M-1, respectively. In contrast to the closely related Fe(phen)32+-PMS reaction, the N-oxide derivative of the ligand (tpyO) does not have any kinetic role in the overall process because of the very slow formation of the N-oxide in the reaction.

Modeling Studies of Inhomogeneity Effects during Laser Flash Photolysis Experiments: A Reaction-Diffusion Approach.

This work presents a rigorous mathematical study of the effect of unavoidable inhomogeneities in laser flash photolysis experiments. There are two different kinds of inhomegenities: the first arises from diffusion, whereas the second one has geometric origins (the shapes of the excitation and detection light beams). Both of these are taken into account in our reported model, which gives rise to a set of reaction-diffusion type partial differential equations. These equations are solved by a specially developed finite volume method. As an example, the aqueous reaction between the sulfate ion radical and iodide ion is used, for which sufficiently detailed experimental data are available from an earlier publication. The results showed that diffusion itself is in general too slow to influence the kinetic curves on the usual time scales of laser flash photolysis experiments. However, the use of the absorbances measured (e.g., to calculate the molar absorption coefficients of transient species) requires very detailed mathematical consideration and full knowledge of the geometrical shapes of the excitation laser beam and the separate detection light beam. It is also noted that the usual pseudo-first-order approach to evaluating the kinetic traces can be used successfully even if the usual large excess condition is not rigorously met in the reaction cell locally.

Formation of 1,10-Phenanthroline-N,N'-dioxide under Mild Conditions: The Kinetics and Mechanism of the Oxidation of 1,10-Phenanthroline by Peroxomonosulfate Ion (Oxone).

This paper confirms the unexpected formation of 1,10-phenanthroline-N,N'-dioxide (phenO2) when 1,10-phenanthroline (phen) is oxidized by peroxomonosulfate ion (PMS) in a neutral aqueous solution. The kinetics of oxidation of phen by PMS features a complex pH dependence. In 1.00 M H2SO4, 1,10-phenanthroline-mono-N-oxide (phenO) is the sole product of the reaction. The rate of the N-oxidation is highly dependent on pH with a maximum at pH ∼6.7. The formation of phenO occurs via two parallel pathways: the rate constant of the oxidation of phen (k = 3.1 ± 0.1 M(-1) s(-1)) is significantly larger than that of Hphen(+) [k = (4.1 ± 0.3) × 10(-3) M(-1) s(-1)] because the two N atoms are open to oxidative attack in the deprotonated substrate while an internal hydrogen bond hinders the oxidation of the protonated form. With an excess of PMS, four consecutive oxidation steps were found in nearly neutral solutions. In the early stage of the reaction, the stepwise oxidation results in the formation of phenO, which is converted into phenO2 in the second step. The formation of phenO2 was confirmed by (1)H NMR and ESI-MS methods. The results presented here offer the possibility of designing an experimental protocol for preparing phenO2.

Construction of a multipurpose photochemical reactor with on-line spectrophotometric detection.

A versatile photoreactor was built for studying homogeneous and heterogeneous photochemical reactions using fiber-optic devices. The reactor was designed to allow simultaneous photochemical initiation and online spectrophotometric monitoring of the reaction using independently controlled excitation and detection lamps. The system consists of a CCD spectrophotometer, a thermostated sample holder, two light sources, and standard 1.00 × 1.00 cm (or possibly smaller) fluorescence cuvettes, all coupled with fiber optic cables. The device can be used as a photoreactor, a diode-array spectrophotometer and also as a spectrofluorimeter. The reactor can be used in flow-through operation modes. Performance tests of the instrument are reported here with a number of known photochemical systems.

Hydrogen Isotope Exchange of Chlorinated Ethylenes in Aqueous Solution: Possibly a Termolecular Liquid Phase Reaction.

This work reports an experimental study of the hydrogen/deuterium exchange in the basic aqueous solutions of trichloroethylene, trans-1,2-dichloroethylene, and cis-1,2-dichloroethylene using (1)H NMR as a monitoring method. 1,1-Dichlorethylene was also investigated but found not to exchange hydrogen isotopes with water. The kinetics of isotope exchange features two different pathways, the first is first order with respect to hydroxide ion, whereas the second is second order. The first pathway is interpreted as a straightforward bimolecular reaction between chloroethylene and hydroxide ion, which leads to the deprotonation of chloroethylene. The second pathway involves a transition state with the association of one molecule of the chloroethylene and two hydroxide ions. It is shown that the second pathway could involve the formation of a precursor complex composed of one chloroethylene molecule and one hydroxide ion, but a direct termolecular elementary reaction is also feasible, which is shown by deriving a theoretical highest limit for the rate constants of termolecular reactions in solution.

The autocatalytic step is an integral part of the hydrogenase cycle.

We earlier proved the involvement of an autocatalytic step in the oxidation of H(2) by HynSL hydrogenase from Thiocapsa roseopersicina, and demonstrated that two enzyme forms interact in this step. Using a modified thin-layer reaction chamber which permits quantitative analysis of the concentration of the reaction product (reduced benzyl viologen) in the reaction volume during the oxidation of H(2), we now show that the steady-state concentration of the product displays a strong enzyme concentration dependence. This experimental fact can be explained only if the previously detected autocatalytic step occurs inside the catalytic enzyme-cycle and not in the enzyme activation process. Consequently, both interacting enzyme forms should participate in the catalytic cycle of the enzyme. As far as we are aware, this is the first experimental observation of such a phenomenon resulting in an apparent inhibition of the enzyme. It is additionally concluded that the interaction of the two enzyme forms should result in a conformational change in the enzyme-substrate form. This scheme is very similar to that of prion reactions. Since merely a few molecules are involved at some point of the reaction, this process is entirely stochastic in nature. We have therefore developed a stochastic calculation method, calculations with which lent support to the conclusion drawn from the experiment.

Detailed kinetics and mechanism of the oxidation of thiocyanate ion (SCN-) by peroxomonosulfate ion (HSO5(-)). Formation and subsequent oxidation of hypothiocyanite ion (OSCN-).

The haloperoxidase-catalyzed in vivo oxidation of thiocyanate ion (SCN(-)) by H(2)O(2) is important for generation of the antimicrobial hypothiocyanite ion (OSCN(-)), which is also susceptible to oxidation by strong in vivo oxidizing agents (i.e., H(2)O(2), OCl(-), OBr(-)). We report a detailed mechanistic investigation on the multistep oxidation of excess SCN(-) with peroxomonosulfate ion (HSO(5)(-) in the form of Oxone) in the range from pH 6.5 to 13.5. OSCN(-) was detected to be the intermediate of this reaction under the above conditions, and a kinetic model is proposed. Furthermore, by kinetic separation of the consecutive reaction steps, the rate constant of the direct oxidation of OSCN(-) by HSO(5)(-) was determined: k(2) = (1.6 ± 0.1) × 10(2) M(-1) s(-1) at pH 13.5 and k(2)(H) = (3.3 ± 0.1) × 10(3) M(-1) s(-1) at pH 6.89. A critical evaluation of the estimated activation parameters of the elementary steps revealed that the oxidations of SCN(-) as well as the consecutive OSCN(-) by HSO(5)(-) are more likely to proceed via 2e(-)-transfer steps rather than 1e(-) transfer.

Stochastic mapping of first order reaction networks: a systematic comparison of the stochastic and deterministic kinetic approaches.

Stochastic maps are developed and used for first order reaction networks to decide whether the deterministic kinetic approach is appropriate for a certain evaluation problem or the use of the computationally more demanding stochastic approach is inevitable. On these maps, the decision between the two approaches is based on the standard deviation of the expectation of detected variables: when the relative standard deviation is larger than 1%, the use of the stochastic method is necessary. Four different systems are considered as examples: the irreversible first order reaction, the reversible first order reaction, two consecutive irreversible first order reactions, and the unidirectional triangle reaction. Experimental examples are used to illustrate the practical use of the theoretical results. It is shown that the maps do not only depend on particle numbers, but the influence of parameters such as time, rate constants, and the identity of the detected target variable is also an important factor.

Stochastic mapping of the Michaelis-Menten mechanism.

The Michaelis-Menten mechanism is an extremely important tool for understanding enzyme-catalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.

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.

Central role of phenanthroline mono-N-oxide in the decomposition reactions of tris(1,10-phenanthroline)iron(II) and -iron(III) complexes.

1,10-Phenanthroline mono-N-oxide (phenO) is a product of the decomposition of tris(1,10-phenanthroline)iron(III), Fe(phen)(3)(3+), and has a slight autocatalytic effect on the overall reaction. The mechanism is proposed to involve Fe(phen)(3)(4+) as a minor intermediate. The addition of phenO significantly influences the kinetic features of the decomposition of Fe(phen)(3)(3+) and the oxidation of Fe(phen)(3)(2+) by HSO(5)(-). The autocatalytic decomposition explains the difficulties in the preparation of Fe(phen)(3)(3+) and may contribute to exotic kinetic phenomena studied using Fe(phen)(3)(3+)/Fe(phen)(3)(3+) as a supposedly innocent indicator.

Thermodynamic, electrochemical, high-pressure kinetic, and mechanistic studies of the formation of oxo Fe(IV)-TAML species in water.

Stopped-flow kinetic studies of the oxidation of Fe(III)-TAML catalysts, [ F e{1,2-X(2)C(6)H(2)-4,5-( NCOCMe(2) NCO)(2)CMe(2)}(OH(2))](-) (1), by t-BuOOH and H(2)O(2) in water affording Fe(IV) species has helped to clarify the mechanism of the interaction of 1 with primary oxidants. The data collected for substituted Fe(III)-TAMLs at pH 6.0-13.8 and 17-45 °C has confirmed that the reaction is first order both in 1 and in peroxides. Bell-shaped pH profiles of the effective second-order rate constants k(I) have maximum values in the pH range of 10.5-12.5 depending on the nature of 1 and the selected peroxide. The "acidic" part is governed by the deprotonation of the diaqua form of 1 and therefore electron-withdrawing groups move the lower pH limit of the reactivity toward neutral pH, although the rate constants k(I) do not change much. The dissection of k(I) into individual intrinsic rate constants k(1) ([FeL(OH(2))(2)](-) + ROOH), k(2) ([FeL(OH(2))OH)](2-) + ROOH), k(3) ([FeL(OH(2))(2)](-) + ROO(-)), and k(4) ([FeL(OH(2))OH)](2-) + ROO(-)) provides a model for understanding the bell-shaped pH-profiles. Analysis of the pressure and substituent effects on the reaction kinetics suggest that the k(2) pathway is (i) more probable than the kinetically indistinguishable k(3) pathway, and (ii) presumably mechanistically similar to the induced cleavage of the peroxide O-O bond postulated for cytochrome P450 enzymes. The redox titration of 1 by Ir(IV) and electrochemical data suggest that under basic conditions the reduction potential for the half-reaction [Fe(IV)L(=O)(OH(2))](2-) + e(-) + H(2)O → [Fe(III)L(OH)(OH(2))](2-) + OH(-) is close to 0.87 V (vs NHE).

Open system approaches in deterministic models of the emergence of homochirality.

Three different general strategies are proposed for kinetic models of the emergence of homochirality in open systems: flow-through reactors, photochemical energy input, and chemical energy input from a sacrificial reagent. Using a simple, second-order chiral autocatalytic core model, it is shown that all these scenarios lead to similar mathematical description despite the fundamentally different chemical background and practically complete homochirality is reached in all of these cases. It is also argued that the photochemical energy input scenario might not be compatible with a sunlight-driven natural process.

Stochastic kinetic analysis of the Frank model. Stochastic approach to flow-through reactors.

The continuous time discrete state stochastic kinetic approach and its extension to flow-through reactors was used to study a straightforward modification of the Frank model to interpret absolute asymmetric synthesis, which is impossible using deterministic approaches. Computational methods for calculating multidimensional probability distributions and expectations for enantiomeric excess were developed. The results showed that narrow focus on the conventionally defined enantiomeric excess could lead to misleading conclusions and the yield-adjusted enantiomeric excess is often more useful. Closed systems proved to be more favorable for the formation of high enantiomeric excesses than flow-through reactors and the importance of mutual antagonism can also be questioned in the original Frank model. It was also shown that a flow-through reactor with a relatively small number of molecules predicts the behavior of much larger systems well.

One- versus two-electron oxidation with peroxomonosulfate ion: reactions with iron(II), vanadium(IV), halide ions, and photoreaction with cerium(III).

The kinetics of the redox reactions of the peroxomonosulfate ion (HSO(5)(-)) with iron(II), vanadium(IV), cerium(III), chloride, bromide, and iodide ions were studied. Cerium(III) is only oxidized upon illumination by UV light and cerium(IV) is produced in a photoreaction with a quantum yield of 0.33 +/- 0.03. Iron(II) and vanadium(IV) are most probably oxidized through one-electron transfer producing sulfate ion radicals as intermediates. The halide ions are oxidized in a formally two-electron process, which most likely includes oxygen-atom transfer. Comparison with literature data suggests that the activation entropies might be used as indicators distinguishing between heterolytic and homolytic cleavage of the peroxo bond in the redox reactions of HSO(5)(-).

Attaining control by design over the hydrolytic stability of Fe-TAML oxidation catalysts.

The iron(III) complexes of tetra amidato macrocyclic ligands (TAMLs) ([Fe{1-X1-2-X2C6H2-4,5-(NCOCMe2NCO)2CR2}(OH2)]- , 1: X1 = X2 = H, R2 = Me2 (a), R2 = (CH2)2 (b); X1 = X2 = Cl, R2 = F2 (c), etc.), which the proton is known to demetalate at pH < 3, are also subject to catalyzed demetalation by Brønsted acid buffer components at pH 4-9 such as H2PO4-, HSO3-, and CH3CO2H, HO2CCH2CO2-. Buffers based on pyridine (py) and tris(hydroxymethyl)aminomethane (TRIS) are catalytically inactive. Where reactions proceed, the products are demetalated TAMLs and iron species of variable composition. Pseudo-first-order rate constants for the demetalation (kobs) are linear functions of the acid concentrations, and the effective second-order rate constants k1,eff have a hyperbolic dependence on [H+] (k1,eff = a1[H+]/(b1+[H+]). The rate of demetalation of 1a in H2PO4-/HPO42- buffer is appreciable, but the kobs values for 1b and 1c are immeasurably low, showing that the rates are strongly affected by the CR2 or "tail" fragments, which are known to potently affect the TAML basicity. The reactivities of 1 depend insignificantly on the aromatic ring or "head" group of 1. The proposed mechanism involves precoordination of the acidic buffer species followed by hydrolysis. The demetalating abilities of buffer species depend on their structures and acidities. Thus, although pyridine-2-carboxylic (picolinic) acid catalyzes the demetalation, its 3- and 4-isomers (nicotinic and isonicotininc acids) are inactive. The difference is rationalized to result from the ability that only coordinated picolinic acid has to deliver a proton to an amidato nitrogen in an intramolecular manner. The reaction order in picolinic acid equals one for 1a and two for 1b. For 1b, "inactive" pyridine and nicotinic acid speed up the demetalation in the presence of picolinic acid, suggesting that the second order arises from the axial binding of two pyridine molecules, one of which must be picolinic acid. The binding of pyridine- and imidazole-type ligands was confirmed by UV/vis equilibrium measurements and X-ray crystallography. The implications of these mechanistic findings for designing superior Fe-TAML oxidation catalysts and catalyst formulations are discussed using the results of DFT calculations.

Inactivation of urease by catechol: Kinetics and structure.

Urease is a Ni(II)-containing enzyme that catalyzes the hydrolysis of urea to yield ammonia and carbamate at a rate 1015 times higher than the uncatalyzed reaction. Urease is a virulence factor of several human pathogens, in addition to decreasing the efficiency of soil organic nitrogen fertilization. Therefore, efficient urease inhibitors are actively sought. In this study, we describe a molecular characterization of the interaction between urease from Sporosarcina pasteurii (SPU) and Canavalia ensiformis (jack bean, JBU) with catechol, a model polyphenol. In particular, catechol irreversibly inactivates both SPU and JBU with a complex radical-based autocatalytic multistep mechanism. The crystal structure of the SPU-catechol complex, determined at 1.50Å resolution, reveals the structural details of the enzyme inhibition.