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.

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.

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.

Kinetics of the autoxidation of sulfur(IV) co-catalyzed by peroxodisulfate and silver(I) ions.

The kinetics and mechanism of the reaction between dissolved oxygen and sulfur(iv) was studied in aqueous acidic medium using co-catalysts peroxodisulfate and silver(i) ions. The presence of both catalysts was required to observe measurable rates in the studied process. The reaction rate was determined through following the UV-absorption of hydrated sulfur dioxide, and the trends were determined as a function of pH, reactant and catalyst concentrations. Individual kinetic curves under conditions where dissolved oxygen was the limiting reagent were close to zeroth-order. A chain mechanism with four chain carriers, sulfite, sulfate, peroxomonosulfate ion radical and silver(ii) ion, is proposed to interpret all the kinetic and stoichiometric findings, and an explicit formula was obtained for the rate law. The role of the co-catalysts is to produce chain carriers, whereas silver(i) and silver(ii) ions also participate in chain propagation steps. Further supporting evidence for the proposed mechanism was gained in laser flash photolysis studies, which showed that sulfate ion radical reacts quite rapidly with silver(i) ion.

Aqueous photochemical reactions of chloride, bromide, and iodide ions in a diode-array spectrophotometer. Autoinhibition in the photolysis of iodide ions.

The aqueous photoreactions of three halide ions (chloride, bromide and iodide) were studied using a diode array spectrophotometer to drive and detect the process at the same time. The concentration and pH dependences of the halogen formation rates were studied in detail. The experimental data were interpreted by improving earlier models where the cage complex of a halogen atom and an electron has a central role. The triiodide ion was shown to exert a strong inhibiting effect on the reaction sequence leading to its own formation. An assumed chemical reaction between the triiodide ion and the cage complex interpreted the strong autoinhibition effect. It is shown that there is a real danger of unwanted interference from the photoreactions of halide ions when halide salts are used as supporting electrolytes in spectrophotometric experiments using a relatively high intensity UV light source.

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.

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.

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.

Detailed mechanism of the autoxidation of N-hydroxyurea catalyzed by a superoxide dismutase mimic Mn(III) porphyrin: formation of the nitrosylated Mn(II) porphyrin as an intermediate.

The in vitro autoxidation of N-hydroxyurea (HU) is catalyzed by Mn(III)TTEG-2-PyP(5+), a synthetic water soluble Mn(III) porphyrin which is also a potent mimic of the enzyme superoxide dismutase. The detailed mechanism of the reaction is deduced from kinetic studies under basic conditions mostly based on data measured at pH = 11.7 but also including some pH-dependent observations in the pH range 9-13. The major intermediates were identified by UV-vis spectroscopy and electrospray ionization mass spectrometry. The reaction starts with a fast axial coordination of HU to the metal center of Mn(III)TTEG-2-PyP(5+), which is followed by a ligand-to-metal electron transfer to get Mn(II)TTEG-2-PyP(4+) and the free radical derived from HU (HU˙). Nitric oxide (NO) and nitroxyl (HNO) are minor intermediates. The major pathway for the formation of the most significant intermediate, the {MnNO} complex of Mn(II)TTEG-2-PyP(4+), is the reaction of Mn(II)TTEG-2-PyP(4+) with NO. We have confirmed that the autoxidation of the intermediates opens alternative reaction channels, and the process finally yields NO(2)(-) and the initial Mn(III)TTEG-2-PyP(5+). The photochemical release of NO from the {MnNO} intermediate was also studied. Kinetic simulations were performed to validate the deduced rate constants. The investigated reaction has medical implications: the accelerated production of NO and HNO from HU may be utilized for therapeutic purposes.

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.

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.

Water exchange rates of water-soluble manganese(III) porphyrins of therapeutical potential.

The activation parameters and the rate constants of the water-exchange reactions of Mn(III)TE-2-PyP(5+) (meso-tetrakis(N-ethylpyridinium-2-yl)porphyrin) as cationic, Mn(III)TnHex-2-PyP(5+) (meso-tetrakis(N-n-hexylpyridinium-2-yl)porphyrin) as sterically shielded cationic, and Mn(III)TSPP(3-) (meso-tetrakis(4-sulfonatophenyl)porphyrin) as anionic manganese(iii) porphyrins were determined from the temperature dependence of (17)O NMR relaxation rates. The rate constants at 298 K were obtained as 4.12 x 10(6) s(-1), 5.73 x 10(6) s(-1), and 2.74 x 10(7) s(-1), respectively. On the basis of the determined entropies of activation, an interchange-dissociative mechanism (I(d)) was proposed for the cationic complexes (DeltaS(double dagger) = approximately 0 J mol(-1) K(-1)) whereas a limiting dissociative mechanism (D) was proposed for Mn(III)TSPP(3-) complex (DeltaS(double dagger) = +79 J mol(-1) K(-1)). The obtained water exchange rate of Mn(III)TSPP(3-) corresponded well to the previously assumed value used by Koenig et al. (S. H. Koenig, R. D. Brown and M. Spiller, Magn. Reson. Med., 1987, 4, 52-260) to simulate the (1)H NMRD curves, therefore the measured value supports the theory developed for explaining the anomalous relaxivity of Mn(III)TSPP(3-) complex. A magnitude of the obtained water-exchange rate constants further confirms the suggested inner sphere electron transfer mechanism for the reactions of the two positively charged Mn(iii) porphyrins with the various biologically important oxygen and nitrogen reactive species. Due to the high biological and clinical relevance of the reactions that occur at the metal site of the studied Mn(iii) porphyrins, the determination of water exchange rates advanced our insight into their efficacy and mechanism of action, and in turn should impact their further development for both diagnostic (imaging) and therapeutic purposes.

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.