Interaction kinetics of peroxides and organic sulphides in atactic polypropylene

Kinetics of the reactions between benzoyl peroxide and sulphides (dilaurylthyodipropionate and dibenzyl sulphide), of the reaction between diphenylethyl hydroperoxide and dibenzylsulphide in atactic polypropylene and of the reaction of benzoyl peroxide with dibenzyl sulphide in polyisobutylene have been studied. The stoichiometry of the reactions was determined and the dependence of the rate constants on the initial concentration of reactant was established. At low reactant concentrations, the rate constants decrease and at high concentration increase with increasing concentration. In model low-molecular-weight hydrocarbon, the reaction rate constants do not change with reactant concentrations. The reaction mechanism is discussed. It is based on specific features of the dissolution of low-molecular additives in polymer.     

H2O(HOD) + Cl→HCl(DCl) + OH(OD)反应动态学的理论研究

用从头算方法, 获得了H2O + Cl→HCl + OH(R1), HOD +Cl→DCl + OH(R2), HOD + Cl→HCl + OD(R3)反应的内禀反应坐标(IRC)。根据传统过渡态、变分过渡态理论及相应的隧道效应校正, 计算了反应的速率常数。对已有实验速率常数值的R1反应, 我们计算的结果和实验一致。根据Truhlar的振动选态公式, 分别讨论了激发HOD中OH, OD振动模式对反应速率的影响,得到激发HOD中的OH振动模式将有利于产物OD + HCl生成, 和实验的结论相一致。     

Quantum Dynamics of Li+HF/DF Reaction Investigated by a State-to-State Time-dependent Wave Packet Approach

Using the reactant coordinate based time-dependent wave packet method, on the APW potential energy surface, the differential and integral cross sections of the Li+DF/HF(v=0, j=0, 1) reactions were calculated over the collision energy range from the threshold to 0.25 eV. The initial state-specified reaction rate constants of the title reaction were also calculated. The results indicate that, compared with the Li+DF reaction, the product LiF of Li+HF reaction is a little more rotationally excited but essentially similar. The initial rotational excitation from j=0 to 1 has little effect on the Li+DF reaction. However, the rotational excitation of DF does result in a little more rotationally excited product LiF. The different cross section of both reactions is forward biased in the studied collision energy range, especially at relatively high collision energy. The resonances in the Li+HF reaction may be identifiable as the oscillations in the product ro-vibrational state-resolved integral cross sections and backward scattering as a function of collusion energy. For the Li+HF reaction, the rate constant is not sensitive to the temperature and almost has no change in the temperature range considered. For the Li+DF reaction, the rate constant increase by a factor of about 10 in the temperature range of 100?300 K. Brief comparison for the total reaction probabilities and integral cross section of the Li+HF reaction has been carried out between ours and the values reported previously. The agreement is good, and the difference should come from the better convergence of our present calculations.     

以交叉分子束及时间切片离子速度成像法研究产物成对相关讯息

A novel experimental technique has been developed to measure the attributes of product pair correlation of bimolecular reactions under the crossed molecular beam condition. The first system that we picked is F + CD4/CHD3 / CH4 reactions. By combining a crossed molecular beam method with a time-sliced ion velocity imaging technique,the product state-resolved pair-correlated differential cross sections were revealed directly from the measurements. Several facets of the product pair correlation have been explored. The dependence on the collisional energy has been elucidated. The pair-correlated angular distributions show strong dependences on the HF/DF vibrational quantum numbers,and weaker yet not negligible dependences on the methyl radical vibrational quantum numbers. For the F + CH4 reaction at collisional energies close to the reaction threshold,the first experimental evidences of a reactive resonance in a polyatomic reaction were discovered. The product pair-correlated information helps us to unravel the complexity of polyatomic reactions and offers the important link between A + BC type of reactions and more general polyatomic reactions.     

Communication: Experimental and theoretical investigations of the effects of the reactant bending excitations in the F + CHD3 reaction

The effects of the reactant bending excitations in the F+CHD(3) reaction are investigated by crossed molecular beam experiments and quasiclassical trajectory (QCT) calculations using a high-quality ab initio potential energy surface. The collision energy (E(c)) dependence of the cross sections of the F+CHD(3)(v(b)=0,1) reactions for the correlated product pairs HF(v('))+CD(3)(v(2)=0,1) and DF(v('))+CHD(2)(v(4)=0,1) is obtained. Both experiment and theory show that the bending excitation activates the reaction at low E(c) and begins to inactivate at higher E(c). The experimental F+CHD(3)(v(b)=1) excitation functions display surprising peak features, especially for the HF(v(')=3)+CD(3)(v(2)=0,1) channels, indicating reactive resonances (quantum effects), which cannot be captured by quasiclassical calculations. The reactant state-specific QCT calculations predict that the v(5)(e) bending mode excitation is the most efficient to drive the reaction and the v(6)(e) and v(5)(e) modes enhance the DF and HF channels, respectively.     

Reversed-phase ion-pair liquid chromatographic method for determination of reaction equilibria involving ionic species: exemplification of the method using ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions

A reversed-phase ion-pair liquid chromatographic method is presented for the determination of reaction equilibria involving ionic species of the same charge sign as reactant and product compounds. It has been demonstrated that ion-exchange chromatography or reversed-phase ion-pair chromatography is a useful tool for the determination of equilibrium constants of chemical reactions involving ionic species such as metal complexation reactions. Previous work with these methods has been based on the assumption that the limiting retention factors of the reactant and product species are constant independent of concentration of the chemical species (X) in the mobile phase, which reacts with the analyte compound. However, when all the reactant and product species are ions of the same charge sign as that of the species X, it is virtually impossible to apply these methods to the equilibrium constant determination because the retention factors of both the reactant and product species may depend on the concentration of X. In this study, an alternative approach was developed that estimates the limiting retention factors of ionic species from the dependence of the retention factor on the ionic strength of the mobile phase. Ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions were used as model reactions to test this method. The equilibrium constants determined by this method are in good agreement with those obtained by a UV-visible spectrophotometric method.     

Kinetics of the reaction of the heaviest hydrogen atom with H2, the 4Heμ + H2 → 4HeμH + H reaction: experiments, accurate quantal calculations, and variational transition state theory, including kinetic isotope effects for a factor of 36.1 in isotopic mass

The neutral muonic helium atom (4)Heμ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (μSR) measurements of the chemical reaction rate constant of (4)Heμ with molecular hydrogen, (4)Heμ + H(2) → (4)HeμH + H, at temperatures of 295.5, 405, and 500 K, as well as a μSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, k(Heμ), are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born-Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born-Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible systematic error, but at 295.5 K the quantum calculations for k(Heμ) are below the experimental value by 2.1 times the experimental uncertainty estimates. Possible reasons for this discrepancy are discussed. Variational transition state theory calculations with multidimensional tunneling have also been carried out for k(Heμ) on the BH surface, and they agree with the accurate QM rate constants to within 30% over a wider temperature range of 200-1000 K. Comparisons between theory and experiment are also presented for the rate constants for both the D + H(2) and Mu + H(2) reactions in a novel study of kinetic isotope effects for the H + H(2) reactions over a factor of 36.1 in isotopic mass of the atomic reactant.     

A simple method for analysis of consecutive reactions with a second order formation and a first order decay of an intermediate

A simple method is developed to evaluate rate constants from absorbance-time traces for a pair of consecutive reactions consisting of a second order formation and a first order decay of an intermediate. Initially, a first order profile is simulated utilizing the data near the end of the reaction. The difference between this simulated and observed profiles provides the absorbance-time data for the initial phase from which a second order rate constant is evaluated. These rate constants were used to simulate composite kinetic curves which were then compared with experimental curves. This method was used to test the reaction between cis-Pt(NH₃)₂(H₂O)₂ ²⁺ and a nonapeptide, ERFKCPCPT. The reaction proceeds through a cysteine coordinated intermediate formed in a second order process (first order with respect to each reactant). The intermediate is then converted to a product through a first order process, in which both cysteines are coordinated to platinum(II).     

Ring opening of cyclohexane over ZSM-zeolites followed by reversed-flow gas chromatography

Summary Kinetic parameters for the ring opening of cyclohexane over modified ZSM-5 zeolites can be measured simultaneously under non-steady state conditions using reversed-flow gas chromatography. At relatively low temperatures, the main product detected and measured was propene. The mathematical relations used for the calculation of adsorption-desorption rate constants, surface reaction rate constants and adsorption equilibrium constants for the reactant cyclohexane are different from previously studied catalytic reactions, owing to the different experimental arrangement for feeding the catalytic bed. The diffusion bands obtained experimentally for reactant or product are described by the sum of two or three exponential functions of time, respectively. From the exponential coefficients of time and the pre-exponential factors, all determined by simple PC programs, the above kinetic parameters are calculated.     

Ring opening of cyclohexane over ZSM-zeolites followed by reversed-flow gas chromatography

Summary Kinetic parameters for the ring opening of cyclohexane over modified ZSM-5 zeolites can be measured simultaneously under non-steady state conditions using reversed-flow gas chromatography. At relatively low temperatures, the main product detected and measured was propene.The mathematical relations used for the calculation of adsorption-desorption rate constants, surface reaction rate constants and adsorption equilibrium constants for the reactant cyclohexane are different from previously studied catalytic reactions, owing to the different experimental arrangement for feeding the catalytic bed. The diffusion bands obtained experimentally for reactant or product are described by the sum of two or three exponential functions of time, respectively. From the exponential coefficients of time and the pre-exponential factors, all determined by simple PC programs, the above kinetic parameters are calculated.     

Reaction of a low‐molecular‐weight free radical with a flexible polymer chain: Kinetic studies on the OH + poly(N‐vinylpyrrolidone) model

This work addresses the issue of kinetics of diffusion‐controlled reactions of small radicals with macromolecules in solution. Attack of pulse‐generated hydroxyl radicals on poly(N‐vinylpyrrolidone)—PVP—chains of various molecular weight in water was used as the model reaction. Pulse radiolysis with spectrophotometric detection was applied to determine the rate constants by competition kinetics. The rate constant depends both on polymer concentration and on its molecular weight. In dilute solutions, a distinct dependence of the rate constant on the molecular weight is observed. In the studied range of molecular weight, the values of reaction radius, calculated using Smoluchowski equation on the basis of experimental kinetic data, are very close to the radius of gyration of polymer coils. We believe that radius of gyration, as an easily determined parameter, could possibly serve for predicting rate constants of diffusion‐controlled reactions of polymers with low‐molecular‐weight compounds in dilute solutions. With increasing polymer concentration and thus increasing spatial overlap of polymer coils the dependence of the rate constant on the molecular weight fades away, and the rate constant values increase with increasing concentration toward the value determined for low‐molecular‐weight model of PVP. Most steep increase approximately coincides with the hydrodynamic critical concentration of a given PVP sample, reflecting the change in reaction geometry from individual coils to a continuous matrix of interpenetrating chains. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 474–481, 2011     

The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

The rates of formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. This surprising result, never formally incorporated in elementary rate expressions over approximately one and a half centuries of quantitative chemical kinetics measurement and calculation is accepted axiomatically and leads to an outline of a theory for the form of the rate constant, in any one given substrate—here the vacuum state. A major deduction is that the long-standing definition of the rate constant for elementary reactions is not complete and is nonlinear, where previous works almost always implicitly refer to the zero density limit for strictly irreducible elementary reactions without any attending concatenation of side-reactions. This is shown directly from MD simulation, where for specially designed elementary reactions without any transition states, density dependence of reactants and products always feature, in contrast to current practice of writing rate equations. It is argued that the rate constant expression without reactant and product dependence is due to historical conventions used for strictly elementary reactions. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions under different state conditions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained under various approximations and conditions. Elementary relations for subspecies equilibria and its relation to the bulk activity coefficient are discussed. From one choice of reaction conditions, estimates of activity coefficients are given which are in at least semi-quantitative agreement with the data for non-reacting Lennard-Jones (LJ) particles for the atomic component. The theory developed is applied to ionic reactions where the standard Brönsted-Bjerrum rate equation and exceptions to this are rationalized.     

O(3P)+HBr(DBr)反应的含时量子散射计算

基于LEPS势能面, 用三维含时量子波包法对O(³P)+HBr(DBr)反应进行了准确的动力学计算. 计算的结果表明, 振动激发对这个反应是有效的, 而转动激发在某一能量范围内具有方位效应. 计算得到了该反应的速率常数和反应截面, 速率常数kO+HBr的计算值同实验值符合得很好. 通过对相应结果的对比, 可以发现这个反应具有比较明显的同位素效应.     

Termination rate constant in free-radical polymerization

The specific rate constant for the termination reaction between two flexible polymer molecules with active chain ends has been considered in relation to the segmental diffusion of chain ends in solution. The probability of reaction between two chain ends per unit time when the centers of gravity of two polymer molecules are at a distance of separation has been calculated by using the Smoluchowski equation and a Gaussian distribution of chain ends. The time during which two polymer molecules are in contact has also been calculated by using the diffusion equation and the potential energy function for intermolecular interaction. The rate constant may then be completely expressed as a complex function of the intramolecular linear expansion factor, molecular weight, and the frictional properties of the reacting polymers' segment. This expression predicts that the rate constant is inversely proportional to solvent viscosity, decreasing with increasing molecular weight to some extent, and is affected by the excluded volume effect and chain flexibility. The complete expression for the rate constant has been simplified and the result compared with experimental data. Close agreement is found between the calculated rate constants and those experimentally obtained.     

Dynamics of reactions between two closed-shell molecules

The crossed molecular beam technique has been utilized to investigate a large number of elementary reactions. However, most of the studied reactions involve atoms or radicals; reactions between two stable molecular reactants are, in fact, seldom studied with the crossed molecular beam method. In this perspective, reactions between two stable molecules are reviewed and discussed. With crossed molecular beams and vacuum UV photoionization, the nascent products have been unambiguously identified. Consistent pictures of the reaction paths have been constructed based on the experimental data and ab initio calculations. Furthermore, there are intriguing features about the reaction barriers. The F(2) + organosulfur reactions are barrierless, demonstrating the first examples of such interactions between two closed-shell reactants. The barrier of F(2) + alkene reaction decreases with more methyl substitution groups at the C=C double bond, yet the absolute barrier heights from experiment and theory disagree with each other by ~2 kcal mol(-1), leaving an issue to be resolved in the future.     

Multi-structural variational transition state theory: kinetics of the 1,5-hydrogen shift isomerization of the 1-butoxyl radical including all structures and torsional anharmonicity

We investigate the statistical thermodynamics and kinetics of the 1,5-hydrogen shift isomerization reaction of the 1-butoxyl radical and its reverse isomerization. The partition functions and thermodynamic functions (entropy, enthalpy, heat capacity, and Gibbs free energy) are calculated using the multi-structural torsional (MS-T) anharmonicity method including all structures for three species (reactant, product, and transition state) involved in the reaction. The calculated thermodynamic quantities have been compared to those estimated by the empirical group additivity (GA) method. The kinetics of the unimolecular isomerization reaction was investigated using multi-structural canonical variational transition state theory (MS-CVT) including both multiple-structure and torsional (MS-T) anharmonicity effects. In these calculations, multidimensional tunneling (MT) probabilities were evaluated by the small-curvature tunneling (SCT) approximation and compared to results obtained with the zero-curvature tunneling (ZCT) approximation. The high-pressure-limit rate constants for both the forward and reverse reactions are reported as calculated by MS-CVT/MT, where MT can be ZCT or SCT. Comparison with the rate constants obtained by the single-structural harmonic oscillator (SS-HO) approximation shows the importance of anharmonicity in the rate constants of these reactions, and the effect of multi-structural anharmonicity is found to be very large. Whereas the tunneling effect increases the rate constants, the MS-T anharmonicity decreases them at all temperatures. The two effects counteract each other at temperatures 385 K and 264 K for forward and reverse reactions, respectively, and tunneling dominates at lower temperatures while MS-T anharmonicity has a larger effect at higher temperatures. The multi-structural torsional anharmonicity effect reduces the final reverse reaction rate constants by a much larger factor than it does to the forward ones as a result of the existence of more low-energy structures of the product 4-hydroxy-1-butyl radical than the reactant 1-butoxyl radical. As a consequence there is also a very large effect on the equilibrium constant. The neglect of multi-structural anharmonicity will lead to large errors in the estimation of reverse reaction rate constants.     

Trace crossings in cyclic voltammetry and electrochemic electrochemical inducement of chemical reactions: Aromatic nucleophilic substitution

Crossing of anodic and cathodic traces is frequently observed on cyclic voltammograms featuring the electrochemical induction of a chemical reaction in the case where the product standard potential is positive to the reactant reduction potential. The theory of this phenomenon has been established in the contaxt of aromatic nucleophilic substitution. The reaction of potassium diethyl phosphite on 4-chlorobenzonitrile in liquid ammonia was investigated as an example illustrating this type of phenomenon and its interpretation. The simulation of the experimental voltammograms demonstrates the proposed mechanistic and kinetic model and allows the rate constants of the various steps to be determined. Much higher rate constants can thus been attained than by the standard application of electrochemical techniques (the gain may reach five or six orders of magnitude). A procedure is derived from these observations and then a rationalization for inducing chemical reactions with a very low electricity consumption as opposed to that which occurs when the electrode potential is settled at the level of the reactant wave.     

Correction for the Concentration Polarization for Simultaneous Reduction of Several Reactants: Platinum(II) Aquachloride Complexes

The reaction of electroreduction of platinum(II) aquachloride complexes on a negatively charged dropping mercury electrode is used to determine specific features of interpretation of experimental data in the case of parallel conversion of several forms of a reactant, connected with the manner of introducing a correction for the concentration polarization. The difference in the charges of species undergoing simultaneous reduction gives rise to ambiguity when analyzing kinetic data on the dependence of current on the supporting-electrolyte concentration at constant electrode charge. A new self-consistent technique for deducing model parameters (ratio between reactant discharge rate constants) is proposed.