Reactant Density Research Articles

On the use of isovalued surfaces to determine molecule shape and reaction pathways

Novel insights into local molecule structure and reactivity can be gained from viewing isovalued surfaces of the molecular electron density, electrostatic potential and molecular orbitals rendered as colored, 3-D objects. For example, drawing positive and negative electrostatic isopotential surfaces partitions the molecule into regions subject to nucleophilic or electrophilic attack. Similarly, coloring isodensity surfaces to indicate the magnitude of the gradient of the electron density maps the molecule surface into regions of high and low electronegativity. A basic understanding of reaction mechanisms can also come from viewing and manipulating isovalued surfaces. A theory of molecular interactions, based upon second-order perturbation theory, provides for the decomposition of the intermolecular interaction energy into steric, electrostatic and orbital interactions. Color figures illustrate the docking of reactant molecular densities, electrostatic potentials and orbitals on low-energy pathways. The figures are used to visualize the steric, electrostatic and orbital contributions to molecular interaction energy. The visualization not only identifies low-energy reaction pathways, but it frequently reveals local interactions which determine the magnitude of the total interaction energy. Similar insight is not easily obtained by simple evaluation of the total interaction energy. Approximate transition states, built from structures along low-energy approach pathways, are excellent starting points for transition state searches.

A comment on mathematical expressions used in solid state reaction kinetics studies by thermal analysis

Computer calculations pertaining to the reaction kinetics analyses of simulated thermoanalytical data, generated under non-isothermal conditions, have been performed. Results obtained by using the two forms of the differential and integral equations descriptive of three different models of rate-controlled solid state reactions: phase boundary movement, nucleation-growth and three-dimensional diffusion, have been examined and compared. Calculations have also been performed to examine the correctness of employing the simple diffusion model equations to analyze data generated by taking into consideration differences in the density of reactant and product. For all models studied and compared, the activation energies are the same, but the pre-exponential factors differ slightly. They can be interconverted by the use of an appropriate multiplicative constant.

Boron monohydride reaction kinetics studied with a high-temperature reactor

The rate coefficients of BH radical reactions with O{sub 2}, CH{sub 4}, C{sub 3}H{sub 8}, C{sub 2}H{sub 4}, NO, and H{sub 2}O were determined over the temperature range 298-750 K in a high-temperature reactor. The BH radicals were generated by the photolysis of BH{sub 3}CO at 193 nm and monitored by laser-induced fluorescence. The absolute bimolecular rate coefficients were obtained from measurement of the BH chemical lifetime as a function of reactant number density. For the reaction of BH with O{sub 2}, a fit of the data to the standard Arrhenius expression k(T) = A exp(-E{sub a}/RT) yielded a preexponential factor of (4.9 {plus minus} 0.6) {times} 10{sup {minus}11} cm{sup 3}/s and an activation energy of 2.4 {plus minus}0.1 kcal/mol over the range 298-750 K. A rate coefficient of (1.9 {plus minus} 0.2) {times} 10{sup {minus}14} cm{sup 3}/s was found for the reaction of BH with CH{sub 4} at 675 K.

Nonlinearity and irreversibility in the theory of the solvent effect of proton transfer dynamics. II. Dissipative system

The quantum-statistical theory of the dynamics of proton transfer in solvated H-bond complexes is formulated. The theory takes into account a H-bond complex interaction with an environmental fast electronic polarisation as well as the coupling to the environment slow degrees of freedom that are connected with vibrational-rotational motion. The equation of motion for a reduced density matrix is derived in the form of a nonlinear generalised master equation. For the dynamics of the proton transfer in a symmetric double-well potential, the kinetic equation for the reactant state probability density has also been derived and solved. Results for different environments and temperatures are presented.

Steady-State Density of Reactants in Diffusion-Limited Reaction A+B->0 with Source

Steady-State Density of Reactants in Diffusion-Limited Reaction A+B->0 with Source

Diffusion-Limited Reaction A + B -> 0 with Source in d Dimensions: Segregation and Density of Reactants

Diffusion-Limited Reaction A + B -> 0 with Source in d Dimensions: Segregation and Density of Reactants

Dynamics and Absolute Cross Sections of Some Hot Hydrogen Atom Reactions

AbstractThe dynamics of chemical reactions with high threshold energies is studied by combining hot atom production by laser photolysis and fast and state selective product detection by laser induced fluorescence. — The nascent OH rotational, vibrational and fine structure (λ‐doublet and spin‐doublet) state distributions produced in the reactions have been measured at collision energies up to 240 kJ/mol (C.M.‐system) with hot H atoms from the Excimer laser photolysis of HJ, and HBr at 193 nm and 248 nm. Absolute reaction cross sections have been obtained by measuring reactant and product densities at short times. Polarization experiments with photolysis‐ and probelaser polarized parallel and perpendicular to each other are performed. — For the reaction H + O2, the experimental results are compared with extensive trajectory calculations on an ab initio potential surface (Melius, Blint 1979).

H+H2O reaction dynamics: state distribution for the OH product

A method has been developed to study the dynamics of high barrier reactions by combining hot-atom production by laser photolysis and fast-product detection by laser induced fluorescence. The nascent OH rotational, vibrational and fine structure state distributions produced in the endothermic reaction\(H + H_2 O \to \underline {OH(K,\upsilon ,f)} + H_2\) have been measured with hot hydrogen atoms from the photodissociation of HBr at 193 nm. OH rotational excitation is low and corresponds to a partitioning of only around 3% of the total reaction energy to OH rotation. OH could only be observed in the vibrational ground state, i.e.σ(v=1)/σ(v=0)≦0.1. The OH spin doublets are produced statistically, but the partitioning in the λ-doublets is very non-statistical with a strong preference for the π+-component (σ(π+)/σ(π−)=3.2±1.0) demonstrating the exit channel of the reaction to be preferentially planar. By measuring reactant and product densities at short times, an absolute total cross-section of 0.24±0.1[A2] has been obtained.

Hot atom-laser induced fluorescence experiments on the reaction of H(2S) with O2

A method has been developed to study the dynamics of reactions with substantial threshold energies by combining hot atom production by laser photolysis and fast product detection by laser induced fluorescence. The nascent OH rotational, vibrational, and fine structure state distributions produced in the endothermic reaction H+O2→OH(K,v, f )+O have been measured with hot hydrogen atoms from the photodissociation of HBr at 193 nm. OH rotational excitation is high and corresponds to the phase space statistical distribution over the measured range of rotational states. Also OH vibrational excitation is substantial. The OH spin doublets are produced statistically, but the partitioning in the λ doublets is very nonstatistical with a strong preference for the π+ component demonstrating the reaction to occur essentially in a plane at high collision energies. By measuring reactant and product densities at short times, an absolute total cross section of 0.42±0.40.2 (Å2) has been obtained.

Study of the mechanism of macroradical reactions in solid polymers: 1. Molecular aspects of reactivity and activation energy model of reactions

A short survey of the problems of post-destruction chemistry is presented from the stand-point of the kinetics and mechanisms of the reactions of macroradicals in solid polymers. Two fundamental hypotheses of mechanism of macroradical decay are discussed in more detail. The philosophy of interpretation of kinetic data is then outlined on the level of activation energy in the terms of a simple kinetic model of decay. In the case of general mechanism of free valence migration, it consists of the physical part which is related to molecular mobility of reactants up to their contact and of the chemical parts which are concerned with redistribution of electron density of reactants on contact. A procedure for calculating the energy barriers of conformational motion in the amorphous phase of a polymer is proposed. Particular contributions are discussed from the molecular point of view in conforming to present knowledge of physical and chemical processes occurring in polymers.

Boron atom reactions. II. Rate constants with O2, SO2, CO2, and N2O

The gas phase reactions of atomic boron with O2, SO2, CO2, and N2O have been studied using a new flow tube apparatus. Boron atoms were produced in a microwave discharge of a 0.02% mixture of diborane in argon. The bimolecular rate constants at 300 °K were obtained by measuring the density of boron down the flow tube as a function of reactant density. The rate constants for the O2, SO2, CO2, and N2O reactions are, in units of cm3 molecule−1 sec−1, 4.6±1.8×10−11, 1.1±0.4×10−10, 7.0±2.8×10−14, and 2.1±0.8×10−14, respectively. These results are compared with the rates measured for the reactions of the group IIA and IVA atoms. The patterns observed in the data are noted and a possible mechanism is discussed.

Zur partialladung adsorbierter spezies der ti-amalgam/ti +-reaktion

The following paper reports on the partial charge of adsorbed species of the T1-amalgam/T1 +-reaction. l- and f-coefficients were determined in a broad potential range and at low reactant concentrations and adsorption densities by impedance measurements. The method of evaluation is presented in detail, including a discussion of the relation of (non-equilibrium) partial charge transfer model to Gibbs adsorption thermodynamics.

Molecular geometry, bond energy and reactivity of conjugated hydrocarbons IV fulvenes

The LCAO-MO-SCF-PPP (π + σ) method developed previously a–c is found to depend fundamentally on the valence state sp 2 carbon ionization potential, and this dependence is discussed. The method is then applied to the fulvenes, dibenzofulvenes, and heptafulvenes, and the calculated bond lengths are analysed systematically in terms of substituent effect, π-electron density distribution, dipolar character and molecular stability. The reactivities of the fulvenes are related to the polarity of the exocyclic double bond. Six reactions of the fulvenes are discussed. Reaction sites are predicted using the SCF π-electron densities of reactants and the calculated energies of possible products. Good agreements are obtained. An Analysis of Component Stabilization is developed to estimate the contribution of composite structural units to the total stabilization as measured by the Empirical Resonance Energy. The Heats of Hydrogenation are calculated in three cross-conjugated fulvenes. Annelation in these 5- and 7-membered ring compounds is found to result in the loss of fulvenic character.

On the analysis of linear pyrolysis experiments

Linear pyrolysis experimental data have been used as surface boundary conditions in the analytical treatment of solid propellant combustion problems. The surface boundary conditions required for the analysis are functional relationships between normal regression velocity, gaseous reactant density, total pressure, temperature, and possibly derivatives of these quantities as well, evaluated at the interface between condensed and gaseous phases during combustion. Available experimental data indicates that a relation based upon equilibrium conditions prevailing at the interface is not generally valid. There are available for many substances, however, hot-plate linear pyrolysis data which give an explicit relation between regression velocity of the condensed phase and a measured hot-plate temperature. This hot-plate temperature has been assumed to be also the temperature at the interface. However, this assumption is thought in some cases to be questionable. In addition, the use of such a rate law in combustion analysis would imply that the total pressure and the gascous reactant partial pressures or densities, which are greatly different for the pyrolysis test as compared to the combustion, have a negligible effect on the rate. This implication again is questionable. The present paper seeks to answer in part these questions on the validity of using linear pyrolysis data. A one-dimensional hot-plate linear pyrolysis experiment is proposed which uses a porous heated plate in place of the present impervious plate. The proposed experiment, having simpler fluid dynamics than present hot-plate experiments, is capable of a reasonably precise analytical description. The analysis is carried out for a general case and is then specialized to simple and chainlike surface gasification processes. Conditions are developed to determine whether the surface process is either a rate process or is one of near-equilibrium. A description is presented of the possible use of data from the proposed pyrolysis experiments to compute the accommodation coefficient and the vacuum sublimation rate as functions of surface temperature. With this information, the surface boundary condition for a given material will then be specified. The pyrolysis rate of potassium chloride is calculated as an example of the use of the derived formulas. If fluid dynamic effects are not too important in the present experiments, and in some respects it is estimated that they are not, interpretation from the results of this analysis serves present pyrolysis data as well. Interpretations are carried out for a number of compounds which have interest in propellant combustion studies. From published data on ammonium perchlorate, for example, revised values are estimated for the heat of sublimation, for the activation energy in linear pyrolysis, and for the difference between the hot-plate temperature and the surface temperature in linear pyrolysis.

Equilibrium of the CO2-NH3-Urea-H2O System under High Temperature and Pressure. I. Equilibrium Pressure of Reaction in Urea-Synthesis from Ammonia and Carbon Dioxide

Abstract (1) In the study of the equilibrium pressure of the CO2-NH3-Urea-H2O system, it was experimentally found that the equilibrium pressure of the system is a function of loading, density of reactants in the reaction vessel at a given temperature. (2) The experimental equations that show the relation between temperature and equilibrium pressure were studied at various loading densities, under conditions that loading mol ratio of carbon dioxide to ammonia was one by two, and at the temperature range 130° to 170°. (3) It was verified that the diversity of the equilibrium pressure of the system is reasonable.

AN INVESTIGATION OF THE HYDROGEN-CHLORIDE-PROPYLENE REACTION IN THE REGION OF THE CRITICAL TEMPERATURE

The reaction between hydrogen chloride and propylene has been studied in the gaseous state above the critical temperature and in the liquid state just below the critical temperature. Pressures were used such that the density of the gaseous mixtures could be made as great as the density of the liquid mixture at some temperature.The rate of reaction above the critical temperature increases slowly with increasing pressure until a certain critical density is attained, after which the rate increases rapidly. In the liquid state the reaction has a positive temperature coefficient except for a 25° temperature range just below the critical temperature. In this region there is a rapid decrease in density of the medium with rise in temperature and a negative temperature coefficient occurs.The density of the liquid reactants at a number of temperatures just below the critical temperature (here defined as the temperature where the visible meniscus disappears) has been reproduced above the critical temperature for a small temperature range. The reaction velocity data obtained under these conditions show a minimum in passing through the critical temperature region.The above results have been interpreted on the basis of a "structure" characteristic of the liquid state which favors higher reaction velocity and which may exist above the critical temperature at sufficiently high densities.