Simple Collision Theory Research Articles

Reconsideration of the Simple Collision Theory Model

Reconsideration of the Simple Collision Theory Model

Theoretical modelling of the chemical reactivity of fresh biomass chars under non-catalytic conditions

This study developed a model for the chemical reactivity of fresh biomass chars, and built a calculation equation for the char gasification rate using simple gas-solid collision theory (SCT). The effects of pore breaks, pore collapse and thermal annealing on the char reactivity were considered in the modelling. Experimental tests for six acid-washed biomass chars were performed under a CO2 atmosphere and used a thermo-gravimetric analyzer (TGA) over the temperature range of 1073–1273 K. The results showed that the reactivity of fresh char could be predicted quantitatively by some characteristic properties of certain kind of biomass and their combined parameters. For the instability of the biomass char structure, the internal pore length and gasification temperature showed a good exponential relationship. Good agreement was achieved, and the applicability of the model was demonstrated by comparing the predicted results with experimental data.

Using molecular dynamics simulations with a ReaxFF reactive force field to develop a kinetic mechanism for ammonia borane oxidation

Ammonia borane is a hydrogen rich compound recently studied as a means for high density hydrogen storage. Ammonia borane also has the potential for increasing performance in a propulsion system when introduced as a fuel. The chemical kinetics of ammonia borane oxidation have been studied using molecular dynamics simulations performed with a ReaxFF reactive force field, which in turn, is based on ab initio data. This approach allows for the development of a continuum model of ammonia borane oxidation, which after refinement can be used to model fundamental experiments, without any prior experimental data. The results of molecular dynamics simulations elucidate the pertinent chemical pathways and intermediate species needed to define the elementary reactions of a simple chemical kinetic mechanism. These simulations show that the gas phase ammonia borane molecule first undergoes two hydrogen elimination steps. Subsequently, the H2 reacts with the O2 in the system, while the boron side of the remaining HNBH molecule is attacked by oxygen, eventually leading to the cleavage of the B–N bond and the formation of the equilibrium products H2O, HOBO, and N2. Density functional theory calculations were used to calculate unknown thermochemical properties, and simple collision theory was used to estimate reaction rate constants. The resulting continuum kinetic model was used to perform simple closed reactor, constant pressure and energy calculations in CHEMKIN, the results of which are consistent with the observations made at the atomistic level in the molecular dynamics simulations. This work demonstrates how a combination between ab initio calculations, molecular dynamics and thermodynamics equilibrium calculations can be employed to elucidate complex combustion reaction kinetics.

SCT reaction kinetics model and diffusion for p.c. combustion in TGA

AbstractRecently, the process of char burnout is extensively concerned. Global model used widely cannot predict the extent of char burnout at the later burning stage. For the need of predicting the burnout degree in industrial pulverized coal (p.c.) fired furnace by making use of the experimental data from such as thermogravimetry analysis (TGA) and drop tube furnace, based on the simple collision theory (SCT) of chemical reaction kinetics, the SCT model is educed. The p.c. combustion is considered as the results of strike and oxidation of oxygen molecules on the surface of p.c. particles, and the frequency of effective strike was determined by Boltzmann factor. Strike and oxidation occur on the oxygen accessible specific surface area (OASA). Chemical regime controlled is at temperature below 1200 K, and molecules diffusion regime controlled is at the temperature above 1600 K, at which OASA corresponds to the specific surface area with pore diameter more than 38 nm of p.c particles in coal‐fired boiler. The OASA of p.c. particles increases with the char burning, for the particles swells, shrinks and cracks. The burning rates calculated based on SCT model have shown good correspondence with experimental data reported. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd.

Comment on “Kinetics of the reactions of Cl atoms with 2-buten-1-ol, 2-methyl-2-propen-1-ol, and 3-methyl-2-buten-1-ol as a function of temperature” by Rodriguez et al. (J. Atmos. Chem. (2008) 59:187–197)

The Arrhenius expressions and the data plotted in Figure 2 of Rodriguez et al. 2008 give rate coefficients of approximately 2 × 10-8 cm3 molecule-1 s-1 at 255 K. Such values are approximately two orders of magnitude larger than expected from simple collision theory (Finlayson-Pitts and Pitts 1986). The rate coefficients reported at sub-ambient temperatures are substantially greater than the gas kinetic limit and are not physically plausible. The rate coefficients reported by Rodriguez et al. imply a long range attraction between the reactants which is not reasonable for reaction of neutral species such as chlorine atoms and unsaturated alcohols. We also note that the pre-exponential A factors (10-23-10-20) and activation energies (−15 kcal mol-1) are not physically plausible. We conclude that there are large systematic errors in the study by Rodriguez et al. (Atmos Chem 59:187–197, 2008).

Radiative Characteristics of N2 Second Positive Bands with Non-Boltzmann Rotational Population Distribution (Modeling Based upon Simple Collision Theory and Effect of Radiative Transition)

The characteristic intensity distribution in the N2 second positive bands observed in high-temperature air plasmas generated by a micro-air plasma-jet generator was reconstructed by the theoretical spectra with predissociation and non-Boltzmann rotational population distribution. In order to construct the precise theoretical spectra, collisional transition rate coefficient that was applicable at high temperatures was proposed based upon a simple collision theory. In addition, the effect of the radiative transition from C3Πu to B3Πg state was included in the master equation. The theoretical spectra with non-Boltzmann rotational population distribution calculated with such factors agreed very well with the experimental ones.

Evaluation of data in terms of two-dimensional random walk model: Interaction between NADH-cytochrome b5 reductase and cytochrome b5

Normally, bimolecular reactions are analyzed in terms of the Smoluchowski theory. However, when one attempts to generalize this analysis to cases where diffusion proceeds in two other than in three dimensions, one soon encounters severe conceptual difficulties. Although kinetic studies of membrane enzymes are generally difficult because the usual kinetic formalism refers to nonaggregated homogenous solutions, a major goal of our research is to define the molecular mechanism(s) by which alterations in membrane-bound substrate contents affect the enzyme activity in the same membrane. For that purpose, a simplified random-walk model was adopted in the present work. The enzyme reaction in the two-dimensional membrane could be calculated theoretically by applying the classical analysis of heat equation. As a result, the theoretical rate equation well accounting experimental findings was derived on the model of the liver microsomal NADH-cytochrome b5 reductase reaction. Furthermore, it was found that the modification of the simple rigid-sphere collision theory by including a term called the steric factor was not necessary in this derived equation.

Diffusion on a nanoparticle surface as revealed by electrochemical NMR.

Surface diffusion of chemisorbed CO (from MeOH electrochemisorption) on pure and Ru-modified nanoscale Pt electrocatalyst surfaces has been investigated by solid-state electrochemical NMR (EC-NMR) in the presence of supporting electrolyte. Temperature-dependent nuclear spin-spin and spin-lattice relaxation measurements enable the diffusion activation energy, E, to be deduced. It is shown that the activation energy E correlates with the steady state current for MeOH electro-oxidation. A simple two-dimensional collision theory model is proposed to explain this intriguing observation, which may provide new mechanistic insights into the promotion of CO-tolerance in Pt/Ru fuel cell catalysts.

Effect of Supercollisions on Energy Transfer in Mixtures of Bath Gases and Laser Excited Complex Molecules

Intensities and decay rates of delayed luminescence (DL) initiated by a pulse of N2 laser were employed to probe collisional relaxation of complex molecules (benzophenone, acetophenone) diluted with bath gases Ar, Kr, Xe, C2H4, SF6, C5H12. It was shown that vibrational relaxation can be interpreted in terms of two consecutive processes: vibration-vibration (V-V) and vibration-translation (V-T). The results clearly demonstrated that fast component of DL can be used to study V-V energy transfer. It was found that at relatively small internal energy the collisional efficiences of V-V process had the values typical for molecular processes in which supercollisions contribute. The average energies transferred per collision, (ΔE), well correlated with predictions of the simple ergodic collision theory of intermolecular energy transfer.

The Rate of Iron Sulfide Formation in the Solar Nebula

The kinetics and mechanism of the reaction H2S(g) + Fe(s)= FeS(s) + H2(g) was studied at temperatures and compositions relevant to the solar nebula. Fe foils were heated at 558–1173 K in H2S/H2gas mixtures (∼25 to ∼10,000 parts per million by volume (ppmv) H2S) at atmospheric pressure. Optical microscopy and X-ray diffraction show that the microstructures and preferred growth orientations of the Fe sulfide scales vary with temperature and H2S/H2ratio. Initially, compact, uniformly oriented scales grow on the Fe metal. As sulfidation proceeds, the scales crack and finer grained, randomly oriented crystals grow between the metal and the initial sulfide scale. The composition of the scales varies from Fe0.90S to FeS with temperature and H2S/H2ratio, in agreement with thermodynamic calculations. The weight gain and thickness change of the samples give nearly identical measures of the reaction progress. Sulfide layers formed in 25–100 ppmv H2S grow linearly with time. Iron sulfides formed in ∼1000 ppmv H2S originally grow linearly with time. Upon reaching a critical thickness growth follows parabolic kinetics. Iron sulfide formation in 10,000 ppmv H2S also follows parabolic kinetics. The linear rate equation for sulfidation of Fe grains (≤20 μm diameter) in the solar nebula isd(FeS)/dt=kfPH2S−krPH2(cm hour−1). The forward and reverse rate constants are (cm hour−1atm−1)kf= 5.6(±1.3)exp(−27950(±7280)/RT) andkr= 10.3(±1.0)exp(−92610(±350)/RT), respectively. The activation energies for the forward and reverse reactions are ∼28 kJ mole−1and ∼93 kJ mole−1, respectively. FeS formation in the solar nebula is rapid (e.g., ∼200 years at 700 K and 10−3bars total pressure for 20 μm diameter Fe grains) as predicted by simple collision theory models of FeS formation.

Combinations of alkyl radicals with alkyl and substituted allyl radicals

In contrast with expectations based upon simple collision theory, reactions of alkyl radicals with substituted allyl radicals yield cross-combination ratios of ϕ=2. Reactions of CH3\ with some C5 radicals give ϕ>2, in accordance with theory.

The nuclear magnetic resonance of 129Xe trapped in clathrates and some other solids

129 Xe NMR spectra were obtained for xenon trapped in the cages of clathrate hydrates and a clathrasil sample. The data, together with shift data for solid xenon, have yielded a linear correlation between the radius of the free space available to the xenon atom and the chemical shift. This observation cannot be rationalized by using simple binary collision theory. In order to account for the observation of anisotropic chemical shifts for xenon trapped in non-spherical environments a simple multiple-site model was developed. Several applications of 129Xe NMR spectroscopy are also presented. These include the identification of new clathrate hydrates, the use of 129Xe NMR to follow changes in site symmetry in a clathrasil and a cyclodextrin inclusion compound, and the observation of trapping sites in crystalline and amorphous solids.

Cross‐reaction and cross‐combination ratios

AbstractA simple collision theory model for reaction between two different radicals shows that the cross‐reaction ratio, ϕ*, is 2 only if the masses and collision diameters of the radicals are identical; for all other combinations of mass and size, ϕ* is greater than 2. The value of ϕ* is shown to depend simply on the ratios of the masses and diameters of the two radicals: which of the two is the heavier or larger is unimportant.Calculated and experimental values of ϕ* are compared for several systems involving small alkyl and fluoroalkyl radicals, and the relationship between ϕ* and ϕ, the cross‐combination ratio, is discussed.

Theory of collisional energy transfer - bromine in low-density inert gases

Classical binary collision trajectory calculations have been carried out to study the energy transfer efficiency between the internal degrees of freedom of highly energized bromine (Br 2) and the translation degrees of freedom of an inert gas (He, Ne, Ar, Kr, Xe) in the low-density limit. The dependence on species (mass, strength of attraction), temperature of the gas ( T = 160, 300, and 1500 K) and internal energy of the bromine (14, 28, 43 kcal/mole; E d = 45.5 kcal/mole) is considered. Global statistical theories overestimate the average energy transferred per collision by an order of magnitude or more. A simple impulsive collision theory is developed and found to account for the magnitudes (typically within a factor of 2–3) and the gross-trends to reasonable accuracy.

Room temperature rate constant for the reaction of Na with Cl2

The room temperature rate constant for the reaction of atomic sodium with Cl2 is measured to be (6.7±0.9)×10−10 cm3 molecule−1 s−1. This experiment is performed in a fast flow reactor where Na is detected using laser-induced fluorescence. The results of this measurement are compared with simple collision theory.

Canonical variational transition state theory for a radical combination reaction on a b i n i t i o potential energy surfaces: H+CH3

Canonical variational transition state theory calculations have been performed for the reaction H+CH3→CH4 on potential energy surfaces based on ab initio calculations. Most vibrations were treated as harmonic. The resulting energy levels and partition functions were compared to empirical rules. For the two rotational degrees of freedom (χ) of CH3 which become bending vibrations in CH4, changing from a harmonic oscillator treatment to a hindered rotor treatment changed the partition functions by an order of magnitude or more for C ⋅ ⋅ ⋅ H distances, R, greater than 0.3 nm. The variation of potential energy with R was taken as a standard Morse function, as a stiff Morse function with a variable parameter β or as a Lippincott function. The value of R for which the rate was minimum was found to vary between 0.25 and 0.5 nm, depending on the temperature and the assumed variation of potential energy with R and χ. Provided the χ bending modes were treated as hindered rotations for large values of R, the limiting values of the rate coefficients were similar to the results of experiments, of classical trajectory calculations, and of a modified version of simple collision theory.

Two-dimensional hindered internal rotations in activated complexes of the form XH2

For reactions of the form X+H2→XH+H, where X represents, H, O, F, or Cl and H represents light hydrogen or deuterium, the usual degenerate, harmonic, bending vibrations of activated complex theory have been replaced by a two-dimensional internal rotation hindered by a sinusoidal potential function. This replacement has the following effects: (a) The zero point energy of the complex is lowered, reducing the Arrhenius activation energy and increasing the reaction rate constant by 45% or less close to room temperature. (b) At very high temperatures, the Arrhenius plot is less strongly curved and the rate constant becomes less than that for the harmonic oscillator case. Provided the best available parameters and tunneling factors are used, the results are in agreement with experiment. At temperatures above about 1000 K, the results of the hindered rotor model approach those of a modified version of simple collision theory. For some reactions, the heat capacity of activation, a measure of Arrhenius plot curvature, exhibits two maxima as a function of temperature; the higher temperature maximum is caused by the hindered internal rotation, the low temperature one by tunneling.

Participation of two-dimensional hindered internal rotations in activated complexes

It is postulated that the bending motions in an activated complex, of the form AB2, may be treated as a two-dimensional internal rotation hindered by a sinusoidal potential function. The Shrödinger equation for these degrees of freedom takes the form of the oblate spheroidal equation. For various values of the barrier to internal rotation, this equation has been solved to find the lowest 231 energy levels. A series expansion has been found for the energies of the bound states. The contributions of these degrees of freedom to the heat capacity, the enthalpy function, and the free energy function have been calculated. Approximations to the latter quantities are also deduced and are shown to be valid in certain temperature ranges. This type of motion has been incorporated into activated complex theory. Replacement of the usual harmonic bending potential by a sinusoidal one has the following effects: (i) the concept of reaction path degeneracy is replaced by nondegenerate states of opposite symmetry, (ii) the zero point energy of the complex is decreased, (iii) at low temperatures, partition functions, activation energies, and Arrhenius plot curvature increase more rapidly with increasing temperature, (iv) at high temperatures, partition functions and activation energies increase less rapidly and curvature declines with increasing temperature. At high temperatures, the expression for the rate constant has the same form as the expression from simple collision theory. Expressions for the collision theory steric factor and activation energy are deduced. As an example, calculations are performed for the reaction of D with H2.

Rates of cholesterol exchange between human erythrocytes and plasma lipoproteins

Rates of exchange of labelled cholesterol between human erythrocytes and three plasma lipoprotein species, LDL, HDL 2 and HDL 3, were measured over a range of lipoprotein concentrations and temperatures. The exchange rates reached limiting, concentration-independent values, which were the same for the three lipoproteins. The temperature dependencies correspond to activation energies of 12 kcal in the limiting rate region, and at lower lipoprotein concentrations to activation energies of 11 to 22 kcal. Calculations based on simple collision theory indicate that energetic barriers to the exchange are far smaller than indicated by these activation energies and that no particular orientation of lipoprotein molecules is required for the exchange. The occurrence of a limiting rate may be a result of the adsorption of lipoprotein molecules onto a limited number of sites on the cell surface, or of a slow process occurring in the membrane, possibly the diffusion of cholesterol. Present data do not permit a choice between these models.

Kinetics and mechanisms of the acid dissolution of goethite (α-FeOOH)

The initial rate of dissolution of several crystalline forms of goethite (α-FeOOH) has been measured as a function of solution conditions. These include hydrogen ion concentration, anion concentration (chloride or perchlorate) and temperature. For dissolution in HClO 4 the rate of reaction is first order with respect to hydrogen ion concentration and is independent of perchloric ion concentration. The rate determining step is thus a protonation of the surface. The activation energy in the presence of perchlorate ion is 23 kcal/mole and the rate of dissolution can be described by the simple collision theory. For dissolution in HCl the kinetics are more complex, the rate again being first order with respect to hydrogen ion concentration but also a function of chloride ion concentration. The results indicate that an adsorption complex is formed before dissolution occurs.