Statistical Rate Theory Research Articles

Adsorption kinetics of propane on energetically heterogeneous activated carbon

The modeling of the adsorption isotherms and kinetics of the adsorbent + adsorbate pair is essential in simulating the performance of a pressurized adsorption chiller. In this work, the adsorption kinetics is analyzed from data measured using a magnetic suspension balance. The Statistical Rate Theory describes the Dubinin–Astakhov (DA) equation and extended to obtain an expression for transient analysis. Hence both the experimental excess equilibria data and the adsorption kinetics data may then be fitted to obtain the necessary parameters to fit the curves. The results fit the data very well within 6% of the error of regression.

Pyrolysis of ethanol: A shock-tube/TOF-MS and modeling study

The pyrolysis of ethanol was studied in a shock tube behind reflected shock waves in the temperature range 1300–1510K at pressures of about 1.1bar by using time-of-flight mass spectrometry for detection. For the first time, concentration–time profiles of C2H5OH, C2H4O, (C2H2+C2H4+C2H6), H2O, and CH4 were simultaneously recorded. It could be shown that under our experimental conditions, the major products are H2O and C2H4, which are mainly formed in the reaction C2H5OH→C2H4+H2O (R1). The rate coefficient of reaction (R1) could be determined for the first time from directly measured concentration–time profiles of H2O in a shock tube. The results can be expressed by the Arrhenius equation k1(T, P ∼1.1bar)=(2.5±1.0)×1010 exp (−23320K/T)s−1 with an estimated uncertainty of ±40%. The multiple-species concentration–time profiles from our experiments can be used for a most rigorous test of ethanol pyrolysis mechanisms. As an exemplary case, we employed the mechanism from Marinov (1999) and found a very good agreement between the experimental and simulation results. We also calculated rate coefficients for the most important decomposition steps of ethanol from statistical rate theory by solving a thermal multichannel master equation. Reaction (R1) as well as the bond fission channels C2H5OH→CH3+CH2OH (R2) and C2H5OH→C2H5+OH (R3) were considered. The specific rate coefficients were obtained from RRKM theory (R1) and the Statistical Adiabatic Channel Model (R2 and R3) with molecular and transition state data from quantum chemical calculations at CCSD(T)-F12/def2-QZVPP//MP2/cc-pVQZ level of theory. The rate coefficient obtained from the ab initio data were slightly fitted to recently published experimental values of k1, k2, and k3 and inserted into Marinov’s mechanism. A similar good representation of the concentration–time profiles as with the original mechanism was obtained.

Synergistic effect of ZnO nanoparticles and triblock copolymer surfactant on the dynamic and equilibrium oil-water interfacial tension.

The present study reports the effects of non-ionic surfactant Pluronic F-127 on the equilibrium and dynamic oil-water interfacial tension in the presence of ZnO nanoparticles. The results show that in the presence of nanoparticles, the decrease of interfacial tension is more. The cooperative behavior of F-127 and ZnO nanoparticles especially at low concentrations increases the surfactant efficiency in lowering the interfacial tension. Statistical rate theory (SRT) and mixed diffusion-kinetic controlled model were used for modeling the dynamic interfacial tension data. The modeling results show that the mechanism of surfactant adsorption is controlled with the mixed diffusion-kinetic model. In addition, the influence of the solution pH on the interfacial tension was investigated. Finally, the effects of F-127 on the contact angle in the absence and presence of ZnO was compared.

Vibrational autodetachment of sulfur hexafluoride anions at its long-lifetime limit

We have investigated the autodetachment of electrons from rovibrationally hot SF${}_{6}{}^{\ensuremath{-}}$ anions using a cryogenic ion-beam trap. Extremely low residual gas densities of ${10}^{4}$ cm${}^{\ensuremath{-}3}$ provided undisturbed observation of the neutralization rates due to vibrational autodetachment (VAD) over almost five orders of magnitude and over times up to 100 ms. We successfully explain our experimental decay curves using statistical rate theory combined with electron attachment data and vibrational frequencies calculated for a ${C}_{4v}$-distorted SF${}_{6}{}^{\ensuremath{-}}$. The unprecedented sensitivity of the experiment to the decay constants at the VAD threshold allows us to infer from the data the adiabatic electron affinity of SF${}_{6}$ to be $(0.91\ifmmode\pm\else\textpm\fi{}0.07)$ eV and to confirm the recently predicted ${C}_{4v}$ symmetry of SF${}_{6}{}^{\ensuremath{-}}$.

The pyrolysis of 2-methylfuran: a quantum chemical, statistical rate theory and kinetic modelling study

Due to the rapidly growing interest in the use of biomass derived furanic compounds as potential platform chemicals and fossil fuel replacements, there is a simultaneous need to understand the pyrolysis and combustion properties of such molecules. To this end, the potential energy surfaces for the pyrolysis relevant reactions of the biofuel candidate 2-methylfuran have been characterized using quantum chemical methods (CBS-QB3, CBS-APNO and G3). Canonical transition state theory is employed to determine the high-pressure limiting kinetics, k(T), of elementary reactions. Rice-Ramsperger-Kassel-Marcus theory with an energy grained master equation is used to compute pressure-dependent rate constants, k(T,p), and product branching fractions for the multiple-well, multiple-channel reaction pathways which typify the pyrolysis reactions of the title species. The unimolecular decomposition of 2-methylfuran is shown to proceed via hydrogen atom transfer reactions through singlet carbene intermediates which readily undergo ring opening to form collisionally stabilised acyclic C5H6O isomers before further decomposition to C1-C4 species. Rate constants for abstraction by the hydrogen atom and methyl radical are reported, with abstraction from the alkyl side chain calculated to dominate. The fate of the primary abstraction product, 2-furanylmethyl radical, is shown to be thermal decomposition to the n-butadienyl radical and carbon monoxide through a series of ring opening and hydrogen atom transfer reactions. The dominant bimolecular products of hydrogen atom addition reactions are found to be furan and methyl radical, 1-butene-1-yl radical and carbon monoxide and vinyl ketene and methyl radical. A kinetic mechanism is assembled with computer simulations in good agreement with shock tube speciation profiles taken from the literature. The kinetic mechanism developed herein can be used in future chemical kinetic modelling studies on the pyrolysis and oxidation of 2-methylfuran, or the larger molecular structures for which it is a known pyrolysis/combustion intermediate (e.g. cellulose, coals, 2,5-dimethylfuran).

Dynamics of the O(3P) + C2H2 reaction from crossed molecular beam experiments with soft electron ionization detection

The reaction between ground state oxygen atoms, O((3)P), and the acetylene molecule, C2H2, has been investigated in crossed molecular beam experiments with mass-spectrometric detection and time-of-flight analysis at three different collision energies, Ec = 34.4, 41.1 and 54.6 kJ mol(-1). From product angular and velocity distribution measurements of the HCCO and CH2 products in the laboratory frame, product angular and translational energy distributions in the center-of-mass frame were determined. Measurements on the CH2 product were made possible by employing for product detection the recently implemented soft electron-ionization (EI) technique with low-energy, tunable electrons, which has permitted suppressing interference coming from the dissociative ionization of reactants, products and background gases. It has been found that the title reaction leads only to two competing channels: H + HCCO (ketenyl) and CO + CH2 (triplet methylene). The branching ratio of cross sections between the two competing channels has been determined to be σ(HCCO)/[σ(HCCO) + σ(CH2)] = 0.79 ± 0.05, independent of collision energy within the experimental uncertainty. This value is in line with that obtained in the most recent and accurate kinetics determination at room temperature as well as with that predicted from recent theoretical calculations based on statistical rate theory and weak-collision master equation analysis and on dynamics surface-hopping quasiclassical trajectory calculations on-the-fly on coupled triplet/singlet ab initio potential energy surfaces. The firm assessment of the branching ratio as a function of translational energy for this important reaction, besides its fundamental significance, is of considerable relevance for the implementation of theoretical models of hydrocarbon combustion.

Application of NRTL activity coefficient model to describe the kinetics of gas adsorption

Abstract The Non-Random Two-Liquid activity coefficient model is applied to describe the kinetics of pure gas adsorption on energetically heterogeneous solid surfaces. The surface energetic heterogeneity has been represented by the Gaussian-like function of the adsorption energy distribution. Two different kinetic isotherms have been presented. One of them, determined by using the statistical rate theory, has been critically discussed. The applicability of the presented approach has been demonstrated by a quantitative analysis of two sets of experimental data previously reported in the literature.

Non-equilibrium phenomena in carbon dioxide expansion

Release of liquid and supercritical carbon dioxide is a fundamental research topic in CCS. Traditional approach is largely based on HEM and, in general, assumes equilibrium from the outlet to the Mach disc. Experimental results have shown that this approach is not always effective in describing the expansion phenomenon; therefore a significant lack of knowledge exists about CO2 properties at the under-expanded jet zone boundary, which is a main focus in process safety. Here, solid formation, vapour quality, sonic velocity and final temperature are generally calculated according to equilibrium saturation condition, and this is generally incorrect. This article deals with non-equilibrium thermodynamics of liquid and supercritical CO2 expansion, illustrating relaxation dynamics through the HRM models, and discussing the very specific singularities of CO2 phase transitions, vapour to liquid and liquid to solid, that result away from the equilibrium condition, due to the rapid phase changes and to the specific properties of CO2 multi phase thermodynamics, including nucleation and particle growth. Statistical rate theory has been applied with the aim at identifying the phase transition energy barrier, resulting in a significant entropy increase. A case study based on HEM conservation equations integrated with the statistical rate approach has been presented, which covers the gap of the equilibrium hypothesis. The objective of the article is to provide a more accurate method to predict the properties of carbon dioxide following an expansion.

On the Thermodynamics of Refrigerant + Heterogeneous Solid Surfaces Adsorption

This Article presents a theoretical framework for the understanding of pressurized adsorption systems using the statistical rate methodology. Utilizing results from the statistical rate theory, basic thermodynamic variables including enthalpy (h(a)), entropy (s(a)), and the specific heat capacity (c(p,a)) of the adsorbed phase are derived using the thermodynamic requirements of chemical equilibrium, Gibbs law, as well as Maxwell relations. A built-in constant (K) describes the adsorbed molecular partition function (q(s)), and it captures the heterogeneous properties of the adsorbent + adsorbate pair at equilibrium states. Improved adsorbed-phase volume considerations were incorporated in the formulations of these variables where they could be utilized with relative ease for analyzing the energetic performances of any practical adsorption system. In this Article, we have demonstrated how derived thermodynamic quantities can bridge the information gap with respect to the states of adsorbed phase, as well as resolved some theoretical inconsistencies that were found in previously derived quantities. Experimentally, the adsorption isotherms of propane (refrigerant) on activated carbon powder (Maxsorb III) for temperatures from 5 to 75 °C and pressures up to 8 bar are presented, and they are used to illustrate the behaviors of the adsorbed-phase during uptakes, temperatures, and pressure excursions or changes.

Source of Temperature and Pressure Pulsations during Sessile Droplet Evaporation into Multicomponent Atmospheres

During sessile droplet evaporation, studies with IR thermography and shadowgraphs have indicated temperature pulsations. We confirm those observations with microthermocouples, but microthermocouples also indicate temperature pulsations in the atmosphere of the droplet. The pressure in this atmosphere pulsated as well and was correlated with the temperature pulsations in the droplet. Also, we find that if a droplet evaporates into its own vapor, there are no temperature or pressure pulsations. The pulsations occur only if the droplet evaporates into an atmosphere with a component having a heat of solution with the droplet when it adsorbs-absorbs. None of the currently proposed mechanisms for the temperature pulsations provide an explanation for the coupling between the temperature pulsations in the droplet and the vapor-phase pressure pulsations, and for the absence of the pulsations when the system is single-component. As a mechanism for the pulsations, we propose that when a droplet is exposed to an atmosphere containing a component that has a heat of solution with the droplet, energy will be released from adsorption-absorption. This energy will cause pulsations in the evaporation flux, and these pulsations could cause the observed temperature and pressure pulsations. We examine this mechanism by showing that, if the measured temperature pulsations in a water droplet exposed to a methanol atmosphere are used as the input to a theory of evaporation kinetics (statistical rate theory), the pressure pulsations of the water vapor in the methanol atmosphere are predicted and agree with those measured with a quadrupole mass analyzer. When the inputs and outputs are reversed in the theory, we find that the temperature pulsations in the droplet are correctly predicted from the measured water vapor pulsations in the atmosphere.

Theoretical Study of Gas Hydrate Decomposition Kinetics—Model Development

In order to provide an estimate of the order of magnitude of intrinsic gas hydrate dissolution and dissociation kinetics, the "Consecutive Desorption and Melting Model" (CDM) is developed by applying only theoretical considerations. The process of gas hydrate decomposition is assumed to comprise two consecutive and repetitive quasi chemical reaction steps. These are desorption of the guest molecule followed by local solid body melting. The individual kinetic steps are modeled according to the "Statistical Rate Theory of Interfacial Transport" and the Wilson-Frenkel approach. All missing required model parameters are directly linked to geometric considerations and a thermodynamic gas hydrate equilibrium model.

Intramolecular Energy Relaxation and Statistical Rate Theory

Statistical rate theory is essentially based on the state counting without any restrictions other than the energy and the angular momentum conservation. In this work, two kinds of restrictions are introduced into the statistical theory. The first restriction is related to the intramolecular energy flow within the reacting molecular system. The excess energy of reaction is made distributed with some bias favoring a specific degree of freedom. That is, the statistical weight of each product state is not equal but biased. The biased product energy distribution observed in various reactions can be well reproduced by using an appropriate form of restriction. The product energy distributions in F+H2 → HF+H and H + F2 → HF +F are treated under such category. In the second restriction, the components of the angular momentum vector of the reaction products are biased so as to express a specific vectorial relation between the departing products and the initial parent system. The vector correlation observed in many photofragment experiments suggests a proper vectorial restriction which can reproduce fragment energy distributions. The photofragmentation of the NO dimer which is known to occur within the molecular plane offers such an example. The energy state distribution of the NO fragments is well reproduced only when the vectorial restrictions are taken into account.

Is gold actor or spectator in the reaction of small AunPd m + clusters with O2?

The reactivity of free binary gold-palladium clusters (AuPd\hbox{$_2^+$}+2, Au2Pd+, Au2Pd\hbox{$_2^+$}+2, and Au2Pd\hbox{$_3^+$}+3) toward molecular oxygen was investigated in an ion trap experiment under multi-collision conditions and compared to the reactivities of bare Au\hbox{$_n^+$}+n and Pd\hbox{$_m^+$}+m (n, m = 2 − 5) clusters. Reaction kinetics measurements revealed that the reaction rate is mainly determined by the number of palladium atoms in the clusters and only weakly influenced by additional gold atoms. The same holds true for the observed reaction product distributions. Most interestingly, the most reactive cluster ions Pd\hbox{$_3^+$}+3, Au2Pd\hbox{$_3^+$}+3, and Pd\hbox{$_5^+$}+5 exhibit a strong preference to form tetroxide products, Au n Pd m O\hbox{$_4^+$}+4. In addition, employing temperature dependent mass spectrometry, a second adsorption species consisting of several weakly bound oxygen molecules was identified for all investigated palladium containing clusters which is, however, only formed at cryogenic temperatures. All these observations suggest that the gold atoms largely act upon a spectator role in the reaction of the binary clusters. Nevertheless, a rough estimation of the relative O2 binding energies via statistical rate theory indicates that the addition of gold to the Pd\hbox{$_n^+$}+n clusters decreases the O2-cluster interaction strength, although the reaction rate stays constant. This effect in the binary clusters may be of importance to a potential activation and dissociation of the adsorbed O2 molecules.

Splitting methods for relaxation two-phase flow models

A model for two-phase pipeline flow is presented, with evaporation and condensation modelled using a relaxation source term based on statistical rate theory. The model is solved numerically using a Godunov splitting scheme, making it possible to solve the hyperbolic fluid-mechanic equation system and the relaxation term separately. The hyperbolic equation system is solved using the multi-stage (MUSTA) finite volume scheme. The stiff relaxation term is solved using two approaches: one based on the Backward Euler method, and one using a time-asymptotic scheme. The results from these two methods are presented and compared for a CO2 pipeline depressurisation case.

Rate of gas absorption on a slippery bubble mattress

We investigate the absorption of a pure gas into a liquid in laminar flow past a superhydrophobic surface consisting of alternating solid walls and micro-bubbles. We experimentally measure and numerically estimate the dynamic mass transfer of gas absorption at stable gas–liquid interfaces for short contacting times. We study the net rate of gas absorption experimentally by in situ measurements of dissolved oxygen concentration profiles in aqueous solutions flowing over oxygen bubbles by fluorescence lifetime imaging microscopy. We numerically analyze the dynamics of interfacial mass transfer of dissolved oxygen by considering (i) kinetic equilibrium conditions at bubble surfaces that are conventionally described by Henry's Law and (ii) non-equilibrium conditions at bubble surfaces using Statistical Rate Theory (SRT). Our experimental results show that kinetic equilibrium is not established for short contact times. Mass transfer of gas into liquid flow past micro-bubbles can be well described by our simulations performed with the non-equilibrium theory for a short exposure time (∼180 μs) of liquid with a microbubble, deviating from the commonly accepted Henry's Law.

A New Theoretical Study of Desorption Kinetics at Solid/Solution Interface by Statistical Rate Theory

Desorption is one of the popular methods for the design and regeneration of catalysts. For better understanding and modeling of this process, it is important to have models with theoretical basis. In the present work kinetics of solute desorption at solid/solution interface has been studied by statistical rate theory (SRT) when the system is close to equilibrium. Based on numerically generated points (t; q) by the SRT equation, it has been shown that the results of numerical analysis are in good agreement with our theoretical derivation of new rate equation for desorption systems close to equilibrium. Finally the results of the present theoretical study were confirmed by analysis of two experimental systems.

An exponential kinetic model for adsorption at solid/solution interface

An exponential kinetic model has been proposed for modeling of adsorption kinetics at the solid/solution interface. This new equation was compared with pseudo first-order (PFO) and pseudo second-order (PSO) equations as the well-known two parametric models. Based on numerically generated data points (t,q) by using of statistical rate theory equation for homogeneous surfaces, it has been shown that we can use the new model for homogeneous solid surfaces as well as the pseudo second-order model. Moreover, the driving force of new model is a combination of driving forces of PFO and PSO equations. However, using Langmuir–Freundlich equation to generate kinetic data for heterogeneous surfaces, it has been shown that the kinetic data can be described by PFO model when the adsorption rate coefficient is smaller than the desorption rate coefficient; but, when the adsorption rate coefficient is bigger than the desorption rate coefficient, which is more favorite for practical application, the new exponential model shows better agreement with kinetic data. The main advantage of using the new model for heterogeneous systems is its simplicity in comparison with Langmuir–Freundlich kinetic model which there is no analytical solution for it. Finally, the results of fitting to the experimental data represent that exponential model can describe kinetics of adsorption for both homo- and heterogeneous systems very well.

The reaction of 2,5-dimethylfuran with hydrogen atoms – An experimental and theoretical study

The kinetics of the reaction of hydrogen atoms with 2,5-dimethylfuran (25DMF), a promising liquid transport biofuel, was experimentally studied in a shock tube at temperatures between 970 and 1240K and pressures of 1.6 and 4.8bar. The hydrogen atoms were produced by pyrolysis of ethyl iodide and monitored by atom resonance absorption spectrometry. From the hydrogen atom concentration–time profiles, overall rate coefficients for the reaction H+25DMF→products (R1) were inferred. The results can be expressed by the Arrhenius equation k1=4.4×10−11exp(−1180K/T)cm−3s−1 with an estimated uncertainty of ±30%. A significant pressure dependence was not observed. The results were analyzed in terms of statistical rate theory with molecular and transition state data from quantum chemical calculations. Three different compound methods were used to characterize the potential energy surface: CBS-QB3, CBS-APNO, and G3. It is found that reaction (R1) mainly (>75%) proceeds via an addition–elimination mechanism to yield 2-methylfuran+CH3. Kinetic parameters for the most important competing channels of the net reaction (R1) were calculated.

Fractal-Like Adsorption Kinetics at the Solid/Solution Interface

The kinetics of adsorption processes at the solid/solution interface has been studied by using a fractal-like concept. For the first time, one possible physical meaning for fractal-like adsorption kinetics which indicates that sorption rate coefficient at solid/solution interface is a function of time is presented. So, new kinetic models have been presented by a combination of the fractal-like approach and integrated kinetic Langmuir equation (IKL), mixed 1,2-order equation (MOE), and statistical rate theory (SRT). The fractal-like SRT rate equation has been solved at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. The new parameter (α) which has appeared in these models affects the rate of sorption. Fractal-like IKL (or fractal-like MOE) and also fractal-like SRT models have been used to analyze different experimental data. The obtained results indicate that the variation of initial concentration of solute and stirring rate of solution affect both “α” and the rate coefficient.

The dissociation/recombination reaction CH4 (+M) ⇔ CH3 + H (+M): A case study for unimolecular rate theory

The dissociation/recombination reaction CH(4) (+M) ⇔ CH(3) + H (+M) is modeled by statistical unimolecular rate theory completely based on dynamical information using ab initio potentials. The results are compared with experimental data. Minor discrepancies are removed by fine-tuning theoretical energy transfer data. The treatment accounts for transitional mode dynamics, adequate centrifugal barriers, anharmonicity of vibrational densities of states, weak collision and other effects, thus being "complete" from a theoretical point of view. Equilibrium constants between 300 and 5000 K are expressed as K(c) = k(rec)/k(dis) = exp(52,044 K/T) [10(-24.65) (T/300 K)(-1.76) + 10(-26.38) (T/300 K)(0.67)] cm(3) molecule(-1), high pressure recombination rate constants between 130 and 3000 K as k(rec,∞) = 3.34 × 10(-10) (T/300 K)(0.186) exp(-T/25,200 K) cm(3) molecule(-1) s(-1). Low pressure recombination rate constants for M = Ar are represented by k(rec,0) = [Ar] 10(-26.19) exp[-(T/21.22 K)(0.5)] cm(6) molecule(-2) s(-1), for M = N(2) by k(rec,0) = [N(2)] 10(-26.04) exp[-(T/21.91 K)(0.5)] cm(6) molecule(-2) s(-1) between 100 and 5000 K. Weak collision falloff curves are approximated by asymmetric broadening factors [J. Troe and V. G. Ushakov, J. Chem. Phys. 135, 054304 (2011)] with center broadening factors of F(c) ≈ 0.262 + [(T - 2950 K)/6100 K](2) for M = Ar. Expressions for other bath gases can also be obtained.