Nonequilibrium Dissociation Rates Research Articles

Application of Reflected Shock Wave Configuration to Validate Nonequilibrium Models of Reacting Air

The direct simulation Monte Carlo (DSMC) method is used to model transient thermal and chemical relaxation behind reflected shock waves in oxygen–argon and air mixtures under conditions reproducing earlier shock-tube experiments. Two vibration–translation and three popular DSMC chemical reaction models are tested. Where possible, model parameters are adjusted to match equilibrium and nonequilibrium relaxation times and reaction rates. A number of factors that impact relaxation and reaction model validation are examined, including gas–surface interactions, time-varying freestream properties, location of the observation point, electronic excitation, and nonequilibrium populations of vibrational states probed in the experiments. Comparison of numerical and experimental results has demonstrated that the reflected shock configuration is a platform very convenient for validation and analysis of high-temperature chemical reaction models. Computations have shown that the Bias reaction model is superior to the total collision energy and quantum kinetic models, providing reasonable agreement with measured absorbance time histories and vibrational temperatures in oxygen–argon mixtures and pure . There are some modeling-versus-experiment differences observed for air that may warrant additional studies focused on Zeldovich reaction rates and oxygen–nitrogen vibrational excitation and nonequilibrium dissociation rate.

Rotation‐translation collision model for DSMC with restricted energy exchange

AbstractIn the standard implementation of Borgnakke–Larsen (BL) rotation and translation energy exchange in DSMC not every rotational mode of each molecule is active in every collision. In some collisions, the rotation mode of one molecule is “frozen” (cannot be changed by the collision); in other collisions the rotation mode of both molecules is frozen. Different relaxation rates are obtained by varying the proportion of frozen‐rotation collisions. In 1974 Larsen and Borgnakke proposed a “restricted exchange” version of BL in which a portion of the energy of each mode is frozen in each collision; the method seemed physically plausible but did not satisfy the detailed balance condition. In 1978 Pullin proposed a general restricted exchange of BL exchange which did satisfy the detailed balance condition; it was more CPU intensive than the original BL scheme. It was seen as “laborius” and “cumbersome” and it seemed to be incompatible with vibration energy‐exchange models. Here a simplified version, a special case, of Pullin's restricted exchange scheme is described. The new method is only 12%–17% more CPU‐intensive than standard BL methods and can be used with the standard DSMC quantum vibration exchange model. It is shown that the elimination of frozen‐rotation collisions changes the high energy distribution of vibration energy in nonequilibrium conditions which may slightly decrease the nonequilibrium dissociation rate when restricted exchange is used with the quantum‐kinetic method for dissociation reactions.

A general form of Macheret–Fridman classical impulsive dissociation model for nonequilibrium flows

The rate of dissociation behind a strong shock in thermochemical nonequilibrium depends on the vibrational excitation of the molecules, hence the rates become a function of translational-rotational and vibrational temperatures. The Macheret–Fridman (MF) model provides analytical expressions for nonequilibrium dissociation rates assuming the collision of molecules to be in the impulsive limit. However, the original form of the model was limited to the dissociation of homonuclear molecules. In this work, we present a general form of the Macheret–Fridman classical impulsive model by considering the dissociation of a heteronuclear molecule and present macroscopic rates applicable for modeling dissociation in computational fluid dynamics (CFD). The nonequilibrium dissociation rates from the MF-CFD model compared well with the available quasiclassical trajectory (QCT) data for some important reactions in the air. Additionally, we also present a comparison of the average vibrational energy removed in a dissociation reaction predicted by the MF-CFD model with QCT data for several reactions in air and propose some improvements to the model. The developed MF-CFD model was used to investigate various nonequilibrium flow problems and the results were compared with available experimental data. In general, the results from the MF-CFD model are promising and the model shows a possibility of becoming the standard tool for investigating nonequilibrium flows in CFD.

Vibrational Energy Transfer and Collision-Induced Dissociation in Collisions

This paper presents molecular dynamics calculations of vibrational energy transfer and nonequilibrium dissociation in collisions. The interactions are modeled using nine potential energy surfaces corresponding to the , , , , , , , , and states, which govern electronically adiabatic collisions of ground-electronic-state collisions of diatomic oxygen with atomic oxygen. Characteristic vibrational excitation times are calculated over a temperature range of to , and nonequilibrium dissociation rate coefficients are calculated over a temperature range of to . Vibrational relaxation rates, specific to each PES, are found to vary by over an order of magnitude, indicating that all spin couplings and spatial degeneracies must be considered for accurate predictions of collisions. It has been observed that the characteristic vibrational excitation time for interactions is weakly dependent on temperature and increases slightly with increasing temperature. Predicted nonequilibrium dissociation rates, during quasi-steady state. Agree well with available experimental data, and the coupling between vibrational energy and dissociation is characterized.

Assessment of Classical Impulsive Models of Dissociation in Thermochemical Nonequilibrium

In strong shock waves in rarefied gases, chemical processes such as dissociation and exchange reactions occur in conditions of thermodynamic nonequilibrium, and the rate coefficients are functions of both translational–rotational and vibrational temperatures. In this work, we reexamine and validate the physical model for nonequilibrium dissociation rates proposed earlier by Macheret et al. The model is based on the classical impulsive approximation and enables analytical formulas for reaction thresholds, probabilities, and multitemperature rate coefficients. The recent quasi-classical trajectory calculations for , , , , and are used to evaluate the Macheret–Fridman dissociation model. The full version of the model that incorporates the reduction of dissociation energy due to rotation of the dissociating molecule as well as the appearance of the centrifugal barrier is found to be in good agreement with quasi-classical trajectory data, whereas the simplified version of the model that ignores the rotational effect significantly underpredicts the dissociation rates in vibrationally cold conditions. The good agreement with quasi-classical trajectory data validates the classical impulsive approximation and implies that details of the potential energy surface are not important for dissociation at high temperatures. Preliminary one-dimensional computational fluid dynamics calculations with the validated dissociation model were conducted for conditions of the shock-tube experiments in pure oxygen by Ibraguimova et al. Generally reasonable agreement was found between the calculations and the experimental data; however, some underprediction of the peak vibrational temperature suggests that some improvement in the model would be desirable.

Assessment of vibration–dissociation coupling models for hypersonic nonequilibrium simulations

The fidelity of three widely-used two-temperature vibration–dissociation coupling models, including the Park model (1988), the Macheret–Fridman model (1994), and the coupled vibration–dissociation–vibration (CVDV) model (1963), is numerically investigated via a comparison with state-specific results and existing shock tube data for oxygen flows. Under the hypothetical condition where a Boltzmann distribution corresponding to a vibrational temperature is assumed, it is found that the CVDV model with a proper parameter is capable of providing the most accurate results, whereas the Park and Macheret–Fridman models present similar prediction accuracy for which the nonequilibrium dissociation rate coefficients could be as much as three orders of magnitude lower than state-specific values. However, for actual postshock flows with intensive vibrational excitation and dissociation processes, the CVDV model still shows significant discrepancies relative to state-specific results and experimental data, presenting a much lower vibrational temperature and a higher degree of dissociation. The essential cause for the disagreement lies in the existence of non-Boltzmann distributions observed when the incubation period is over and dissociation starts to dominate. Recommendations on further modification of two-temperature vibration–dissociation coupling models are presented.

Effect of O2 + O ab initio and Morse additive pairwise potentials on dissociation and relaxation rates for nonequilibrium flow calculations

This work quantifies the sensitivity of O2 + O dissociation rates and relaxation to interatomic potential energy surfaces at high-enthalpy, nonequilibrium flow conditions. State-to-state cross sections are obtained by quasi-classical trajectory (QCT) calculations with two potential surfaces. The first is a Morse additive pairwise potential for O3 that is constructed based on O2(3Σg−) spectroscopic measurements and the second is a double many-body expansion potential by Varandas and Pais [Mol. Phys. 65, 843–860 (1988)]. The QCT calculations of cross sections and rates with the two surfaces are compared to each other and shock tube measurements. It is found that, at temperatures between 2500 K and 20 000 K, the equilibrium dissociation rates predicted by the two potentials agree within 12%, and they are bound by experimental dissociation measurements. In contrast, above 10 000 K, ab initio based equilibrium dissociation rates are about a factor of two higher than the widely used Park’s model. The nonequilibrium dissociation rates calculated by the two potentials are within 70% while phenomenological models differ by two orders of magnitude for vibrationally cold conditions of shocks. The analyses provide an approach for improving accuracy of nonequilibrium high-enthalpy flow modeling when ab initio potentials are not available.

A review of non-equilibrium dissociation rates and models for atmospheric entry studies

The appropriate simulation of vibrational exchange and dissociation processes in high-temperature (above 1000 K) plasmas mandates the application of more detailed state-to-state models, when compared with those based on first-order theories, utilized for the simulation of low-pressure plasmas. Such can be achieved through the application of approaches such as the forced harmonic oscillator model, or the quasi-classical trajectory model. This allows obtaining multiquantum state-resolved rates significantly more accurate at high temperatures, as compared with rates issued from first-order perturbation theories. This work reviews the more recent high-temperature datasets proposed by several groups, including our own. Such datasets have then been applied to the simulation of dissociation processes in high-temperature shock-heated nitrogen flows, and a comparison against traditional multi-temperature models has been carried out, for post-shock temperatures ranging from 20 000–100 000 K. Differences between the results predicted by the state-resolved and macroscopic models are significant, except in the high-temperature limit.

Nonequilibrium dissociation and recombination rates in nitrogen: From shock waves to discharge conditions

A discussion about the validity of state-to-state and total weighted dissociation and recombination rate coefficients under nonequilibrium conditions is presented, both for the cases of high translational temperatures, in a shock wave, and of moderate and low temperatures, in a electrical discharge. Accurate data for these processes are obtained in N 2 using the semiclassical nonperturbative analytic method known as forced harmonic oscillator (FHO) for V– V– T and V– T energy exchanges.

On-chip non-equilibrium dissociation curves and dissociation rate constants as methods to assess specificity of oligonucleotide probes

Nucleic acid hybridization serves as backbone for many high-throughput systems for detection, expression analysis, comparative genomics and re-sequencing. Specificity of hybridization between probes and intended targets is always critical. Approaches to ensure and evaluate specificity include use of mismatch probes, obtaining dissociation curves rather than single temperature hybridizations, and comparative hybridizations. In this study, we quantify effects of mismatch type and position on intensity of hybridization signals and provide a new approach based on dissociation rate constants to evaluate specificity of hybridized signals in complex target mixtures. Using an extensive set of 18mer oligonucleotide probes on an in situ synthesized biochip platform, we demonstrate that mismatches in the center of the probe are more discriminating than mismatches toward the extremities of the probe and mismatches toward the attached end are less discriminating than those toward the loose end. The observed destabilizing effect of a mismatch type agreed in general with predictions using the nearest neighbor model. Use of a new parameter, specific dissociation temperature (Td-w, temperature of maximum specific dissociation rate constant), obtained from probe–target duplex dissociation profiles considerably improved the evaluation of specificity. These results have broad implications for hybridization data obtained from complex mixtures of nucleic acids.

Non-equilibrium dissociation rates in expanding flows

In this Letter, non-equilibrium dissociation rates in expanding gas flows are studied taking into account state-to-state vibrational–chemical kinetics. A comparison of the results obtained in the state-to-state approach with the ones based on the quasi-stationary two-temperature vibrational distributions for harmonic and anharmonic oscillators and on the thermal equilibrium one-temperature distribution is presented. The influence of vibrational energy transition probabilities and nozzle profiles on vibrational level populations and dissociation rates is also discussed.

Optimization of single-base-pair mismatch discrimination in oligonucleotide microarrays.

The discrimination between perfect-match and single-base-pair-mismatched nucleic acid duplexes was investigated by using oligonucleotide DNA microarrays and nonequilibrium dissociation rates (melting profiles). DNA and RNA versions of two synthetic targets corresponding to the 16S rRNA sequences of Staphylococcus epidermidis (38 nucleotides) and Nitrosomonas eutropha (39 nucleotides) were hybridized to perfect-match probes (18-mer and 19-mer) and to a set of probes having all possible single-base-pair mismatches. The melting profiles of all probe-target duplexes were determined in parallel by using an imposed temperature step gradient. We derived an optimum wash temperature for each probe and target by using a simple formula to calculate a discrimination index for each temperature of the step gradient. This optimum corresponded to the output of an independent analysis using a customized neural network program. These results together provide an experimental and analytical framework for optimizing mismatch discrimination among all probes on a DNA microarray.

Optimization of an oligonucleotide microchip for microbial identification studies: a non-equilibrium dissociation approach.

The utility of a high-density oligonucleotide microarray (microchip) for identifying strains of five closely related bacilli (Bacillus anthracis, Bacillus cereus, Bacillus mycoides, Bacillus medusa and Bacillus subtilis) was demonstrated using an approach that compares the non-equilibrium dissociation rates ('melting curves') of all probe-target duplexes simultaneously. For this study, a hierarchical set of 30 oligonucleotide probes targeting the 16S ribosomal RNA of these bacilli at multiple levels of specificity (approximate taxonomic ranks of domain, kingdom, order, genus and species) was designed and immobilized in a high-density matrix of gel pads on a glass slide. Reproducible melting curves for probes with different levels of specificity were obtained using an optimized salt concentration. Clear discrimination between perfect match (PM) and mismatch (MM) duplexes was achieved. By normalizing the signals to an internal standard (a universal probe), a more than twofold discrimination (> 2.4x) was achieved between PM and 1-MM duplexes at the dissociation temperature at which 50% of the probe-target duplexes remained intact. This provided excellent differentiation among representatives of different Bacillus species, both individually and in mixtures of two or three. The overall pattern of hybridization derived from this hierarchical probe set also provided a clear 'chip fingerprint' for each of these closely related Bacillus species.

Semiclassical modeling of state-specific dissociation rates in diatomic gases

A nonempirical, containing no adjustable parameters, theoretical model is suggested for calculations of state-specific dissociation rates in diatomic gases. Effects of molecular rotation and three dimensionality of collisions are consistently accounted for. The model is based upon a modified forced harmonic oscillator (FHO) scaling, with anharmonic frequency correction and energy symmetrization. The FHO scaling allows close-coupled calculations of multiquantum transitions between vibrational states, and it requires evaluation of collisional energy transfer to classical oscillator. Three-dimensional classical energy transfer models in both free-rotation and impulsive (sudden) approximations were used in conjunction with the FHO quantum scaling. The new theory describes the role of various degrees of freedom in dissociation both qualitatively and quantitatively. One of the predictions is that at low and moderate temperatures, dissociation is strongly preferential, with state-specific rates sharply increasing with vibrational energy; however, at high temperatures, the rate dependence on vibrational energy becomes less steep, turning into a virtually nonpreferential. Calculated thermal (equilibrium) and nonequilibrium dissociation rates of oxygen and nitrogen show a very good agreement with shock-tube experimental data taken from the literature.

Discordant measures of androgen-binding kinetics in two mutant androgen receptors causing mild or partial androgen insensitivity, respectively.

We have characterized two different mutations of the human androgen receptor (hAR) found in two unrelated subjects with androgen insensitivity syndrome (AIS): in one, the external genitalia were ambiguous (partial, PAIS); in the other, they were male, but small (mild, MAIS). Single base substitutions have been found in both individuals: E772A in the PAIS subject, and R871G in the MAIS patient. In COS-1 cells transfected with the E772A and R871G hARs, the apparent equilibrium dissociation constants (Kd) for mibolerone (MB) and methyltrienolone are normal. Nonetheless, the mutant hAR from the PAIS subject (E772A) has elevated nonequilibrium dissociation rate constants (k(diss)) for both androgens. In contrast, the MAIS subject's hAR (R871G) has k(diss) values that are apparently normal for MB and methyltrienolone; in addition, the R871G hAR's ability to bind MB resists thermal stress better than the hAR from the PAIS subject. The E772A and R871G hARs, therefore, confer the same pattern of discordant androgen-binding parameters in transfected COS-1 cells as observed previously in the subjects' genital skin fibroblasts. This proves their pathogenicity and correlates with the relative severity of the clinical phenotype. In COS-1 cells transfected with an androgen-responsive reporter gene, trans-activation was 50% of normal in cells containing either mutant hAR. However, mutant hAR-MB binding is unstable during prolonged incubation with MB, whereas normal hAR-MB binding increases. Thus, normal equilibrium dissociation constants alone, as determined by Scatchard analysis, may not be indicative of normal hAR function. An increased k(diss) despite a normal Kd for a given androgen suggests that it not only has increased egress from a mutant ligand-binding pocket, but also increased access to it. This hypothesis has certain implications in terms of the three-dimensional model of the ligand-binding domain of the nuclear receptor superfamily.

Numerical investigation of thermal and chemical nonequilibrium flows past slender blunted cones

A steady laminar axisymmetric flow of viscous, heat conducting, nonequilibrium, partially dissociated, and ionized air past a thin slender sphere-cone is considered. The flowfield characteristics with the interplay between reactions and vibrational relaxation taken into account are investigated. An adiabatic dissociation model accounting for both nonequilibrium excitation of vibrational modes and equilibrium excitation of rotational modes of the air molecules is used to calculate thermal nonequilibrium dissociation rate constants. In the case of thermal equilibrium, the model yields a good agreement of dissociation constants with experimental data widely used in hypersonic calculations. The combined effect of the multicomponent diffusion with real binary diffusion coefficients on the heat transfer rates has been evaluated. Quantitative assessments of the influence of thermal nonequilibrium on the flow parameters have been obtained at various freestream conditions. The influence of the body surface activity with respect to accommodation of vibrational energy on the heat transfer rate has been evaluated.

Nonequilibrium dissociation rates behind strong shock waves: classical model

A model is suggested for the analytical calculation of dissociation rates behind shock waves where the vibrational temperature T v is less than the gas temperature T. The model is based on an analysis of the threshold translational energy for collision-induced dissociation as a function of initial vibrational and rotational energies. The threshold function method combined with a classical impulsive model for energy exchange yields explicit formulae for the rate coefficient k( T v, T) and the mean vibrational energy removed in dissociation. The mechanism of nonequilibrium dissociation is predicted to change during vibrational relaxation: dissociation from low vibrational levels dominates at low T v/ T, while dissociation from all levels contributes almost equally as T v/ T approaches unity. The formulae obtained exhibit an explicit dependence on the mass ratio of the dissociating molecule and its collision partner, the lighter mass of the partner making dissociation from high levels more favorable. Dissociation in a molecular gas at T > T v is demonstrated to occur predominantly via noncollinear collisions with simultaneous transfer of rotational and translational energy to the vibrational mode of the dissociating molecule.

Deactivation dynamics of vibrationally excited nitrogen molecules by nitrogen atoms. Effects on non-equilibrium vibrational distribution and dissociation rates of nitrogen under electrical discharges

The non-equilibrium vibrational distribution and the dissociation kinetics of N 2 in electrical discharges has been calculated by solving an appropriate vibrational master equation. Attention has been devoted to the role of nitrogen atoms in deactivation the vibrational distribution. To this end, a complete set of V—T (vibration—translation) deactivation rates of vibrationally excited molecules by nitrogen atoms has been calculated using a quasiclassical trajectory technique. The results show that nitrogen atoms formed by electron impact are able to deactive the high vibrational levels ( v > 25) of N 2 strongly affecting the heavy particle dissociation kinetics of N 2.

Calculation of nonequilibrium distribution functions and dissociation rate of diatomic molecules in a boundary layer

The effect of the nonequilibrium velocity and rotation distributions of the dissociating molecules on the population of the upper vibrational levels and the dissociation rate, when the reaction kinetics are strongly influenced by the motion of the gas, is analyzed by solving the Boltzmann equation by a method permitting the calculation of the distribution function under conditions of strong disequilibrium.

Monte Carlo trajectory and master equation simulation of the nonequilibrium dissociation rate coefficient for Ar+H2→Ar+2H at 4500 K

Thermally averaged rate coefficients for state-to-state rovibrational transitions and dissociation from individual states in Ar+para-H2 collisions at 4500 K are derived from Monte Carlo quasiclassical trajectory calculations. The problem of multidimensional interpolation of state-to-state rate constants is discussed, and the rate matrix is completed by nonlinear least-squares fitting. The relaxation time, the induction time, and the steady dissociation rate are calculated by a matrix eigenvalue solution of the master equation simulating a shock wave experiment on para-H2 dilute in Ar. Rotational–vibrational nonequilibrium effects are fully included. We have found that multiquantum transitions play a very significant role in determining the observable dissociation rate and that the master equation eigenmodes representing internal energy redistribution are little affected by the reaction process. The final steady dissociation rate is 2.8 times less than at local equilibrium. Various lumping schemes are tested, and we show that the original 162-state system can be well approximated by a 10-state model which predicts a factor of 2.4 for the nonequilibrium effect. However, we are unable to find equally successful models involving smaller numbers of states, and the popular vibrational ladder model and the corresponding rotational ladder model do not reproduce the full results even qualitatively.