Microcanonical Statistical Model Research Articles

Automated identification and calculation of prompt effects in kinetic mechanisms using statistical models

The kinetics of prompt dissociation involves rovibrationally excited species (generally formed by exothermic reactions) which may dissociate or isomerize prior to thermalization via collisions with the bath gas. Treating such rovibrationally excited species (so-called “hot” species) with standard kinetic phenomenology may result in incorrect macroscopic representation of their reactivity. This work presents the first fully automated methodology for the calculation of prompt effects of a chosen species in a kinetic mechanism, including (i) reaction selection; (ii) theoretical calculation of rate constants and prompt branching fractions; and (iii) final rate constant fitting. The energy partition between hot fragments is estimated using a variety of statistical models, including a new physically sound microcanonical statistical model based on the rovibrational density of states of the fragments. The methodology is validated against literature data for the prompt dissociations of HCO and C3H7 radicals. The microcanonical statistical model is in better agreement with trajectory simulations for larger species and is thus applicable for practical systems that typically involve large molecules, for which direct dynamics calculations are impractical. The automated workflow is applied to the evaluation of the effects of prompt dissociation for two isomeric radicals C4H71-3 (1-methylallyl) and C4H71-4 (3-buten-1-yl). Twelve H-atom abstraction reactions are selected and the corresponding rate constants are computed with first principles theory. The microcanonical statistical model predicts that prompt dissociations of C4H71-3 and C4H71-4 are already significant at 1000 K, resulting in differences of up to an order of magnitude at 2000 K with respect to the phenomenological thermal rate constants. To illustrate the effects of prompt dissociation on simulations of experimental data, the calculated prompt rate constants are implemented in both CRECK and C3MechV3.3 kinetic mechanisms. Simulations of experimental flame data illustrate the noticeable impact of prompt dissociation kinetics on the high-temperature combustion reactivity of C4H8-1 and C4H8-2.

Microcanonical Statistical Model for Fragmentation of Small Neutral Carbon Clusters

We present the microcanonical statistical model to study fragmentation of small neutral carbon clusters Cn (n ≤ 9). This model describes, at a given energy, the phase space associated with all the degrees of freedom accessible to the system (partition of the mass, translation and ro- tation, spin and angular momentum of the fragments). The basic ingredients of the model (cluster geometries, dissociation energies, harmonic frequencies) are obtained, for both the parent cluster and the fragments, by an ab initio calculation. The fragmentation channels probabilities obtained as a function of the excitation energy, were compared with the experimental data at the Orsay Tandem. The deposited energy distributions were adjusted so that the experimental measure- ments were optimally reproduced. Two algorithms were used: Non-Negative Least Squares and Bayesien backtracing. The comparison of the theoretical and experimental probabilities shows a good global agreement. Both algorithms result in deposited energy distributions showing peaks. These peaks could be the signatures of specific molecular states which may play a role in the clus- ter fragmentation.

ChemInform Abstract: State Resolved Photofragmentation of Ni(CO)4 at 193, 248, and 308 nm: A Detailed Study of the Photodissociation Dynamics.

The vibrational, rotational, and translational energy distributions for the CO photofragments from the 193, 248, and 308 nm photolysis of Ni(CO)4 in a supersonic molecular beam have been determined by vacuum ultraviolet laser‐induced fluorescence. The measured product energy distributions appeared to be statistical, with equilibrium between the degrees of freedom investigated. The distributions were significantly colder than those calculated with a microcanonical statistical model using published bond energies. To model the measured distributions, it was necessary to postulate that the unsaturated nickel carbonyl products are formed in a stable electronically excited state. By using an excited state energy consistent with published fluorescence experiments, excellent agreement was obtained between the measured distributions and those calculated using a microcanonical statistical model. These results indicate that for 193 nm photolysis, essentially all of the Ni(CO)n products are electronically excited, wi...

Freeze-out properties of multifragmentation events

Freeze-out properties of multifragmentation events produced in central 129Xe + natSn collisions at different beam energies (32, 39, 45 and 50 A MeV) were estimated by means of a simulation based on the experimental data collected by the 4 π INDRA multidetector. A rapid increase (between 32 and 45 A MeV) of the fraction of particles emitted at freeze-out is deduced. The existence of a limitation of excitation energy for fragments around 3.0–3.5 A MeV is confirmed. A comparison with the results of a microcanonical statistical model is also performed to verify the overall physical coherence of the present approach.

Microcanonical hadron production inppcollisions

We apply a microcanonical statistical model to investigate hadron production in $pp$ collisions. The parameters of the model are the energy $E$ and the volume $V$ of the system, which we determine via fitting the average multiplicity of charged pions, protons, and antiprotons in $pp$ collisions at different collision energies. We then make predictions of mean multiplicities and mean transverse momenta of all identified hadrons. Our predictions on nonstrange hadrons are in good agreement with the data, the mean transverse momenta of strange hadron as well. However, the mean multiplicities of strange hadrons are overpredicted. This agrees with canonical and grand-canonical studies, where a strange suppression factor is needed. We also investigate the influence of event-by-event fluctuations of the $E$ parameter.

Charge transfer, excitation and evaporation in low energy collisions of simple metal clusters and fullerenes with atomic targets

We present charge transfer, excitation and evaporation cross sections in low energy collisions of small and medium-size metal clusters (Nanq+, Linq+) and C60 with atomic targets (H+, He2+ and Cs) using a molecular close-coupling formalism and a post-collision rate equation model. The theoretical model benefits from different time scales associated with the collision and the internal motion of the cluster nuclei. The collision description includes the many-electron aspect of the problem and makes use of a realistic cluster potential obtained with density functional theory and a spherical jellium model. The evaporation model takes into account the non-harmonic effects of the ionic motion and describes sequential evaporation to any order within the framework of the microcanonical statistical model of Weisskopf. We show that the relative abundance of different fragments depends critically on the cluster temperature and the spectrometer time of flight window. We have found good agreement with recent experimental results [Eur. Phys. J. D 12 (2000) 185].

Evaporation of hot mesoscopic atomic metal clusters

The evaporation times of hot mesoscopic sodium clusters are estimated using the microscopic and microcanonical statistical model of Weisskopf and the macroscopic canonical kinetic gas theory. The level density of liquid sodium clusters as function of the internal excitation energy is computed from the experimentally known thermodynamic quantities of the bulk matter. In using the known temperature dependent surface tension and standard thermodynamics, both theories are corrected to take into account finite size effects. By this method it is possible to obtain decay rates and internal level densities of mesoscopic clusters at excitations where any harmonic approximation breaks down. For clusters having more than about 200 atoms, the evaporation times obtained from the two models are practically equal.

Calculated patterns for multifragment reduced velocity correlation functions

We have investigated the utility of multifragment reduced velocity correlation functions as probes for nuclear fragmentation. Within the framework of the microcanonical statistical model, correlation functions for fragment multiplets (three or more fragments) are found to exhibit characteristic signatures which are strongly enhanced compared to those for two-fragment correlation functions. Further, it is demonstrated that a “pure multiplet” contribution can be extracted from high-order reduced velocity correlation functions. It is proposed that these new/enhanced signatures can provide good probes for multifragment disassembly.

State resolved photofragmentation of Ni(CO)4 at 193, 248, and 308 nm: A detailed study of the photodissociation dynamics

The vibrational, rotational, and translational energy distributions for the CO photofragments from the 193, 248, and 308 nm photolysis of Ni(CO)4 in a supersonic molecular beam have been determined by vacuum ultraviolet laser-induced fluorescence. The measured product energy distributions appeared to be statistical, with equilibrium between the degrees of freedom investigated. The distributions were significantly colder than those calculated with a microcanonical statistical model using published bond energies. To model the measured distributions, it was necessary to postulate that the unsaturated nickel carbonyl products are formed in a stable electronically excited state. By using an excited state energy consistent with published fluorescence experiments, excellent agreement was obtained between the measured distributions and those calculated using a microcanonical statistical model. These results indicate that for 193 nm photolysis, essentially all of the Ni(CO)n products are electronically excited, with about 2.8 eV of electronic excitation. The Ni(CO)n products from 248 nm photolysis are formed in both the ground and excited states, with a 3:1 branching ratio. The data taken at 308 nm also indicate the presence of both channels, with the excited state channel still important. These results are consistent with predictions of earlier ab initio work, although the detailed mechanism is somewhat different. This earlier work is discussed in light of the present results.