Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties-A Review.

It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures Ti (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows.

Quasi-Classical Trajectory Study of the CN + NH3 Reaction Based on a Global Potential Energy Surface.

Based on a combination of valence-bond and molecular mechanics functions which were fitted to high-level ab initio calculations, we constructed an analytical full-dimensional potential energy surface, named PES-2020, for the hydrogen abstraction title reaction for the first time. This surface is symmetrical with respect to the permutation of the three hydrogens in ammonia, it presents numerical gradients and it improves the description presented by previous theoretical studies. In order to analyze its quality and accuracy, stringent tests were performed, exhaustive kinetics and dynamics studies were carried out using quasi-classical trajectory calculations, and the results were compared with the available experimental evidence. Firstly, the properties (geometry, vibrational frequency and energy) of all stationary points were found to reasonably reproduce the ab initio information used as input; due to the complicated topology with deep wells in the entrance and exit channels and a "submerged" transition state, the description of the intermediate complexes was poorer, although it was adequate to reasonably simulate the kinetics and dynamics of the title reaction. Secondly, in the kinetics study, the rate constants simulated the experimental data in the wide temperature range of 25-700 K, improving the description presented by previous theoretical studies. In addition, while previous studies failed in the description of the kinetic isotope effects, our results reproduced the experimental information. Finally, in the dynamics study, we analyzed the role of the vibrational and rotational excitation of the CN(v,j) reactant and product angular scattering distribution. We found that vibrational excitation by one quantum slightly increased reactivity, thus reproducing the only experimental measurement, while rotational excitation strongly decreased reactivity. The scattering distribution presented a forward-backward shape, associated with the presence of deep wells along the reaction path. These last two findings await experimental confirmation.

VTST and RPMD kinetics study of the nine-body X + C2H6 (X ≡ H, Cl, F) reactions based on analytical potential energy surfaces.

Thermal rate constants of nine-atom hydrogen abstraction reactions, X + C2H6 → HX + C2H5 (X ≡ H, Cl, F) with qualitatively different reaction paths, have been investigated using two kinetics approaches - variational transition state theory with multidimensional tunnelling (VTST/MT) and ring polymer molecular dynamics (RPMD) - and full dimensional analytical potential energy surfaces. For the H + C2H6 reaction, which proceeds through a noticeable barrier height of 11.62 kcal mol-1, kinetics approaches showed excellent agreement between them (with differences less than 30%) and with the experiment (with differences less than 60%) in the wide temperature range of 200-2000 K. For X = Cl and F, however, the situation is very different. The barrier height is either low or very low, 2.44 and 0.23 kcal mol-1, respectively, and the presence of van der Waals complexes in the entrance channel leads to a very flat topography and, consequently, imposes theoretical challenges. For the Cl(2P) reaction, VTST/MT underestimates the experimental rate constants (with differences less than 86%), and RPMD demonstrates better agreement (with differences less than 47%), although the temperature dependence is opposite to the experiment at low temperatures. Finally, for the F(2P) reaction, available experimental information shows discrepancies, both in the absolute values of the rate constants and also in the temperature dependence. Unfortunately, kinetics theories did not resolve this discrepancy. Different possible causes of these theory/experiment discrepancies were analyzed.

The hydrogen abstraction reaction H + C2H6→ H2(v,j) + C2H5. Part I. A full-dimensional analytical potential energy surface based on ab initio calculations.

Using as input data high-level structure electronic calculations, a new full-dimensional analytical potential energy surface (PES), named PES-2018, was developed for the title reaction, which is a valence bond/molecular mechanics based surface that depends on a set of adjustable parameters. The title reaction is practically thermoneutral, -0.18 kcal mol-1, with a high barrier, 11.62 kcal mol-1, and it presents features that make it very interesting for kinetics and dynamics studies. The PES simulates the high-level ab initio calculations used in the fitting process, with differences of less than 0.5 kcal mol-1. The quality of the fitting and the analytical expression was tested by comparing the results from this PES to different ab initio data. In the light of these results we believe that the new PES-2018 surface presents great versatility and satisfactory behaviour for the description of the nine-body reactive system. Based on this PES, in a forthcoming paper (Part II) an exhaustive kinetics and dynamics study of the title reaction will be presented.