Surface electron gas model

Pyzhov Equation. Temkin is also known for the theory of complex steady-state reactions. His model of the surface electronic gas related to the nature of adlay-ers presents one of the earliest attempts to go from physical chemistry to chemical physics. A number of these findings were introduced to electrochemistry, often in close cooperation with -> Frumkin. In particular, Temkin clarified a problem of the -> activation energy of the electrode process, and introduced the notions of ideal and real activation energies. His studies of gas ionization reactions on partly submerged electrodes are important for the theory of -> fuel cell processes. Temkin is also known for his activities in chemical -> thermodynamics. He proposed the technique to calculate the -> activities of the perfect solution components and worked out the approach to computing the -> equilibrium constants of chemical reactions (named Temkin-Swartsman method). 

Nevertheless, except in these extreme cases (very slow ions and grazing incidence geometry) in which the ion does not get close enough to the surface, it can be considered a weak perturbation, no effect related to the insulator character of the target could be observed. In other words, the same free electron gas model that is used to obtain the stopping power of slow ions in metals showed to be applicable in the case of insulators [65,66]. 

In distinction from the more refined, and thus much more complicated lattice-gas model, the form of the model of the surface electronic gas provides possibilities for its application to chemisorption of gas mixtures and thus to modelling of kinetics of complex reactions. Derivation of multicomponent chemisorption isotherms based on thermodynamic approach was presented in the previous chapter. Within the framework of this model the following generalized elementary reaction A+ZI+Z=>S is considered. This reaction is written as a three-body collision, which is highly improbable, but is presented here only for illustrative purposes of how to express the reaction rate... 

According to the elementary free-electron gas model of a metal, the metal electrons move in a flat, position-independent potenti2d. The average charge density due to the positive nuclear charges is equal to that of the negative charge of the electrons. At the surface the attractive potential is zero. The potential model is illustrated in Fig.(2.14). 

If the energy is assumed to be independent of the z component of the momentum, we obtain the two-dimensional electron gas model, Et = h kl+ k y)l2m. The Fermi surface is a cylinder with diameter 2kp. The functional form of x(q) is... 

In addition for the noble metals further extension of the free electron gas model is necessary for higher frequencies co > cop. Though the response is essentially determined by free s-electrons, the filled d-band close to the Fermi surface represent a highly polarizable background which can be described by a dielectric constant s c (typically 1 < oo < 10), and we can write ... 

Decay rates in a 3D electron gas model (Pegm, see Eq. (6.22)) of holes with the energy of the Shockley surface-state at P are also displayed. From Ref [37]. 

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

Since each atom in a f.c.c. array of purely metallic atoms is the same as every other atom (except at the surface), only a representative positive ion needs to be considered. Let it interact with a spherical portion (radius = R) of the electron gas which has a density of one electron per ion. This is called the jellium model. 

In the past the theoretical model of the metal was constructed according to the above-mentioned rules, taking into account mainly the experimental results of the study of bulk properties (in the very beginning only electrical and heat conductivity were considered as typical properties of the metallic state). This model (one-, two-, or three-dimensional), represented by the electron gas in a constant or periodic potential, where additionally the influence of exchange and correlation has been taken into account, is still used even in the surface studies. This model was particularly successful in explaining the bulk properties of metals. However, the question still persists whether this model is applicable also for the case where the chemical reactivity of the transition metal surface has to be considered. 

The most basic information that is needed for constructing a global potential energy surface for gas phase MD simulations is the structures and vibrational frequencies. The earliest information about gas-phase RDX molecular structures was obtained from theoretical calculations [54-58]. In 1984 Karpowicz and Brill [59] reported Fourier transform infrared spectra for vapor-phase (and for the a - and p -phase) RDX in 1984, however, their data precluded a complete description of the molecular conformations and vibrational spectroscopy. More recently, Shishkov et al. [60] presented a more complete description based on electron-scattering data and molecular modeling. They concluded that the data were best reproduced by RDX in the chair conformation with all the nitro groups in axial positions. 

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