Transmission coefficient, definition

Unfortunately, there are usually large discrepances in the different treatments of activated complex theory, concerning the definitions and the results of calculations of the "transmission coefficient" or the"tunneling correction"/19/ ... 

The conditions (133.HI) mean that the tunneling through the adiabatic potential barriers (99.HI) is neglected however, the non-adiabatic transitions from a lower to a higher electronic state are not excluded. The reflexion effects due to the reaction path curvature may be simply included in the dynamical definition (121.11) of the reaction coordinate. An adiabatic separation of that coordinate may be also used as an approximation at these conditions. Then, the "transmission coefficient — 1 takes into account only sudden changes... 

The terms, electromechanical coupling factor, energy transmission coefficient, and efficiency are sometimes confused (5. All are related to the conversion rate between electrical energy and mechanical energy, but their definitions are different [6]. 

We will demonstrate later that the transmission coefficient (or transmittance, cf. Sec. 5.3a) is identical, from a physical standpoint, with our previous definition of the albedo [cf. Eq. (5.111)]. It is appropriate, then, to use the same symbol. 

The tunnel correction is not now a fundamentally defined number rather it is defined by the equation Q = kobJk, where kobs is the observed rate constant for a chemical reaction and k is that calculated on the basis of some model which is as good as possible except that it does not allow tunnelling. In this chapter the definition used for k is that calculated by absolute reaction rate theory [3], i.e., k = KRT/Nh)K where X is the equilibrium constant for the formation of the transition state. The factor k, the transmission coefficient, is also a quantum correction on the barrier passage process, but it is in the other direction, that is k < 1. We shall here follow the customary view (though it is not solidly based) that k is temperature-independent and not markedly less than unity. The term k is used following Bell [1] the s stands for semi-classical, that is quantum mechanics is applied to vibrations and rotations, but translation along the reaction coordinate is treated classically. 

The attenuation of tunneling-ray power in Eq. (7-3) depends on the product y(P, l)z, where the attenuation coefficient is the ratio of the transmission coefficient r to the ray half-period Zp. For the step profile, the latter is given in Table 2-1, page 40, and we use the linear approximation of Eq. (7-21) for T, which is an excellent approximation for all but the most weakly tunneling rays. If we express k in terms of the fiber parameter using the definition inside the front cover, then... 

Tunneling rays whose radiation caustics are not too far from the interface of a circular fiber have a transmission coefficient given by Eq. (35-49b). We replace the ray invariants in the exponent by their definitions of Eq. (2-7) in terms of the angles shown... 

The transmission coefficient must be the same for the forward and reverse reaction (this vanishes in the equilibrium constant definition, which is the ratio of two rate coefficients). Useful information regarding a can therefore be deduced from the study of the reverse reaction. It has led authors to define the theoretical transmission coefficient as ... 

Thickness. The traditional definition of thermal conductivity as an intrinsic property of a material where conduction is the only mode of heat transmission is not appHcable to low density materials. Although radiation between parallel surfaces is independent of distance, the measurement of X where radiation is significant requires the introduction of an additional variable, thickness. The thickness effect is observed in materials of low density at ambient temperatures and in materials of higher density at elevated temperatures. It depends on the radiation permeance of the materials, which in turn is influenced by the absorption coefficient and the density. For a cellular plastic material having a density on the order of 10 kg/m, the difference between a 25 and 100 mm thick specimen ranges from 12—15%. This reduces to less than 4% for a density of 48 kg/m. References 23—27 discuss the issue of thickness in more detail. 

Permeability is defined as the product of the diffusion constant and the solubility coefficient. Water vapor permeability (WVP] is defined as the time rate of water vapor transmission through unit area of flat material with a definite unit thickness induced by unit vapor pressure difference between two specific surfaces, and under indicated temperature and humidity conditions. (ASTM E 96, Standard Test Method for Water Vapor Transmission of Materials]. 

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