Energy diffusion theory

Guo, Y., Thompson, D. L. and Miller, W. (1999) Thermal and microcanonical rates of unimolecular reactions from an energy diffusion theory approach, J.Phys.Chem. A, 103, 10308-10311. 

Thus, Ij. is the contribution to the effective group cross section for group / due to process x from all resonances of sequence (i). It is shown in Section IV that, if < ( ), the energy-dependent neutron flux, is known exactly, then, as is well known, this definition of the multigroup cross sections leads to exactly the same value of the multiplication constant as the continuous energy diffusion theory. 

It has been suggested that a sensitive test of the diffusion model would be found in the evolution of the eh yield (Schwarz, 1969). Early measurements by Hunt and Thomas (1967) and by Thomas and Bensasson (1967) revealed -6% decay within the first 10 ns and 15% decay in 50 ns. The diffusion theory of Schwarz predicts a very substantial decay ( 30%) in the first nanoseconds for instantaneous energy deposition. Schwarz (1969) tried to mitigate the situation by first integrating over pulse duration (-4.2 ns) and then over the detector response time (-1.2 ns). This improved the agreement between theory and experiment somewhat, but a hypothesis of no decay in this time scale would also agree with experiment. Thus, it was decided that a crucial test of the diffusion theory would... 

Several authors have made restricted comparisons between experiment and calculations of diffusion theory. Thus, Turner et al. (1983, 1988) considered G(Fe3+) in the Fricke dosimeter as a function of electron energy, and Zaider and Brenner (1984) dealt with the shape of the decay curve of eh (vide supra). These comparisons are not very rigorous, since many other determining experiments were left out. Subsequently, more critical examinations have been made by La Verne and Pimblott (1991), Pimblott and Green (1995), Pimblott et al. (1996), and Pimblott and LaVeme (1997). These authors have compared their... 

This is related by elementary diffusion theory to the migration coefficient A and the root-mean-square energy-displacement a according to... 

Kramers [67], Northrup and Hynes [103], and also Grote and Hynes [467] have considered the less extreme case of reaction in the liquid phase once the reactants are in collision where such energy diffusion is not rate-limiting. Let us suppose we could evaluate the (transition state) rate coefficient for the reaction in the gas phase. The conventional transition state theory needs to be modified to include the effect of the solvent motion on the motion of the reactants as they approach the top of the activation barrier. Kramers [67] used a simple model of the... 

Shalashilin and Thompson [46-48] developed a method based on classical diffusion theory for calculating unimolecular reaction rates in the IVR-limited regime. This method, which they referred to as intramolecular dynamics diffusion theory (IDDT) requires the calculation of short-time ( fs) classical trajectories to determine the rate of energy transfer from the bath modes of the molecule to the reaction coordinate modes. This method, in conjunction with MCVTST, spans the full energy range from the statistical to the dynamical limits. It in essence provides a means of accurately... 

Somewhat closer to the designation of a microscopic model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller cells of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable average length of the elementary diffusion jump must be known. But in the framework of this type of microscopic model, it is not possible to determine this parameter from first principles . 

Diffusion Theory. The diffusion theory of adhesion is mostly applied to polymers. It assumes mutual solubility of the adherend and adhesive to form a true interpliase. The solubility parameter, the square root of the cohesive energy density of a material, provides a measure of the intemiolecular interactions occurring witliin the material. Thermodynamically, solutions of two materials are most likely to occur when the solubility parameter of one material is equal to that of the other. Thus, the observation that "like dissolves like." In other words, the adhesion between two polymeric materials, one an adherend, the other an adhesive, is maximized when the solubility parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubility between adhesive and adherend. The diffusion theory is not applicable to substantially dissimilar materials, such as polymers on metals, and is normally not applicable to adhesion between substantially dissimilar polymers. 

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