Thiele theory

These points need emphasizing, for the use of free valence as a measure of reactivity was first introduced on intuitive grounds, based on the Thiele theory of partial valence. On this basis there seems no obvious reason why free valence should serve as a measure of reactivity only for compounds of one type. The perturbational treatment given above shows that the validity of the correlation is due merely to a fortuitous coincidence which holds only for alternant hydrocarbons. 

Furthermore, it can be shown that Qv can be predicted on the basis of the Thiele theory for irreversible first order reaction. 

I hc Ov value is found to vary mainly with the type of catalyst and pore size. This variation can be predicted by the Thiele theory. 

Thiele Theory of diffusion and reaction in porous solids... 

However, the behavior of the catalysts measured in this work is different. At temperatures above 400 K the catalytic activity becomes limited, in agreem t with the Thiele theory. However, the apparent activation energy gradually decreases from 94 to 6 kJ/mol, rather than to 50 kJ/mol, which implies that the apparent activation energy of diffusion is exhibited. Nevertheless, the size of the wider pores in the pellet does appear to affect strongly the activity. Therefore, it is impossible that merely external diffusion limitation, that is, diffusion from the bulk of the gas flow to tiie external surface of the catalyst body, is rate-determining. Since the catalyst spheres had the same diameter, the activity of all catalysts should be equal if external transport is determining the activity. As the concentration of reactants inside the particle is nearly zero, the pore size should be of no importance. However, this is in contradiction with the measurements. 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Meohanios (Adv. Chem. Phys. XCiti) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

Thiel, W., 1998. Thermochemistry from Semiempirical MO Theory, In Irikura, K. K. Frurip, D. J. Eds., 1998. Computational Thermochemistry. American Chemical Society, Washington, DC. 

Note that this parameter has the same form as the Thiele number which occurs in the theory of diffusion/reac tion in catalyst pores. 

This by no means exhausts the list of structures proposed for benzene. The remainder, however, such as the structure of Thiele based upon his theory of partial valence and that of Collie based upon a dynamic model, are usually complicated and cannot be represented in any simple valence scheme. 

Problem P7.06.02 reproduces one result from the literature. There it is apparent that in some ranges of the parameters, effectiveness can be much greater than unity, and also that at low values of Thiele modulus several steady states are possible. When both external and internal adiabatic diffusion occur, moreover, other studies find that half a dozen or more steady states can exist. Those kinds of findings involve much computer work. A book by Aris (Mathematical Theory of Diffusion and Reaction in Permeable Catalysts,... 

Thus in 1899, Johannes Thiele extended his valence theory of double bonds to include colloids. Thiele suggested that in such materials as polystyrene the molecules of styrene were bound together merely by association of the double bonds. He referred to this association as "partial valence" (21). In 1901, Rohm concluded that the transformation of acrylic esters into polymers was from an "allotropic alteration" and not a chemical reaction (22). Schroeter, working with salicylides just as Kraut, Schiff, and Klepl before him, concluded that the tetrameric salicylide was formed by "external forces about the monomeric molecules", and that the chemical structures of the monomers were unaltered (23). Thus the association theory rapidly grew in popularity. 

According to K. H. Meyer, this surprising reactivity—which is also encountered amongst the enols—is explained by the fact that the OH-group activates the double bond adjacent to it and the two neighbouring double bonds of the conjugated system (Thiele s theory) are also involved in this activation. Phenol, therefore, can yield 1 2- and 1 4-substitution products with bromine, addition reactions first taking place ... 

A classic example is the dimerization of methyl cyclopentadienylcarboxylate (37) to Thiele s ester (38)67. Although diene 37b should be more reactive than 37c according to the FMO theory, it was diene 37c that reacted with diene 37b (equation 17). 

H. Lin, J. Zheng, and W. Thiel, Mol. Phys., 2005, 103, 359], and it makes use of dipole moment surfaces calculated ab initio. We apply the theory to NH3 and demonstrate that the theoretical results show good agreement with experimental findings. 

M. Korth and W. Thiel. Benchmarking semiempirical methods for thermochemistry, kinetics, and noncovalent interactions OMx methods are almost as accurate and robust as DFT-GGA methods for organic molecules, J. Chem. Theory Comput., 7 2929-2936 (2011). 

A. Kazaryan, Z. G. Lan, L. V. Schafer, M. Filatov, and W. Thiel. Surface hopping excited-state dynamics study of the photoisomerization of a light-driven fluorene molecular rotary motor, J. Chem. Theory Comput., 1 2189-2199 (2011). 

M. R. Silva-Junior and W. Thiel. Benchmark of electronically excited states for semiempirical methods MNDO, AMI, PM3, OMl, OM2, OM3, INDO/S, and INDO/S2, J. Chem. Theory Comput., 6 1546-1564 (2010). 

Thiel WJ. The theory of fluidization and application to the industrial processing of pharmaceutical products. Int J Pharm Tech Prod Manuf 1981 2(5). Thiel WJ. Solids mixing in gas fluidized beds. Int J Pharm Tech Prod Manuf 1981 2(9). 

This study employed conventional diffusion-reaction theory, showing that with diffusion-limited reactions the internal effectiveness factor of a heterogeneous catalyst is inversely related to the Thiele modulus. Using a standard definition of the Thiele modulus [100], the observed reaction rate of an immobilized-enzyme reaction will vary with the square root of the immobilized-enzyme concentration in a diffusion-limited system. In this case, a plot of the reaction rate versus the enzyme loading in the catalyst formulation will be nonlinear. 

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