Lindemann and

There is, however, little exact data for its application. Lindemann and Magnus found that C, could be fairly well represented by adding to Einstein s equation an arbitrary term... 

M. Doch, A. Hammerschmidt, A. Lindemann and B. Krebs, Phys. Chem. 

Infra-red, microwave, and X-ray photoelectron spectroscopy Infra-red and ultra-violet spectroscopy has been widely used for investigating the structure of intermolecularly hydrogen-bonded complexes in the solid state (Novak, 1974) and in solution (Zundel, 1976, 1978 Clements et al., 1971a,b,c Pawlak et al., 1984). By analysing the infra-red spectra of equimolar liquid mixtures of amines with formic or acetic acid, the relative importance of structures [10] and [11] was estimated (Lindemann and Zundel, 1977). It was proposed that [10] and [11] make equal contributions to the observed structure of the complex when the p -value of the carboxylic acid is approximately two units lower than that of the protonated amine. 

The use of centrifuges for isotope enrichment was suggested by Lindemann and Aston as early as 1919, but success required the development of vacuum centrifuges in the late 1930s. The rotors in such devices are suspended in vacuum chambers and gas is introduced and withdrawn through metal capillaries. Introductory discussions have been given by London (1961) and Benedict et al. (1981). 

P. Ruther, M. Ehmann, T. Lindemann, and O. Paul. Dependence of the Temperature Distribution in Micro Hotplates on Heater Geometry and Heating Mode , Proc. IEEE Transducers 03, Boston, MA, USA (2003), 73-76. 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

Fig. 3.49 Graphical display of chemicals shifts for classes of paraffins. Data reproduced from L. P. Lindemann and J. Q. Adams (1971). Analyt. Ckem., 43(10), 1251.

M. D. Lindemann, and J. H. Wilson, Effectiveness of Natuphos phytase in improving the bioavailabilities of phosphorus and other nutrients in soybean metal-based semipurified diets for young pigs,/. Anim. Sci. 1996a, 74, 1601-1611. 

This problem was resolved in 1922 when Lindemann and Christiansen proposed their hypothesis of time lags, and this mechanistic framework has been used in all the more sophisticated unimolecular theories. It is also common to the theoretical framework of bimolecular and termolecular reactions. The crucial argument is that molecules which are activated and have acquired the necessary critical minimum energy do not have to react immediately they receive this energy by collision. There is sufficient time after the final activating collision for the molecule to lose its critical energy by being deactivated in another collision, or to react in a unimolecular step. 

How thermal activation can take place following the Lindemann and the Lindemann-Hinshelwood mechanisms. An effective rate constant is found that shows the interplay between collision activation and unimolecular reaction. In the high-pressure limit, the effective rate constant approaches the microcanonical rate... 

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