Lindemann

The correct treatment of the mechanism (equation (A3.4.25), equation (A3.4.26) and equation (A3.4.27), which goes back to Lindemann [18] and Hinshelwood [19], also describes the pressure dependence of the effective rate constant in the low-pressure limit ([M] < [CHoNC], see section A3.4.8.2). 

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

This approxunation is generally valid if For the Lindemann mechanism of unimolecular reactions... 

Lindemann F A 1922 Discussion on the radiation theory of chemical reactions Trans. Faraday Soo. 17 598-9... 

This ensures the correct connection between the one-dimensional Kramers model in the regime of large friction and multidimensional imimolecular rate theory in that of low friction, where Kramers model is known to be incorrect as it is restricted to the energy diflfiision limit. For low damping, equation (A3.6.29) reduces to the Lindemann-Flinshelwood expression, while in the case of very large damping, it attains the Smoluchowski limit... 

Lindemann F 1922 A discussion on the radiation theory of chemicai action Trans. Faraday Soc. 17 598-606... 

Nitration of a series of methyl-1,2-benzisoxazoles was studied by Tahkar and Bhawal using fuming nitric acid and sulfuric acid in acetic acid at 100 °C. 3-Methyl-1,2-benzisoxazole gave a mixture of 5-nitro- and 5,7-dinitro-3-methyl-l,2-benzisoxazole, with the 5-nitro isomer predominant. The product obtained from 3,5-dimethyl-1,2-benzisoxazole was the 4-nitro derivative and not the 7-nitro compound as proposed by Lindemann (26LA(449)63). The synthesis of the 7-nitro compound by an alternative method was used as structural proof. Two products were obtained from 3,6-dimethyl-l,2-benzisoxazole and these were the 5-nitro and 5,7-dinitro derivatives. 3,7-Dimethyl-l,2-benzisoxazole was converted into the 5-nitro derivative (Scheme 25) (77lJC(B)l06l). 

Sample cells include Lindemann/capillary tubes (normally < 1 mm in diameter) and aluminium holders. In the latter, thin aluminium windows sandwich the sample in a cylindrical aluminium sample holder. The diffraction from the aluminium is observed in this case, and may be used as a calibration standard. For low-temperature materials, the aluminium window can be replaced by the polymer Kapton. Beryllium may also be used [14]. Sample volumes of between 50 and 100 pL are typically required. 

Lothar Lindemann, Marius C. Hoener F. Hoffinann-La Roche, Pharmaceuticals Division, Discovery Neuroscience, Basel, Switzerland... 

Lindemann L, Hoener MC (2005) A renaissance in trace amines inspired by a novel GPCR family. Trends Pharmacol Sci 26 274-281... 

The method just described leads to the mean specific heats over a fairly large range. Nernst, Koref, and Lindemann (1910) have recently described a method of measuring the true specific heat at a given low temperature. The substance is contained in a block of copper cooled to the requisite temperature in liquid carbon dioxide, liquid air, etc., and energy is supplied by a heating spiral of platinum wire carrying an electric current, the measurement of the resistance of which serves at the same time to determine the temperature. 

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... 

Lindemann <8> has made an interesting application of the new theory in the determination of the frequency of atomic vibration, r, from the melting-point. He assumes that at the melting-point, T the atoms perform vibrations of such amplitude that they mutually collide, and then transfer kinetic energy like the molecules of a gas. The mean kinetic energy of the atom will then increase by RT when the liquid is unpolymerised and the fusion occurs at constant volume this is the molecular heat of fusion. 

That this is not the case follows from the experimental data discussed by A. Russell (9), and F. Koref (10) has attempted to calculate the change of frequency of an element when it enters into combination by means of the alteration of melting-point and atomic volume. According to Lindemann s equation, for the combined atom ... 

Page 14, line 2 The method of Nernst, Koref, and Lindemann, by the use of the copper-calorimeter, determines the mean specific heat over a range of temperature. The mode of procedure is the same as in ordinary calorimetry, except that a hollow block of copper, the temperature of which is determined by means of inserted thermoelements, is used instead of a calorimetric liquid, and the method therefore made applicable to very low temperatures. 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

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