Lindemann approach

As we already mentioned, similar considerations can be suggested and analogous expressions can be obtained for reverse processes, i.e., for reactions, which are usually considered as dissociation under the conditions of hydrocarbon oxidation. Typical examples are hydrogen peroxide and alkyl hydroperoxide decomposition. Despite existing difficulties, the Lindemann approach can be recommended as it allows ... 

In the equation above, F = 1 in the Lindemann approach and the reduced pressure... 

The ratio of the decomposition products varies with pressure as follows What would be predicted if the Lindemann approach was verified ... 

For the Lindemann approach the rates k and k would be independent of energy. In terms of ideal gas law one would have [D]/[S] = d// s[M] = RTkjk P and one should expect a linear relation of [D]/[S] versus P. This is not verified the plot has a pronounced downward curvature. The rate of decomposition should increase with an increase in the vibrational energy. 

Here MX, Y designates an outer sphere or second sphere complex. There is every reason to suppose that formation and dissociation of MX, Y occurs at rates approaching the diffusional-control limit so that the slow conversion to MY is a negligible perturbation on the equilibrium of the first step. There is a similarity here the Langmuir, the Michaelis-Menten and the Lindemann-Hinshelwood schemes. 

In the preceding expression, log(FJ is related to the depression of the fall-off curve at the center relative to the L-H expression in a og k/k ) vs. log(2f/(l -I- X)) plot. The values for F<. can then be related to the properties of specific species and reaction and temperature using methods discussed in Gardiner and Troe (1984). In Fig. 19, values of F for a variety of hydrocarbon decompositions are presented. As evident from this figure, in the limit of zero or infinite temperatures and pressures, all reactions exhibit Lindemann-Hinshelwood behavior and F approaches unity. From this figure, it is clear that L-H analysis generally does an adequate job in... 

The sequence of chapters mirrors the steps in a standard directed-evolution experiment. In the beginning, various methods for the creation of molecular diversity are considered. S. Brakmann and B.F. Lindemann (Chapter 2) present protocols for the generation of mutant libraries by random mutagenesis. Two chapters deal with the particularly powerful approach of in-vitro recombination. H. Suenaga, M. Goto, and K. Furukawa (Chapter 3) describe the application of DNA shuffling, and M. Ninkovic (Chapter 4) presents DNA recombination by the S tEP method. 

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... 

France, D. L., Griffin, T. J., Swanburg, J. G Lindemann, J. W., Davenport, G. C Trammell, V., et al. (1997). NecroSearch revisited further multidisciplinary approaches to the detection of clandestine graves, in Forensic Taphonomy The Postmortem Fate of Human Remains (W. D. Haglund and M. H. Sorg, Eds.). Boca Raton, FL CRC Press, 497-509. 

Another approach to liquid glass transition is the self-consistent phonon theory or density functional theory applied to aperiodic structures [112-114]. These theories predict the Lindemann stability criterion for the emergence of a density wave of a given symmetry. Although the finite Lindemann ratio implies a first-order phase transition, the absence of latent heat in glassy systems suggests the presence of an exponentially large number of aperiodic structures that are frozen in at Tg [94,95,110,111],... 

Some of the continuing approaches to reaction-rate theory that differ from either the simple collisional theory or the transition-state theory discussed here are cited on pages 98-112 of [4]. Examples of differing approaches may be found in particular in theories for rates of three-body radical-recombination processes [61]. Advances in methods for calculating rate constants relevant to the Lindemann view of unimolecular processes also are providing new information relevant unimolecular and bimolecular rates. Future work may be expected to produce further results of use in combustion problems. 

Troe proposed a similar approach to the calculation of the fall-off curve. In this case the zero-order approximation is the Lindemann-Hinshelwood model, formulated with the correct high and low-pressure limiting rate coefficients ... 

The lattice vibrations have a complex spectrum in various applications it is often replaced by an effective frequency t>o, and ro is taken as its reciprocal. Several approaches and formulae have been proposed for calculation of its value. In particular, Lindemann [7] proposed the relationship... 

Another approach proposed by Lindemann (1922) suggests the extended description of such reactions, which includes an explicit accounting of the formation of the excited species (marked with an asterisk) and two channels of its degradation... 

There are also some other methods that provide a more accurate description of the fall-off region than does the simple Lindemann form. The details can be found in corresponding publications (see, for example, Allison, 2005 Gilbert et al., 1983 Stewart et al., 1989 Wagner and Wardlaw, 1988). Some kinetic simulation packages (e.g., CHEMKIN) optionally realize these approaches for representation of three-body reaction rates (Kee et al., 1996). 

We have calculated the addition channel rate constant using the RRKM approach to unimolecular reaction rate theory, as formulated by Troe ( ) to match RRKM results with a simpler computational approach. The pressure dependence of the addition reaction (1) can be simply decribed by a Lindemann-Hinshelwood mechanism, written most conveniently in the direction of decomposition of the stable adduct ... 

The approach of Lindemann is based on coUisional activation of molecules as a result of energy transfer. C. N. Hinshelwood (Nobel Prize in 1956) extended this approach to include changes in vibrational energies that can be distributed internally to supply sufficient energy to the bond being broken. This approach provided a better fit to observed kinetics in the region of low pressure. 

A) + /a]. At sufficiently low pressures, where /2(A) 3, the reaction should appear to be second order, since — > i(A) and - d A)/dt = /i(A). If we refer to the Lindemann scheme, the high-pressure constancy of / corresponds to the rate-determining slow decomposition preceded by a rapid activation-deactivation step. As the pressure is decreased, the activation-deactivation step becomes slower as the binary-collision frequency decreases quadratically with pressure. Thus the rate of this activation-deactivation step tends to approach that of the decomposition step, which decreases linearly with pressure. In principle, the rate of the unimolecular decomposition of A may become rapid relative to the activation-deactivation step, and the overall reaction is then characterized by the slow bimolecular step and follows a second-order rate law. 

Simon in the meantime had been working to convert a skeptical Lindemann. At Simon s suggestion Peierls had written to Lindemann on June 2. Together at Oxford later in June they approached Lindemann in person. I do not know him sufficiently well to translate his grunts correctly, Peierls reported of the meeting. But he felt sure he had convinced him that the whole thing ought to be taken seriously. ... 

On the other hand, the strong collision treatment is quite poor in describing the shapes of the fall-off in rate with pressure for the reactions of many simpler molecules, as is shown for the case of the thermal dissociation of nitrous oxide in Figure 8.1 here, the experimental measurements [66.0] lie rather close to a strict Lindemann curve, whereas the strong collision shape exhibits a much more gradual decline. This approach to strict Lindemann behaviour is easily understood in terms of a sequential activation process as the pressure declines and we enter the fall-off region, the states just above threshold decay so quickly... 

Pyda et al. (1998) studied in detail the heat capacity of PTT by adiabatic calorimetry, standard DSC and temperature-modulated differential scanning calorimetry (TMDSC) for this measurement. The computation of the heat capacity of solid PTT is based on an approximate group vibrational spectrum and the general Tarasov approach for the skeletal vibrations, using the well-established Advanced Thermal Analysis System (ATHAS) scheme. The experimental heat capacity at constant pressure is first converted to heat capacity at constant volume using the Nemst-Lindemann approximation... 

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