Lindemann-Hinshelwood expression

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

The reaction of OH with nitric acid has been smdied extensively (Margitan et al., 1975 Smith and Zellner, 1975 Wine et al., 1981 Ravishankara et al., 1982 Margitan and Watson, 1982 Kurylo et al., 1982 Jourdain et al., 1982 Marinelli and Johnston, 1982 Smith et al 1984 Devolder et al., 1984 Connell and Howard, 1985 Jolly et al., 1985 Stachnik et al., 1986 Brown et al., 1999 Carl et al., 2001). The rate coefficient of the reaction has been found to be pressure and temperature dependent. Below 350 K, the reaction shows a negative temperature dependence with small pressure dependence at ambient temperature, and sttong pressure dependence at lower temperatures (Brown et al., 1999). The recommended pressure dependence of the rate coefficient is obtained by combining a low pressure bimolecular limit, ko, with a Lindemann-Hinshelwood expression (Brown et al., 1999 Sander et al., 2(X)6) ... 

Equation (2.11) can be considered as a switching function describing the transition of k from feo to k with a value of k = k /2 at the center of the fall-off curve. We call Eq. (2.11), which is based on the model for unimolecular reactions that was first given 50 years ago by Lindemann and Hinshelwood, the Lindemann-Hinshelwood expression. It is shown in Fig. 2. 

Here log F ent gives the depression of the fall-off curve at the center relative to the Lindemann-Hinshelwood expression in a log k/k y sAog x) plot like Fig. 2. It turns out that F ent is a weak function of T and the nature of M that can be estimated by theory. Experimental fall-off curves can be fitted to the form of Eq. (2.13) and characterized by the three quantities ko, k, and F enf In essence, Eq. (2.13) is a first step beyond the Lindemann-Hinshelwood expression. Still more realistic, but more complex, expressions are given in Section 5. 

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... 

In the Lindemann-Hinshelwood theory the Lindemann expression for the uni-molecular rate constant, Eq. (9), is still assumed to be correct, but an improved activation rate coefficient is obtained from the Hinshelwood formulation. The shape of the fall-off curve should therefore still be the simple form predicted by Lindemann. Reference to Fig. 2 shows that, for the cyclobutane decomposition reaction, the change in the activation rate coefficient brings the theory much closer to the experimental results, particularly at low pressure. However, the shape of the fall-off curve is still not correct the Lindemann-Hinshelwood model predicts a faU-off region that is too narrow, the true fall-off is broader. 

There is no reason for this expression to be consistent with the Lindemann straight line plot, but it is instructive to examine the physical reasons for the curvature. The low pressure limit is the same as in the Lindemann-Hinshelwood theory because the rate determining step is activation, which is dealt with in the same way in the two theories. This can be seen by taking the low pressure limit of Eq. (21). 

Bimolecular steps involving identical species yield correspondingly simpler expressions. A3.4.8.2 THE LINDEMANN-HINSHELWOOD MECHANISM FOR UNIMOLECULAR REACTIONS... 

The expression for N t, E) in equation (A3.12.67) has been used to study [103.104] how the Porter-Thomas P k) affects the collision-averaged monoenergetic unimolecular rate constant k (Si, E) [105] and the Lindemann-Hinshelwood unimolecular rate constant T) [47]. The Porter-Thomas P k) makes k, E) pressure... 

Lindemann-Hinshelwood theory makes the assumption that a single collision with a bath gas molecule M is sufficient to deactivate AB to AB. In reality, each collision removes only a fraction of the energy. To account for the fact that not all collisions are fully deactivating, Troe (1983) developed a modification to the Lindemann-Hinshelwood rate expression. In the Troe theory, the right-hand side of... 

We concentrate attention first on the broadening factor defined in Eq. (2.13), which defines the depression of the fall-off curve at the center relative to the Lindemann-Hinshelwood function. F ent can be expressed to good approximation by the three parameters and is defined... 

In Hinshelwood s treatment, the molecule A is allowed to acquire an amount of energy El at an enhanced rate. The rate at which A converts to A is independent of that energy. Let us take the expression for first order rate constant given by Lindemann s theory, i.e. 

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