Strong collision assumption

The next step in the Hinshelwood model is to invoke the strong collision assumption. This says that after every collision, the molecule s final energy is uncorrelated with its energy before the collision. Such collisions establish an equilibrium (i.e., Boltzmann) population distribution as in Eq. 10.114. From the steady-state analysis earlier, Eq. 9.107, the fraction of molecules excited with energy e or above is... 

The collisional stabilization (de-activation) efficiency is assumed to be unity, which is consistent with the strong collision assumption. Thus the stabilization rate constant ks is equal to the hard-sphere rate constant kHS, and Eq. 10.120 becomes... 

Consistent with the finding in the previous section, we assume that the rate coefficient for the excitation step is not a constant. It is assumed to depend on n, the total number of vibrational quanta transferred to the excited intermediate C. The analysis to this point has also included a strong collision assumption, basically that all collisions are effective enough to deactivate the excited intermediate. In actuality this is often not the case. A collision efficiency will be introduced to account for this fact. 

The strong collision assumption is often invoked to equate ks with the hard-sphere rate constant kns This approximation assumes that every collision of C (n) with another molecule M will completely stabilize (deactivate) the excited molecule. It fact different collision partners are more or less effective in such deactivation. A collision efficiency fi is introduced to account for this effect ... 

Figure 1.2 Pressure dependence of the unimolecular rate constant for CH3NC CH3CN isomerization. For clarity, the 260° and 200° curves are displaced by one log unit to the left and right, respectively. (All three curves are nearly identical.) The solid lines through the data are RRKM calculated rates with the strong collision assumption. Taken with permission from Schneider and Rabinovitch (1962).

Thus, a plot of (k pp) versus the gas pressure [M] yields a straight line with intercept ( a[/iv]) > and slope k /(k [hv]k(E)). Since the photoactivation rate, k [hv] is known from the intercept, the slope permits the determination of the ratio kJk(E). An example of such a Stem-Volmer plot is shown in Figure 5.17 for the isomerization of the previously mentioned allyl isocyanide reaction, C3H5NC —C3H5CN, in which k [hv] k pp is plotted. This results in an intercept of 1.0 and a slope of kJk(E). The quantity of interest, k(E), can be extracted if we know the deactivation rate, k. This is generally taken to be equal to the gas kinetic collision rate constant (strong collision assumption), which is typically about 10 cm3/(molec sec). 

The rate results from Stem-Volmer plots depend directly upon the assumption that k is equal to the collision rate. This can be checked by diluting the sample gas with different inert collision partners. Unfortunately, because the product yield drops as the pressure is increased, these experiments have generally been done with neat samples. However, the Stem-Volmer plot also contains an internal check on the strong collision assumption. Suppose that a single collision does not completely stabilize the excited molecule so that it can continue to react, but at a lower rate. Residual reactivity at the... 

Since the collisional and the intramolecular reaction steps enter into the experimental observables, one has to adc how sensitively the measured quantity depends on Ae particular collisional model, Z(E) and P(E /E), and the specific rate constants k E) of the intramolecular process. If the measured quantity is essentially given by some ratio of the effective rate constants of the two processes, the one factor cannot be derived better than the other. This trivial statement has been violated frequently specific rate constants k(E) have been determined under the (often inadequate) strong-collision assumption properties of collisional energy transfer have been derived on the basis of (often uncertain) calculated specific rate constants k E). These uncertainties cannot be removed as long as the competing processes are not measured separately in time-resolved experiments. 

The review of pressure-dependent reactions, which so far was based on the strong collision assumption, is readily adapted to more sophisticated collision models. Here, we discuss the description of unimolec-ular reactions in form of the ME. Our initial scheme... 

The (modified) strong collision assumption allows us to separate this reaction into several steps... 

This complex contains, as internal energy, energy that is released as the Rad -Rad2 bond forms. Here ku is assumed to be independent of the internal energy of (RadiRad this is often referred to as the strong collision assumption . 

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