Energy-Transfer-Limited Processes

Many association reactions, as well as their reverse unimolecular decompositions, exhibit rate parameters that depend both on temperature and pressure, i.e., density, at process conditions. This is particularly the case for molecules with fewer than 10 atoms, because these small species do not have enough vibrational and rotational degrees of freedom to retain the energy imparted to or liberated within the species. Under these conditions, energy transfer rates affect product distributions. Consequently, the treatment of association reactions, in general, would be different than that of the fission reactions. 

Energy transfer limitations have long been recognized to affect the rates and mechanisms of fission and association reactions (Robinson and Holbrook, 1972 Laidler, 1987). In addition, it is increasingly being recognized that many exothermic bimolecular reactions can exhibit pressure-(density)-dependent rate parameters if they proceed via the formation of a bound intermediate. When energy transfer limitations exist, the rate coefficients exhibit non-Arrhenius temperature dependencies—i.e., the plots of ln(k) as a function of l/T are curved. 

The importance of energy transfer limitations can be illustrated best by 

The presence of additional product channels can also be considered. In this analysis M represents any collision partner ([M] = P/RT), the parameters and kj are the rate coefficients for energization and de-energization of A as a consequence of intermolecular collisions, and fi represents the efficiency of collisional energy transfer given by (Gardiner and Troe, 1984) 

Average Collisional Energies Transferred for Various Gases (from Gardiner and Troe, 1984) 

---

It is convenient initially to classify elementary reactions either as energy-transfer-limited or chemical reaction-rate-limited processes. In the former class, the observed rate corresponds to the rate of energy transfer to or from a species either by intermolecular collisions or by radiation, or intramolecular-ly due to energy transfer between different degrees of freedom of a species. All thermally activated unimolecular reactions become energy-transfer-limited at high temperatures and low pressures, because the reactant can receive the necessary activation energy only by intennolecular collisions. 

Since the development of fundamental working equations for energy-transfer-limited reactions requires the knowledge of the rates of chemical processes, we will discuss the latter first. 

Based upon the electrodics, the exchange current density is related to the activation energy (16. pp.ll52). For an Arrhenius relation for the effect of temperature upon corrosion rate, AG and AG j are analogous to activation energy and equal 6.44 kcal/mol and 4.30 kcal/mol, respectively. The literature indicates activation energies for mass transfer limited processes range between 1 and 3 kcal/mol and for reaction limited between 10 and 20 kcal/mol (12). Based upon this criteria, corrosion of the 304 S.S. in pure water in the experimental system may lie between the mass transfer and reaction rate limited cases. 

As mentioned earlier, in laboratory reactors the global rate is measured directly, and the question is whether these rates are influenced by extenlal physical processes. In this section we shall consider the method of solution for an isothermal case. Combined mass- and energy-transfer limitations are discussed in Sec. 10-4. 

After we have fuUy characterized the pseudocomponent and any tme components in the process model, we must choose a thermodynamic model. The thermodynamic model here refers to a framework that allows us to describe whether a particular mixture of components forms one phase or two phases, the distribution of components within these phases and material and energy flows of these phases given a set of process conditions. Process thermodynamics also set material and energy transfer limits on various fractionation and reaction units in the model and in the actual plant itself... 

Note that in the low pressure limit of iinimolecular reactions (chapter A3,4). the unimolecular rate constant /fu is entirely dominated by energy transfer processes, even though the relaxation and incubation rates... 

CFIDF end group, no selective reaction would occur on time scales above 10 s. Figure B2.5.18. In contrast to IVR processes, which can be very fast, the miennolecular energy transfer processes, which may reduce intennolecular selectivity, are generally much slower, since they proceed via bimolecular energy exchange, which is limited by the collision frequency (see chapter A3.13). 

The method of exchange-luminescence [46, 47] is based on the phenomenon of energy transfer from the metastable levels of EEPs to the resonance levels of atoms and molecules of de-exciter. The EEP concentration in this case is evaluated by the intensity of de-exciter luminescence. This technique features sensitivity up to-10 particle/cm, but its application is limited by flow system having a high flow velocity, with which the counterdiffusion phenomenon may be neglected. Moreover, this technique permits EEP concentration to be estimated only at a fixed point of the setup, a factor that interferes much with the survey of heterogeneous processes associated with taking measurements of EEP spatial distribution. 

Before terminating the discussion of external mass transfer limitations on catalytic reaction rates, we should note that in the regime where external mass transfer processes limit the reaction rate, the apparent activation energy of the reaction will be quite different from the intrinsic activation energy of the catalytic reaction. In the limit of complete external mass transfer control, the apparent activation energy of the reaction becomes equal to that of the mass transfer coefficient, typically a kilocalorie or so per gram mole. This decrease in activation energy is obviously... 

Ehrenfest dynamics with the MMVB method has also been applied to the study of intermolecular energy transfer in anthryl-naphthylalkanes [85]. These molecules have a naphthalene joined to a anthracene by a short alkyl —(CH)n— chain. After exciting the naphthalene moiety, if n = 1 emission is seen from both parts of the system, if n = 3 emission is exclusively from the anthracene. The mechanism of this energy exchange is still not clear. This system is at the limits of the MMVB method, and the number of configurations required means that only a small number of trajectories can be run. The method is also unable to model the zwitterionic states that may be involved. Even so, the calculations provide some mechanistic information, which supports a stepwise exchange of energy, rather than the conventional direct process. 

---