Efficiency collisions

The ratio kq/kf can now be identified as ki9/k9a. We can calculate an upper limit for kl9 from ion-molecule reaction rate theory by assuming that this reaction occurs with a collision efficiency. This leads to k9il < 1 X 109 sec. -1 (7). 

Several explanations for this seeming inconsistency can be offered. By far the most attractive is based on unreactivity of certain intermediate ions, and this interpretation is supported by the observation that the reaction of butene ion with ethylene (Reaction 8) appears to occur with a collision efficiency of only about 0.015. The mass spectrometric observation of Reaction 17c (16) indicates that there may be similar low efficiency reactions in sequences initiated by other ions as well. 

The existence of a single step with a collision efficiency of 10 2 in the sequence of reactions would be insufficient to account for the absence of ionic polymerization since an over-all efficiency of about 10 5 is required by this mechanism within the first five reactions. Thus, at least two low efficiency steps are required in each series. Although... 

The first possibility is an increase in the pre-exponential factor, A, which represents the probability of molecular impacts. The collision efficiency can be effectively influenced by mutual orientation of polar molecules involved in the reaction. Because this factor depends on the frequency of vibration of the atoms at the reaction interface, it could be postulated that the microwave field might affect this. Binner et al. [21] explained the increased reaction rates observed during the microwave synthesis of titanium carbide in this way ... 

The two major theories of flocculation, the bridging model (1) and the electrostatic patch model (2, 3 ), provide the conceptual framework for the understanding of polymer-aided flocculation, but they do not directly address the kinetics of the process. Smellie and La Mer (4) incorporated the bridging concept into a kinetic model of flocculation. They proposed that the collision efficiency in the flocculation process should be a function of the fractional surface coverage, 0. Using a modified Smoluchowski equation, they wrote for the initial flocculation rate... 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

The first term on the right-hand side of Equation (2) describes the formation rate of k-flocs, and the second term is the disappearance rate. In the present study the flow was turbulent, and an effective shear rate was calculated as (e/v) / (19), where e is the energy dissipation, W/kg, and v is the kinematic viscosity, m /s. Equation (2) was also extended to include a collision efficiency factor, a, defined as... 

Theoretical collision efficiencies as a function of shear rate and particle size were based on theory derived for spherical particles in simple shear (20,21). Effective floe size radii (22) were calculated according to... 

Particle collision frequency due to Brownian motion was estimated to be less than 1% of the collision frequency due to shear. The effects of Brownian motion could therefore be neglected in the flocculation rate calculations. However, for the smallest molecular size, radius of gyration 14 nm (see Table I), the effect of Brownian motion on the particle-polymer collision efficiency was of the same order of magnitude as the effect of shear. These two contributions were assumed to be additive in the adsorption rate calculations. Additivity is not fundamentally justified (23) but can be used as an interpolating... 

Adsorption rates were not significantly affected by molecular weight, but flocculation was about 25% faster for the high molecular weight polymer. Two shear rate levels were tested 1800 s-1 and 8000 s-. The absolute adsorption and flocculation rates increased with shear rate as expected. The "pseudo" OFC appeared to be shifted to a higher value for the higher shear rate. Collision efficiencies were affected by both molecular weight and shear rate, as discussed below. 

Table I. Relative Collision Efficiencies Estimated from Fitting the Mathematical Model to Experimental Data ...

Summary plot of experimentally derived stability ratios, Wexp, of hematite suspensions, as a function of added electrolyte or adsorbate concentration at pH around 6.5 (pH = 10.5 for Ca2+ and Na+). Hematite concentration is about 10-20 mg/ . The stability ratio, Wexp, was determined from measurements on the coagulation rate it is the reciprocal of the experimentally determined collision efficiency factor, a. 

To what extent can theory predict the collision efficiency factor Two groups of researchers, Derjagin and Landau, and Verwey and Overbeek, independently of each other, have developed such a theory (the DLVO theory) (1948) by quantitatively evaluating the balance of repulsive and attractive forces that interact most effective tool in the interpretation of many empirical facts in colloid chemistry. 

Coagulation a Collision efficiency volumetric concentration of suspended particles G Velocity gradient t time i... 

Elimelech, M., and Ch. R. O Melia (1990), "Effect of Particle Size on Collision Efficiency in the Deposition of Brownian Particles with Electrostatic Energy Barriers", Langmuir 616,1153-63. 

The reaction probabilities for O and OH with soot particles have been measured by Roth and co-workers in a series of shock tube experiments [58-60], They have found that both radicals react with soot particles with a collision efficiency of between 0.10 and 0.20. In contrast, the reaction probability with 02 is at least an order of magnitude lower [55], Of course, at lower temperatures and sufficiently lean mixtures, soot oxidation by radical species becomes small and oxidation by 02 is important (though slow). Consequently, soot that passes through or avoids the primary reaction zone of a flame (e.g., due to local flame quenching) may experience oxidation from 02 in the post-flame gases. Analysis of soot oxidation rates in flames [54-57] has supported the approximate value of the OH collision efficiency determined by Roth and co-workers. 

The arenium ion/(R)-(— )-2-chlorobutane adducts. A crucial question concerns the chemical identity and the relative spatial arrangement of the components of a microsolvated system, two features of paramount importance to assess the kinetic and the mechanistic role of the corresponding ion-dipole pairs in solution. In the example reported in this section, Cacace and coworkers consider the ion-molecule complexes involved in the classical Friedel-Crafts alkylation of arenes." " At 300 K and under FT-ICR conditions, the benzenium ion CeH reacts with 2-chlorobutane C4H9CI to give the CloHj5 ion with a rate constant of 5 X 10 cm molecule corresponding to a collision efficiency of 2.5% (equations (33) or (34)). ... 

His keen analysis of the hydrogen chlorine reaction has also had support in the recent work of Rodebush and Klingelhoefer on the collision efficiency of the reaction Cl + H2. It is found that this reaction goes in one every 10 collisions, whereas the value suggested by Bodenstein was 10. ... 

The 1997 recommendations for the OH + N02 rate constants (DeMore et al., 1997 Atkinson et al., 1997a, 1997b) may be systematically high (e.g., Donahue et al., 1997) at temperatures below 240 K. Thus, recent measurements at temperatures characteristic of the upper troposphere give rate constants that are smaller than the recommendations by 10-30% (Brown et al., 1999a Dransfield et al., 1999). In addition, 02 appears to be only about 70% as efficient a third body as N2 in the termolecular reaction. Using a modified form of the semiempirical equation for the rate constant in the falloff region (Chapter 5, Eq. (C)), which takes into account the variable collision efficiency /3,... 

Based on a molecular kinetic model, Schweikert derives equations which. describe both the process of detonation in a condensed expl and that of the burning of a colloidal powder These processes are shown to differ primarily in the magnitude of the collision efficiency. Relations are derived which relate the max deton vel and pressure with molecular props... 

Schweikert s theory differs radically from the conventional thermohydrodynamic Chapman-Jouguet theory in that it provides for a continuous transition from burning to deton. In Section I entitled "Introduction , the author criticizes the validity of the C-J theory for condensed expls. In Section II the burning rate constants of a colloidal propint are related to fundamental parameters such.as specific surface vol of the powd, the most probable molecular vel, and the collision efficiency c. Schweikert arrives in Section III at the conclusion that burning deton differ primarily in the magnitude of c i.e. c l in a deton and is a much. smaller value in a burning process A surprisingly simple relation is derived in Section IV for the upper boundary of the deton vel Dm of a condensed expl ... 

The first quantitative calculation of a high collision efficiency for methyl radical recombination was made by Gorin4 who treated the collision pair as being stabilized by a polarization interaction at relatively large distances. From this point of view the transition state for the reaction corresponds to what might be termed a loose transition state in which there is relatively free libration or rotation of the two methyls relative to each other. 

It thus seems reasonable to expect that in the process of separation of CjH into 2 CHS radicals there is a distance in the neighborhood of 2.0 to 2.5 A. in which the system has a considerable amount of ionic character. It is our feeling that only such intermediates, particularly of the H-bonded type, are capable of explaining the very high A factors for C2H6 pyrolysis and the high collision efficiencies for radical-radical recombinations. 

This is a possible explanation for the observation that the recombinations 2N(L - NtOt and NO2 4- NO3 - N 05 have collision efficiencies lower by about a factor of 50 than those for the alkyl radicals. 

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