Collision efficiency factor

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 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... 

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. 

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. 

It is often the case that certain species have enhanced collisional efficiencies. For example, for reaction 9.74 it is found that when H2O is the third body collision partner the rate of reaction is increased by a factor of 15 over the rate when other species participate as the collision partner M.2 Thus a collisional efficiency akl is introduced. Such enhanced collision efficiencies result in an effective concentration of third bodies that can be higher than the actual concentration [M]. 

TJhe aggregation of particles in a colloidal dispersion proceeds in two distinct reaction steps. Particle transport leads to collisions between suspended colloids, and particle destabilization causes permanent contact between particles upon collision. Consequently, the rate of agglomeration is the product of the collision frequency as determined by conditions of the transport and the collision efficiency factor, the fraction of collisions leading to permanent contact, which is determined by conditions of the destabilization step (2). Particle transport occurs either by Brownian motion (perikinetic) or because of velocity gradients in the suspending medium (orthokinetic). Transport is characterized by physical parame-... 

Figure 5. The variation of relative colloid stability, expressed as collision efficiency factor, with A1(III) dosage as compared with colloid surface coverage from adsorption of Al(lll)...

The rate constant kp is given in terms of physical parameters (Boltzmann Constant KB, the absolute temperature T, and the absolute viscosity rj) that characterize these transport conditions. In the case of not completely destabilized colloids, when according to v. Smoluchowski so-called slow coagulation is observed, the rate constant contains in addition the collision efficiency factor, p, the fraction of collisions leading to permanent attachment under perikinetic conditions ... 

According to this kinetic model the collision efficiency factor p can be evaluated from experimentally determined coagulation rate constants (Equation 2) when the transport parameters, KBT, rj are known (Equation 3). It has been shown recently that more complex rate laws, similarly corresponding to second order reactions, can be derived for the coagulation rate of polydisperse suspensions. When used to describe only the effects in the total number of particles of a heterodisperse suspension, Equations 2 and 3 are valid approximations (4). 

The equation derived by Troelstra and Kruyt is only valid for coagulating dispersions of colloids smaller than a certain maximum diameter given by the Rayleigh condition, d 0.10 A0. Equation 4 applies in cases where particles are transported solely by Brownian motion. Furthermore, the kinetic model (Equations 2 and 3) has been derived under the assumption that the collision efficiency factor does not change with time. In the case of some partially destabilized dispersions one observes a decrease in the collision efficiency factor with time which presumably results from the increase of a certain energy barrier as the size of the agglomerates becomes larger. 

The rate constant k0 for orthokinetic coagulation is determined by physical parameters (velocity gradient du/dz, floe volume ratio of the dispersed phase, = sum over the product of particle number and volume), and the collision efficiency factor a0 observed under orthokinetic transport conditions ... 

The collision efficiency factors, describing the extent of the colloid destabilization, within certain limits are equal under perikinetic and orthokinetic conditions (3). 

The rate of coagulation depends upon the collision frequency, which is controlled by physical parameters describing perikinetic or ortho-kinetic particle transport (temperature, velocity gradient, number concentration and dimension of colloidal particles), and the collision efficiency factor a measuring the extent of the particle destabilization which is primarily controlled by chemical parameters. 

Figure 9. Relative effects of collision efficiency factor and velocity gradient on...

The coagulation rate depends upon physical parameters (temperature, velocity gradient, number and dimension of colloid), determining the collision frequency and upon chemical parameters (pH, Al(III) dosage, surface concentration of dispersed phase S), affecting the collision efficiency factor a... 

Light absorbance in 4 cm. cell Collision efficiency factor... 

Collision efficiency factor, measured under orthokinetic conditions... 

The first factor in Eq. [87] is the free molecular limit for the rate of collisions between particles of mass mp, whereas the second factor can be interpreted as the collision efficiency (sticking probability). The collision efficiency becomes negligible for very small particles, since in such cases the overall interaction potential becomes vanishingly small. 

---