Probability of chain propagation

The Fischer Tropsch kinetics of product formations are best understood as a non trivial surface polymerization. The basic kinetic interrelations are well described by an ideal model with carbon number independent probability of chain propagation. The pecularities of real Fischer Tropsch systems are then described as deviations from the ideal model. In this paper (because of space limitations) only the Anderson two slope distributions are discussed and explained by a readsorption extension of the ideal model. The full model including chain branching and formation of olefins, alcohols and aldehydes is being published shortly (ref. 28). 

In all the above ethylene oligomerizations, Schulz-Flory distributions of oUgomers are observed which can be quantified by the a value, which represents the probability of chain propagation [117, 118]. The magnitude of a can be experimentally determined by the ratio of two oligomer fractions Eq. (5.1). The a value is usually preferred to be in the range of about 0.6 to about 0.8 to make a-olefins of the most commercial interest... 

The kernel (26) and the absorbing probability (27) are controlled by the rate constants of the elementary reactions of chain propagation kap and monomer concentrations Ma(x) at the moment r. These latter are obtainable by solving the set of kinetic equations describing in terms of the ideal kinetic model the alteration with time of concentrations of monomers Ma and reactive centers Ra. 

Table I. The Reaction Rate Constants for Propagation and Termination Expressed as a Function of Turnover Frequencies, Probability of Chain Growth, Steady-State Surface Coverage of the Precursor A, and the Equilibrium Constant K.

Table II. Minimum Reaction Rate Constants for Propagation Caknlated from the Data of Turnover Frequency and Probability of Chain Growth Published in the...

The simplest oxidative reactions occur in hydrocarbon polymers. This free-radical process generally follows the same path as the oxidation of low molecular weight compounds. The difference, however, is in the propagation of the reaction. In oxidation of low-molecular weight hydrocarbons, each step of chain propagation results in transfer of active center from on molecule to another. In polymers, however, the probability of such a transfer is low. Instead, the oxidation propagates along the polymer backbone [520]. 

Some polymers, such as poly(vinyl chloride) or poly(acrylonitrile), are insoluble in their own monomers. In bulk polymerization, therefore, the polymer is precipitated at relatively low conversions. Since newly produced free radicals still have monomer available to them, the polymerization continues, but the kinetics of polymerization is complicated. Part of the growing chain resides in the precipitated phase, and thus the probability of chain termination is small. On the other hand, the rate of diffusion of the monomer to the growing chain end is considerably reduced, so that the propagation reaction is also affected. 

At that the participation of catalyst NF(acac)2XMSt in micro steps of chain propagation and, probably, in chain termination must also be taken into account. [2]. The results found in [14] illustrate the possibility that redox-inactive metal ions can be used to facilitate the activation of dioxygen (see the abstract scheme of [14], above), which will be coordinated with our data. 

The FTS product distribution is determined by the probability of chain growth, which is the ratio of the rate of propagation to the overall reaction rate. 

The kinetic curves for the polymerization of butadiene and isoprene with the titanium catalytic system in the absence of US irradiation (Method 1) are almost coincident (Fig. 4.9). US irradiation (Method 2) brings about an increase in the initial rates of butadiene and isoprene polymerization and accelerates accumulation of the polymer in the system. In this case, the initial rates of polymerization of butadiene and isoprene increase owing to an increase in the rate constant of chain propagation without any marked changes in the concentration of active sites. This result correlates with the estimation of dispersity of the catalytic system, specifically, with the absence of changes in the most probable size of catalyst particles. In the case of polymerization of butadiene via Method 2, the munerical values of rate constants of chain termination increase. 

Effects of compounds observable at lower concentrations ai e probably connected with the effect on the initiation/termination stages (transition metals in TMB-0, reaction with photoinitiation, UDMH in the same reaction with chemical initiation), while the compounds influencing only at higher concentrations may affect chain propagation stages. 

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