Number of Active Centers

The coordinated anionic catalysis is one of the few examples of heterogeneous catalysis in which it is possible to estimate the actual number of active centers, present on the catalyst surface, which directly take part in the chemical catalytic process. 

In the stereospecific polymerization of propylene, such active centers, which are formed by treating a-TiCU with alkylaluminum, have been determined by using C-labeled alkylaluminum. The two systems studied were 

In both cases the determination of active centers has been performed by means of absorption tests of C-labeled alkylaluminum on samples of ground a-titanium trichloride. In the first case, two a-TiCh samples were used, one of them (sample A) having low catalytic activity, the other one (sample B) high activity. In the second case, only the sample A was used, and the determination of active centers was also made by a kinetic method, still using labeled alkylaluminum. 

Direct determination of C-labeled ethyl groups bound on the surface of titanium trichloride samples, treated either with triethylaluminum or di-ethylaluminum monochloride solutions, at different temperatures. 

Determination of active centers by the number of C-labeled —CjHs 

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Reactions that are catalyzed by solids occur on the surfaces of the solids at points of high chemical activity. Therefore, the activity of a catalytic surface is proportional to the number of active centers per unit area. In many cases, the concentration of active centers is relatively low. This is evident by the small quantities of poisons present (material that retards the rate of a catalytic reaction) that are sufficient to destroy the activity of a catalyst. Active centers depend on the interatomic spacing of the solid structure, chemical constitution, and lattice structure. 

Mejzlik, J., Lesna, M. and Kratochvila, J. Determination of the Number of Active Centers in Ziegler-Natta Polymerizations of Olefins. Vol. 81, pp. 83 — 120. 

It is necessary to note the limitation of the approach to the study of the polymerization mechanism, based on a formal comparison of the catalytic activity with the average oxidation degree of transition metal ions in the catalyst. The change of the activity induced by some factor (the catalyst composition, the method of catalyst treatment, etc.) was often assumed to be determined only by the change of the number of active centers. Meanwhile, the activity (A) of the heterogeneous polymerization catalyst depends not only on the surface concentration of the propagation centers (N), but also on the specific activity of one center (propagation rate constant, Kp) and on the effective catalyst surface (Sen) as well ... 

It is evident [see Eq. (5), Section II[] that for catalysts of the same or similar composition the number of active centers determined must be consistent with the catalytic activity it can be expected that only in the case of highly active supported catalysts a considerable part of the surface transition metal ions will act as propagation centers. However, the results published by different authors for chromium oxide catalysts are hardly comparable, as the polymerization parameters as a rule were very different, and the absolute polymerization rate was not reported. 

Several determinations of the number of propagation centers by the quenching technique have been carried out (98, 111). As a quenching agent methanol, labeled C14 in the alkoxyl group, proved to be suitable in this case. The number of active centers determined by this technique at relatively low polymerization rates (up to 5 X 102 g C2H4/mmole Cr hr at 75° and about 16 kg/cm2) (98, 111, 168) in catalysts on silica was about... 

The number of active centers determined by the quenching technique was dependent on the polymerization temperature (98) that was the reason for the difference between the overall activation energy and the activation energy of the propagation step. 

Fig. 57.—Weight percent (100 w ) vs. number of units for polymers formed by successive addition of monomers to a fixed number of active centers, as calculated from Eq. (33) for the values of p indicated. The p = 500 curve is drawn to the scales along the upper and right-hand margins scales for the other curves are given along the lower and left-hand margins. The broken curve represents a most probable distribution, 5n = 101, shown for comparison.

Both of these reactions involve the production of two active centers where there was only one before. When reactions of this type occur to a significant extent, the total number of active centers present in the system can increase very rapidly, since a multiplication effect sets in as the chains propagate. The growth of chain carriers in a branched chain reaction is pictured below. 

The energy of an adsorbed species is the same anywhere on the surface and is independent of the presence or absence of nearby adsorbed molecules. This assumption implies that the forces between adjacent adsorbed molecules are so small as to be negligible and that the probability of adsorption onto an empty site is independent of whether or not an adjacent site is occupied. This assumption usually implies that the surface is completely uniform in an energetic sense. If one prefers to use the concept of a nonuniform surface with a limited number of active centers that are the only points at which chemisorption occurs, this is permissible if it is assumed that all these active centers have the same activity for adsorption and that the rest of the surface has none. 

With increasing size of the alkali cation, the left-hand side is favored, lowering the chance of Fe-OH hydrogenation. Thereby the number of active centers with mechanism 2, and thus f2, is increased. This effect may explain the increasing promoter effect on f2 in the order H < Li Na < K Cs. 

A wide variation exists for the number of active centers of oxidation in polymer samples. This reflects the statistical nature of the catalyst residues in polymer particles. On the contrary, the spreading rate coefficient b is approximately constant for the studied samples of PP. The coefficient a is probably sensitive to the morphology of the particles. 

Finite number of active centers, often well characterized, can in many cases be modeled, good understanding of chemistry at a molecular level... 

In the fabrication of printed circuit boards the sensitizer is applied to the substrate S by immersion of the substrate into the solution for 1 to 3 min. Alternatively, the surface of a nonconductor may be sprayed with sensitizer. Addition of aged stannic chloride (SnC ) solution to the tin sensitizer solution results in an improved sensitizer (17). The improved sensitizer yields a greater number of active centers per unit surface area (greater density) and a more uniform distribution. The density of adsorbed centers, using the conventional and improved sensitizers, is 10 and 10 particles per square centimeter, respectively. The diameter of adsorbed particles for both types of sensitizers is about 10 to 15 A. 

B. Determination of the Number of Active Centers by a Kinetic Method... 56... 

This adjustment period has been explained on the assumption that crystals and aggregates of a-TiCh are smashed and cleaved under the mechanical action of growing polymeric chains, so that we have a consequent increase up to a constant value, in the number of active centers which directly participate in the polymerization. 

It has also been found that the polymer formed from the beginning of the reaction is already prevaiUngly isotactic. This means that, from the start of the reaction, there exist a certain number of active centers on the solid a-TiCU surface which immediately yield iso tactic polymer consequently, it can be excluded that, at least for the active centers present on the initial free surface of a-titanium trichloride, there is an initial activation process, whose rate is slow enough to be observed even when operating at low temperature (30°). 

The result is due to the fact that the alkylaluminum, in the concentrations considered above, is always in excess with respect to the number of active centers existing on the surface of the solid catalyst. 

Before carrying out such determinations in an attempt to estimate the number of active centers correctly, it has been necessary to define the magnitude of the eventual radioactive contaminations of the polymers, caused by phenomena extraneous to the polymerization process. 

The number of ethyl groups, and, therefore, the number of the corresponding active centers found in the catalytic system diethylaluminum monochloride-a-titanium trichloride, is smaller than the one found in the system triethylaluminum-a-titanium trichloride. It is interesting to notice that for the two samples of a-TiCh (A and B), the activity ratio in the propylene polymerization is almost equal to the ratio (determined from ethyl groups) between the number of active centers (Table XI) (38). 

It has already been noticed that the number of active centers, which the monomer can directly reach, on the surface of the catalyst, may vary after the start of the polymerization, until it assumes to a constant value. 

The previously described method for the determination of the number of active centers gives, therefore, a value that may not correspond to the number of active centers found in steady-state conditions. 

The method employed to calculate the total number of active centers relies upon the determination of the variation occurring in the ratio between ethyl groups (deriving from the alkylaluminum) which are present in the polymer and the whole amount of polymerized propylene, on increasing the time of polymerization. 

The evaluated number of active centers C does not depend in practice on the polymerization time. In fact, the curve of Fig. 34, drawn by assuming C = 0.6 X mol. of —CaHs per mol. of a-titanium trichloride and... 

Therefore, with the catalyst under consideration, ground a-titanium tri-chloride-AlCl(CjH6)2, the totality of active centers is involved in the catalytic process, once the polymerization starts. We may deduce from the time constancy of the polymerization rate from the very beginning of the reaction that, in this case, the number of active centers is invariable and that the calculated value corresponds to the number of conventional active centers involved in the polymerization, in steady-state conditions. 

A. Detbemination of the Mean Lifetime from THE Number of Active Centers... 

The data summarized in the previous paragraphs (namely, over-all polymerization rate, average polymerization degree for isotactic polymer, and number of active centers) enabled us to evaluate the mean lifetime of the... 

Equation (8) can be generalized by considering more than two kinds of centers. If there are many different kinds of active centers, their relative proportions may be represented approximately by a continuous distribution function, as has been suggested by Constable (2). In particular, it may be assumed that their relative numbers decrease exponentially with decreasing activation energy A . Thus the number of active centers dn involving activation energies between A and AE -+ dAE can be assumed to be... 

The implication is that where hydride ion abstraction is indicated, the probable true initiator is the add HSbCl6 or HPFS. Dreyfuss et al. further point out that one cannot make the apriori assumption that the reactivity of the dialkyl oxonium ion (THF HSbCle) is comparable to the reactivity of the trialkyl oxonium ion (i.e. the propagating species). In fact, it may be slower (46). Thus any assumptions about the rate of initiation, or about the number of active centers formed, or any attempts to correlate the degree of polymerization of the resulting polymer with the amount of carbonium ion salt or aryl diazonium salt initiators charged should be made with extreme caution. Again, for theoretical studies of the polymerization, the use of preformed trialkyloxonium salts is to be preferred. 

Rozenberg et al. (51) used the reaction shown in equation 35 to explain the large increase in the viscosity of the reaction mixture that they observed after most of the monomer had polymerized. As evidence they offered the observation that the addition of an amount of metha-nolic KOH comparable to the number of active centers caused a marked reduction of viscosity. They associated this with a breakdown of the product of equation 35. Sims (37) has made similar observations. He suggests that the breakdown may be associated with a hydrolysis of the phosphate linkages in the chain of the final product shown in equation 8. Equation 6 a suggests that the explanation for Rozenberg s observations may be similar to Sims, i. e. a hydrolysis of borate esters occurs. 

Obviously the number of active centers postulated until now are fewer than the number of protomers, but there is fair evidence for at least eight active regions per molecule of crystalline enzyme or one catalytic region in a (2n) unit. 

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