Distribution of active centers

Anisotropy in interface roughness and in a roughening transition. Anisotropic distribution of active centers for growth, such as lattice defects, which contribute to growth. 

It is seen from these figures that as the concentration of the additive increases, the value of E and Kq increase at first, simultaneously reach a maximum, and then drop again. The range of values covered by E and K0 are quite extensive and these effects, as pointed out by Cremer, cannot be explained by an exponential distribution of active centers on a surface. 

It can be seen that the methods outlined in this Section allow determination of average values of C, kp and other rate constants. A distribution of active center reactivities can be elucidated using molecular weight distribution data as shown by Keii et al.23 . 

As an alternative to the suspension process. Witco GmbH developed (1995) a technique which immobilizes the active compounds on a spray-dried silica support by utilizing a fluidized bed reactor. They claimed to produce supported metallocene catalysts with a controllable distribution of active centers achieved by using the three different supporting methods. Controlling the addition of tri-methylaluminum and water in the different reactor... 

Distribution of Active Centers on Propagation Rate Craistants and Their Stereospecificity. 125... 

Extensive fragmentation and uniform particle growth are key indications that the replication process is proceeding as desired. Good replication requires the high support surface area, homogeneous distribution of active centers throughout the particle, and free access of the monomer to the innermost zones of the particle. 

The type, density and energy distribution of active center of catalyst, dynamic behavior and reaction mechanism of reaction molecules. 

A continuous defect distribution must be understood as follows a distribution of structural defects with different local environment exists on an heterogeneous solid surface like MgClj. These defects give rise to a distribution of active centers after titanium fixation. Moreover, the titanium fixed on the surface may correspond to 1,2 or several different chemical structures. Among the properties that may distinguish the defects, we have mentioned the steric hindrance, but the acidity (which is possibly related) is easier to characterize. The acidity is evidenced for instance by the displacement of the IR... 

Most Kaminsky catalysts contain only one type of active center. They produce ethylene—a-olefin copolymers with uniform compositional distributions and quite narrow MWDs which, at their limit, can be characterized by M.Jratios of about 2.0 and MFR of about 15. These features of the catalysts determine their first appHcations in the specialty resin area, to be used in the synthesis of either uniformly branched VLDPE resins or completely amorphous PE plastomers. Kaminsky catalysts have been gradually replacing Ziegler catalysts in the manufacture of certain commodity LLDPE products. They also faciUtate the copolymerization of ethylene with cycHc dienes such as cyclopentene and norhornene (33,34). These copolymers are compositionaHy uniform and can be used as LLDPE resins with special properties. Ethylene—norhornene copolymers are resistant to chemicals and heat, have high glass transitions, and very high transparency which makes them suitable for polymer optical fibers (34). 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

A great variety of suitable polymers is accessible by polymerization of vinylic monomers, or by reaction of alcohols or amines with functionalized polymers such as chloromethylat polystyrene or methacryloylchloride. The functionality in the polymer may also a ligand which can bind transition metal complexes. Examples are poly-4-vinylpyridine and triphenylphosphine modified polymers. In all cases of reactively functionalized polymers, the loading with redox active species may also occur after film formation on the electrode surface but it was recognized that such a procedure may lead to inhomogeneous distribution of redox centers in the film... 

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.

The process described above is expected to produce a random distribution of active and passive spots on the electrode interface. But the electrode surface may also be artificially patterned prior to anodization in order to form nucleation centers for pore growth. This may be a lithographically formed pattern in said passive film or a predetermined pattern of depressions in the electrode material itself, which become pore tips upon subsequent anodization. The latter case applies to silicon electrodes and is discussed in detail in Chapter 9, which is devoted to macropore formation in silicon electrodes. 

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. 

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... 

Diphenylmethylcarbanions. The carbanions based on diphenyknethane (pKa = 32) (6) are useful initiators for vinyl and heterocyclic monomers, especially alkyl methacrylates at low temperatures (94,95). Addition of lithium chloride or lithium /W -butoxide has been shown to narrow the molecular weight distribution and improve the stability of active centers for anionic polymerization of both alkyl methacrylates and tert-huXyi acrylate (96,97). Surprisingly, these more stable carbanions can also efficiendy initiate the polymerization of styrene and diene monomers (98). 

Temperature effects on the polymerization activity and MWD of polypropylene have been examined in the range of —78 °C to 3 °C 82 The MWD of polypropylene obtained at temperatures below —65 °C was close to a Poisson distribution, while the MWD at higher temperatures above—48 °C became broader (Slw/IWIii = 1.5-2.3). At higher temperatures the polymerization rate gradually decreased during the polymerization, indicating the existence of a termination reaction with deactivation of active centers. It has been concluded that a living polymerization of propylene takes place only at temperatures below —65 °C. 

This produces a rise in the concentration of active centers and a corresponding increase in the propagation rate. Chains produced at this stage are longer, and this leads to a broadening of the molar mass distribution. The term gel effect is widely used to describe this effect, although no gel is actually formed in the system. The effect is also called the Trommsdorff effect (see Chapter 5). 

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