Slow initiation step, kinetics

The Landolt reaction (iodate + reductant) is prototypical of an autocatalytic clock reaction. During the induction period, the absence of the feedback species (Irere iodide ion, assumed to have virtually zero initial concentration and fomred from the reactant iodate only via very slow initiation steps) causes the reaction mixture to become kinetically frozen . There is reaction, but the intemiediate species evolve on concentration scales many orders of magnitude less than those of the reactant. The induction period depends on the initial concentrations of the major reactants in a maimer predicted by integrating the overall rate cubic autocatalytic rate law, given in section A3.14.1.1. 

Kinetic curves relative to polymerization reactions in the solid state commonly show a sigmoidal shape with a slow initiation step followed by a steep increase, even by two orders of magnitude, of the reaction rate. A reaction with this kind of kinetic curve is said to have an autocatalytic behavior. 

The macromolecular silyl chloride reacts with sodium in a two-electron-transfer reaction to form macromolecular silyl anion. The two-electron-trans-fer process consists of two (or three) discrete steps formation of radical anion, precipitation of sodium chloride and generation of the macromolecular silyl radical (whose presence was proved by trapping experiments), and the very rapid second electron transfer, that is, reduction to the macromolecular silyl anion. Some preliminary kinetic results indicate that the monomer is consumed with an internal first-order-reaction rate. This result supports the theory that a monomer participates in the rate-limiting step. Thus, the slowest step should be a nucleophilic displacement at a monomer by macromolecular silyl anion. This anion will react faster with the more electrophilic dichlorosilane than with a macromolecular silyl chloride. Therefore, polymerization would resemble a chain growth process with a slow initiation step and a rapid multistep propagation (the first and rate-limiting step is the reaction of an anion with degree of polymerization n[DP ] to form macromolecular silyl chloride [DP +J, and the chloride is reduced subsequently to the anion). 

With acetaldehyde, step 1 must be the slowest1 since it has been shown that in spite of the fact that two molecules of aldehyde undergo reaction, the kinetics of the transformation is first order in aldehyde.2 A slow initial step is in agreement with the fact that no deuterium becomes at-... 

Another possibility, as Hogan proposes, is that the first chain is somehow different from those that follow. Hence the kinetics of polymerization shown in Figure 1 could result from a slow initiation step. 

Non-stationary kinetics. A complex kinetic scheme has been developed by Chirkov et al (32) and used to determine C for the VCly(Al(i-Bu)y propylene syst. The settling period is attributed to a slow initiation step and hence C is evaluated from the initial non-stationary period of the polymerization. The method is limited in that it depends on this particular kinetic interpretation and in any case many polymerization systems show no settling period. 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

Up to now it has not been possible to prove a mechanism which is able to explain all these effects. Neither intramolecular termination alone, nor a combination of intramolecular termination and monomer termination fit the data. However, they can be fitted by a hypothetical kinetic scheme which assumes that a slow reaction takes place between the living end and a deactivating species which is produced in the initial stage of the reaction. The dependence of the rate of termination on the initial monomer concentration can only be explained on the basis of a side reaction occuring in the initiation process. To verify this model, however, the deactivating species has to be identified by analyzing the oligomers produced in the initiation step. 

Dilution with toluene slowed the copolymerization rate, and kinetic measurements were carried out in toluene at 0°-30°C. As reported previously (II), the over-all activation energy of the spontaneous copolymerization of CPT and S02 was calculated to be 16.5 kcal/mole from the Arrhenius plot of the initial rate vs. polymerization temperature. Dependence of the intial rate of copolymerization upon monomer concentration was checked at various monomer concentrations and found to be quite high (II) this could not be explained without participation of the monomer in the initiation step. 

Polymer Adsorption. A review of the theory and measurement of polymer adsorption points out succinctly the distinquishing features of the behavior of macromolecules at solid - liquid interfaces (118). Polymer adsoiption and desorption kinetics are more complex than those of small molecules, mainly because of the lower diffusion rates of polymer chains in solution and the "rearrangement" of adsorbed chains on a solid surface, characterized by slowly formed, multi-point attachments. The latter point is one which is of special interest in protein adsoiption from aqueous solutions. In the case of proteins, initial adsoiption kinetics may be quite rapid. However, the slow rearrangement step may be much more important in terms of the function of the adsorbed layer in natural processes, such as thrombogenesis or biocorrosion / biofouling caused by cell adhesion. 

The fast initiation step is followed by an equally fast propagation reaction. While the rate constant of the former has been measured by Kunitake and Takarabe the dimerisation kinetics have not been measured for this particular system. The following slow reactions consist of the proton transfer between the dimeric cation and the monomer to gjve alternatively the unsaturated dimer or the indanylic one. Finally, the protonated dimer can isomerise to a more stable configuration due to the direct interaction of the two phenyl groups through space polarisation effects Thus ... 

Lubricants used in watches usually consist of long-chain hydrocarbons. Oxidation by air forms solid polymers that eventually destroy the effectiveness of the lubricants. It is believed that one of the initial steps in the oxidation is removal of a hydrogen atom (hydrogen abstraction). By replacing the hydrogen atoms at reactive sites with deuterium atoms, it is possible to substantially slow down the overall oxidation rate. Why (Hint Consider the kinetic isotope effect.)... 

Kinetic runs in step b in Fig. 8c started with a very fast reduction of approximately e per molecule, after which a slow reductioh took place, yielding sigmoidal reduction curves. This, indicates that reduction of Co2+ to Co° is controlled by the formation and slow growth of reduction nuclei of metallic cobalt on. the surface of the reduced phase in step a (nucleation model). Initially, the reduction rate increases because of the growth of nuclei already formed and the appearance of new ones. At a certain point the reduction nuclei start to overlap at the inflection point, the interface of. the oxidized and reduced phases and the reduction rate both begin to decrease. Reduction of this type is described by the Avrami-Erofeev equation (118)... 

It should be pointed out that this mechanism accounts for the observed first order kinetics (based on the sum of all deuterated products), since the rate of the hydrogen transfer step (8) depends on the first power of the concentration of isobutane in the gas phase, i.e., the rate of adsorption of isobutane. Probably the hydrogen transfer step (8) is the slow step in the overall reaction, since the activation energy of the overall deuterium exchange reaction is not affected by the initiating step involving olefin. 

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