Monomolecular kinetics

Concerning the nature of electronic traps for this class of ladder polymers, we would like to recall the experimental facts. On comparing the results of LPPP to those of poly(para-phenylene vinylene) (PPV) [38] it must be noted that the appearance of the maximum current at 167 K, for heating rates between 0.06 K/s and 0.25 K/s, can be attributed to monomolecular kinetics with non-retrapping traps [26]. In PPV the density of trap states is evaluated on the basis of a multiple trapping model [38], leading to a trap density which is comparable to the density of monomer units and very low mobilities of 10-8 cm2 V-1 s l. These values for PPV have to be compared to trap densities of 0.0002 and 0.00003 traps per monomer unit in the LPPP. As a consequence of the low trap densities, high mobility values of 0.1 cm2 V-1 s-1 for the LPPPs are obtained [39]. 

Since chlorine is always in more than a hundred-fold excess compared to bromine the reaction is occurring by pseudo monomolecular kinetics. The reaction occurs via nucleophilic aromatic substitution by an addition-elimination mechanism, the so-called SjsfAr mechanism (ref. 24). 

Table 13.9 Monomolecular kinetics for alkane cracking when surface reaction controls the rate.

For every monomolecular kinetic system, the Jordan cell for zero eigenvalue of matrix K is diagonal and the maximal number of independent linear conservation laws (i.e. the geometric multiplicity of the zero eigenvalue of the matrix K) is equal to the maximal number of disjoint ergodic components (minimal sinks). 

Until the geminate pairs start to mix, i.e., at relatively short times r relative diffusion coefficient, the monomolecular kinetics reads n(t) = n(0)u>(t), with n(0) = nA(0) = ne(0) being initial particle concentration. The distinctive feature of this stage is the linearity of the recombination kinetics n(t) with respect to the irradiation dose n(0). 

The kinetics captured in disordered systems like polymers, glasses and poly-cristalline structures has been often described in terms of continuous relaxation times and exciton diffusion at recombination centers [10]. Assuming a <5— pulse function, the temporal data are best fitted by a monomolecular kinetic equation,... 

The next type of the reaction investigated was hydrogen elimination by macroradicals. We have used cumene (isopropylbenzene) vapours at 1 mm Hg as hydrogen donor. The reaction kinetics was determined from the intensity decrease of the initial radical spectra. Since diffusion coefficients of cumene in our polymers are very low, one could expect that the reaction between macroradicals and cumene takes place only on the polymer surface. Experiment actually shows that radical decay is in exact agreement with monomolecular kinetics. In contrast to the... 

The rate constant for the isomerization of /ra/i.v-stilbene in the S, state is also affected by solvent viscosity and has served as a favorite prototype for the investigation of solvent dynamics in fast monomolecular kinetic processes (Saltiel and Sun, 1990). 

In case of dominant recombination, or A m > A N - n), eq. (5) gives / =pn. This is the case offirst-order kinetics called also monomolecular kinetics. Vox A (N — n) A m, i.e. for the situation in which retrapping is dominant, I is nearly proportional to n, which is the case of second-order kinetics or bimolecular kinetics. 

If we assume a monomolecular kinetics for the process (4) we may easily justify the experimental increase of r brought about by an increase in P/D. In fact the relaxation equation for process... 

Another example requiring the solution of linear algebraic equations comes from the analysis of complex reaction systems that have monomolecular kinetics. Fig. 2.2 considers a chemical reaction between the three species, whose concentrations are designated by Fj, Fj, taking place in a batch reactor. 

Weis [85AHC(38)1, pp. 70-73] has also studied the kinetics of 1,4-dihydro to 1,6-dihydro transformation quantitatively using H NMR line-shape analysis. The results indicated that two mechanisms (monomolecular and bimolecular reactions) are involved in the process, for which all the kinetic parameters were calculated. 

In the process of radical polymerization a monomolecular short stop of the kinetic chain arises from the delocalization of the unpaired electron along the conjugated chain and from the competition of the developing polyconjugated system with the monomer for the delivery of rr-electrons to the nf-orbitals of a transition metal catalyst in the ionic coordination process. Such a deactivation of the active center may also be due to an interaction with the conjugated bonds of systems which have already been formed. 

Figure 6.22. Model predicted electrochemical promotion kinetic behaviour for a monomolecular reaction of an electron donor (left) and an electron acceptor (right) absorbate.

Immobilizing the catalyst on the electrode surface is useful for both synthetic and sensors applications. Monomolecular coatings do not allow redox catalysis, but multilayered coatings do. The catalytic responses are then functions of three main factors in addition to transport of the reactant from the bulk of the solution to the film surface transport of electrons through the film, transport of the reactant in the reverse direction, and catalytic reaction. The interplay of these factors is described with the help of characteristic currents and kinetic zone diagrams. In several systems the mediator plays the role of an electron shuttle and of a catalyst. More interesting are the systems in which the two roles are assigned to two different molecules chosen to fulfill these two different functions, as illustrated by a typical experimental example. 

The usual kinetic law for S/v Ar reactions is the second-order kinetic law, as required for a bimolecular process. This is generally the case where anionic or neutral nucleophiles react in usual polar solvents (methanol, DMSO, formamide and so on). When nucleophilic aromatic substitutions between nitrohalogenobenzenes (mainly 2,4-dinitrohalogenobenzenes) and neutral nucleophiles (amines) are carried out in poorly polar solvents (benzene, hexane, carbon tetrachloride etc.) anomalous kinetic behaviour may be observed263. Under pseudo-monomolecular experimental conditions (in the presence of large excess of nucleophile with respect to the substrate) each run follows a first-order kinetic law, but the rate constants (kQbs in s 1 ruol 1 dm3) were not independent of the initial concentration value of the used amine. In apolar solvents the most usual kinetic feature is the increase of the kabs value on increasing the [amine]o values [amine]o indicates the initial concentration value of the amine. 

Table 13.8 Monomolecular and bimolecular kinetics of alkane cracking [92],...

With increasing reaction severity, the concentrations of the individual isomers approach their equilibrium values. The monomolecular route is the most effective for achieving high yields of PX, which is typically the most desirable for petrochemical applications. The schematic above shows the stepwise interconversion of OX to MX and MX to PX, which is consistent with a 1,2-methyl shift route. However, the results of kinetics studies provide some indications in favor of a reaction step that directly converts OX to PX [62]. It is not clear what the form of the reaction intermediate for this transformation is. Some in situ time-resolved spectroscopic methods have been used to look at how modification of zeoMtes like MFl affects the monomolecular mechanism by constraining the diffusion of MX [63]. 

The first quantum-chemical investigation of the mechanism of olefin epoxidation in flnoroalcohols was carried out by Shaik et al. [54], In the absence of kinetic data, a monomolecular mode of activation by the fluorinated alcohols for aU reaction pathways was assnmed [54],... 

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