Concentration of carbenium ion

For this reason carbenium ion polymerisations with conveniently observable half-lives involve concentrations of carbenium ions in the range 10"9 to 10"6 mol l"1. 

If concentrations of carbenium ions are too low to be observed directly, they must be detected indirectly in kinetic studies of the racemiza-tion of optically active dormant species, ligand exchange and/or detailed studies of the effect of substituents, solvent and salts. Some of the most convincing and elegant work in this area was presented in Chapter 2 using primarily benzhydryl derivatives. As discussed in the next section, correlations between ionization rates and equilibrium constants, rates of solvolysis and rate constants of electrophilic addition can be interpolated and in some cases extrapolated to cationic polymerizations of alkenes to evaluate the reactivities of various active species and the dynamics of their isomerization. 

Acid adds slowly to styrene to form covalent esters, which have been detected directly by, 9F NMR [101]. Carbenium ions capable of propagation are then generated by ionization of the covalent esters with excess acid. However, the concentration of carbenium ions is too low to detect directly by spectroscopy, and propagation was initially proposed to occur by a nonionic mechanism. 

Carbenium ions with a-aromatic substituents (e.g., styrene derivatives) absorb at very different UV-visible wavelengths compared to the corresponding monomers and polymer chains. In such cases, UV-visible spectroscopy can be used to quantitatively determine the concentration of growing carbenium ions. Because the extinction coefficients of these carbenium ions are typically e = 10,000 to 30,000 moI l L cm 1, they can be detected only at concentrations higher than [C + ] = 10-6 mol, -L. In some of the systems discussed in this chapter, the concentration of carbenium ions are below the detection limit of UV. On the other hand, those systems with carbenium ion concentrations [C+] = 10-5 mol-, L will propagate very rapidly because kp 105 mol" Lsec-. The resulting half-lifetimes 1 sec) will require rapid detection techniques, such as... 

If Kd = 10 6 mol/L, free ions will dominate when the concentration of carbenium ions is less than 10" 6 mol/L. However, dissociation is strongly suppressed by adding salts with common ions. For example, addition of 10 3 mol/L of salt with common anion decreases the concentration of free ions from approximately I0-6-10 9 mol/L. Ion pair dissociation may also be suppressed by the counterions of adventitious oxonium ions formed by alkylation or protonation of impurities such as moisture. Even 10 5 mol/L of such oxonium ions reduces the concentration of free ions considerably. 

The equilibrium constants with nucleophiles such as tertiary amines are so large, that carbenium ions practically do not exist. Thus, tertiary amines and pyridine apparently react with carbenium ions irreversibly and therefore terminate carbocationic polymerizations. Somewhat weaker nucleophiles such as 2,6-dimethylpyridine (lutidine), sulfides, and tris(p-chlorophenyl)phosphine are good deactivators in vinyl ether polymerizations because they react reversibly with monomer, thus maintaining a low concentration of carbenium ions without causing elimination. However, the equilibrium constants in styrene and isobutene polymerizations with amines, sulfides, and phosphines are too large to generate a sufficient stationary concentration of carbenium ions to complete polymerization in a reasonable amount of time. 

If ionization is strongly exothermic, polymerization may be faster at lower temperatures due to the increased concentration of carbenium ions. Temperature affects kinetics by the activation enthalpy of propagation (AHP ) and by the enthalpy of the ionization equilibrium (AH). The apparent activation enthalpy is therefore a sum of both components and may become negative, if AH > AH/ ... 

Despite the vast amount of work which has recently been done on the protonation of olefins in the context of the search and characterisation of carbenium ions, very little information is available on the kinetics of this proton transfer process in non-aqueous media. A study of this nature requires the use of an analytical stem capable of detecting quantitatively small concentrations of carbenium ions and possessing an adequate time response. Two t es of investigation have been carried out, namely those using polymerisable monomers and those using olefins which cannot be polymerised. We will not analyse here reactions in such basic sdvents as methanol, althou an excellent study has been conducted in this medium °° because they are outside our scope. 

It is reasonable to expect that under specific experimental conditions certain Lewis acids mi t promote the ionisation of alkyl halides. Chlorinated hydrocarbons are frequently used as solvents in cationic polymerisation, and one can conceive that in the presence of a Lewis acid they mi t produce a small but sufficient concentration of carbenium ions capable of attacking the monomer in a solvent-cocatalysed initiaticm. Indeed, the reaction... 

It can be seen that at equilibrium, the concentration of carbenium ions is independent of the stannic chloride concentration in this scheme. However, if chloride ion exchange can occur between the Lewis acid and HClj, the sequence of equilibria is shifted to the ri t and a dependence is established between carbenium ion concentration and amount of SnCL used ... 

The existence of the pentachlorostannate anion in well known, but to the best of our knowledge this species has never been characterised in a polymerising system. If we consider its presence in this context as plausible, the concentration of carbenium ions at equilibrium will be determined by the overall relationship ... 

Finally, we can envisage that HCI2 is never formed, i.e. stannk chloride assists in all mechanisms the release of the chloride anion in the step leading to the formation of the active cationic species. In this event, only the first step is different between the two alternatives (complexation with the double bond by either acid) and of course the acid reformed at the end wiU be the one responsible for the initial interaction. The equilibrium concentration of carbenium ions will be given by the expressions ... 

The H transfer, that is a typical route of transfer in cationic vinyl polymerization, is not important in the polymerizations proceeding with the participation of tertiary oxonium ions as active species. This type of transfer may, however, occur in special cases where the presence of carbenium ions cannot be excluded. Such situations may appear in the cationic polymerization of suitably substituted oxiranes when the presence of low concentration of carbenium ions in equilibrium with oxonium ions has been postulated (Scheme 13). 

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