Carbenium theory

This same ability to recognise hidden, unexploited treasure induced me to develop the first comprehensive theory of the polymerisations by ionising radiations [146]. None of the original researchers had stood back from their own findings, seen that their rather primitive theory was incompatible with the results of others, and set about constructing the general theory that was evidently needed. My effort [146] eventually produced a much-refined model of the propagating carbenium ion in solution and its different modes of reaction. 

At the IUPAC Polymer Symposium in Helsinki in 1972, I put forward a new theory concerning the initiation of cationic polymerisations by metal halides [1]. This comprised three principal ideas (a) Initiating metal halides undergo self-ionisation in solution, (b) Metal halide cations formed in this way can be the principal initiators in certain circumstances, and act by combining additively with the monomer to give a metalated carbenium ion. (c) The metal halides form complexes with the monomers. 

The second part of the theory, which is a logical consequence of the first, is that monomers that have more than one basic site, e.g., an aromatic ring or an oxygen atom, can form more than one type of complex with the carbenium ion this idea was first proposed by Plesch (1990) in the context of chemically initiated polymerizations. It helps to explain why aryl alkenes and alkyl vinyl ethers polymerize more slowly than isobutene and cyclopentadiene. The reason is that all the complexes formed by the alkyl alkenes are propagators, whereas for the aryl alkenes and vinyl ethers only a fraction of the population of complexes can propagate. 

As mentioned in Section 2.2, the complexing of carbenium ions with monomers is a well-accepted feature of the theory of cationic polymerisations, but it has not been realised clearly until recently that this implies the coexistence of first-order and second-order propagation reactions in certain systems over certain concentration ranges, i.e., the existence of (at least) dieidic polymerisations. 

In developing his theory of the polymerisations by ionising radiations Plesch now distinguishes between the mono-alkenes and other monomers, thus if a monomer, such as styrene, contains two donor groups, then both of these can be involved in the complex formation with the carbenium ion, but only the Jt-complex involving the double-bond can propagate. This means that Equation (40) must be replaced by... 

It is appropriate to point out here just why it is not valid to assume (as is commonly done) that throughout the propagation step a paired cation will remain paired and that the resulting newly formed carbenium ion will therefore start its life paired (see, e.g., Mayr et al. [13]). On the contrary, if we follow the assumption made by the founders of Transition State Theory that the transition state can be treated as a thermodynamically stable species, it follows that because in the transition state the positive charge is less concentrated than in the ground state and because therefore the Coulombic force holding... 

The author s theory which has been used here was developed in detail to explain the polymerisations by ionising radiations of some alkyl vinyl ethers, the polymerisations of which proceed by secondary ions. Although it was shown that the theory is also perfectly serviceable for the tertiary carbenium ions considered here, it must be realised that there is a fundamental difference between these two types of carbenium ions. When one of the bonds of the carbenium ion is a C—H bond, the solvators, especially of course an ion, can get much closer to the positive centre, and they are therefore correspondingly more firmly held to which effect is added that of a smaller steric hindrance. The most researched monomer propagating by secondary cations, apart from the alkyl vinyl ethers, is, of course, styrene. Thus, Mayr s many studies with diaryl methylium cations are directly relevant to the polymerisation of styrene. 

The two main versions of the ions-at-any-price rival theories, namely the large concentration of invisible ions view and the minute concentration of conventional carbenium ions view are both shown to be incompatible with all the facts. It is emphasised that many industrial cationoid oligomerisations and polymerisations are pseudo-cationic. 

We wish to emphasise that the formation of esters (E) from alkenes (M) and acids (HA), the catalysis of the reactions of E by HA or MtXn, and the activation of E, such as organic chlorides, by the co-ordination of a Lewis acid, such as A1C13, are all very familiar chapters in conventional organic chemistry. It follows that the pseudo-cationic theory is nothing more than a generalisation of conventional organic-chemical ideas and a revival of some pre-Whitmore interpretations which had become occulted by the usefulness and novelty of the carbenium ion concept. 

Pseudo-cationic polymerisations are reactions in which an alkene is inserted between the positive carbon atom and the negative heteroatom of a polar bond at the growing end of a polymer chain, without the formation of a carbenium ion they do not differ essentially from the well-known additions of esters to alkenes. The theory of these reactions was devised by Gandini and Plesch [2] and has been brought up to date by Plesch [3]. 

The recent theory of Penzcek, which involves co-ordinated oxy-carbenium ions, is also shown not to be applicable to the systems considered here. The heuristic value of the ring-expansion theory is illustrated briefly by reference to a new method of synthesising crown ethers from 1,3-dioxacycloalkanes, which arose from it. 

We now examine the theory recently put forward by Penczek [6]. Strictly, we would not need to concern ourselves with it, as the system to which it is said to apply does not involve initiation by perchloric acid, but by triphenylmethyl salts. None the less, it is useful to consider it briefly. Penczek believes that the propagating species in his systems is an oxy-carbenium ion stabilised by co-ordination of two oxygens from a polymer molecule, as shown in structure 6 ... 

Also shown in Figure 2 are the GIAO-MP2/tzp/dz values of the isotropic 13C chemical shifts. The predicted chemical shift for C2 and C3 is 255.3 ppm, which compares to the experimental value of 250 ppm. For C2, theory predicts a chemical shift of 152.8 ppm, whereas the experimental value is 148 ppm. The CH2 carbons are predicted to have isotropic chemical shifts of 50.0 ppm which compare to the measured values of 33 ppm. Finally, the methyl carbons have theoretical values of 28.9 ppm, whereas the experimental chemical shifts are 24 ppm. In all cases the theoretical values are downfield of the experimental chemical shifts. The differences are generally =5 ppm, with the exception of C3. The source of this larger difference is not clear. Still, the agreement is sufficient to verify the presence of the 1,3-dimethylcyclopentyl carbenium ion within the zeolite. 

Theory helps the experimentalists in many ways this volume is on chemical shift calculations, but the other ways in which theoretical chemistry guides NMR studies of catalysis should not be overlooked. Indeed, further theoretical work on two of the cations discussed above has helped us understand why some carbenium ions persist indefinitely in zeolite solid acids as stable species at 298 K, and others do not (25). The three classes of carbenium ions we were most concerned with, the indanyl cation, the dimethylcyclopentenyl cation, and the pentamethylbenzenium cation (Scheme 1), could all be formally generated by protonation of an olefin. We actually synthesized them in the zeolites by other routes, but we suspected that the simplest parent olefins" of these cations must be very basic hydrocarbons, otherwise the carbenium ions might just transfer protons back to the conjugate base site on the zeolite. Experimental values were not available for any of the parent olefins shown below, so we calculated the proton affinities (enthalpies) by first determining the... 

The. S n 1 hydrolysis of 5-methoxyacenaphthylene 1,2-oxide was found to occur preferentially via the 7.73 kcal mol-1 more stable carbenium ion,8 as confirmed by B3LYP/6-31G calculation. The predominant formation of the less stable c/s-diol is a consequence of kinetic control and explained by calculations at the MP2/6-31G // MP2/6-31G level of theory, which reveal the stabilizing influence of the hydrogen bonding that occurs between the attacking water molecule and the /3-OII group on the carbenium ion in the transition state. 

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