Functional groups, concept equal reactivity

The concept of equal reactivity of functional groups, Chap. 5. 

One of the main assumptions which have been made in the study of polyesterifications is the concept of equal reactivity of functional groups. It was first postulated by Flory1 who, studying various polyesterifications and model esterifications, found the same orders of reaction and almost the same rate constants for the two systems. He concluded that the reaction rate is not reduced by an increase in the molecular weight of the reactants or an increase in the viscosity of the medium. The concept of equal reactivity of functional groups has been fully and carefully analyzed by Solomon3,135 so that we only discuss here its main characteristics. Flory clearly established the conditions under which the concept of equal reactivity can be applied these are the following ... 

There are instances where some or all parts of the concept of equal reactivity of functional groups are invalid [Kronstadt et al., 1978 Lovering and Laidler, 1962], The assumption of equal reactivities of all functional groups in a polyfunctional monomer may often be incorrect. The same is true for the assumption that the reactivity of a functional group is... 

The product of a polymerization is a mixture of polymer molecules of different molecular weights. For theoretical and practical reasons it is of interest to discuss the distribution of molecular weights in a polymerization. The molecular weight distribution (MWD) has been derived by Flory by a statistical approach based on the concept of equal reactivity of functional groups [Flory, 1953 Howard, 1961 Peebles, 1971]. The derivation that follows is essentially that of Flory and applies equally to A—B and stoichiometric A—A plus B—B types of step polymerizations. 

The kinetic treatment revealed that the reactivity of pendant allyl groups of the prepolymer is approximately equal to that of the monomer. The ratios ri = kii/kii and r2 = kn/kn have been estimated to be 1.0 and 0.9, respectively [67]. A similar result was also observed for the post-copolymerization of DAI prepolymer with ABz [68]. Now, we can conclude that the concept of equal reactivity of functional groups belonging to the monomer and polymer is valid for the radical polymerization of diallyl aromatic dicarboxylates at an early stage of polymerization, at least up to the theoretical gel point. However, in the case of the highly branched prepolymer formed at a late stage of polymerization, i.e. far beyond the theoretical gel point, the reactivity of pendant allyl groups may be reduced by steric hindrance. 

Imphcit in these equations is the assumption that the functional group on the end of a monomer has the same reactivity as a similar group on a n-mer of any size and that the reactivities of both functional groups of bifunctional species (e.g., COOH groups of a diacid and OH groups of a diol) in the reaction mixture are the same. These simplifying assumptions are known as the concept of equal reactivity of functional groups. Experimental evidence and theoretical justifications have been provided in support of this concept (Flory, 1953 Odian, 1991). 

Applying the concept of equal reactivity of all functional groups, the rate of polycondensation according to the general Equation 2.4 may be expressed in terms of the extent of reaction by the rate equation 2.8. 

Floty s concept of equal functional group reactivity (see Flory, Polymer Chemistry, Cornell University Press, 1953) states that the intrinsic reactivity of a functional group is unalTected by the size of the molecule to which it is attached. However the reaction conditions for the modification of cellulose are usually heterogeneous and topochemical in nature. Discuss, in some detail, the reasons for this aspect of cellulose chemistry. 

---