Equal reactivity of functional groups

Equal reactivity of functional groups irrespective of the size of the molecule to which the group is attached. 

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 ... 

The prindple of equal reactivity of functional groups originates in the comparison by Flory of the results obtained for monoesterifications and polyesterifications. This means that it is particularly important to check whether Flory hypotheses are corred and whether the study of a polyesterification must be limited to the last stages of the reaction. 

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 molecular weight distribution and/or PDI has been described for several cases where the assumption of equal reactivity of functional groups is not valid. Unequal reactivity is easily handled by the Macosko-Miller method. For the A—A + B—B + B B system described in the previous section, we simply redefine the relationship between P and y by... 

The most useful and most commonly employed simplified approach dates back to Flory [27,28] and is based on the premise of equal reactivity of functional groups and statistical growth. The most important application is to polymerization of bifunctional monomers and can be sketched as follows (Flory s derivation is more elaborate). 

Equal reactivity of functional groups has been demonstrated by measurements of reaction rates of several series of reactants which differ in molecular weight. Further evidence is provided by the occurrence of interchange reactions under... 

In the theoretical treatment, an equal reactivity of functional groups belonging to the monomer and polymer is assumed. So, any reduction of the reactivity of pendant allyl groups of the prepolymer compared with the monomer may beeome one of the reasons for a greatly delayed actual gel point. The reaetivity of DAP prepolymer was evaluated kinetically from the post-copolymerization with ABz which has equivalent reaetivity to one allyl group of DAP monomer [62]. 

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. 

In several instances, discussed in more detail later in this section, experimental evidence strongly indicates that the principle of equal reactivity of functional groups is not obeyed for all chain lengths, and that the equilibrium constant may itself be a function of the degree of polycondensation. 

Problem 5.30 A mixture of equivalent amounts of glycerol and tricarballylic acid is condensed to the extent of 65% conversion. Assuming equal reactivity of functional groups, calculate (a) weight fractions of sol and gel in the mixture, and (b) weight fractions of the monomer and the dimer in the sol fraction. 

Molecular weight distributions in step-growth polymerization described so far in this chapter are all based on the probability approach of Flory [1,15] and Stockmayer [19]. Starting with the assumptions of equal reactivity of functional groups and no intramolecular reactions, they used combinatorial arguments to derive expressions for the distribution of all species as a function of the reaction extent and then used these distributions to calculate the average properties (Mn, Mw, and PDI). For cases of practical importance these distribution functions become quite complex [19]. 

Poly(decamethylene adipate) obtained in Exercise 5.4 was subjected to alcoholysis with 5% of its own weight of (a) ethylene glycol and (b) n-octyl alcohol in the presence of p-toluene sulfonic acid catalyst till there was no further change in viscosity. Estimate the limiting Xn of the mixture. Assume equal reactivity of functional groups. 

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). 

Stepwise Polymerizations For stepwise polymerizations of stoichiometric formulations of comonomers with / and g active sites per molecule exhibiting an ideal behavior (equal reactivity of functional groups, absence of both substimtion effects and intramolecular cycles), the gel conversion (Xg i) is given by ... 

While deriving the dynamic batch-reactor models in Tables 7.3 and 7.4, the equal-reactivity-of-functional-groups assumption was made, so that kp is the rate constant for all forward linear polyamidation reactions and Ay is the rate constant for all reverse hydrolysis reactions involving amide links on linear chains. Let the rate constant for the forward cychzation reaction be Ay and the rate constant for hydrolysis of an amide link on cyclic oligomers be A . In practice all of these rate constants depend on the reactor temperature and... 

---