Unequal Reactivity of Functional Groups

2-7e Effect of Reaction Variables on MWD 2-79-1 Unequal Reactivity of Functional Groups 

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 

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As mentioned previously, the behavior of systems containing bifunctional as well as trifunctional reactants is also governed by the equations developed above. The variation of wx for the polymerization of bifunctional monomers, where the branching coefficient a is varied by using appropriate amounts of a trifunctional monomer, is similar to that observed for the polymerization of trifunctional reactants alone. The distribution broadens with increasing extent of reaction. The effect of unequal reactivity of functional groups and intramolecular... 

The polymerization temperature, often called the cure temperature, affects both transitions in different ways. In Chapter 3 it was shown that the gel conversion does not depend on temperature for ideal stepwise polymerizations but may show a small dependence on temperature for the case where unequal reactivity of functional groups or substitution effects vary... 

Flory Fgei = /(/- ) Neglects unequal reactivities of functional groups, polydrsperse oligomers (Flory, 1941). 

In aromatic diisocyanates, such as toluene dissocyanate (TDI), one isocyanate gronp can modify the activity of the other, and the activity of both groups can depend on the other snbstituents of the aromatic ring. For a mixture of 2,4 and 2,6 isomers of TDI (industrially, it is difficult to separate the two), 12 reactions with primary and secondary lOH groups of the polyols have been identified. The rate constants for these reactions have been measured experimentally and are summarized in Table 3.4. Significant differences can be observed in the reactivity of the two —NCO groups the equal reactivity hypothesis is definitely not followed. There have been several fundamental studies to model the unequal reactivity of functional groups in urethane formation. It has been shown that such reactivity has considerable influence on the polymer formed. 

For a fixed extent of reaction, the presence of multifunctional monomers in an equimolar mixture of reactive groups increases the degree of polymerization. Conversely, for the same mixture a lesser extent of reaction is needed to reach a specified with multifunctional reactants than without them. Remember that this entire approach is developed for the case of stoichiometric balance. If the numbers of functional groups are unequal, this effect works in opposition to the multifunctional groups. 

Stockmayer 25 subsequently developed equations relating to branched-chain polymer size distributions and gel formation, whereby branch connectors were of unspecified length and branch functionality was undefined. An equation was derived for the determination of the extent of reaction where a three-dimensional, network ( gel ) forms this relation was similar to Flory s, although it was derived using another procedure. Stockmayer likened gel formation to that of a phase transition and noted the need to consider (a) intramolecular reactions, and (b) unequal reactivity of differing functional groups. This work substantially corroborated Flory s earlier studies. 

This chapter has discussed the analysis of reactors for step-growth polymerization assuming the equal reactivity hypothesis to be valid. Polymerization involves an infinite set of elementary reactions under the assumption of this hypothesis, the polymerization can be equivalently represented by the reaction of functional groups. The analysis of a batch (or tubular) reactor shows that the polymer formed in the reactor cannot have a polydispersity index (PDI) greater than 2. However, the PDI can be increased beyond this value if the polymer is recycled or if an HCSTR is used for polymerization. A comparison of the kinetic model with experimental data shows that the deviation between the two exists because of (1) several side reactions that must be accounted for, (2) chain-length-dependent reactivity, (3) unequal reactivity of various functional groups, or (4) comphca-tions caused by mass transfer effects. 

The last topic to be treated is unequal reactivity by substitution effects. As a first example, the effect of an infinitely negative substitution effect in C due to a reaction with an h group (so I CD Kqj = 0) is compared with the case of equal (random) reactivity of the two functional groups in C for formulation F40. This is suggested as an example of polyesterification with an anhydride and a carboxylic acid, respectively. Figure 15 gives the dramatic effect on... 

The statistical approach has been applied to systems containing reactants with functional groups of unequal reactivity [Case, 1957 Macosko and Miller, 1976 Miller and Macosko, 1978 Miller et al., 1979]. In this section we will consider some of the results for such systems. Figure 2-15 shows a plot of Mw vs. extent of reaction for the various values of s at r = 1 for the system... 

Compare the gel points calculated from the Carothers equation (and its modifications) with those using the statistical approach. Describe the effect of unequal functional groups reactivity (e.g., for the hydroxyl groups in glycerol) on the extent of reaction at the gel point. 

Polymerization reactions of multifunctional monomers such as those used in dental restorations occur in the high crosslinking regime where anomalous behavior is often observed, especially with respect to reaction kinetics. This behavior includes auto acceleration and autodeceleration [108-112], incomplete functional group conversion [108,109,113-116], a delay in volume shrinkage with respect to equilibrium [108, 117,118], and unequal functional group reactivity [119-121]. Figures 3 and 4 show a typical rate of polymerization for a multifunctional monomer as a function of time and conversion, respectively. Several distinctive features of the polymerization are apparent in the rate profiles. 

Branching and crosslinking processes can be treated as a combinatorial problem which is not too complicated when the functionalities are equally reactive and unreacted functionalities are considered as the only kind of defects. If loop formation (intra-molecular cyclization) is involved, the complexity increases considerably. The same holds if the monomers contain groups of unequal reactivity or if the reactivity is influenced by substitution effects. 

With two functional groups of unequal reactivity, the more reactive can always be made to react alone. 

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