Unequal functional group reactivity

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. 

The observed values as in many other similar systems fall approximately midway between the two calculated values. The Carothers equation [12] gives a high value for p. The experimental p values are close to but always higher than those calculated from the Flory equation [13]. Two reasons can be given for this dilference first the occurence of intramolecular cyclization and second unequal functional group reactivity. Both factors were ignored in the theoretical derivations for p. 

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. 

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 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 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... 

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... 

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. 

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

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

Most theoretical kinetic studies on step polymerizations have in the past considered the reacting species to have equal reactivity. Recently, however, the step polymerization of two kinds of difunctional monomers, one in which the reactive functional groups have unequal reactivities and the other for which monomeric function groups react at a rate that is different from those that are present as chain ends, have been dealt with. The effect of the non-equivalent reactivity of the two functional groups in a difunctional monomer on the kinetics of polymerization with a symmetric monomer and molecular-weight distribution of the product have also been calculated theoretically. ... 

This model has been extended by Gordon et al. by taking into account unequal reactivity and substitution effects within monomer units and by a mean field treatment of very restricted cyclization. However, all these models are limited to systepis which can be described by Markovian statistics without any long range correlations affecting the apparent reactivity of a functional group. 

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