Step-Growth Kinetics

Consider the condensation of two monomers, A-A and B-B, such as a dicarboxylic acid and a diol to make a polyester. We assume that a trace amount of acid catalyst is present, and the concentration of the catalyst is a constant and so can be absorbed into the rate constant, giving the rate law of Eq. 13.6. This is just the familiar second-order rate law (see Eq. 7.32). Note that [A] and [B] are the concentrations ot functional groups, not of monomers. We assume that the starting concentrations of each functional group are the same, and define Co as the initial concentration and c for the concentration at a particular time in the reaction. This makes it possible to simplify Eq. 13.6. We define the extent of reaction as p, and express c in terms of p as in Eq. 13.7. The treatment is then as in Eq. 13.8, giving the final rate law in Eq. 13.9. 

If our assumptions are correct, a plot of 1 / (1 - p) vs. time should be linear, and indeed this is empirically observed for step-growth polymerizations. To determine p you need a method that can follow the conversion of all functional groups in the monomers to all the associated functional groups in the polymer, such as carboxylic acids to esters in the formation of polyester. 

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The term stepwise kinetics, or step-growth kinetics, refers to polymerizations in which the polymer s molecular weight increases in a slow, stepwise manner as reaction time increases. 

The reaction was shown to follow step-growth kinetics in its early stages and to stop abruptly at the length defined by the template. No products were detected in the absence of any template. As the hydrogen bonding between the nucleobases and the imine formation are reversible, error correction occurs to some extent in this system. In this sense, this report matches the spirit of DCC more closely than many others. Unfortunately, no follow-up using the entire nucleic acid alphabet has been published hitherto. 

Although many step polymerizations do involve condensation reactions, e.g. in the formation of polyesters and polyamides, there are examples where this is not the case. The formation of polyurethanes from diols and diisocyanates, and the formation of polyphenylene oxides (PPO) shows step growth kinetics. 

Tsvetkova, I. V., and Lipkind, M. A., 1973, Studies on the role of myxovirus neuraminidase in virus-cell receptor interaction by means of direct determination of sialic acid split from cells. 3. One-step growth kinetics of accumulation of the sialic acid liberated from NDV-infected chick embryo cells. Arc/ . Gesamte Virusforsch. 42 125. 

The preceding discussions of the kinetics and molecular weight distributions in the step-growth polymerization of AB monomers are clearly exemplified by the esterification reactions of such monomers as glycolic acid or co-hydroxydecanoic acid. Therefore one method for polyester synthesis is the following ... 

Acrylic adhesives cure by a free radical chain growth mechanism. In contrast, epoxy and urethane adhesives cure by a step growth mechanism. This has a major impact on the cure kinetics, as well as the composition of the adhesive during cure ([9], pp. 6-9). Cyanoacrylate adhesives (such as Super Glue ) also cure by chain growth, but the mechanism is ionic with initiation by surface moisture. 

Step-growth polymerizations have widely been developed in industrial applications whereas knowledge of their mechanisms and of their kinetics has remained far below that of chain polymerization reactions. 

Why are the kinetics of chain growth polymerization more difficult to study than those of step growth polymerization What simplification do we use to treat the kinetics of the chain growth process How does this simplification reduce the complexity of the problem and what are the limitations of this method ... 

The resin system selected to initiate these studies is a step-growth anhydride cured epoxy. The approach to the kinetic analysis is that which is prevalent in the chemical engineering literature on reactor design and analysis. Numerical simulations of oligomeric population density distributions approximate experimental data during the early stages of the cure. Future research will... 

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