The Kinetics of Step-Growth Polymerization

But it isn t Experimental measurements show that the (overall) reaction is actually third-order (rate constant = kf) because the reaction is catalyzed by acids (so one of the reacting components also acts as a catalyst— Equation 4-12). 

Note two important things. First, the rate of the reaction is described m terms of the disappearance of one of the functional groups, in this case the A s or acids. Because A s only react with B s and the stoichiometry is 1 1, we could have just as easily chosen the B s to follow. Second, the quantities [A] and [ ] are the concentrations of functional groups, not monomers or molecules. In this reaction, there are two functional groups per monomer, so if some nasty, sadistic professor was to set you a homework question where the concentration of monomers was given, you would have to multiply these numbers by two to get the concentration of functional groups. 

Now let s consider the important case where we have exactly equal concentrations of functional groups, so we can put c = [A] = [B]. Instead of Equation 4-12 we can write Equation 4-13. 

And if the initial concentration (time, t = 0) of monomer is cQ then we can integrate this equation as shown in Equations 4-14. 

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ADMET has been shown to be a step-growth polycondensation reaction [31[. The kinetics of step-growth polymerization and consequences thereof are completely different than those of chain polymerizations. Since ROMP and many other single-site transition metal-catalyzed polymerizations discussed in this book proceed... 

If a volatile monomer is used in an ADMET polymerization, a condenser should be used to return monomer vapor to the reaction mixture. The kinetics of step-growth polymerization dictate that the concentration of monomer falls very quickly to produce dimer, trimer, and so forth. Nevertheless, monomer will be present for some time after the start of the polymerization. If the monomer is particularly volatile, a dry ice-isopropanol condenser is useful. This can be constructed in any glass shop by attaching a cup-shaped cooling reservoir to a vacuum valve or other cylindrical glass tube with the required joints and valve. If the monomer is only slightly volatile, or the carrier gas method is used, a water-cooled condenser is sufficient to retain monomer in the flask, while allowing ethylene to escape. 

The kinetics of step-growth polymerization can be derived from a polyesterification reaction that follows the same course as all acid-catalyzed esterifications. ... 

A-A/B-B Step Growth If the two functional groups are on different monomer units, the kinetics of step-growth polymerization are more complex. If two monomers are used, one with two A functional groups and one with two B functional groups, the polymerization is described as A-A/B-B step-growth polymerization. An example is nylon 66. The polymerization may be represented as ... 

The rate of a step-growth polymerization is the sum of the rates of reactions which take place between molecules of different size, therefore, in this case the kinetics is difficult to analyze. However, the kinetics of step-growth polymerization can be considered identical to those of analogous small molecule reaction and can be... 

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 ... 

Kinetic considerations are of paramount importance in understanding the mechanism of step-growth polymerization. As stated in Chapter 1, chain-growth polymerizations take place in discrete steps. Each step is a reaction between two functional groups for instance, in a polyesterification reaction it is a reaction between -COOH and -OH. The increase in molecular weight is slow. The first step is a condensation between two monomers to form a dimer ... 

Mechanism and Kinetics of Step-Growth Polymerization and, the molecular weight distribution is ... 

A few papers have appeared on the subject of the kinetics of step growth or condensation polymerization without reference to any particular polymer system and these will be considered first. 

If the mechanism of termination is disproportionation then the degree of polymerization is the same as the kinetic chain length. The initial reaction between the radical and the first monomer molecule is fast and so only subsequent additions need be considered. The molecule M, has been formed by (/ - 1) addition reactions. The probability that one of these reactions has taken place is a and so using the analogy of step-growth polymerization the probability that (/ - 1) successive addition reactions have taken place is The probability that the last reaction is... 

Recently, several research groups exploited the analogy between NP self-assembly and step-growth polymerization reactions. The theory of step-growth polymerization has been applied to a different extent to the formation of nanowires and chains of NPs. The resemblance between the formation of NP chains and the polymerization of monomer molecules is more straightforward, as it does not include the recrystallization of self-assembled NPs. Therefore, below we will describe the results of studies of the kinetics of the formation of chains that are bonded due to the physical or chemical interactions between the ligands. 

To a different extent, the theory of step-growth polymerization was also applied to interpret the kinetics and the mechanism of OA of NPs, in which NPs with common... 

Based on the experimental results of Table 3.1, we can postulate a simple kinetic model for the study of step-growth polymerization in which all of the rate constants are assiuned to be independent of chain length. This is referred to as the equal reactivity hypothesis. The following section shows that this assumption leads to a considerable simplification of the mathematical analysis. However, there are several systems in which this hypothesis does not hold accmately, and the analysis presented here must be accordingly modified [2,8-14]. 

There are some fundamental differences in the engineering of step-growth and chain-growth polymerizations because of basic distinctions in the mechanisms of these reactions. A propagation reaction (Section 6.3.2) in a kinetic chain sequence must be fast or the series of monomer additions will not be long enough to produce... 

There is general similarity between the kinetics of many ring-opening polymerizations and those of step-growth polymerizations that are discussed in Chapter 6. Some kinetic expressions in ring-opening polymerizations, on the other hand, resemble chain-growth ionic ones. 

The Stille reaction-based polymerization, by its polycondensation nature, falls into the major category of step-growth polymerization. Thus, characteristics concerning step-growth polymerization still exist and related fundamental principles apply, such as reaction kinetics, molecular-weight distribution and control, and end-group modifications. We will briefly discuss the latter two in the context of Stille polymerizations. 

The reactions taking place during the synthesis of a polymer are rather complex in nature. The description of the chemistry of a polymerization reaction often involves over 20 different elementary reactions. This means that control of the overall reaction rate that governs the process safety may be rather complicated. Nevertheless the kinetically determining step in polymerization reactions is the chain growth reaction. 

Flory outlined [3] that the definition of polycondensation is necessarily based on kinetic aspects and not on the structure of polycondensates, because numerous polycondensates can also be prepared by ROP which usually proceeds as chain-growth polymerization. Flory s definition of step-growth polymerization is limited to polycondensations and polyadditions in the melt or in solution, and does not include solid-state polycondensations. Hory s definition of step-growth polymerizations is based on point 1. 

In this chapter, we have presented the kinetics of reversible step-growth polymerization based on the equal reactivity hypothesis. We have found that the polymerization consists of infinite elementary reactions that collapse into a single one involving reaction between flmctional groups. This kinetic model has been tested extensively against experimental data. It is found that in most of the systems involving step-growth polymerization, there are either side reactions or the equal reactivity hypothesis does not hold well. This chapter presents the details of chemistry for some industrially important systems motivated readers are referred to advanced texts for mathematical simulations. 

In all of the four elasses of ehain-reaetion polymerization, the distinguishing feature is the existenee of the propagation step between the polymeric growing center and the monomer moleeule. This ehapter discusses in detail the kinetics of these different polymerizations and the differenees between the four modes of ehain growth polymerization. 

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 ... 

Elsewhere in this chapter we shall see that other reactions-notably, chain transfer and chain inhibition-also need to be considered to give a more fully developed picture of chain-growth polymerization, but we shall omit these for the time being. Much of the argumentation of this chapter is based on the kinetics of these three mechanistic steps. We shall describe the rates of the three general kinds of reactions by the notation Rj, Rp, and R for initiation, propagation, and termination, respectively. 

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