Extent reaction, polycondensation

Hydroxy-terminated PDMS, however, has disadvantages. The monofunctional ends limit the number of connections between the polymer (or oligomer) molecule and the glass network to two. This limitation raises the possibility that some PDMS molecules are not tied at both ends to the glass network if the polycondensation does not go to completion i.e. there may be "dangling" or loose PDMS chains in the final sol-gel material. This occurance of free ends would indeed be anticipated since the extent of reaction most likely is not 100%. Hence, the physical properties, specifically the mechanical behavior of the overall material, would be expected to suffer as a result of loose PDMS chains in the system. Disregarding this potential problem, the mechanical behavior of the sol-gel hybrids are, ultimately, influenced by the mechanical behavior of the modifying elastomer ... 

Fig Number-fraction distribution of chain molecules at different extents of reaction in polycondensation... 

Table Effect of extent of conversion on degree ofpolymerisation for polycondensation reaction...

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

The chemical constraint reduces the number of possible reactions considerably, and consequently it leads to a much narrower molar mass distribution. Furthermore, the extent of reaction a of the A-group can cover all values from zero to unity, but the extent of reaction P of the equally reactive 5-groups cannot become larger than P=a/(f-l). One important consequence of this strict constraint is that gelation can never occur [1,13]. A much higher branching density than by random polycondensation can be achieved. For this reason one nowadays speaks of hyperbranching. 

Again, we have made use of 0n = which holds for Gaussian chains. Equation (E.4) is formally identical to the equation for linear polycondensates. It differs, however, essentially in the meaning of a that is no longer the overall extent of reaction, which would be proportional to the monomer consumption, but is instead a conditional probability that an activated monomer has formed a bond with another monomer. This probability is only weakly dependent on the monomer conversion and cannot be determined by titration but has to be determined from kinetic measurements107. ... 

In other words, of the initial charge of isopropyl chloride, 34% of the carbon is converted to propane under these conditions. A comparable sample of 1-chloropropane under identical reaction conditions, of excess alkyl halide Lewis acid, was converted after five minutes to the extent of 18% to propane. After 15 minutes the relative amount of "propane" had decreased as a result of further acid catalyzed polycondensation reactions. Similarly, isopropyl chloride reacts in HBr-AlBr3 at room temperature to give a gas product which is entirely propane after 2 min. In this system we again begin to see a buildup of heavier hydrocarbon species with time. The fact that the reaction proceeds so rapidly here can probably be attributed to a homogeneous hydrocarbon/acid liquid phase. This last result and additional experiments are summarized in Table IV. 

This chapter will attempt to survey critically the major areas of experimentally determined kinetic data which are available on polycondensation reactions and their mechanisms, and to emphasize the mechanistic similarities of many of the reactions. The statistics of polycondensation reactions will be touched on only to the extent that it helps understand the reactions and their kinetics. The general approach to the subject of kinetics is designed to be of primary use and interest to those polymer chemists who are concerned with the synthesis of products having desired properties, and with the understanding of their synthetic processes. 

In the statistical analysis of polycondensation the extent of reaction, p, is defined as the probability that a functional group has reacted at time t. (In kinetic treatments p is often used as the equivalent expression, the fraction of functional groups which has reacted.) It follows that (1—p) is the probability of finding a functional group unreacted. 

This last equation is the statistical number-distribution function for a linear polycondensation reaction at the extent of reaction p. 

This is the statistical weight-distribution function for a linear polycondensation reaction at the extent of reaction p. The number-distribution and weight-distribution functions are illustrated in Figs. 1 and 2 for values of p. 

A wide range of carbonyl addition reactions is available to the polymer synthesis chemist. To the extent that reactants having functionalities of two or higher are available, these reactions may be suitable for polycondensation. A simplified scheme is... 

Reversible reactions involve both formation of polyester and the reverse reaction of the polymer with the liberated low-molecular-weight product. The so-called polycondensation equilibrium occurs, of course, when the rates of the forward and reverse reactions are the same. This equilibrium determines the extent of conversion to polymer, d the position of the equilibrium determines the molecular weight of the product. In the case of monofunctional reactants, the equilibrium governs only the yield of the product. 

In all the synthetic approaches reviewed here, and indeed in all polycondensation reactions, various side reactions can influence the formation of polymer to a greater or lesser extent. Among these side reactions are loss of functionality as in decarboxylation or in the oxidation of an aliphatic hydroxyl group, the formation of volatile intermediates, the formation of unreactive intermediates, crosslinking, and other reactions. These reactions are examined in more detail in the relevant sub-sections. 

Many factors affect the progress of the interfacial polymerization reaction, including choice of solvent, the use of detergents as emulsifiers, temperature, rate of addition of one monomer, and rate of stirring [6]. However, no major study has yet been made of reaction rates, the extent of formation of unreactive cyclic oligomers, and the nature and extent of various possible side reactions in this class of polycondensation. 

FIGURE 20.3 Relationship between X and extent of reaction, p, for various reaction times during a typical polycondensation. 

The lack of dependence of the reaction rate for polycondensation on the extent of reaction (to a first approximation) allows a simple bimolecular reaction mechanism to be employed. Noting, from the previous section, that the reaction mechanism for simple esterification reactions (Scheme 1.1) had as the rate-determining step the second reaction, namely... 

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