Polymerization reactions and kinetic considerations

Whether a particular monomer can be converted to polymer depends on both thermodynamic and kinetic considerations. The polymerization will be impossible under any and all reaction conditions if it does not pass the test of thermodynamic feasibility. Polymerization is possible only if the free-energy difference AG between monomer and polymer is negative (Sec. 3-9b). A negative AG does not, however, mean that polymerization will be observed under a particular set of reaction conditions (type of initiation, temperature, etc.). The ability to carry out a thermodynamically feasible polymerization depends on its kinetic feasibility—on whether the process proceeds at a reasonable rate under a proposed set of reaction conditions. Thus, whereas the polymerization of a wide variety of unsaturated monomers is thermodynamically feasible, very specific reaction conditions are often required to achieve kinetic feasibility in order to accomplish a particular polymerization. 

It is possible to balance all of these thermodynamic, kinetic, and mechanistic considerations and to prepare well-defined PTHF. Living oxonium ion polymerizations, ie, polymerizations that are free from transfer and termination reactions, are possible. PTHF of any desired molecular weight and with controlled end groups can be prepared. 

In order to formulate an answer to the obviously important question of the length of this interval of acceleration and to ascertain under what conditions it may be long enough to observe experimentally, we shall examine the non-steady-state interval from the point of view of reaction kinetics. Let us suppose, however, that the polymerization is photoinitiated, with or without the aid of a sensitizer. It is then possible to commence the generation of radicals abruptly by exposure of the polymerization cell to the active radiation (usually in the near ultraviolet), and the considerable period required for temperature equilibration in an otherwise initiated polymerization can be avoided. Then the rate of generation of radicals (see p. 114) will be 2//a s, and the rate of their destruction 2kt [M ]. Hence... 

Rate considerations have enormous practical implications to anyone working with polymers. As an example, it may be possible to make an incredible new polymer, but would we be able to profitably commercialize this super new polymer if its polymerization took weeks, months, or even years to occur Rather obviously, the answer is no . Therefore, we must study the rates of reactions in an effort to understand how to produce materials in the time scales we have at our disposal. The study of kinetics provides us with the tools and the knowledge necessary to understand the rates of the polymerization reactions that are important to us. Kinetic studies allow us to understand the energetic considerations necessary for a reaction to progress. We also gain the tools to propose mechanisms that describe how a reaction actually occurs at the molecular level. 

A quantitative kinetic model of the polymerization of a-pyrrolidine and cyclo(ethyl urea) showed,43 that two effects occur the existence of two stages in the initiation reaction and the absence of an induction period and self-acceleration in a-pyrrolidine polymerization. It was also apparent that to construct a satisfactory kinetic model of polymerization, it was necessary to introduce a proton exchange reaction and to take into consideration the ratio of direct and reverse reactions. As a result of these complications, a complete mathematical model appears to be rather difficult and the final relationships can be obtained only by computer methods. Therefore, in contrast to the kinetic equations for polymerization of e-caprolactam and o-dodecalactam discussed above, an expression... 

We first consider the polymerization where each kinetic chain yields one polymer molecule. This is the case for termination of the growth of macroradicals by disproportionation and/or chain transfer (A,c = 0). The situation is completely analogous to that for linear, reversible step-growth polymerization described in Section 5.4.3. If we randomly select an initiator residue at the end of a macromolecule, the probability that the monomer residue which was captured by this primary radical has added another monomer is S and the probability that this end is attached to a macromolecule which contains at least i monomers is S . The probability that this macromolecule contains exactly i monomers equals the product of 5 and the probability of a termination or transfer step. The latter probability must be equal to (I — S) since it is certain that the last monomer under consideration will undergo one of these three reactions. That is, the probability that a randomly selected molecule contains t monomer units is 5 (l — S). Since such probabilities are equal to the corresponding mole fraction of this size molecule, jc,, we have the expression... 

Engineering of polymerization reactions requires a detailed knowledge of the phenomena that take place in the polymer reactor. This entails a model of the polymerization kinetics and the heat and mass transfer features of the particular polymerization and process. Polymerization reactions are usually complex and a certain degree of mathematical sophistication is required for effective modeling. Excursions into the details of particular reactions or modeling techniques are beyond the scope of this introductory text and this chapter is therefore limited to a review of the special considerations that apply in the case of various polymerizations and processes. Most of the following discussions are necessarily qualitative, for space reasons. 

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