Step polymerization equilibrium considerations

Many, if not most, step polymerizations involve equilibrium reactions, and it becomes important to analyze how the equilibrium affects the extent of conversion and, more importantly, the polymer molecular weight. A polymerization in which the monomer(s) and polymer are in equilibrium is referred to as an equilibrium polymerization or reversible polymerization. A first consideration is whether an equilibrium polymerization will yield high-molecular-weight polymer if carried out in a closed system. By a closed system is meant one where none of the products of the forward reaction are removed. Nothing is done to push or drive the equilibrium point for the reaction system toward the polymer side. Under these conditions the concentrations of products (polymer and usually a small molecule such as water) build up until the rate of the reverse reaction becomes equal to the polymerization rate. The reverse reaction is referred to generally as a depolymerization reaction other terms such as hydrolysis or glycolysis may be used as applicable in specific systems. The polymer molecular weight is determined by the extent to which the forward reaction has proceeded when equilibrium is established. 

The propagation step in ionic polymerizations is considerably more comphcated than in free radical polymerization (5). In addition to monomer structure and temperature, solvent and counter ion type are of importance. The separation between the counter ion and the active polymer chain end is the primary rate determining factor it can be represented schematically as an equilibrium between four species of different level of separation ... 

Equation (5.49) indicates the limitation imposed by equilibrium on the synthesis of a high-molecular-weight polymer. Thus, according to this equation even for a high equilibrium constant of 10, a degree of polymerization of only about 100 can be obtained in a closed system. A consideration of the equilibrium constants for various step polymerizations [4, 8-12] readily shows that polymerizations to obtain high-molecular-weight polymer cannot be carried out as closed systems. For example, K for a polyesterification... 

Many step-growth polymerizations are carried out by mass or bulk-type polymerization. This is commonly done not only for convenience, but also because it results in minimum contamination. Few step-growth reactions are highly exothermic, so thermal control is not hard to maintain. Because equilibrium considerations are very important, the reactions are usually carried out in a way that allows continuous removal of the byproduct. Occasionally, the polymerizations are carried out in dispersion in some convenient carriers. Solution polymerizations are sometimes used as a way of moderating the reactions. 

The first step in the analysis of copolymer crystallization is the development of quantitative concepts that are based on equilibrium considerations. Subsequently, deviations from equilibrium and a discussion of real systems will be undertaken. Problems involving the crystallization and melting of copolymers cannot in general be uniquely formulated since two phases and at least two species are involved. The disposition of the species among the phases needs to be specified. It cannot be established a priori by theory. This restraint is not unique to polymeric systems. It is a common experience in analyzing similar problems that involve monomeric components.(2) Thus, in the development of any equilibrium theory a decision has to be made prior to undertaking any analysis of the disposition of the co-units between the phases. Theoretical expectations can then be developed based on the assumptions made. 

Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

Since alkylate compositions from the four butene isomers are basically similar, the butenes are thought to isomerize considerably, approaching equilibrium composition prior to isobutane alkylation. Such a postulation is at variance v/ith previously published alkylation mechanisms. The Isomerization step yields predominantly isobutene which then polymerizes and forms a 2,2,4-trimethylpentyl carbonium ion, a precursor of 2,2,4-trimethylpentane, the principal end product. The 2,2,4-trimethylpentyl ion is also capable of isomerization to other trimethylpentyl ions and thus yields other trimethylpentanes, principally 2,3,4-trimethyl-pentane and 2, 3, 3-trimethylpentane. 

It is interesting that the reaction epimerizes 75% of the M residues, but not more. No solvent deuterium incorporation into M residues during the epimerization reaction could be detected, which indicates that the proton abstraction that is the necessary first chemical step in the reaction is irreversible. However, the enzyme does not epimerize all of the M residues in the substrate. The equilibrium constant for epimerizations is usually close to one for reactions that involve simple substrates, so one might expect the epimerase reaction to reach equilibrium when the M content of the alginate is equal to the G content. The fact that the reaction occurs on a polymeric substrate made up of chiral monomers complicates considerations of the energetics of the reaction somewhat. Nonetheless, it is difficult to reconcile the apparent irreversibility of proton abstraction with the 1 3 M G ratio in the product, unless one proposes that the conformation of the polymer becomes such that it can no longer bind to the enzyme. 

In this chapter we will focus on the economic implications of the process. In general it is not needed to add solvents to the process in reactive extrusion. During the major part of the process the monomer acts as a solvent for the polymer, and therefore no extensive separation step has to be used after the process. Nevertheless, also in reactive extrusion some devolatilization is generally still necessary to remove remaining monomers, but this is only a fraction of the amount to be removed in, for instance, solution polymerization. The amount of residual monomer that has to be removed can be connected to the equilibrium of the reaction and to the ceiling temperatures, but it can also be connected to a limited residence time in the extruder. The choice between extra devolatilization or the use of a longer extruder has to be based on economic considerations. However, devolatilization of monomer in reactive extrusion is from an economic point of view always much more attractive than the complete separation step needed when solution polymerization is considered. 

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