Reaction networks polymerization

The Fischer-Tropsch synthesis follows a polymerization mechanism where a Q unit is added to the growing chain. A simplified representation of the reaction network is shown in Fig. 1, where the key points are termination by either H-abstraction to give a-olefins or by hydrogenation to give w-paraffins. 

As implied by the name, one of the fundamental distinctions between macromolecules and small molecules lies in their mass, or molecular weight, M. The lower limit for the molecular weight of a macromolecule is ill defined, but it is often considered to lie in the range M = 103-104. The upper limit for the molecular weight of a macromolecule is unbounded, and for all practical purposes it can be considered to be infinite. Of course, an infinite molecular weight is unattainable with a finite amount of material. However, molecular masses in covalently bound polymeric networks are conveniently expressed in units of kg molecule-1, rather than units of kg mol-1, and they are certainly an acceptable approximation to infinite in the context of this work. These polymeric networks contain numerous branch points, either as a consequence of the use of multifunctional monomers during the polymerization or as a consequence of crosslinking reactions after polymerization has occurred. In such systems, the molecular mass is of less fundamental interest than the mass of the network chains between crosslinks. 

The four materials are (1) polymer 1 linear and polymer 2 crosslinked (2) polymer 1 crosslinked and polymer 2 linear (3) and (4) are obtained by interchanging polymers 1 and 2. In each case the second polymerized material is grafted to the first polymerized material. Equations 9-14 and the related discussion result in 72 possibilities. The difference lies in the counting or omission of the time sequence of events. The reaction network scheme does not consider the importance of the time-order of events. Thus Equation 31 yields the minimum number of distinguishable materials. 

This chapter addresses the establishment of practical mathematics of kinetics for given pathways and networks. The complementary problem of establishing pathways or networks from observed kinetic behavior will be taken up in the next chapter. The discussion of special aspects of catalysis, chain reactions, and polymerization is deferred to Chapters 8 to 10. 

Approximate reaction networks have become customary for modeling reactions in which the species are too numerous for a full accounting or chemical analysis. Lumped components or continuous distributions commonly take the place of single components in process models for refinery streams (Wei and Kuo 1969 Weekman 1969 Krambeck 1984 Astarita 1989 Chou and Ho 1989 Froment and Bischoff 1990). Polymerization processes are described in terms of moments of the distributions of molecular weight or other properties (Zeman and Amundson 1965 Ray 1972, 1983 Ray and Laurence 1977). Lumped components, or even hypothetical ones, are also prevalent in models of catalyst deactivation (Szepe and Levenspiel 1968 Butt 1984 Pacheco and Petersen 1984 Schipper et al. 1984 Froment and Bischoff 1990). 

As shown earlier in Section 3.2.2, scanning temperamre DSC provides a mpid method for measuring the total heat of reaction for network polymerization, and there are many such applications to provide baseline data for polymer chemorheoiogy. For example, in the... 

Chemical reactions may involve large numbers of steps and participants and thus many simultaneous rate equations, all with their temperature-dependent coefficients. The full set of rate equations is easily compiled as shown in Section 2.4, and to obtain solutions by numerical computation poses no serious problems. With a large number of equations, however, it may become too much of a task to verify the proposed network and obtain values for all its coefficients. Therefore, every available tool must be brought to bear to reduce the bulk of mathematics, and that without unacceptable sacrifice in accuracy. The present chapter critically reviews the principal tools for such a purpose stoichiometric constraints and the concepts of a rate-controlling step, quasi-equilibrium steps, and quasi-stationary states. Other tools useful in catalysis, chain reactions, and polymerization will be discussed in the context of those reactions (see Sections 8.5.1, 9.3, 10.3, and 11.4.1). 

Precipitate can also form fiom a step reaction. Precipitation polymerizations of prepolymers to form crosslinked, thermoset polymers is a very common commercial reaction of the epoxy resins and phenol-methanal, network polymers covered in this book. These reactions work best when the reaction is slow, mildly exothermic, and undergoes a viscous to solid transformation late in the synthesis. 

Bifunctional monomers, such as A-A, B-B and A-B, yield linear polymers. Branched and crosslinked polymers are obtained from polyfunctional monomers. For example, polymerization of formaldehyde with phenol may lead to complex architectures. Formaldehyde is commercialized as an aqueous solution in which it is present as methylene glycol, which may react with the trifunctional phenol (reactive at its two ortho and one para positions). The type of polymer architecture depends on the reaction conditions. Polymerization imder basic conditions (pH = 9-11) and with an excess of formaldehyde yields a highly branched polymer (resols. Figure 1.8). In this case, the polymerization is stopped when the polymer is still liquid or soluble. The formation of the final network (curing) is achieved during application (e.g., in foundry as binders to make cores or molds for castings of steel, iron and non-ferrous metals). Under acidic conditions (pH = 2-3) and with an excess of phenol, linear polymers with httle branching are produced (novolacs). 

Formally speaking, the reaction of polymerization seems most effective at P -> oo, and on the T vs V2 state diagram (Figure 3.59), the asymptote T —> oo corresponds to v n responding to P ,c. At lower uj < V2,n, the curve A of the solution-gel transition heis a positive first derivative. The specific shape of the curve A depends on the model s details. J his curve ends on the binodal curve of the two-phase gel state due to the elasticity forces of the network chains and the interaction between polymer and LMWL (see above). The numerical values of g have been determined for different types of lattice. It has also been established that the inequality f J/j < V2,c holds true (de Gennes, 1979). 

Instead of using compartment models, the flow pattern in the reactor also can be calculated via computational fluid dynamics (CFD). However, when using CFD, relatively small reaction networks are often used to reduce the computational cost. An exception is gas-phase polymerization, such as the production of low-density polyethylene). For more details on the application of CFD calculations for polymerization processes, the reader is referred to Asua and De La Cal (1991), Fox (1996), Kolhapure and Fox (1999), and Pope (2000). 

The reaction conditions can be varied so that only one of those monomers is formed. 1-Hydroxy-methylurea and l,3-bis(hydroxymethyl)urea condense in the presence of an acid catalyst to produce urea formaldehyde resins. A wide variety of resins can be obtained by careful selection of the pH, reaction temperature, reactant ratio, amino monomer, and degree of polymerization. If the reaction is carried far enough, an infusible polymer network is produced. 

We noted above that the presence of monomer with a functionality greater than 2 results in branched polymer chains. This in turn produces a three-dimensional network of polymer under certain circumstances. The solubility and mechanical behavior of such materials depend critically on whether the extent of polymerization is above or below the threshold for the formation of this network. The threshold is described as the gel point, since the reaction mixture sets up or gels at this point. We have previously introduced the term thermosetting to describe these cross-linked polymeric materials. Because their mechanical properties are largely unaffected by temperature variations-in contrast to thermoplastic materials which become more fluid on heating-step-growth polymers that exceed the gel point are widely used as engineering materials. 

---