Advanced Stage of Polymerization

In several cases (e.g., in the manufacture of polyethylene terephthalate), the equilibrium constants of the reactions are such that one must remove the volatile condensation products by application of a vacuum in order to obtain a polymer 

Equations (4.4.1) and (4.4.4) can be solved numerically using the Runge-Kutta technique when n is known. In order to do so, the mass transfer problem in the film is first solved. This is discussed in Appendix 4.1, where an analytical solution is developed using a similarity transformation. From these results, it is possible to prepare a computer program that gives n . 

Example 4.3 Write material balance equations in terms of Eq. (4.1.6) and solve 

Note that the value of Aqo of the interface cannot be time independent if wq at the point is assumed to be fixed. Because the variation of [i.e., Eq. Ad.l.lb) is governed by a partial differential equation which does not have any derivative with respect to y, the time variation of Ago l e interface is given by 

This chapter has discussed the analysis of reactors for step-growth polymerization assuming the equal reactivity hypothesis to be valid. Polymerization involves an infinite set of elementary reactions under the assumption of this hypothesis, the polymerization can be equivalently represented by the reaction of functional groups. The analysis of a batch (or tubular) reactor shows that the polymer formed in the reactor cannot have a polydispersity index (PDI) greater than 2. However, the PDI can be increased beyond this value if the polymer is recycled or if an HCSTR is used for polymerization. A comparison of the kinetic model with experimental data shows that the deviation between the two exists because of (1) several side reactions that must be accounted for, (2) chain-length-dependent reactivity, (3) unequal reactivity of various functional groups, or (4) comphca-tions caused by mass transfer effects. 

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Observe that for monomer concentrations of up to 40%, plots show that first-order kinetics is followed. However, at higher initial monomer concentrations, a sharp increase in rate is observed at an advanced stage of polymerization. At the same time, high-molecular-weight polymers are produced. Autoacceleration is particularly pronounced with methyl methacrylate, methyl acrylate, and acryhc acid. It occurs independent of an initiator and is observed even rmder isothermal conditions. In fact, where there is no effective dissipation of heat, autoacceleration results in a large increase in temperature. 

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