The Kinetics of CRP Processes

Analysis of the kinetics of CRP reactions is more complex than for conventional radical polymerizations consequently, a detailed derivation of the basic equations will not be given here. The fundamental activation-deactivation pseudoequilibria that control the living characteristics of the various CRPs have been outlined in Equation 3.31 to Equation 3.33, and if the steady state is to be achieved rapidly, then the rates of activation and deactivation must be considerably larger than the rates of the initiation and termination reactions. In successful CRP reactions, the time taken to reach the equilibrium steady state is estimated to be in the range 1 to 100 ms. 

The application of a steady-state analysis to these polymerization reactions leads to a series of rate equations that can be simplified for certain reaction conditions. If the rate of initiation is finite (Vj 0), i.e., when a conventional radical iiutiator is used to start the reaction, and the concentration of the persistrait radical X ] or [AX Jo is initially zero, then Equation 3.35 is obtained 

For CRP reactions that have no conventional initiator present, i.e., v, = 0, two limiting cases can be considered. 

If [X ] or [AX ] are large, then the eonvCTsion index is again first order in /, Equation 3.37 

Stationary state kinetics can also be used to derive a relation for the polydispersity index of the form 

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