Rate constants free radical termination

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

A characteristic reaction of free radicals is the bimolecular self-reaction which, in many cases, proceeds at the diffusion-controlled limit or close to it, although the reversible coupling of free radicals in solution to yield diamagnetic dimers has been found to be a common feature of several classes of relatively stable organic radicals. Unfortunatly, only the rate constants for self-termination of (CH3)jCSO (6 x 10 M s at 173 K) and (CH3CH2)2NS0 (1.1 X 10 M s at 163K) have been measured up to date by kinetic ESR spectroscopy and consequently not many mechanistic conclusions can be reached. 

A case classically associated with radical chain polymerization for which a (pseudo)steady state is assumed for the concentration of active centers this condition is attained when the termination rate equals the initiation rate (the free-radical concentration is kept at a very low value due to the high value of the specific rate constant of the termination step). The propagation rate, is very much faster than the termination rate, so that long chains are produced from the beginning of the polymerization. For linear chains, the polydispersity of the polymer fraction varies between 1.5 and 2. 

Baxendale, Evans and coworkers reported in 1946 that the polymerization of methyl methacrylate (MMA) in aqueous solution was characterized by homogeneous solution kinetics, i.e. where mutual termination of free radicals occurred, in spite of the fact that the polymer precipitated as a separate phase. Increases in the rates of polymerization upon the addition of the surfactant cetyl trimethyl ammonium bromide (CTAB) were attributed to the retardation of the rate of coagulation of particles, which was manifested in a reduction in the effective rate constant for mutual termination,... 

Once least squares values of the /3 s were obtained, it was desirable to extract from them as much information as possible about the original parameters. To do so, we make one further statement concerning the relations between the rate constants for mutual termination of polymeric radicals of different size. It has been shown (2) that termination rates in free radical polymerizations are determined by diffusion rates rather than chemical factors. The relative displacement of two radicals undergoing Brownian motion with diffusion coefficients D and D" also follows the laws of Brownian diffusion with diffusivity D = D -J- D" (11). It... 

In solving the problem for this case, use the stationary-state hypothesis for the intermediates (free radicals Cl, RH, RHCl ) to obtain rate equations for Trhj and ErhiCi analogous to the rate equations for the first-order and second-order cases. Note that the rate constant for the termination steps is usually much less than that for the propagation steps. 

Figure 20-2. Dependence of the rate constant for polymerization termination by mutual deactivation of two polymer free radicals on the viscosity of the solvent for styrene (STY), methyl methacrylate (MMA), benzyl methacrylate (BMA) polymerizations at 2(fC. (After G. V. Schulz.)...

To develop their model, Wen and McCormick adopted a number of simplifying assumptions. These are (1) initiation produces two equally reactive radicals, (2) chain transfer reactions are neglected, (3) the rate constants for radicals of different sizes are assumed identical, (4) the propagation rate constant kp, termination rate constant kp and the rate constant for radical trapping kb are all simple functions of free volume as shown below, and (5) there is no excess free volume. The material balance equations for the initiator, the functional group, the active radical, and the trapped radical concentrations... 

The core of the derivation for the rate of polymerization expression is the assumption that the rate of initiation equals the rate of termination, equation 46 in its simplified form. This assumption is mandatory for the establishment of a constant free radical concentration (eq. 54). 

Although the steady state is reached within a couple of seconds after starting the initiation process, the generation of free radicals exceeds their loss by termination (ie the preeffect) in this period. Therefore, the concentration of free radicals [R ] is not constant but a function of time. The rate of free radical production is the rate of initiation minus the rate of termination, as given by equation 61 ... 

Cross Termination n In free radical copolymerization, termination by reaction of two radicals terminated by monomer units of the opposite type, i.e., A -h B termination, by combination or disproportionation with rate constant /cab- Cross-termination is often favored over termination by reaction between two like radicals due to polar effects. 

Polymer propagation steps do not change the total radical concentration, so we recognize that the two opposing processes, initiation and termination, will eventually reach a point of balance. This condition is called the stationary state and is characterized by a constant concentration of free radicals. Under stationary-state conditions (subscript s) the rate of initiation equals the rate of termination. Using Eq. (6.2) for the rate of initiation (that is, two radicals produced per initiator molecule) and Eq. (6.14) for termination, we write... 

We saw in the last chapter that the stationary-state approximation is apphc-able to free-radical homopolymerizations, and the same is true of copolymerizations. Of course, it takes a brief time for the stationary-state radical concentration to be reached, but this period is insignificant compared to the total duration of a polymerization reaction. If the total concentration of radicals is constant, this means that the rate of crossover between the different types of terminal units is also equal, or that R... 

It can be seen from equation (2) that when y 0 the model falls into the classical expression for the rate of conversion of free radical polymerization. Equation (la) shows that this will be the case whenever all macroradicals have the same high mobility (i.e., as n tends to infinity) or when both entangled and non-entangled radicals have the same termination rate constant (i.e. a is equal to unity). 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

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