Radical exit

If a chain transfer reaction is the actual event, as shown in Fig. 9, a monomeric or a CTA radical is formed. Neglecting the difference between monomeric and CTA radicals, the probability of radical exit when the chain transfer reaction occurs is given by ... 

It is evident from Eq. 85 that the condition =l/(kp[M]pFe) < Cm is needed to apply the CLD method to emulsion polymerization. Note that the radical entry rate may be increased through the radical exit. Even when these conditions are satisfied, a higher polymer concentration than for the corresponding bulk polymerization may result in more occurrences of the polymer transfer reaction. 

The parameter c is a measure of the rate of radical entry relative to the rate of bimolecular termination within loci. Similarly, the parameter m is a measure of the rate of radical exit relative to the rate of bimolecular teimiDatioD within loci. The ratio tjm = ojk is a measure of the rate of radical entry relative to radical exit. The so-called Case I, Case 2, and Case 3 of Smith and Ewart (1948) correspond to the following circumstances Case I m large relative to a ... 

The kinetics of emulsion polymerization is complex, involving a large number of species and at least two phases. The first quantitative approach to emulsion polymerization kinetics led to extensions by many others.The important events to consider are 1) the free-radical reactions of chain formation initiation, propagation, chain transfer, and termination and 2) the phase transfer events that control particle formation radical entry into particles from the aqueous phase, radical exit into the aqueous phase, radical entry into micelles, and the aqueous phase coil-globule transition. In free-radical emulsion polymerization, the fundamental steps are shown schematically in Fig. 1... 

The early kinetic model by Smith and Ewart was based on Harkin s mechanistic understanding of the batch process. The particle population balances were written for a stationary state assuming that the rate of formation of particles with n radicals equals the rate of their disappearance (see equation at the bottom of this page). Where / , is the rate of radical entry into a particle (m /sec) is the rate constant for radical exit (m/sec) S is the particle surface area (m ) ktp is the rate constant for bimolecular termination in the particles (m /sec) and o is the particle volume. According to Smith and Ewart three limiting cases can be identified ... 

Case / Where the rate of radical exit from the particle is greater than the rate of radical entry... 

The population of no-type particles is increased by the entry of radicals (oligomeric or exited) into n and nj -type particles. They are also formed when monomeric radicals exit an n -type particle (a process that occurs with a rate constant diu)- The population of notype particles is decreased when oligomeric radicals enter an existing particle (to form an nj -type particle), or when an exited radical enters to form an n -type particle. 

It must be noted tliat, even with an extremely hydrophobic catalyst, catalyst-free particles would be formed by radical exit and nucleation of new particles, and thus uncontrolled polymerization would occur. On the other hand, it is also proposed that with more hydrophilic ligands (such as Meg-TREN, or pentamethyl diethylenetriamine (PMDETA) [221]) all the catalyst is located in the aqueous phase, and uncontrolled polymerization occurs in the hydrophobic polymer particles. However, these ligands are also ineffective in controlling the aqueous polymerization of water-soluble monomers (see above), hinting that ligand dissociation might also occur in these systems [215]. 

The kinetics of onulsion polymerizations initiated by oil-soluble irutiators has received considerable attention for some time [56-61]. It seems fairly well established that the main kinetic features obtained with oil-soluble initiators closely resemble those foimd with water-soluble initiators, although some ccxiflicting views exist concerning the importance of radicals generated in the aqueous phase, radicals exited firom the particles and tomination in the water phase (see Chapter 2). 

O Toole [128] revised Stockmayer s solution and ctmcluded that the values of n calculated from Stockmayer s expressions taking radical exit into account were too large for small particles although results were idraitical for large particles. 

Desorption results in a decrease in the concentration of growing radicals inside the particles, and causes the rate of polymerization to decrease. It is strongly connected to the probability of chain transfer to monomer as smaller radicals cross the interface faster than larger radicals. For monomers with higher chain-transfer rates to monomer (such as ethylene, vinyl acetate, or vinyl chloride), radical exit represents the major process of reducing n to values much less than 0.5. However, for styrene also, the correct kinetic description requires the consideration of radical desorption. Exit is not only literally, but also mechanistically, the opposite of entry the radical must reach the particle surface and must then overcome the barrier for desorption exerted by the interface. 

Radical exit occurs by chain transfer to a small molecule followed by diffusion of the small radical to the aqueous phase. The rate of radical desorption from a particle with n radicals is... 

In the first situation (Case 1), where the particles are small or the monomer is substantially water-soluble, and desorption of radicals from the particle is likely, n is very low, and polymerisation is slow. In the second situation. Case 11, radical exit is negligible. When a radical enters a particle, polymerisation occurs until a second radical enters, and both are instantaneously terminated (zero-one kinetics). Under these conditions, n is equal to V2. In the third situation. Case III, the particles are large enough that two or more radicals may coexist within the same particle without... 

The photoreduction of henzophenone triplets in micellar solution leads to the generation of isolated radical pairs, the behaviour of which resembles that of biradicals (Scaiano et al. 1982). Radical pair decay is controlled by intersystem crossing and by radical exit from the micelle. 2-Hydroxy-4-metho-xybenzophenone, a commonly used sunscreen, was neither genotoxic in the Drosophila somatic mutation and recombination test nor clastogenic in the cytogenetic assay in rat bone marrow cells (Robison et al. 1994). 

Fig. 9.10. Observed and simulated TOF profiles of a molecular beam of OH radicals exiting the Stark decelerator when the deceierator is operated at a phase angie of 70° for a synchronous molecule with an initial velocity of 470m/s (o), 450m/s (6), 430 m/s (c) and 417 m/s (d). The molecules that are accepted by the decelerator are split off from the molecular beam and arrive at later times, and with the final velocities as indicated, in the detection region. (Reproduced from S.Y.T. van de Meerakker et with permission. 2006 by Annual Reviews www.annuaireviews.org.)...

Chain-transfer reactions to monomers and chain-transfer agents lead to the formation of small and mobile radicals that can exit the polymer particle. Radical desorption leads to a decrease in the average number of radicals per particle. Equation (10), where is the rate coefficient for radical exit [Eq. (11)] [25], gives the rate of radical exit from a population of particles with an average number of radicals per particle n. In Eq. (11), X is an overall mass-transfer rate coefficient, y/rj the ratio between the rate of generation of small radicals by chain transfer and the rate of consumption of these radicals (mostly by propagation), m the partition coefficient of the small radicals between the polymer particles and the aqueous phase, [M] the concentration of monomer in the aqueous phase, km, the termination rate constant in the aqueous phase, and [R] the concentration of radicals in the aqueous phase. 

The presence of radical byproducts such as Cl radicals and the formation of unsaturated and defect structures in PVC point to a complex polymerization mechanism. The partitioning of the volatible radicals (monomeric. Cl,..) between vapor, water and polymer particles may vary the radical concentration in particles and the aqueous phase. Exit of radicals from the particles and the aqueous phase to the vapor phase probably negatively influences the growth events in the system. The low concentration of monomer in the vapor phase favors more termination. The decrease of the chain transfer to monomer with decreasing reactor pressure (at subsaturation pressures) favors the hypothesis that the volatile radicals exit to the vapor phase. The chain transfer is constant at saturation pressure and decreases with increasing pressure at subsaturation conditions. 

Write the contribution to W, Xj, iV, and Y, from polymerization, radical entry, radical exit, chain transfer, and bimolecular termination. 

---