Radical entry rate

The rates of propagation and termination in the aqueous phase were also calculated. The radical entry rate, radical generation rate, and aqueous propagation rate were then used to develop an algebraic equation for the rate of formation of primary precursors. This equation is an extension to copolymers of the homogeneous nucleation equation derived by Hansen and Ugelstad (7.) for a homopolymer. 

Radical Entry Rate. The rate of transport of the active oligomers from the aqueous phase to the particles have been... 

It is accepted that the radical entry rate coefficient for miniemulsion droplets is substantially lower than for the monomer-swollen particles. This is attributed to a barrier to radical entry into monomer droplets which exists because of the formation of an interface complex of the emulsifier/coemulsifier at the surface of the monomer droplets [24]. The increased radical capture efficiency of particles over monomer droplets is attributed to weakening or elimination of the barrier to radical entry or to monomer diffusion by the presence of polymer. The polymer modifies the particle interface and influences the solubility of emulsifier and coemulsifier in the monomer/polymer phase and the close packing of emulsifier and co emulsifier at the particle surface. Under such conditions the residence time of entered radical increases as well as its propagation efficiency with monomer prior to exit. This increases the rate entry of radicals into particles. 

The higher the hydrophilicity of macromonomer, the lower the final conversion. This may be attributed to the formation of hydrophilic or surface active oligomer radicals and the low or high radical entry rate. In the system with hydrophilic C1-(EO)17-MA, the limiting conversion was ca. 60%. Thus the low rate of polymerization at ca. 50 or 60% conversion may be discussed in terms of the solution polymerization, a strong bimolecular termination and the low radical entry rate. 

Maxwell et al. [ 11 ] proposed a radical entry model for the initiator-derived radicals on the basis of the following scheme and assumptions. The major assumptions made in this model are as follows An aqueous-phase free radical will irreversibly enter a polymer particle only when it adds a critical number z of monomer units. The entrance rate is so rapid that the z-mer radicals can survive the termination reaction with any other free radicals in the aqueous phase, and so the generation of z-mer radicals from (z-l)-mer radicals by the propagation reaction is the rate-controlling step for radical entry. Therefore, based on the generation rate of z-mer radicals from (z-l)-mer radicals by propagation reaction in the aqueous phase, they considered that the radical entry rate per polymer particle, p p=pJNp) is given by... 

Another important problem that has been debated for a long time is whether or not the electric charges and the emulsifier layers on the surfaces of the polymer particles affect the radical entry rate of a charged radical (p). It is now con-... 

On the other hand, several reports have been published that point out that when a polymeric surfactant acting as an electrosteric stabilizer is used, the rate of radical entry into a polymer particle should decrease due to a diffusion barrier of the hairy layer built up by the polymeric surfactant adsorbed on the surface of the polymer particles [34-36]. Coen et al. [34] found that in the seeded emulsion polymerization of St using a PSt seed latex stabilized elec-trosterically by a copolymer of acrylic acid (AA) and St, the electrosteric stabilizer greatly reduced the radical entry rate p compared to the same seed latex... 

In our illustrative calculated results, chain transfer reactions are neglected in order to highlight unique characteristics of emulsion polymerization. However, the radical entry rate into a polymer particle is often much smaller than the chain transfer frequency in emulsion polymerization usually. In such cases, dead polymer chain formation is dominated by chain transfer reactions, and the instantaneous weight fraction distribution is given by the following most probable distribution ... 

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 transfer of free radicals out of the particles is assumed to be negligible. Also, the rate of mutual termination of two radicals inside a particle is taken to be very much faster than the free-radical entry rate, as is reasonable for small particles. 

Consider a monodispersed latex, where water-phase termination is negligible and termination is instantaneous when a radical enters a polymer particle containing one radical. By definition, IV2 = IV3 = — = 0 and the total radical entry rate per liter of latex equals p. Application of the stationary-state hypothesis gives... 

The question remains as to the cause of the increased radical entry rate when polymer is present in the droplets. Two possibilities have been suggested which are related to the surface and bulk properties of the droplets respectively. The former explanation contends that the polymer disrupts the packing of the SLS/CA... 

Recently, Durant et al. [55] developed a mechanistic model based on the classic Smith-Ewart theory [48] for the two-phase emulsion polymerization kinetics. This model, which takes into consideration complete kinetic events associated with free radicals, provides a delicate procedure to calculate the polymerization rate for latex particles with two distinct polymer phases. It allows the calculation of the average number of free radicals for each polymer phase and collapses to the correct solutions when applied to single-phase latex particles. Several examples were described for latex particles with core-shell, inverted core-shell, and hemispherical structures, in which the polymer glass transition temperature, monomer concentration and free radical entry rate were varied. This work illustrates the important fact that morphology development and polymerization kinetics are coupled processes and need to be treated simultaneously in order to develop a more realistic model for two-phase emulsion polymerization systems. More efforts are required to advance our knowledge in this research field. 

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