Radical entry

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

However, some of these models have been refuted, and two major entry models are currently widely accepted. One is the diffusion-controlled model, which assumes that the diffusion of radicals from the bulk phase to the surface 

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Radicals generated from water-soluble initiator might not enter a micelle (14) because of differences in surface-charge density. It is postulated that radical entry is preceded by some polymerization of the monomer in the aqueous phase. The very short oligomer chains are less soluble in the aqueous phase and readily enter the micelles. Other theories exist to explain how water-soluble radicals enter micelles (15). The micelles are presumed to be the principal locus of particle nucleation (16) because of the large surface area of micelles relative to the monomer droplets. 

Radical Concentration in Particles. The radical concentration in the particles is also needed to calculate the reaction rates. The average number of radicals per particle was calculated by the O Toole (16) equation which accounts for radical entry, desorption, and termination. 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

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... 

Examples of radical-mediated C-alkylations are listed in Table 5.4. In these examples, radicals are formed by halogen abstraction with tin radicals (Entries 1 and 2), by photolysis of Barton esters (Entry 3), and by the reduction of organomercury compounds (Entry 4). Carbohydrate-derived, polystyrene-bound a-haloesters undergo radical allylation with allyltributyltin with high diastereoselectivity (97% de [41]). Cleavage from supports by homolytic bond fission with simultaneous formation of C-H or C-C bonds is considered in Section 3.16. 

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. 

Particles that contain one distinguished and one nondistin-guished growing chain are produced at t,=0 by radical entry into particles containing one free radical or by chain transfer from either of the free radicals in particles containing two free radicals ... 

Note that if it is possible to cause free radical entry events to occur much more frequently than chain transfer to monomer events (e.g., for styrene, at a rate greater than 1 per second), then the polymer will be controlled primarily by bimolecular termination. Note, too, that if chain stoppage is dominated by chain transfer, the molecular weight of the polymer produced would be independent of particle volume. Morton et al. (16) have obtained data for styrene that support this conclusion. 

Equation(2) can include this expression by supposing that k = TTd and k = TTd2. We have, therefore, the following expressions for e according Fo the mechanism of radical entry into micelles and particles. 

Case D Ugelstad states that radical entry into micelles and particles is, under some conditions, proportional to their volumes. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

Smith and Ewart [4] first proposed that the transfer of free radical activity into the interior of a polymer particle takes place by the direct entry of a free radical into a polymer particle. They pointed out that the rate of radical entry into a polymer particle is given by the rate of diffusion of free radicals from an infinite medium of concentration into a particle of diameter dp with zero radical concentration. 

On the other hand, Nomura and Harada [14] proposed a kinetic model for the emulsion polymerization of styrene (St), where they used Eq. 7 to predict the rate of radical entry into both polymer particles and monomer-swollen micelles. In their kinetic model, the ratio of the mass-transfer coefficient for radical entry into a polymer particle kep to that into a micelle kem> K lk,... 

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... 

Two major entry models - the diffusion-controlled and propagation-controlled models - are widely used at present. However, Liotta et al. [28] claim that the collision entry is more probable. They developed a dynamic competitive growth model to understand the particle growth process and used it to simulate the growth of two monodisperse polystyrene populations (bidisperse system) at 50 °C. Validation of the model with on-line density and on-line particle diameter measurements demonstrated that radical entry into polymer particles is more likely to occur by a collision mechanism than by either a propagation or diffusion mechanism. 

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-... 

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