Absorption of free radicals

In comparison with Eq. (3.3), a smaller population of latex particles (Np,i) is obtained from Eq. (3.5) due to the competitive absorption of free radicals. 

It should be noted that the derivation of Eq. (3.5) is based on the assumption that free radicals are captured by monomer-swollen micelles or particle nuclei at a rate that is proportional to their surface area (termed the collision theory [15]). In this case, there is no free radical concentration gradient surrounding the colloidal particle. It would be more appropriate to use the diffusion theory [17,18] to calculate the rate of entry of free radicals into micelles or particle nuclei if this concentration gradient does exist. The diffusion theory proposes that the rate of entry of free radicals into a colloidal particle is equal to 2ndpDy R y, where dp is the diameter of the particle, D is the diffusion coefficient of free radicals in water, and [R ] , is the bulk concentration of free radicals in water. It is generally accepted that the diffusion theory is more realistic to describe the absorption of free radicals by micelles or particle nuclei [19]. The detailed reaction mechanisms involved in the entry of free radicals into monomer-swollen micelles or particle nuclei will be discussed in Chapter 4. 

Nomura and co-workers [20] studied the competitive absorption of free radicals by micelles and particle nuclei. In addition to the basic assumptions made in the Harkins-Smith-Ewart theory, the bimolecular termination reac-... 

Figure 3.2. A schematic model for the competitive absorption of free radicals by monomer-swollen micelles and particle nuclei. (-10° nm in diameter), O (-10 nm in diameter), and (-10 nm in diameter) represent the monomer-swollen micelles, inactive polymer particle nuclei, and active polymer particle nuclei, respectively. The symbol represents the free radicals in the continuous aqueous phase.

The ratio kepNpKJce m) signifies the competitive absorption of free radicals by micelles and particle nuclei. Only those kinetic events involving the entry of free radicals into micelles contribute to the formation of particle nuclei. Eq. (3.11) is reduced to Equation (3.3) when the ratio kepNpl(ke i) is much smaller than one. On the other hand, the rate of particle nucleation can be written as... 

At low values of a, the emulsion polymerization system is characterized by (a) the very slow overall rate of absorption of free radicals by the latex particles and/or the very large population of latex particles (i.e., pJNp ) and (b) the very large rate constant for desorption of free radicals out of the latex particles and/or the very large ratio of the surface area to volume of a single latex particle (i.e., /CdesV p ) tliis regime, desorption of free radicals out of the latex particles plays an important role in the emulsion polymerization kinetics. The value of n is smaller than 0.5 [Smith-Ewart Case 1 kinetics, Eq. (4.6)] and n increases rapidly with increasing a. At medium values of a, the emulsion polymerization system is characterized by (a) the very small rate... 

It should be noted that the rate of absorption of free radicals by the latex particles from the continuous aqueous phase (p or a ) is not equal to the rate of generation of free radicals in the continuous aqueous phase (p, or a) when desorption of free radicals out of the latex particles (m) and/or the bimolecular termination of free radicals in the continuous aqueous phase (Y) cannot be neglected in the emulsion polymerization system. In addition to the particle nucleation mechanisms discussed in Chapter 3, to gain a fundamental understanding of transport of free radicals in the heterogeneous reaction system (e.g., absorption of free radicals by the latex particles, desorption of free radicals out of the latex particles and reabsorption of the desorbed free radicals by the latex particles) is thus required to predict the emulsion polymerization... 

A number of models dealing with absorption of free radicals by the latex particles were proposed. They are (a) the collision-controlled model [1,17,18], (b) the diffusion-controlled model [19], (c) the surfactant displacement model [20], (d) the colloidal model [21], and (e) the propagation-controlled model [22, 23]. The dependence of the rate constant for absorption of free radicals by the latex particles on the particle diameter d ) predicted by these models is summarized in Table 4.1 [24]. At present, the most widely accepted models... 

Table 4.1. Dependence of the Rate Constant for Absorption of Free Radicals by the Latex Particles Predicted by the Models [24]...

Smith and Ewart [1] proposed that the rate of absorption of free radicals by a latex particle is expressed as follows ... 

The concept of free radical capture efficiency was incorporated into the work of Hansen and Ugelstad [26,27], Based on the mechanism of mass transfer with simultaneous chemical reactions, the net rate of absorption of free radicals by a single latex particle (pJNp) can be written as... 

Table 4.2. Some Representative Data Regarding the Absorption of Free Radicals by the Monomer-Swollen Micelles and Polymer Particles...

Unzueta and Forcada [31] studied the emulsion copolymerization of methyl methacrylate and n-butyl acrylate. It was assumed that both micellar nucle-ation and homogeneous nucleation are operative in this emulsion polymerization system. Based on the experimental data and computer simulation results, the values of the free radical capture efficiency factors for monomer-swollen micelles (f ) and polymer particles (Fj) that serve as adjustable parameters in the kinetic modeling work are approximately 1(T and 10, respectively. The reason for such a difference in the free radical capture efficiency factors is not available yet. Table 4.2 summarizes some representative data regarding the absorption of free radicals by the monomer-swollen micelles and polymer particles obtained from the literature. 

As mentioned above, the two most popular reaction mechanisms involved in the absorption of free radicals by the monomer-swoUen micelles and polymer particles are the diffusion- and propagation-controlled models. Nevertheless, liotta et al. [39] were inclined to support the colUsion-controlled model. A dynamic competitive particle growth model was developed to study the emulsion polymerization of styrene in the presence of two distinct populations of latex particles (i.e., bimodal particle size distribution). Comparing the on-line density and particle size data with model predictions suggests that absorption of free radicals by the latex particles follows the collision-controlled mechanism. 

Reabsorption of the desorbed free radicals by the latex particles may contribute to the emulsion polymerization kinetics, as proposed by Ugelstad and Hansen [19], According to Gilbert [55], the overall rate of absorption of free radicals by the latex particles (pa) can be written as... 

Strictly speaking, any model based on the time-independent thermodynamics cannot be used to adequately predict the concentration of monomer in latex particles during Smith-Ewart Interval II. This is because the free radical polymerization of monomer in the discrete latex particles is governed by the simultaneous kinetic events such as the generation of free radicals in the continuous aqueous phase, the absorption of free radicals by the particles, the propagation of free radicals with monomer molecules in the particles, the bimolecular termination of free radicals in the particles, and the desorption of free radicals out of the particles. The equilibrium (or saturation) concentration of monomer in the growing latex particles may not be achieved if the rate of consumption of monomer in the major reaction loci is much faster than that of diffusion of monomer molecules from the monomer droplets to the reaction loci. Therefore, the equilibrium concentration of monomer in the latex particles represents an upper limit that is ultimately attainable in the course of polymerization. Nevertheless, the general... 

The application of these comprehensive models to the prediction of the emulsion polymer molecular weight distribution requires a fundamental understanding of the very conaplex reaction mechanisms and knowledge of various kinetic parameters (e.g., the rate coefficients for the absorption of free radicals by the latex particles, the desorption of radicals out of the particles, and the bimolecular termination reaction). However, these mathematical models in combination with the polymer molecular weight distribution data may serve as a useful tool for estimating the values of the kinetic parameters involved in emulsion polymerization. 

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