Rate coefficient for desorption

The rate coefficient for desorption of monomeric radicals may be written as a function of the diffusivity of monomer both in the water phase and inside the particle, the aqueous monomer concentration, the monomer concentration in the particle, and the swollen radius ... 

Rate coefficient for desorption of monomeric radicals from particles (s )... 

The rate coefficient for desorption of a monomeric radical from a particle, can be simply derived [27] by considering the equilibrium between capture of an aqueous phase radical at the diffusion-controlled rate, and desorption of that radical by diffusion away from the particle. One then obtains, from microscopic reversibility,... 

Now one can write the rate of adsorption rp, to be proportional to the pressure of A and the number of vacant sites on the surface N — 0), where N is the total number of sites, ka is the adsorption rate coefficient and is the rate coefficient for desorption. Thus ... 

First-order rate coefficient for the desorption of adatoms [see eqn. (1)]. 

Second-order rate coefficient for the desorption of molecules by recombination of adatoms [see eqn. (14)]. constant of proportionality defined by eqn. (89) to give the rate of change of pressure in an atomisation system, rate coefficient for the production of atoms per unit are of surface at temperature T and gas pressure P2. rate coefficient for wall trapping of thermally excited molecules per unit area of filament, masses of atom (X) and molecule (X2), respectively, rate coefficient for the Rideal recombination mechanism [see equation (60)]. 

On the other hand, Casey and Morrison et al. [52,96] derived the desorption rate coefficient for several limiting cases in combination with their radical entry model, which assumes that the aqueous phase propagation is the ratecontrolling step for entry of initiator-derived free radicals. Kim et al. [53] also discussed the desorption and re-entry processes after Asua et al. [49] and Maxwell et al. [ 11 ] and proposed some modifications. Fang et al. [54] discussed the behavior of free-radical transfer between the aqueous and particle phases (entry and desorption) in the seeded emulsion polymerization of St using KPS as initiator. 

As we discuss later in Section 3.3.3, Nomura et al. [45,47] first derived the rate coefficient for radical desorption in an emulsion copolymerization system by... 

In the case where all the desorbed A-monomeric radicals reenter the polymer particles, the desorption rate coefficient for A-monomeric radicals kf is given by... 

Ldpez et al. [55] investigated the kinetics of the seeded emulsion copolymerization of St and BA in experiments where the diameter and number of seed particles, and the concentration of initiator were widely varied. The experimental data were fitted with a mathematical model in which they used the desorption rate coefficient developed by Forcada et al. [56] for a copolymerization system. The desorption rate coefficient for the A-monomeric radical that they used was a modification of Eq. 22 and Eq. 23, and is given by... 

The average rate coefficient for radical desorption, k, is defined using the equations... 

Recently, Ugelstad et al. l969i proposed a semiempirtcal rate coefficient for radical desorption in vinyl chloride emulsion polymerization. On the other hand, Nomura et al. (1971, 1976) have derived a rate coefficient for radical desorption theoretically with both stochastic and deterministic approaches and have successfully applied it to vinyl acetate emulsion polymerization. They also pointed out that radical desorption from the particles and micelles played an important role in micellar particle formation, Fiiis et al. 1973 also derived the rate coefficient for radical desorption in a different way. Lift et al. (1981) discussed in more detail the chemical reactions incorporated in the physical process of radical desorption in the emulsion polymerization of vinyl acetate. 

In this chapter, the polymerization rate equations for emulsion polymerization will be reviewed briefly. Then, the rate coefficient for radical desorption from tbe panicles will be derived theoretically, and the effect of rathcal desorption on the rate of emulsirai polymerization and the micellar particle formation will he discussed. 

The rate coefficient for radical desorption from the particles kf is defined as... 

It is clear from the discussion so far that as long as the value of the rate coefficient for radical desorption from the particles kf cannot be estimated quantitatively, the rate of emulsion polymerization is impossible to predict. In the next section, therefore, the quantitative expression for kf will be derived. 

Derivation of Rate Coefficient for Radical Desorption from Particles... 

As shown in Fig. 1, the value of n becomes independent of the value of kf in the range of n 0.5. This means that tbe rate coefficient for radical desorption from the particles is important in Ibe range (n < 0.5) where the polymer particle contains at most one radical. For this reason, we consider an emulsion polymerization system where (i) the particles contain at most one radical and (ii) instantaneous termination takes place when another radical enters the particle that already contains a radical. 

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