Radical desorption rate

The newly formed short-chain radical A then quickly reacts with a monomer molecule to create a primary radical. If subsequent initiation is not fast, AX is considered an inhibitor. Many have studied the influence of chain-transfer reactions on emulsion polymerisation because of the interesting complexities arising from enhanced radical desorption rates from the growing polymer particles (64,65). Chain-transfer reactions are not limited to chain-transfer agents. Chain-transfer to monomer is ia many cases the main chain termination event ia emulsion polymerisation. Chain transfer to polymer leads to branching which can greatiy impact final product properties (66). 

Radical Desorption Rate. It is evaluated, according to the law proposed by Nonura (36), as the result of three stages in series Chain transfer of a growing chain to monomer, diffusion of the active, low molecular weight product to the particle surface and diffusion in the aqueous phase. The resulting expression has been extended to the multlconponent case as follows ... 

General. In this section, a mathematical dynamic model will be developed for emulsion homopolymerization processes. The model derivation will be general enough to easily apply to several Case I monomer systems (e.g. vinyl acetate, vinyl chloride), i.e. to emulsion systems characterized by significant radical desorption rates, and therefore an average number of radicals per particle much less than 1/2, and to a variety of different modes of reactor operation. 

Figure 4 shows the influence of radical desorption from particles (the parameter y) on . The shape of the curves are, as expected, quite similar to those reported by Ugelstad et al. In this case two parameters, 3 and Y, are fixed. Dubner et al. also report that the radical desorption rate (as accounted for by y) could have a very substantial influence on the PSD of the CSTR effluent latex. Figure 5 illustrates this effect. The distributions are plotted in terras of a dimensionless diameter, that is, particle diameter divided by seed-particle diameter. 

Equilibrium radical desorption The equilibrium desorption of a radical takes into account the different solubility of the radicals between the polymer particles and the aqueous phase. The rate coefficient of equilibrium radical desorption (ko ) can be related to the simple radical desorption rate coefficient by ... 

For Case 1, n 0.5, and it corresponds to a system in which the radical desorption rate is much faster than the rate of radical entry. In Case 2, n = 0.5 corresponding to a system in which the radical desorption rate is zero, and instantaneous termination occurs when a radical enters a polymer particle already containing one radical. In Case 3, the concentration of radicals in the polymer particle approaches that of bulk polymerization (n 0.5). For Case 2, the polymerization rate is proportional to the number of particles and the molecular weight also increases with Np. For Cases 1 and 3 the polymerization rate is independent of the number of polymer particles if radical termination in the aqueous phase is negligible, and increases with Np when it is significant. In Case 1, the molecular weights are determined by chain transfer, and in Case 3, the molecular weights are similar to those in bulk. 

It is noteworthy that a basic assumption made in the derivation of the free radical desorption rate constant is that the adsorbed layer of surfactant or stabilizer surrounding the particle does not act as a barrier against the molecular diffusion of free radicals out of the particle. Nevertheless, a significant reduction (one order of magnitude) in the free radical desorption rate constant can happen in the emulsion polymerization of styrene stabilized by a polymeric surfactant [42]. This can be attributed to the steric barrier established by the adsorbed polymeric surfactant molecules on the particle surface, which retards the desorption of free radicals out of the particle. Coen et al. [70] studied the reaction kinetics of the seeded emulsion polymerization of styrene. The polystyrene seed latex particles were stabilized by the anionic random copolymer of styrene and acrylic acid. For reference, the polystyrene seed latex particles stabilized by a conventional anionic surfactant were also included in this study. The electrosteric effect of the latex particle surface layer containing the polyelectrolyte is the greatly reduced rate of desorption of free radicals out of the particle as compared to the counterpart associated with a simple... 

During Stages II and III the average concentration of radicals within the particle determines the rate of polymerization. To solve for n, the fate of a given radical was balanced across the possible adsorption, desorption, and termination events. Initially a solution was provided for three physically limiting cases. Subsequentiy, n was solved for expHcitiy without limitation using a generating function to solve the Smith-Ewart recursion formula (29). This analysis for the case of very slow rates of radical desorption was improved on (30), and later radical readsorption was accounted for and the Smith-Ewart recursion formula solved via the method of continuous fractions (31). 

The photoreactivity of the involved catalyst depends on many experimental factors such as the intensity of the absorbed light, electron-hole pair formation and recombination rates, charge transfer rate to chemical species, diffusion rate, adsorption and desorption rates of reagents and products, pH of the solution, photocatalyst and reactant concentrations, and partial pressure of oxygen [19,302,307], Most of these factors are strongly affected by the nature and structure of the catalyst, which is dependent on the preparation method. The presence of the impurities may also affect the photoreactivity. The presence of chloride was found to reduce the rate of oxidation by scavenging of oxidizing radicals [151,308] ... 

Case 1 h < 0.5. The average number of radicals per particle can drop below 0.5 if radical desorption from particles and termination in the aqueous phase are not negligible. The decrease in n is larger for small particle sizes and low initiation rates. 

Hayashi et al., 1989], involving the addition of monomer and initiator to a previously prepared emulsion of polymer particles, is especially useful for this purpose since it allows the variation of certain reaction parameters while holding N constant. Thus, h in seeded styrene polymerization drops from 0.5 to 0.2 when the initiator concentration decreases from 10-2 to 1CT5 M. At sufficiently low Ru the rate of radical absorption is not sufficiently high to counterbalance the rate of desorption. One also observes that above a particular initiation rate ([I] = lO-2 M in this case), the system maintains case 2 behavior with h constant at 0.5 and Rp independent of Ri. A change in Ri simply results in an increased rate of alternation of activity and inactivity in each polymer particle. Similar experiments show that h drops below 0.5 for styrene when the particle size becomes sufficiently small. The extent of radical desorption increases with decreasing particle size since the travel distance for radical diffusion from a particle decreases. 

In the catalytic mechanism, the two consecutive reactions are likely to have radically different rate constants. If the reaction for the proton discharge is relatively small compared with that for the catalytic desorption, the former reaction will determine the rate of the overall reaction in steady state. The catalytic reaction will react quickly when there are adsorbed H atoms to deal with. Since the recombination reaction is assumed here to have a relatively high rate constant (k2), then as soon as some H atoms arrive on the surface, they will form adsorbed H, which will recombine to H2. After gathering a few H2 s together, these will nucleate to form a tiny bubble, which will grow and detach itself from the electrode surface. Because the recombination rate constant is large, the adsorbed H is quickly removed, and 0H remains small. 

Copolymerization of styrene and butyl acrylate was successfully carried out by Huang et al. using the redox initiator system (NH SjOg/NaHSC at lower temperature [68]. The rate of the miniemulsion polymerization increases with increasing butyl acrylate concentration and decreases with increasing styrene concentration. This was attributed to differences in the water solubility. The lower water solubility of styrene either increases the desorption rate of the radicals or reduces the radical absorption of the monomer droplet [81]. 

The desorption (exit) of free radicals from polymer particles into the aqueous phase is an important kinetic process in emulsion polymerization. Smith and Ewart [4] included the desorption rate terms into the balance equation for N particles, defining the rate of radical desorption from the polymer particles containing n free radicals in Eq. 3 as kftiN . However, they did not give any... 

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... 

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