Radicals desorption

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 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. 

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. 

As long as the distribution of radicals among the particles approximates a steady state situation (a condition that may be violated during periods of rapid acceleration in latices), one may use Stockmayer s result (7) to compute n. When radical desorption is insignificant and water phase termination of radicals is neglected,... 

We now report on some experiments using seeded emulsion polymerization of styrene in which conditions were carefully chosen to ensure that Smith-Ewart Case 2 kinetics (6) would obtain throughout, in the absence of chain transfer/radical desorption effects. Various hydrocarbons were investigated for their effects on kinetics of polymerization and equilibrium swelling of the latex particles. 

A much simpler model for the radical capture (absorption) efficiency F can be derived by introducing the concept of radical desorption from a polymer particle, developed in Section 3.2.1. The probability F for a radical to be captured inside a particle containing n radicals by any chemical reaction (propagation or termination) is given by... 

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... 

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... 

As we discussed in Sect. 3.1.1, Hansen et al. [15] made significant improvements to the concept of the radical capture efficiency proposed by Nomura et al. [ 14]. Taking this concept into consideration, they examined the effect of radical desorption on micellar particle formation in emulsion polymerization [ 65 ]. Assuming that radical entry is proportional to the x power of the micelle radius and the polymer particle radius, they proposed the following general expression for the rate of particle formation ... 

Moreover, when both radical termination in the water phase and radical desorption from the particles are neghgible, Eq. 47 is reduced to... 

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

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