Phase termination

Emulsion Polymerization. Emulsion polymerization takes place in a soap micelle where a small amount of monomer dissolves in the micelle. The initiator is water-soluble. Polymerization takes place when the radical enters the monomer-swollen micelle (91,92). Additional monomer is supphed by diffusion through the water phase. Termination takes place in the growing micelle by the usual radical-radical interactions. A theory for tme emulsion polymerization postulates that the rate is proportional to the number of particles [N. N depends on the 0.6 power of the soap concentration [S] and the 0.4 power of initiator concentration [i] the average number of radicals per particle is 0.5 (93). 

Z( = zero phase sequence or residual impedance. This is measured between the three-phase terminals of a star winding shorted together and the neutral (Figure 20.9(b)) and is calculated by... 

The steps involved in entry of a radical into the particle phase from an aqueous phase initiator have been summarized in Section 3.1.11. Aqueous phase termination prior to particle entry should be described by conventional dilute solution kinetics (Section 5.2,1.4.1). Note that chain lengths of the aqueous soluble species are short (typically <10 units). 

Even though the chemical reactions are the same (i.e. combination, disproportionation), the effects of compartmentalization are such that, in emulsion polymerization, particle phase termination rates can be substantially different to those observed in corresponding solution or bulk polymerizations. A critical parameter is n, the average number of propagating species per particle. The value of h depends on the particle size and the rates of entry and exit. 

Entry = Desorption + Initiation—Water Phase Termination... 

If one neglects water phase termination, the first of (III-4) becomes ... 

In the field of solid-state chemistry an important group of substances is represented by the intermetallic compounds and phases. In binary and multi-component metal systems, in fact, several crystalline phases (terminal and intermediate, stable and metastable) may occur. A few introductory remarks about these substances will be presented in relation to the mentioned figures. 

In the previous chapter we looked at some questions concerning solid intermetallic phases both terminal (that is solubility fields which include one of the components) and intermediate. Particularly we have seen, in several alloy systems, the formation in the solid state of intermetallic compounds or, more generally, intermetallic phases. A few general and introductory remarks about these phases have been presented by means of Figs. 2.2-2.4, in which structural schemes of ordered and disordered phases have been suggested. On the other hand we have seen that in binary (and multi-component) metal systems, several crystalline phases (terminal and intermediate, stable and also metastable) may occur. 

Since a radical is consumed and formed in reaction (3.3) and since R represents any radical chain carrier, it is written on both sides of this reaction step. Reaction (3.4) is a gas-phase termination step forming an intermediate stable molecule I, which can react further, much as M does. Reaction (3.5), which is not considered particularly important, is essentially a chain terminating step at high pressures. In step (5), R is generally an H radical and R02 is H02, a radical much less effective in reacting with stable (reactant) molecules. Thus reaction (3.5) is considered to be a third-order chain termination step. Reaction (3.6) is a surface termination step that forms minor intermediates (T) not crucial to the system. For example, tetraethyllead forms lead oxide particles during automotive combustion if these particles act as a surface sink for radicals, reaction (3.6) would represent the effect of tetraethyllead. The automotive cylinder wall would produce an effect similar to that of tetraethyllead. 

In this higher temperature regime and in atmospheric-pressure flames, the eventual fate of the radicals formed is dictated by recombination. The principal gas-phase termination steps are... 

The rest of the mechanism proposed by Tibbitt et al. " is also shown in Table 6. Two assumptions were introduced to simplify the mechanism. The first is that the extent of gas phase termination is very small and consequently, that essentially all of the radicals formed in the gas phase are adsorbed on the polymer surface. The second assumption is that the concentrations of adsorbed monomer and free radical are proportional to the gas phase concentrations of these species. These relationships are expressed by... 

At low pressures surface termination is predominant, and altering the size, shape and nature of the surface has a major effect. Addition of inert gas cuts down diffusion to the surface, decreasing the rate of surface termination. As the pressure increases diffusion to the surface decreases, and gas phase termination becomes increasingly important until it is predominant at high pressures. 

Gas phase terminations generally have very low, zero or negative activation energies, and their rate constants are governed by their pre-exponential factors. In contrast, surface terminations have a much wider range of activation energies. 

Standard mechanisms for chain reactions generally miss out the surface termination steps, but these should be included. Such terminations are written as first order in radical since diffusion to the surface or adsorption on the surface are rate determining, rather than the second order bimolecular step of recombination of the two radicals adsorbed on the surface. A complete mechanism will also include the need for a third body in any unimolecular initiation or propagation steps, and in any gas phase termination steps. 

Steps 7 and 8 are rate determining for surface termination, being diffusion of each type of radical to the surface or adsorption of each radical on to the surface, whichever is the slower process. The recombinations of adsorbed R and R by like-like and like-unlike radical recombinations are the fast steps in the surface termination process. Consequently surface termination consists of the two steps, 7 and 8, in contrast to the gas phase termination, which consists of the three steps, 4, 5 and 6. 

Steady state procedures will be carried out under stylized schemes ignoring the need for third bodies, assuming one recombination step to be dominant, and taking gas and surface terminations separately. This simplified analysis is sufficient to demonstrate that the order can change if gas or surface phase termination is dominant, or if both are significant. In reality, actual reactions are more complex. 

The reaction is now second order in contrast to 3/2 order when gas phase termination is dominant. 

The conclusion drawn from Worked Problem 6.14 is that changing the type of termination step from gas to surface alters the kinetics. This is because the order with respect to the radical differs between the second order recombination of the gas phase termination and surface termination where diffusion to the surface or adsorption on the surface is rate determining and first order. If, however, the rate-determining step in surface termination were bimolecular recombination on the surface, the order would not change between gas and surface termination. This is because both recombinations would now have the same order, i.e. 2 4[R ]2 and 2 7[R ]2, with the total rate of termination if both contributed being 2(k + 7)[R ]2. 

The third pressure limit, when it exists, occurs at even higher pressures. At the third limit, i.e. at pressures greater than at d, the reaction moves back into an explosive region which is in part thermal, and in part the result of some dramatic change in radical concentration. This results from another set of reactions coming into play so that gas phase termination can no longer cope with this new production of radicals. 

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,... 

However, at high rates of radical desorption, the effect of water phase termination on the average number of radicals per particle is much more prominent when the radicals are produced in the water phase. 

All quantitative theories based on micellar nucleation can be developed from balances of the number concentrations of particles, and of the concentrations of aqueous radicals. Smith and Ewart solved these balances for two limiting cases (i) all free radials generated in the aqueous phase assumed to be absorbed by surfactant micelles, and (ii) micelles and existing particles competing for aqueous phase radicals. In both cases, the number of particles at the end of Interval I in a batch macroemulsion polymerization is predicted to be proportional to the aqueous phase radical flux to the power of 0.4, and to the initial surfactant concentration to the power of 0.6. The Smith Ewart model predicts particle numbers accurately for styrene and other water-insoluble monomers. Deviations from the SE theory occur when there are substantial amounts of radical desorption, aqueous phase termination, or when the calculation of absorbance efficiency is in error. 

Case 2, assumes instantaneous termination of the existing radical with an entering radical. In this case, each particle will contain either zero or one radical, and n becomes 0.5. Styrene generally follows Case 2 kinetics. Smith and Ewart Case 3 assumes that both desorption from particles and aqueous phase termination may be neglected, and so n 1.0. This occurs with large particles, and in the limit results in bulk kinetics. 

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