Free-radical distributions

Asua, J.M., Rodriguez, V.S., Sudol,E.D.,andEl-Aasser, M.S. 1989. The free radical distribution in emulsion polymerization using oil-soluble initiators. J. Polym. Sci. A 27 3569-3587. 

Data for the normal, skewed, and free radical distributions was generated with 50 linearly spaced delay times (channels), while 100 channels were used for the bimodal cases. To realistically model experimantal data approximately 1% random noise was added to the AC data. Each of the AC data sets, with 0 and 1% noise levels, were then analyzed for a MWD using constrained regularization, subdistribution, and GEX fit techniques. 

Figure 6 Results of the analyses for the classical free radical distribution with 0 and 1% noise in the AC function.

The use of gaseous tritiated radical scavengers to determine the secondary free radical distribution in y-irradiated lyo-philized macromolecules has been explored. For proteins the similarity of the tritium distributions obtained with tritiated H2S and HI as well as studies with H235S, support the assumption that these distributions are an approximate measure of the secondary radical distribution. Radical distributions of several native proteins were characteristically different, those of denatured proteins approximately the same, thus demonstrating a pronounced effect of conformation. In contrast to proteins, the reaction of irradiated dry DNA with tritiated H2S or HI gave approximately 100 times more tritium label on the DNA than expected from the initial concentration of free radicals in the DNA. 

Although the reasons underlying this spatial relationship are not known, its existence is additional evidence for conformation as a significant factor in determining the free radical distribution. 

Tkdc followed the free radical distribution in the molten phase as well as in the pre-flame and flame zones of a burning specimen of polypropylene rod by ESR spectroscopy. Using several entrapping techniques for the radicals, he detected free radicals, bi-radicals, and non-radical fragments leaving the molten phase for the gas phase where they may be combined with traces of oxygen on the surface into peroxy radicals or recombined by cyclization as well as by intermolecular reactions. 

For transfer-dominated systems the shape of the polymer distribution is the same as that of the free radical distribution, [Rj ] [Pp], keeping in mind that the chain length i equals the degree of polymerization, P. It tnms out that this situation is in fact more general Clay and Gilbert (497) have shown that for partly termination controlled distributions also, the following equation holds true, in which the slope of the logarithmic number distribution (Xp = [Pp]/Xlp =o[Rf ]) i correlated with the kinetic parameters ... 

When an oil-soluble initiator is used, free radicals distribute themselves, in a stochastic sense, more uniformly in the latex particles. The subsequent emulsion polymerization then yields a morphological structure in which the post-formed polymer appears not only near the latex particle surface layer but also inside the composite particle, as observed by Merkel et al. [14]. 

This free radical distribution function, determined via a Monte Carlo technique, was then incorporated into the two-phase emulsion polymerization kinetics model developed by Nelson and Sundberg [44, 45] to predict the monomer conversion versus time data available in the literature. Thus, the only difference between the kinetic model characterized by the following major governing equations [47] and that of Nelson and Sundberg is the method used for calculation of the average free radical population in each polymer phase. 

The Smith and Ewart-Stockmayer-O Toole treatments [48-50] (see Chapter 4) that are widely used to calculate the average number of free radicals per particle (n) are based on the assumption that the various components of the monomer-swollen latex particles (e.g., monomer, polymer, free radicals, chain transfer agent, etc.) are uniformly distributed within the particle volume. A latex particle in emulsion homopolymerization of styrene involves uniform distribution of monomer and polymer within the particle volume except perhaps for a very thin layer near the particle surface. In the case of free radicals, this uniform distribution would only hold in a stochastic sense. However, as illustrated in Eq. (8.1), free radicals are not distributed uniformly in the latex particles when water-soluble initiators are used to initiate the free radical polymerization. The assumption of uniform distribution of free radicals in the latex particles would be valid only if the particles are very small or chain transfer reactions are the dominate mechanism for producing free radicals. If such a nonuniform free radical distribution hypothesis is accepted, the very basis of the Smith and Ewart-Stockmayer-O Toole methods might be questioned. Despite this potential problem, the Stockmayer-O Toole solutions for the average number of free radicals per particle have been used for kinetic studies of many emulsion polymerization systems. The theories seem to work reasonably well and have been tested extensively with monomers such as styrene. 

Chem and Poehlein [52] developed a kinetic model based on the nonuniform free radical distribution function to predict the grafting efficiency of the emulsion emulsion polymerization of styrene in the presence of polybutadiene seed latex particles. The predominant grafting reaction appears to be the attack of growing polystyrene chains on the allyl hydrogen atoms of... 

The association of the observed free radical distributions with apparent chain length distributions requires the smallest number of additional assumptions. If it were to be assumed that the microfibrils contained a monodisperse distribution of... 

At elevated temperatures (250-400°C) bromine reacts with thiazole in the vapor phase on pumice to afford 2-bromothiazole when equimolecu-lar quantities of reactants are mixed, and a low yield of a dibromothiazole (the 2,5-isomer) when 2 moles of bromine are used (388-390). This preferential orientation to the 2-position has been interpreted as an indication of the free-radical nature of the reaction (343), a conclusion that is in agreement with the free-valence distribution calculated in the early application of the HMO method to thiazole (Scheme 67) (6,117). 

The molecular weight distribution for a polymer like that described above is remarkably narrow compared to free-radical polymerization or even to ionic polymerization in which transfer or termination occurs. The sharpness arises from the nearly simultaneous initiation of all chains and the fact that all active centers grow as long as monomer is present. The following steps outline a quantitative treatment of this effect ... 

Figure 6.11 Comparison of the number distribution of n-mers for polymers prepared from anionic and free-radical active centers, both with f = 50.

That the Poisson distribution results in a narrower distribution of molecular weights than is obtained with termination is shown by Fig. 6.11. Here N /N is plotted as a function of n for F= 50, for living polymers as given by Eq. (6.109). and for conventional free-radical polymerization as given by Eq. (6.77). This same point is made by considering the ratio M /M for the case of living polymers. This ratio may be shown to equal... 

Polyamides, like other macromolecules, degrade as a result of mechanical stress either in the melt phase, in solution, or in the soHd state (124). Degradation in the fluid state is usually detected via a change in viscosity or molecular weight distribution (125). However, in the soHd state it is possible to observe the free radicals formed as a result of polymer chains breaking under the appHed stress. If the polymer is protected from oxygen, then alkyl radicals can be observed (126). However, if the sample is exposed to air then the radicals react with oxygen in a manner similar to thermo- and photooxidation. These reactions lead to the formation of microcracks, embrittlement, and fracture, which can eventually result in failure of the fiber, film, or plastic article. 

Eree-radical initiation of emulsion copolymers produces a random polymerisation in which the trans/cis ratio caimot be controlled. The nature of ESBR free-radical polymerisation results in the polymer being heterogeneous, with a broad molecular weight distribution and random copolymer composition. The microstmcture is not amenable to manipulation, although the temperature of the polymerisation affects the ratio of trans to cis somewhat. 

Various techniques have been studied to increase sohds content. Hydroxy-functional chain-transfer agents, such as 2-mercaptoethanol [60-24-2], C2HgOS, reduce the probabihty of nonfunctional or monofunctional molecules, permitting lower molecular-weight and functional monomer ratios (44). Making low viscosity acryhc resins by free-radical initiated polymerization requires the narrowest possible molecular-weight distribution. This requires carehil control of temperature, initiator concentration, and monomer concentrations during polymerization. 

Mechanism. The thermal cracking of hydrocarbons proceeds via a free-radical mechanism (20). Siace that discovery, many reaction schemes have been proposed for various hydrocarbon feeds (21—24). Siace radicals are neutral species with a short life, their concentrations under reaction conditions are extremely small. Therefore, the iategration of continuity equations involving radical and molecular species requires special iategration algorithms (25). An approximate method known as pseudo steady-state approximation has been used ia chemical kinetics for many years (26,27). The errors associated with various approximations ia predicting the product distribution have been given (28). 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

A further feature of anionic polymerisation is that, under very carefully controlled eonditions, it may be possible to produee a polymer sample which is virtually monodisperse, i.e. the molecules are all of the same size. This is in contrast to free-radical polymerisations which, because of the randomness of both chain initiation and termination, yield polymers with a wide molecular size distribution, i.e. they are said to be polydisperse. In order to produce monodisperse polymers it is necessary that the following requirements be met ... 

A mass of polymer will contain a large number of individual molecules which will vary in their molecular size. This will occur in the case, for example, of free-radically polymerised polymers because of the somewhat random occurrence of ehain termination reactions and in the case of condensation polymers because of the random nature of the chain growth. There will thus be a distribution of molecular weights the system is said to be poly disperse. 

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