Chain polydispersity index

The minimum polydispersity index from a free-radical polymerization is 1.5 if termination is by combination, or 2.0 if chains ate terminated by disproportionation and/or transfer. Changes in concentrations and temperature during the reaction can lead to much greater polydispersities, however. These concepts of polymerization reaction engineering have been introduced in more detail elsewhere (6). 

Silane radical atom transfer (SRAA) was demonstrated as an efficient, metal-free method to generate polystyrene of controllable molecular weight and low polydispersity index values. (TMSlsSi radicals were generated in situ by reaction of (TMSlsSiH with thermally generated f-BuO radicals as depicted in Scheme 14. (TMSlsSi radicals in the presence of polystyrene bromide (PS -Br), effectively abstract the bromine from the chain terminus and generate macroradicals that undergo coupling reactions (Reaction 70). 

In industrial reactors, the full equilibration of the chain length distribution is prevented by incomplete mixing, as well as by the residence time distribution, thus resulting in considerable deviations from the equilibrium polydispersity index. These deviations are generally higher for continuous plants than for batch plants and increase with increasing plant capacity as demonstrated in Figure 2.2. 

The degree of polymerization depends on the duration of the process. After 7 min, the molecular mass is equal to 9400 (the polydispersity index is 5.30). When the reaction is carried out for 15 min, the molecular mass of the polymer increases to 37,000 and the polydispersity index reaches 7.31 (Bauld et al. 1996). Depending on whether cation-radical centers arise at the expense of intramolecular electron transfer or in a stepwise intermolecular lengthening, polymerization can occur, respectively, through a chain or a step-growth process (Bauld and Roh 2002). In the reaction depicted in Scheme 7.17, both chain and step-growth propagations are involved. 

Hence, cation-radical copolymerization leads to the formation of a polymer having a lower molecular weight and polydispersity index than the polymer got by cation-radical polymerization— homocyclobutanation. Nevertheless, copolymerization occnrs nnder very mild conditions and is regio-and stereospecihc (Bauld et al. 1998a). This reaction appears to occnr by a step-growth mechanism, rather than the more efficient cation-radical chain mechanism proposed for poly(cyclobutanation). As the authors concluded, the apparent suppression of the chain mechanism is viewed as an inherent problem with the copolymerization format of cation-radical Diels-Alder polymerization. ... 

The simplest measure of the breadth of a distribution is the ratio of two different types of average molecular weight. Specifically the ratio of Mw to Mn is by far the most widely used for this purpose, and is called the polydispersity index. It has a minimum value of unity (for a monodisperse material in which all the chains have exactly the same length). The extent to which it exceeds unity is a measure of the breadth of the distribution. Typical values are in the range 1.5-2.0, but many polymerizations yield considerably larger values. 

First Order Stoppage Alone. If stoppage is determined solely by a first order process, such as transfer, the foregoing analysis predicts a nearly exponential distribution function. The polydispersity index must then be very close to 2.00. The same result is obtained for bulk and solution polymerizations dominated by chain transfer. Compartmentalization thus has no major effect on the polydispersity of the polymer produced, as was recognized by Gerrens (11), if the stoppage process is dominated by chain transfer. This contrasts with the significant effects of compartmentalization if bimolecular events dominate termination. 

It can be established by the following reasoning. If n = %, each particle contains at most one free radical. Growing chains in the latex particles can thus either grow or be terminated instantaneously by entrant free radicals. These mutually exclusive kinetic events immediately prescribe the Flory most probable distribution function for the growing chains (12) this is an exponential distribution function with a polydispersity index of 2.00 (13). 

The termination process occurs instantaneously via entrant free radicals of (near) zero molecular weight. These radicals do not perturb significantly the distribution of chain lengths in converting growing chains to dead polymer. Indeed, termination in this instance is equivalent to chain transfer, which gives an identical value for the polydispersity index. 

Displayed in Figure 3 are the results for the polydispersity index for an emulsion polymerization system in which chain stoppage occurs by a combination of chain transfer ( tr= 1 reciprocal time unit) and disproportionation (c = 100 reciprocal time units). These results were obtained by varying p and thus n. The results suggest how it might be possible to tailor a distribution to some desired polydispersity index. 

The experimental results on the polymer produced in emulsion polymerizations published thus far are both confusing and contradictory. Several factors may be responsible for this first, many surfactants behave as chain transfer agents, which has often not been recognized second, measurements have often been made on samples that contain polymer from Intervals I, II and III, which leads to a significant increase in the polydispersity index becauseis sensitive to the presence of lower molecular weight species tRird, direct measurements of the MWD have only recently become possible with the advent of gel permeation chromatography. 

Figure 3. Polydispersity index of the polymer produced in Interval II of an emulsion polymerization as a function of the average number of free radicals per particle. Chain stoppage occurs by chain transfer (k,r = 1 reciprocal time unit) and disproportionation (cd/k = 100).

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

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