Stockmayer molecular weight distribution

It is observed that Bueche s equation in combination with the g1/2 rule explains the results of this work whereas in combination with g3/2 it does not. The correction to g for polydispersity brings closer the agreement between the data and the seventh power relation. The difference of a few percent between the expected and observed slopes of 7 and 6.4 may be attributed to an undercorrection for polydispersity in this regard according to Graessley s findings current theories do not sufficiently account for the reduction in viscosity with polydispersity, whether the Beasley or the Stockmayer molecular weight distribution is employed (29). 

A large number of papers has dealt with the question of molecular weight and molecular weight distribution in polyacrylonitrile. Recent discussions are those of Onyon 108), Krigbaum and Kotliar 90), Booth and Beason 33), Bamford, Jenkins, Johnston and White 19) and Kobayashi 87). The intrinsic viscosity vs. molecular weight relationship of Cleland and Stockmayer 41) is probably as well supported as any. Fortunately, much of the material in this review does not depend heavily on detailed knowledge of molecular weights or of their distributions. 

Molecular weight distributions in step-growth polymerization described so far in this chapter are all based on the probability approach of Flory [1,15] and Stockmayer [19]. Starting with the assumptions of equal reactivity of functional groups and no intramolecular reactions, they used combinatorial arguments to derive expressions for the distribution of all species as a function of the reaction extent and then used these distributions to calculate the average properties (Mn, Mw, and PDI). For cases of practical importance these distribution functions become quite complex [19]. 

The results above are only valid for tetrafunctional crosslinking of monodisperse polymer. However, in many thermoreversible systems the crosslinks have functionalities that are much larger than four. Moreover, the polymers used are not monodisperse in general. In order to be able to calculate network parameters the present author [39—44] extended the Flory-Stockmayer model for polydisperse polymer which is crosslinked with f-functional crosslinks. It was possible to calculate network parameters for polymers of various molecular weight distributions (monodisperse polymer with D s M, /r3 = 1, a Schulz-Flory distribution with D = 1.5, a Flory distribution with D = 2, a cumulative... 

Stockmayer, W.H.J., 1945. Distribution of chain lengths and compositions in copolymers. Chem. Phys. 13,199-207. Tobita, H., 1993. Molecular weight distribution in free radical polymerization with long-chain branching. J. Polym. Sci. B Polym. Phys. 31, 1363-1371. 

We next consider the condensation reaction of polyfunctional molecules of the type R A/. The molecular weight distribution for the special case / = 3 was first studied by Flory [10], The result was later extended to the general case of / by Stockmayer [11] under the assumption of no intramolecular cycle formation. Their theories are called the classical theory of gelation reaction. 

Classical Theory explains the theory developed by Flory and Stockmayer to account for the gel point and the molecular-weight distribution in the sol. The most important deficiency of this model is that it neglects the formation of closed loops within the growing clusters, and this leads to unrealistic predictions about the geometry of the polymers. 

D. Molecular Weight Distribution in Condensation Polymers The Stockmayer Distribution... 

D. MOLECULAR WEIGHT DISTRIBUTION IN CONDENSATION POLYMERS THE STOCKMAYER DISTRIBUTION FUNCTION... 

Presently available information is insufficient to permit deciding whether the high molecular weight polymers obtained in ordinary polymerizations of cycloolefins consist of macrocyclics alone or mixtures of rings and chains. Nevertheless, the intentional introduction of known amounts of chain ends via addition of vinylenic olefins should result in ring-chain equilibrium of the type presented in Reaction 11. For this type of equilibrium, the weight fractions and size distributions of rings and chains present in the system may be compared with the Jacobson and Stockmayer theory (8). Experiments to test theory in this area are currently underway. 

This result is the same as that which Stockmayer [19] obtained by tortuous combinatorial arguments and manipulation of distribution functions. If some of the starting species are oligomers, with a distribution of molecular weight, average molecular weights must be used in Eq. (5.200) [33]. 

Kurata, Stockmayer, and Roig have employed an equivalent ellipsoid model, in which the polymer chain is replaced by a uniform distribution of unconnected segments within an ellipsoid of revolution whose dimensions are chosen to give the correct principal radii of gyration of the chain. They then use equation (38) to obtain the molecular-weight dependence over the entire solvent range. 

Fig. 26. Top bivariate distribution of chain sizes and compositions for poly(MMA-co-BA) obtained at high conversions. Bottom corresponding contour map. The random copolymer was fractionated by SEC and the average molecular weight and average composition of each fractions were determined by MALDI-TOF MS and NMR, respectively. The mol fraction of MMA was calculated according to the Stockmayer s theoretical prediction. Reproduced from [142] with permission...

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