Molecular weight distributions most probable distribution

This distribution is known as the Schultz-Flory or most probable distribution.2S The moments of the molecular weight distribution are ... 

The molecular weight distribution in Fig. 5.3 a) exhibits a most probable molecular weight distribution , which is characteristic of polymers produced by metallocene catalysts. This distribution contains relatively few molecules with either extremely high or low molecular weights. Products made with this type of distribution are relatively difficult to process in the molten state, exhibit modest orientation, and have good impact resistance. 

Resins with a bimodal molecular weight distribution, as illustrated in Fig. 5.3 b), are more readily processed than those with a most probable molecular weight distribution, but are more likely to be oriented in the solid state and have a somewhat reduced impact resistance. 

The equations relating Mn and Mw to radiation dose which are most frequently used apply to all initial molecular weight distributions for Mn, but only to the most probable distribution (Mw/Mn = 2) for Mw. However, equations have been derived for other initial distributions, especially for representation by the Schulz-Zimm distribution equation. 

No restriction is made to the same molecular weight distribution. Instead of this, the natural distributions for f > 2 and f = 2 are taken. For star-molecules, f = 2 corresponds to the monodisperse linear chain or to a linear chain that obeys the most probable distribution, and in the case of random polycondensates, f > 2 corresponds to the branched non-fractionated sample, and f = 2 to the linear polycondensate. The g and h-factors so defined no longer have the appearance of shrinking factors in all cases, as may be recognized from Figs. 43 and 44. For star-molecules, both factors decrease as... 

In the range of these experiments, the molecular-weight distribution narrows as oligomer degree of polymerization increases. When the reaction is allowed to proceed to high molecular weight, bisphenol-A homopolycarbonate is obtained this product has a molecular-weight distribution of 2.3, comparable with the most probable value of 2 predicted for polycondensation reactions. 

It was established, in unpublished results, that the PMMA polymerization process yielded a random, most probable distribution of molecular weights, and therefore it was assumed that the relationship... 

The most probable distribution of molecular weights is expected in condensation polymerization of bifunctional monomers when the principle of the equal reactivity of all... 

Chains with monodisperse molecular weight distribution (Mw/Mn = 1.00) can occur in idealized conditions when all polymerizing centers initiate instantaneously and chain termination is absent. In these cases the catalyst is actually an initiator. These living polymerizations are quite rare among transition metal catalysts. More often, random chain termination leads to many chains formed per metal atom. A Schulz-Flory most probable distribution of polyalkene molecular weights (Mw/Mn = 2.00) is the result. In cases when more than one type of active site is present, bimodal or multimodal distributions of molecular weights result (Mw/Mn > 2.00). 

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