Molecular weight distribution most probable

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

Because of the absence of chain limiter, the catalyst itself may initially act as the chain limiter (Fig. 8.22). The catalyst reacts with the olefinic regions of the polymer backbone and causes chain scission to occur, forming two new chains. The reactive carbene which is produced then moves from chain to chain, forming two new chains with each scission until the most probable molecular weight distribution is reached (Mw/Mn = 2), producing linear chains end capped with [Ru] catalyst residues. 

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. 

Resins with a significant low molecular weight tail, as shown in Fig. 5.3 c), exhibit similar melt flow characteristics to the most probable molecular weight distribution, but may be more flexible in the solid state due to the plasticizing effect of the shorter chains. 

In practice, product developers often blend two or more resins together in order to obtain a product that has the required melt flow and solid-state characteristics. Thus, we frequently combine metallocene catalyzed linear low density polyethylene, having a most probable molecular weight distribution, with low density polyethylene, having a broad molecular weight distribution. The linear low density polyethylene provides good impact resistance, while the low density polyethylene improves melt flow characteristics. 

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. 

SOLUBLE/INSOLUBLE (GEL) FRACTION. If crosslinking predominates over scission (when G(crosslink) > 4 G(scission)), the decrease in soluble fraction above the gel dose, may be used to derive G values for both processes. An equation was derived by Charlesby and Pinner for the most probable molecular weight distribution and similar equations have been derived for other distributions. 

The results of the various methods used to determine the molecular weight and degree of functionality of the diamine are shown in Table II. All of this evidence is consistent with the conclusion that the purified, isolated diamine possesses high difunctionality. When the diamine was chain extended with terephthaloyl chloride, a polymer product with a symmetrical molecular weight distribution was obtained (D.P. a 10). Inexact stoichiometry is most probably responsible for the limited extent of chain extension. 

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. 

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