Breadth of MWD

Evaluation of the series summation in Eq. (5.76) at fixed p yields (see Appendix 5.1)  

The breadth of the molecular weight distribution curve is then given by 

The ratio X jX-n is synonymous with the ratio M /Mn discussed in Chapter 4. 

An expression of X. in terms of p is then obtained by combining Eqs. (5.73) and (5.82) and performing series summation (see Problem 5.15)  

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In some systems it is necessary to add a large amount of salts to obtain polymers with low polydispersities. This happens when salts participate in ligand/anion exchange (special salt effect) and when they enhance ionization of covalent compounds through the increase of ionic strength. The special salt effect may either reduce or enhance ionization. Strong rate increases observed in the polymerization of isobutyl vinyl ether initiated by an alkyl iodide in the presence of tetrabutylammonium perchlorate or triflate can be explained by the special salt effect [109]. The reduction in polymerization rate of cyclohexyl vinyl ether initiated by its HI adduct in the presence of ammonium bromide and chloride can be also ascribed to the special salt effect [33]. The breadth of MWD depends on the relative rate of conversion of ion pairs to covalent species and is affected by the structure of the counterions. 

MIR melt index ratio (HLMI/MI) an indicator of the breadth of MWD of a polymer, used mostly with PE... 

MW fraction increases the melt flow, thus improving the processability but at the cost of toughness, stiffness, and stress crack resistance. In addition, the improvement in performance through narrowing the MWD is restricted by the catalyst, the process hardware, and the process control limitations. Dow has developed a reactor grade HDPE of optimized breadth, peak, and shape of MWD... 

A mathematical model for this polymerization reaction based on homogeneous, isothermal reaction is inadequate to predict all of these effects, particularly the breadth of the MWD. For this reason a model taking explicit account of the phase separation has been formulated and is currently under investigation. 

Graessley and his co-workers have made calculations of the effects of branching in batch polymerizations, with particular reference to vinyl acetate polymerization, and have considered the influence of reactor type on the breadth of the MWD (89, 91, 95, 96). Use was made of the Bamford and Tompa (93) method of moments to obtain the ratio MJMn, and in some cases the MWD by the Laguerre function procedure. It was found (89,91) that narrower distributions are produced in batch (or the equivalent plug-flow) systems than in continuous systems with mixing, a result referrable to the wide distribution of residence times in the latter. 

The breadth of the molecular weight distribution is described by the ratio of the weight and number average molecular weights or degrees of polymerization, and is referred to as the polydispersity index (PDI) or molecular weight distribution (MWD) [Eq. (8)]. 

Dividing HLMI by MI affords the melt index ratio (MIR), a dimensionless number which gives an indication of breadth of molecular weight distribution. As MIR increases, MWD broadens. 

This dimensionless number measures the breadth of the MWD. It is 1 for amonodis-perse population (e.g., for monomers before reaction) and 2 for many polymerization... 

Evidently, the effect of [TiCl4] on the breadth of the GPC traces is insignificant under the conditions examined. Evidently the increase in [TiCU] reduces but does not eliminate the undersirable MWD broadening effect of slow initiation (see Fig. 33B). The relatively broad MWDs may also be due to the low temperature of the experiment where very rapid propagation by the nonliving ionic species is dominating. 

It is apparent that the breadth of the MWD is highly dependent on the extent of reaction (conversion) attained in these reactions, as B increases with the conversion. At low conversions, the MWD for an AB system corresponds to a Flory distribution (B 2) however, B trends toward infinity as full conversion is approached. Eor trifunctional monomers, including equally reactive A3 monomers and ABC monomers with reactivity differentials, the MWD also depends on the DP but in a different way B is proportional to DP in an A3 system, while for an ABC system it is proportional to (DP) [49, 50]. 

The molecular weight distribution (MWD), also discussed earlier, is an indication of the relative proportions of molecules of different weights/ lengths. It shows the breadth of distribution, or the ratio of large, medium, and small molecular chains in the resin. If most of the molecules have about the same MW, the MWD is classified as narrow. A wide or broad MWD implies a large variation in MW. Figure 1-5 compares wide and narrow MWDs. The MWD is independent of both density and melt index (MI) (see Chapter 10), and must be taken into account in considerations of both processing and product performance. A narrow MWD enables much better. 

The last two columns of Table 1 give the values of M /M obtained by the two mthods this ratio is a measure of the breadth of the MWD... 

The primary intent of studying the modulus data was to use the information to examine changes in the molecular weight distribution. As described earlier, it has been reported that the G - G" crossover, Gc, point in the terminal zone can be used to measure the polydispersity index, PI (eq. 1). The breadth of the MWD has a direct relationship with PI and an inverse relationship with Gc. Consequently, as Gc shifts down it indicates a broadening of the MWD. 

Swell represents a recovery of stored elastic energy. The molecular structure, in particular molecular weight and long chain branching, has a profound effect on the swell characteristics, but to date there is no consistent theory to explain the relationships. Early investigations into the phenomenon of swell showed that HDPE appeared to behave in a similar fashion to polystyrene (PS), where an increase in the breadth of the MWD of PS... 

The value of is sensitive to the presence of higher molecular masses, whereas the value of ilf, is sensitive to the lower molecular masses. The ratio of M and Jlf, is often used as a measure of the breadth of the molecular-weight distribution (MWD) and times is referred to as the polydispersity index. In monodisperse systems, MJM = 1, whereas in the examples discussed in Sections 1.1.2A and 1.1.2B, MJMn = 2.5 (550,000/220,000), indicating that it is a polydisperse system. 

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