Polydispersity index distributions, breadth

It may be shown that M > M. The two are equal only for a monodisperse material, in which all molecules are the same sise. The ratio MI /MI is known as the polydispersity index and is a measure of the breadth of the molecular weight distribution. Values range from about 1.02 for carefully fractionated samples or certain polymers produced by anionic polymerization, to 20 or more for some commercial polyethylenes. 

A measure of the breadth of the molecular mass distribution is given by the ratios of molecular mass averages. The most commonly used ratio Mw/Mn — H, is called the polydispersity index. Wiegand and Kohler discuss the determination of molecular masses (weights) and their distributions in Chapter 6. 

A consideration of the preceding equations indicates that high polymer (i.e., large values of X and Xw) will be produced only if p is close to unity. This is certainly what one expects from the previous discussions in Sec. 3-5. The distributions described by Eqs. 2-86, 2-88, and 2-89 have been shown in Figs. 2-9 and 2-10. The breadth of the size distribution Xw/X [also referred to as the polydispersity index (PDI)] has a limiting value of two as p approaches unity. 

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. 

The ratio Mw/ Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index. Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/ Mn is in the range 1.5-2, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/ Mn = 1.00. 

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)]. 

If all species in a polymer sample have same molecular weight (that is, the polymer is monodisperse) then Mn = M i — Mz- Such monodispersity is, however, unknown in synthetic polymers and it is always true that Mz > Mw > Mn- The ratio Mu,/M , or (A/ /M ) , is commonly taken to be a measure of the polydispersity of the sample. This ratio, called the polydispersity index (PDI), is not a sound statistical measure, however, and it is easy to make incorrect inferences from the magnitude of the M a/Mn ratio. The breadth and shape of the distribution curve are characterized most efiiciently with parameters derived from the moments of distribution. 

The Z-average molecular weight gives a measure of the upper limit of the polymer molecular weight distribution. The ratio Mw/M can be used as a measure of the breadth of the molecular weight distribution or polydispersity and is sometimes referred to as a polydispersity index (PDI). 

Polydispersity n. The breadth of the molecular-weight distribution of a polymer. Two measures of polydispersity are in common use (1) the ratio of the weight-average and number-average molecular weights MJM y and (2) the g-index. 

Both Mjj and are useful values, and their ratio, MJM called the polydispersity index, provides a measure of the breadth of the molecular-weight distribution. When the MJM ratio is equal to one, all the polymer molecules in a sample are the same length, and the polymer is said to be monodisperse. No synthetic polymers are ever monodis-perse unless the individual molecules are carefully fractionated using time-consuming, rigorous separation techniques based on molecular size. On the other hand, natural polymers, such as polypeptides and DNA, that are formed using biological processes are monodisperse polymers. 

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. 

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. 

He then defined a polydispersity index of relaxation times as (r )/(r ) and pointed out that this parameter increases as the MWD becomes broader. In an entangled melt, if we limit our attention to the plateau and terminal zones, and if the relaxation spectrum function is known over the full range of times, it can be shown that this ratio of times is equal to /f. As we have seen, the product /° G indicates the breadth ofthe molecular weight distribution of a linear polymer and can be calculated directly from rheological data. For example, if the relaxation modulus in the plateau and terminal zones is represented by a single exponential ... 

Zeichner and coworkers [33,34] developed a measure of the breadth of the molecular weight distribution that is based on the curves of storage and loss moduli versus frequency. Based on data for a series of polypropylenes made by Ziegler-Natta catalysts and degraded by random chain scission, they found that the polydispersity index, i.e., the ratio Af /M , was related to the crossover modulus, G, as shown in Eq. 5.8... 

The most primitive measure of the breadth of a molecular weight distribution (MWD) is the polydispersity index PI, which is defined as the ratio of the weight to the number... 

The polydispersity index is a measure of the breadth of mole fraction (or molecular weight) distribution. For a monodisperse polymer, Q is unity commercial polymers may have a value of Q lying anywhere between 2 and 20. 

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