Molecular weight 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. 

The breadth of the molecular weight distribution is often discussed in terms of the dispersity (Z>) and is expressed in terms of the moments as shown in eq. 15 ... 

This dimensionless number measures the breadth of the molecular weight distribution. It is 1 for a monodisperse population (e.g., for monomers before reaction) and is 2 for several common polymerization mechanisms. 

The breadth of the molecular weight distribution may be measured by the ratio MJMn. Show that this ratio is given by... 

Figure 15 Morphological map of linear polyethylene fractions. Plot of molecular weight against crystallization temperature. The types of supermolecular structures are represented by symbols. Patterns a, b and c represent spherulitic structures with deteriorating order from a to c. Patterns g and d represent rods or sheet-like structures whose breadth is comparable to their length g or display a different aspect ratio d. Pattern h represents randomly oriented lamellae. Neither h nor g patterns have azimuthal dependence of the scattering. Reproduced with permission from Ref. [223]. Copyright 1981 American Chemical Society. (See Ref. [223] for full details.) Note the pattern a is actually located as o in the figure this was an error on the original.

The breadth of the Molecular weight distribution curve can be obtained as follows. The degree of polymerisation in given by... 

For polydisperse sample, situation becomes a bit more complex, but a detailed analysis can yield average Molecular weights with different weightings such as > Mn, Mz which are useful measures of breadth of distribution. 

Consider the polymerization of styrene initiated by di-t-butyl peroxide at 60°C. For a solution of 0.01 M peroxide and 1.0 M styrene in benzene, the initial rates of initiation and polymerization are 4.0 x 10 11 and 1.5 x 10 7 mol L 1 s 1, respectively. Calculate the values of (jkj), the initial kinetic chain length, and the initial degree of polymerization. Indicate how often on the average chain transfer occurs per each initiating radical from the peroxide. What is the breadth of the molecular weight distribution that is expected, that is, what is the value of Xw/Xnl Use the following chain-transfer constants ... 

Definition of a Complex Polymer. A simple polymer is one vrtiich has at most one broad molecular property distribution (e.g., a broad molecular weight distribution). A complex polymer is one which has two or more broad molecular property distributions (e.g., a broad molecular weight distribution and a broad copolymer composition distribution) ( ). Properties such as molecular weight and composition, Aiich can be in so much variety in a polymer that they must be described as a distribution, are here termed "distributed properties". It is the presence of simultaneous breadth (i.e., variety) in more than one distributed property which is the defining characteristic of a "complex" polymer and the source of analysis difficulties. 

Axenic bacterial cultures that grow on HMW PAHs of four or more fused rings have been reported. Many studies also suggest that this breadth includes cometabolism or fortuitous metabolism. This is a process in which enzymes responsible for the initial oxidation of a particular PAH fortuitously oxidize other, higher-molecular-weight PAHs, even though these latter substrates may not ultimately be used as a source of carbon and energy for the cells. In addition,... 

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 variance measures the absolute breadth of the distribution, but properties that depend on the width of the distribution would depend on the width relative to the average. For this reason the dispersion index is defined as the ratio of the weight to the number average molecular weight, which is related to the variance as follows ... 

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