Breadth of Molecular Weight Distribution

The breadth of the molecular weight distribution is then given by 

The ratio Xw/Xn is synonymous with the ratio MwfMn discussed in Sec. 1-4. It is a measure of the polydispersity of a polymer sample. The value of Xw/Xn increases with the extent of reaction and approaches 2 in the limit of large extents of reaction. The ratio XwfX is also referred to as the polydispersity index (PDI). 

The most probable distribution of Flory is generally well established, although its experimental verification has been somewhat limited. Direct evidence for the most probable 

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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. 

The ratio of Mw/Mn is taken as a measure of the polydispersity or the breadth of molecular weight distribution of the polymer. The... 

While the polydispersity, Q, is by far the most commonly employed measure of the breadth of molecular weight distributions, several others are available and are more revealing in some cases. 

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 ... 

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... 

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

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. 

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