Molecular weight distribution breadth

Hence, the preferred measure of the molecular weight distribution breadth is... 

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. 

In a very interesting paper, Ray (42) has applied the methods of optimal design, for instance, minimizing the breadth of the molecular weight distribution within other constraints. He used generating functions to solve for the moments of the distribution and peak-seeking methods for reaching the optimum. One and two CSTR s were considered with combination termination as well as transfer to monomer. 

Block length polydispersity indices"for blends were calculated on the assumption that the block polymers, as prepared, were composed of monodisperse blocks. This is, of course, an approximation justified only by the narrowness of the molecular weight distribution in polymerizations of the present type. The block heterogeneity indices given here should, therefore, be regarded as relative measures of breadth of distribution. 

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)]. 

Complete description of a molecular weight distribution implies a knowledge of all its moments. The central tendency, breadth, and skewness may be summarized by parameters calculated from the moments about zero U, U[, U 2, and These moments also define the molecular weight averages Mn, and M. Note that A/n and My, can be measured directly wiihoul knowing the distribution but it has not been convenient to obtain A j of synthetic polymers as a direct measurement of a property of the sample. Thus, some information about the breadth of the number... 

Assume that each fraction is monodisperse and calculate Mn, and a measure of the breadth of the number distribution for the recovered polymer. Note-. This is not a recommended procedure for measuring molecular weight distributions. The fractions obtained by the method described will not be monodisperse and the molecular weight distributions of successive fractions will overlap. The assignment of a single average molecular weight to each fraction is an approximation that may or may not be useful in particular cases.)... 

The term A h in Eq. (3-62) is called Huggins constant. Its magnitude can be related to the breadth of the molecular weight distribution or branching of the solute. Unfortunately, the range of A h is not large (a typical value is 0.33) and it is not determined very accurately because Eq. (3-62) fits a chord to the curve of Eq. (3-64), and the slope of this chord is affected by the concentration range in which the curve is used. 

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. 

---