8.7 Average Molecular Weights and Distributions
A major distinguishing feature of high polymers is their enormous molecular weight. Molecular weights of 20,000 Daltons are routine,and values as high as 2,000,000 Daltons are not uncommon. However,unlike small molecules such as benzene or chloroform,or biological polymers like enzymes,a sample of a synthetic polymer has no single,fixed molecular weight. Instead,there is a distribution of different molecular weights in the same sample of material (Figure 8-3). For this reason,it is necessary to speak of average molecular weights rather than a single defining value.
Figure 8-3 Molecular Weight Distributions
Several different types of average molecular weights are used in polymer chemistry,the most important of which are known as number average,,and weight average,,values. They are defined as shown in equations (8-4) and (8-5):
where Ni is the number of molecules of molecular weight Mi,and Xi is the number fraction or mole fraction of molecules having molecular weight Mi,and where wi is the weight of molecules of molecular weight Mi,and Wi is the weight fraction of molecules with molecular weight Mi.
In general, values are higher than because the calculations for give more emphasis to the larger molecules,while calculations give equal emphasis to all molecules.
The fraction (called the polydispersity) is a measure of the molecular weight distribution. If the value of is close to 1(1.01 or 1.02 for instance),the distribution is very narrow. If it is,say,2 or higher,the distribution is considered to be very broad. The molecular-weight distribution affects several important polymer properties. For example,polymers with very broad distributions are less prone to crystallize than their narrow distribution counterparts,and they often have lower solidification temperatures. The shorter chains plasticize the bulk material and make it softer. Thus,together with the glass transition temperature,Tg,and the crystalline melting temperature,Tm (see below), is a crucial characteristic of any synthetic polymer.