The Number Molecular Mass Distribution

In the basic molecular mass distribution, N(M), the number N of molecules in a sample is plotted vs. their molecular mass, M. Figure 1.2 presents a sketch of a... 

Figure 1.2. A number molecular mass distribution N (M) of an ideal chain polymer. N (M) is defined for integer multiples of Mm, the monomer mass. The integer factor, P, is called the degree of polymerization... 

Now the function displays the number fraction of molecules with a certain molecular mass. Its integral is 1 by definition. Nevertheless, we still call it the number molecular weight distribution because the factor /N (A/) dM is nothing but a constant. 

The narrow molecular mass distributions are usually obtained by polymerizing these materials directly to obtain a narrow distribution (i.e. by ionic polymerization techniques), rather than by using any fractionation techniques. As these polymerization techniques are limited in their applicability, there are technical as well as commercial reasons for the limited range of polymer types for which narrow MMD calibrants are available. The manufacturers of these narrow-distribution calibrants will undoubtedly seek to extend the number of chemical types and the molecular mass range available, but commercial considerations will inevitably limit this expansion. 

The structure parameter g was determined over the complete molecular mass distribution, and the number of long-chain branches per macromolecule, n, calculated. The degree of long-chain branching did not appear to vary by much over all ten specimens or with molecular weight. A marked difference was observed between LDPE in that EVA showed an absence of branching at low molecular mass. All the evidence thus pointed to EVA being a random copolymer. 

The concentration of the synthase or the number of enzyme copies has been assumed to have an influence on the molecular mass and molecular mass distribution of the synthesized polymer [33],but this has not been confirmed. The only variables found so far to control the molecular mass of the polymer are the initial ratio of substrate to enzyme levels, and the concentration of inducing factors in the culture medium [34-36] cf. also Chap. 9 of this book. 

Solution viscosity measurements for Mn are calibrated from the flow characteristics of linear molecules of the equilibrium molecular weight distribution. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. One, therefore, expects different flow properties as branching increases, hence causing the viscosity numbers to become less and less accurate and so should only be used for trends - not exact calculations. 

When does this process start to play a significant role When the relaxation time of such an elastic deformation exceeds the time scale at which the deformation takes place, which is the reciprocal shear rate 1/f. We have seen before that for a number of similar polymers with the same shape of molecular mass distribution, the deviation from Newtonian behaviour starts with the same value of the shear stress, thus (according to 7= r/p) at values of /which are inversely proportional to the (zero)viscosity p. It seems plausible to suppose that (again with similar mol mass distributions) the relaxation time of the elastic deformation is proportional to the viscosity (see also next section), so that the above mentioned observation is explained. 

Let s compare proteins to the polymers that were discussed in Chapter 24. One difference is that all the molecules of a particular protein are identical that is, they have the same molecular mass and contain the same number of amino acids connected in the same sequence. Recall that a typical condensation polymer consists of molecules containing many different numbers of monomers. More important, proteins are enormously more complex than simple condensation polymers because they are formed from a combination of 20 different monomer units. And these monomers are not randomly distributed in the protein. Rather, each molecule of a particular protein has an identical sequence of amino acid units. The exact sequence is of critical importance because it is the order of the side chains that determines the shape and function of that particular protein. 

The chains of the produced polymer are lengthened by combination, but not by disproportionation. This affects the molecular mass distribution but the differences are not very large, differing by a factor of 2 at most. Due to the inaccuracies in molecular mass determinations, it is almost impossible to make estimates of the relation between termination and disproportionation from the distributions. Even labelling of the initiator and determination of the average number of its fragments in a macromolecule (one for disproportionation and two for combination) is usually unsafe because of transfer. 

Figure 10 Number of possible amino acid compositions (peptide combinations) as a function of the peptide monoisotopic molecular mass for [M] = 1000 Da ([M] is the nominal molecular mass, i.e., lower integer mass value). The histogram is built with a 10-mDa step. The top density of the distribution is 230 peptide compositions per mDa or per ppm. (Reprinted from Ref. 100.)...

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