Weight and Degree of Polymerization

The molecular weight (M) of a polysaccharide is the gram mole or molar mass of 6.023 X 1023 molecules (Avogadro s number) that ideally are of a single size. Extracted, isolated, and purified polysaccharides in the same class, from the same sampling source, are seldom uniform in shape and size and are therefore preferably characterized by an average molecular weight M. 

The high number of monomers constituting M and M is referred to as the degree of polymerization (DP). Being predetermined by the manufacturer s methodologies, the average DP is constant but widely distributed from the mean, and is thus unsuitable without fractionation for most experiments involving purchased samples. 

M and M are not related only to mass they are equally a function of charge, solvent activity, and concentration. Some generalizations can nevertheless be made about the DP the lowest DP stimulates the highest kinetic activity at the same weight concentration low DP polysaccharides are more soluble and reactive than high DP polysaccharides a high DP is necessary for dispersion viscosity measurably above that of water. 

M and M are alternatively characterized by the radius of gyration (J ), which is visualized as the radius of a thin circle transversely excised from an imaginary molecular cylinder, having a proximal end fixed at the center and a distal end traveling randomly along the circumference. The mass density is highest at the proximal end (Tanford, 1961). Random-walk theory indicates that the distal end will eventually maintain an equilibrium distance in the vicinity of the proximal end. 

The importance of M is unmistakable when it is recalled that 180 g glucose in 10s g water [1 molal (m)] lowers the freezing point by 1.86°C, whereas the same weight of polysaccharide (1.80 X 10 3 m, assuming M = 105 g) has no such effect and, moreover, it is difficult if not impossible to disperse 105 g of any polysaccharide in 103 g water. Identical arguments hold for boiling-point elevation and osmotic pressure. However, polysaccharides at much lower concentrations exercise influences, most prominently by 

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The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

After the initial reaction of a radical with the first monomer unit, a series of propagation steps follows, rapidly building up the molecular weight and degree of polymerization. The important part of this mechanism is therefore the (3), (3), etc. noted. This is what makes the polymer With unsymmetrical monomers the head-to-tail addition is preferred because whatever it is in the R group that stabilized the radical once will do so each time a propagation step happens. 

This exponential decrease in molecular weight and degree of polymerization with time can be expressed by an empirical relationship of the form... 

The structure, molecular weights, and degrees of polymerization, m, of these compounds are unknown. Some may be 6-heteropolymolybdates — for example, the P+3 and As+3 complexes. 

A 1% aqueous solution of gum arabic (simplest formula CigHo-jOu) was found to have an osmotic pressure of 7.2 mm Hg.. What are tlie average molecular weight and degree of polymerization of the solute ... 

Table 6.5. The dependence of elastic constant ratios of nematic PBG solution on the average molecular weight and degree of polymerization (4> 0.16).

In use of abbreviations, we have attempted to use accepted and common forms. When molecular weight and degree of polymerization have been cited, the abbreviations for the text and equations have been respectively MW and DP and M and P. This designation in equations avoids complications particularly where subscripts are used. 

Calculate number average and weight-average molecular weights and degree of polymerization for a specified polymer. 

Computations of Average Molecular Weights and Degree of Polymerization... 

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