Determination of Molecular-Weight Distribution by Fractionation

For m 00, the critical value is identical with that in a fl solvent, i.e., A2 = 0 and X = 0.5. Since the solubility of macromolecules decreases with increasing molecular weight, it is possible to separate these materials with respect to their molecular weights by changing the composition of the solvent and/or the temperature. In general, one roughly distinguishes between two methods, namely fractional precipitation and fractional extraction. 

To fractionate a polymer by precipitation, a precipitant is slowly added to the polymer solution (concentration of polymer 0.1-1 wt.%) at constant temperature until a persistent cloudiness appears. After some time the droplets separate as a second liquid (or swollen gel) phase. This fraction contains the highest molecular weight components and is separated by decantation or centrifugation. Further precipitant is then added to the majority layer until further phase separation is observed. Then the above procedure is repeated several times until all polymer is separated off. A disadvantage of fractional precipitation is that the residual solutions become more and more dilute so that separation of the late fractions might be difficult. Furthermore, the method is rather time consuming since the formation of the gel phase occurs very slowly. 

In some cases the molecular-weight distribution can be determined by turbidi-metric titration, a technique which is based on the fractional precipitation. A precipitant is added to a very dilute solution of the polymer, and the resulting 

Once the amounts and molecular weights of the fractions have been determined, the molecular-weight distribution of a polydisperse material can be expressed graphically in the form of a distribution curve. The mass distribution function is written as  

For example, to obtain the value of I(P) for fraction 5 in Table 2.9 one adds the percentage amounts of fractions 8, 7, and 6 (3.4 + 3.7 + 7.3 = 14.4) and adds half the amount of fraction 5 (14.4 + 8.4 = 22.8). The integral distribution curve (see Fig. 2.17) is obtained by plotting I(P) values obtained in this way, versus the corresponding degree of polymerization. 

In some cases the molecular-weight distribution can be determined by turbi-dimetric titration, a technique which is based on the fractional precipitation. A precipitant is added to a very dilute solution of the polymer, and the resulting turbidity is measured as a function of the amount of added precipitant the preparative separation of the fractions is thereby avoided. If the polymer is chemically homogeneous, the mass distribution function can then be calculated. Tur-bidimetric titration is also suitable as a means for establishing the best fractionation conditions (e.g., choice of solvent/precipitant combination, size of fractions, etc.), before carrying out a full-scale fractionation by precipitation. 

Fractional extraction is free from the disadvantages encountered in fractional precipitation. Here, the technique consists in extracting the polymer with a series of solvent/precipitant mixtures, the proportion of solvent being increased stepwise. Since one begins with the poorest solvent mixture - in contrast to fractional precipitation - the first fraction contains the low-molecular-weight com- 

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