368 BELL SYSTEM TECHNICAL JOURNAL 



Molecular Weight Distribution l\ GR-S 



Unlike the linear polyesters whose molecular weight distributions can be 

 calculated from simple assumptions (Fig. 1), the distribution of molecular 

 sizes present in polymerization polymers cannot, at the present state of our 

 knowledge at least, be accurately predicted. With linear polymers of 

 uniform composition it is possible to determine experimentally the approxi- 

 mate molecular weight distribution by fractional precipitation of the dis- 

 solved polymer from dilute solution. This procedure, to yield good results, 

 must be carried out under very careful control, and requires considerable 

 time. The usual procedure is to prepare a solution of the polymer to be 

 studied and add to it portions of a precipitant. The successive fractions 

 of the whole polymer precipitated are then examined for average molecular 

 weight by some suitable method. This procedure can give only a crude 

 separation but often furnishes useful information. More accurate results 

 require the use of very dilute solutions and the precipitation is best carried 

 out by lowering the temperature to produce insolubility at each step. The 

 experimental distribution curve is then obtained by plotting as ordinate the 

 weight fraction and as abscissa the average molecular weight (weight average 

 or number average) corresponding to each fraction. In this way an integral 

 curve is obtained which on differentiation gives differential curves of the 

 type shown in Fig. 1. 



In GR-S, such a fractionation procedure is complicated by the fact that 

 all of the molecules of the copolymer are not of the same t}^e. For as we 

 have seen we may encounter differences not only in structure between 

 molecules but also in composition either of which alone will, independently 

 of molecular size per se, influence solubility. 



In fact experiments have shown that fractions separated from (iR-S 

 actually do exhibit differences in styrene content attesting to the special 

 compUcations of determining molecular distributions in copolymers b}' this 

 method. In spite of this, fractionations of GR-S have been made whicli 

 no doubt have quahtative value. As a result of such experiments it has 

 been found that molecular size distribution in GR-S is highly dependent on 

 impurities present during the reaction as well as on other factors. When, . 

 however, the process and raw materials are suitably controlled it is likely 

 that the shape of the curve does not vary greatly. Under these circum- 

 stances the number average molecular weight determined by osmotic pres- 

 sure furnishes a measure of molecule size. 



If the molecules are not too highly branched, we may employ viscosit}- 

 measurements to furnish a "viscosity average" molecular weight. Since 

 the latter measurements are the simplest to make they are generally em- 

 ployed^'-, although care must be used to insure proper interpretation of 

 results. In general, the average molecular weight given b}' the viscosity will 



