A Proposed Method for Estimating Polymer Molecular Weight Distribution without Fractionation

The close agreement which Green has demonstrated between results from the Schulz binomial and the Tung distribution and the applicability of the latter to a variety of fractionation data for different polymers both seem to outweigh possible objection that the present method assumes a particular distribution function. Green's results suggest to us that the apparent exceptions found by Tung for some polyethylenes containing large amounts of low molecular species may possibly be attributed to fractionation inefficiency, rather than to the inadequacy of his function. The internal consistency or smoothness of data does not, of course, constitute proof of precise fractionation. In fact, one can safely say it is no easy matter to find complete fractionation data, of established precision, that can provide a critical test of a distribution function over the entire molecular weight domain. In his study of polyethylenes, Tung suggested that his function tends to exaggerate the low molecular weight end of the distribution, in the sense that the Mn values calculated from his parameters were only about half as large as those obtained by summation of the experimental data for the fractions. His calculated and experimental values of Mw, on the other hand, were in satisfactory agreement. One might be tempted to use this to reconcile the Mn values of the SBR system in Table II with the higher values reported by others. However, this procedure would be indefensible because simply doubling the Mn values would give polydispersity values of less than unity. It would therefore seem incorrect to generalize that the Tung function gives abnormally small Mn values for all polymers, especially when there is some reason to believe that it is better than it seems, even for polyethylenes. Much more likely, the differences between the average molecular weights and the polydispersity of the peroxide-SBR system of Table II, and the corresponding quantities reported by Bueche and Harding for sulfur-SBR and by Booth and Beason for uncompounded SBR, are real and are due to chemical and other factors already mentioned. Although the meager data at hand leave some question as to the accuracy with which the present method can predict absolute values of the various average molecular weights, the key to the matter seems to be the ratio of the true to the physically measured crosslink density for polymers in general, rather than the particular distribution function employed here. Less uncertainty is attached to the polydispersity, since this is a function of only one parameter, b, which is quite insensitive even to large errors in ρ. The method may therefore be useful, even in its present state, for comparative studies in a given system. These might include, for example, the effect of synthesis or processing variables on distribution characteristics and product properties or the effects of stabilizers in aging or other degradative processes.