ISSN:
0022-3832
Keywords:
Chemistry
;
Polymer and Materials Science
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
A number-average property such as a number-average diffusion constant Dn cannot be defined in terms of weight-related weighting factors (such as concentrations in weight per unit volume) without postulating a functional relationship between the molecular weight and that property. Conversely, an analogous statement holds concerning any weight-average property and number-related weighting factors such as mole fractions. Ordinarily the molecular weight distribution is not known initially for a given sample under study, so that assignment of any such a relationship under these circumstances would be quite arbitrary. It is proposed that the number average analog [Σci/(Σci/Qi)], which is equal to the true number average Qn only when Qi is directly proportional to the molecular weight Mi within the sample considered, be designated the number-analogous average Qx to distinguish it from Qn. (In this, ci is a weighting factor proportional to the polymer weight fraction having the value Qi of the intensive physical or chemical property under discussion.) Mn is of course necessarily equal to Mx. However, designation of Dx as the number-average diffusion constant is particularly unreasonable because it implies direct proportionality between the molecular weight and the diffusion constant. Although such a relation may hold for a specific case, in general, other factors being usual, the diffusion constant is inversely related to molecular weight. Discussion of a specific illustration shows the following: Qx may be the same for heterogeneous systems having different values of Qn. Qn cannot in general be found by analyzing a material distribution by means of a property such as the refractive index that is proportional to the mass concentration rather than to the number of molecules in a given volume. Qx sometimes can be found from such data. Although the sedimentation and diffusion constants, with the partial specific volume, define the molecular weight of a homogeneous sample, the average sedimentation and diffusion constants of a mixture do not uniquely determine its average molecular weights. Values found from weight-, number-, or number-analogous average sedimentation and diffusion constants may be either higher or lower than the weight- and number-average molecular weights, even though these latter have been deduced to be limiting values for certain postulated molecular weight distributions. In a given instance, heterogeneity indexes calculated from true weight- and number-averages of sedimentation and diffusion constants more closely approximate the ratio of the weight-average to number-average molecular weights than if the more readily determined number-analogous averages are used.
Additional Material:
1 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/pol.1957.1202410502
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