ISSN:
0022-3832
Keywords:
Chemistry
;
Polymer and Materials Science
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
The authors have developed a statistical model for a branched polymer built from a monomeric unit (such as glucose) which has two types of reactive groups (aldehydic and alcoholic). The treatment differs from that of Flory's in that the different B groups in the A-R-Bf-1 monomer have differing reactivities instead of equal reactivities. The mole fraction of a particular x-mer having b1, b2,…bf-1 linkages at their respective B1, B2,…Bf-1 functional groups is: \documentclass{article}\pagestyle{empty}\begin{document}$N_{b1,b2,...b_{{\rm f} - 1}} = \frac{1}{x}\prod\limits_{i = 1}^{{\rm f} - 1} {\left({\begin{array}{*{20}c} x \\ {b_i} \\ \end{array}} \right)} p_i^{b_i} (1 - p_i)^{x - b_i}$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$ x = 1 + \sum\limits_{i = 1}^{f - 1} {b_i}$\end{document} is the total number of monomer units per molecule and p1,p2,…pf-1 are the probabilities that any monomer unit is linked at the B1, B2,…Bf-1 functional group. From the above, x̄n, the number-average DP, x̄w, the weight-average DP, x̄z, the Z-average DP, and wx, the weight fraction of an x-mer, have been obtained. It is shown that the limit of x̄z/x̄w is 3 and the limit of x̄w/x̄n is infinity as the degree of polymerization increases for all cases where “f” is greater than two. These results were used for the randomly branched polymers, amylopectin and glycogen, where the functionality of the monomer in both cases is three. p4 and p6 were used to represent the probabilities that any glucose unit is linked at the 4 or 6 position. Using values of p6 = 0.05 and p4 = 0.94933, x̄n = 1500, M̄n = 243,000, M̄w=35,100,000, and M̄z = 104,500,000, giving M̄w/M̄n = 140 and M̄z/M̄w = 2.99. Literature values for molecular weights of amylopectin and glycogen are compared with the above statistical model and with less random statistical models.
Additional Material:
4 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/pol.1956.120209402
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