2017 Fall Problem 5 (20 points). Chemical evidence for chain folding in polyethy

Question

2017 Fall Problem 5 (20 points). Chemical evidence for chain folding in polyethylene crystals is obtained by etching polymer crystals with fuming nitric acid, which cleaves the chain at the fold surface. The resulting chain fragments are separated chromatographically and their molecular weights determined by osmometry. The folded chain is pictured as crossing through the crystal, emerging and folding back, then reentering and recrossing the crystal, and so on. According to this picture, the shortest chain showing up in the chromatograms should equal the crystal thickness in length. The second shortest chain exceeds twice this value by some amount, which measures the length of the loop made by the chain outside the crystal. Molecular weights for the two shortest chains observed in an experiment of this sort were 1260 and 2530. Since the cleaved chains end in nitro and carbok,/l groups, 60 should be subtracted from each of these molecular weights to give polyethylene chain weight. Calculate the degree of polymerization of each molecule and the chain length (use the length of the unit cell along the chain axis, 2.53 A, as the distance per repeat unit). Compare the latter with the crystal thickness determined by x- ray diffraction, 105 A. What does the ratio of chain lengths for the first and second peaks 24270 suggest about the tightness of folding?

Explanation / Answer

degree of the polymerization can be calculated using the formula

degree of the polymerization = molecular weight of (C2H4)n/C2H4

degree of the polymerization of 1st chain = (1260-60)/28 = 42.85

degree of the polymerization of 2nd chain = (2530-60)/28 = 88.21

Chain length of the first chain = 42.85 * 2.53Å =108.41Å (corresponds to the thickness), which is nearly the same as determined by the X-Ray diffraction technique

Chain length of the second chain = 88.21 * 2.53Å = 223.17Å (corresponds to the length of the loop)

Ratio of the chain length is approximately 1:2, which is suggestive of the quite tight folding)

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