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Molecular weight data for some polymer are tabulated here. Compute (a) the number average molecular weight, and (b) the weight-average molecular weight. (c) If it is known that this material's degree of polymerization is $477,$ which one of the polymers listed in Table 14.3 is this polymer? Why? $$\begin{array}{ccc} \hline \text {Molecular Weight} & & \\ \text {Range }(\mathrm{g} / \mathrm{mol}) & \boldsymbol{x}_{\boldsymbol{i}} & \boldsymbol{w}_{\boldsymbol{i}} \\ \hline 8,000-20,000 & 0.05 & 0.02 \\ 20,000-32,000 & 0.15 & 0.08 \\ 32,000-44,000 & 0.21 & 0.17 \\ 44,000-56,000 & 0.28 & 0.29 \\ 56,000-68,000 & 0.18 & 0.23 \\ 68,000-80,000 & 0.10 & 0.16 \\ 80,000-92,000 & 0.03 & 0.05 \\ \hline \end{array}$$
For each of the following pairs of polymers do the following: (1) state whether or not it is possible to determine whether one polymer has a higher melting temperature than the other; (2) if it is possible, note which has the higher melting temperature and then cite reason(s) for your choice; and (3) if it is not possible to decide, then state why. (a) Branched polyethylene having a numberaverage molecular weight of $850,000 \mathrm{g} / \mathrm{mol}$; linear polyethylene having a number-average molecular weight of $850,000 \mathrm{g} / \mathrm{mol}$ (b) Polytetrafluoroethylene having a density of $2.14 \mathrm{g} / \mathrm{cm}^{3}$ and a weight-average molecular weight of $600,000 \mathrm{g} / \mathrm{mol}$; PTFE having a density of $2.20 \mathrm{g} / \mathrm{cm}^{3}$ and a weight-average molecular weight of $600,000 \mathrm{g} / \mathrm{mol}$ (c) Linear and syndiotactic poly(vinyl chloride ) having a number-average molecular weight of $500,000 \mathrm{g} / \mathrm{mol} ;$ linear polyethylene having a number-average molecular weight of $225,000 \mathrm{g} / \mathrm{mol}$ (d) Linear and syndiotactic polypropylene having a weight-average molecular weight of 500,000 g/mol; linear and atactic polypropylene having a weight-average molecular weight of $750,000 \mathrm{g} / \mathrm{mol}$
Polyethylenes A, B, and C from three sources are to be blended to achieve a weight-average molecular weight of 210,000 and a polydispersity index (PDI) of 3.0. How much of each polymer should be used to obtain 10,000 kg blend? Polyethylene A B C Weight-average mol. wt. A = 130,000 B = 220,000 C = 400,000 PDI A = 2.50 B = 2.00 C = 2.50
Sri K.
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