For each of the following pairs of polymers do the following: (1) State whether 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 numberaverage molecular weight of \(225,000 \mathrm{~g} / \mathrm{mol}\) (d) Linear and syndiotactic polypropylene having a weight-average molecular weight of 500,000 \(\mathrm{g} / \mathrm{mol}\); linear and atactic polypropylene having a weight-average molecular weight of \(750,000 \mathrm{~g} / \mathrm{mol}\)

Understanding the concept of polymer crystallinity is crucial when predicting the melting temperature of polymers. Crystallinity refers to the degree to which the molecules in a polymer are orderly packed. In polymers with higher crystallinity, the regular arrangement of their long-chain molecules allows for strong intermolecular interactions and thus, increases the melting temperature. This is because a greater amount of energy is required to disturb the orderly structure and cause the polymer to transition from a solid to a liquid state.

For instance, in the case of polypropylene, the structure of the molecules significantly affects its crystallinity. Linear and syndiotactic polypropylene, which have a more regular arrangement of molecules, will exhibit higher crystallinity compared to linear and atactic polypropylene that has a random arrangement. As a result, the melting temperature of the more crystalline syndiotactic polypropylene will be higher than that of the atactic form, despite any differences in their molecular weights.

The molecular weight of polymers plays a significant role in determining their physical properties, including the melting temperature. Generally, a higher molecular weight implies longer polymer chains, which can lead to increased van der Waals forces between the chains. Thus, generally, polymers with higher molecular weights require higher temperatures to melt because more energy is needed to overcome these forces.

However, it's important to note that molecular weight is not the sole determinant of melting temperature. As the exercise solution indicated, when comparing polymers of similar molecular weights, such as branched and linear polyethylene both at 850,000 g/mol, other structural factors like the degree of branching or crystallinity must be considered. These structural aspects can affect the ease with which the chains slide past one another, thereby influencing the melting temperature.

Intermolecular forces in polymers include van der Waals forces, hydrogen bonding, and dipole-dipole interactions. These forces significantly affect the thermal and mechanical behaviors of polymers, including their melting temperatures. In polymers such as Polytetrafluoroethylene (PTFE), which contains highly electronegative fluorine atoms, the intermolecular forces are relatively strong due to the presence of dipole-dipole interactions. As a result, a higher temperature is needed to overcome these interactions during melting.

In the example provided, PTFE with a higher density suggests tighter packing and stronger intermolecular forces, leading to a greater melting temperature in comparison to a less dense PTFE with identical molecular weight. Such comparisons highlight how minute changes in molecular structure or composition can result in significant differences in the properties of polymers.