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 \(750,000 \mathrm{g} / \mathrm{mol}\)

Step by step solution

01

(a) Branched vs. Linear Polyethylene

For both branched and linear polyethylene, they have the same number-average molecular weight of 850,000 g/mol. Since linear polymers generally have higher crystallinity than their branched counterparts, they also have higher melting temperatures. In this case, linear polyethylene has a higher melting temperature than branched polyethylene due to its higher crystallinity.

02

(b) PTFE (Polytetrafluoroethylene) with different densities

In this case, both PTFE samples have the same weight-average molecular weight of 600,000 g/mol but different densities, 2.14 g/cm³ and 2.20 g/cm³. The one with a higher density (2.20 g/cm³) has a more compact molecular structure, which causes stronger intermolecular forces. As a result, PTFE with a density of 2.20 g/cm³ has a higher melting temperature.

03

(c) Linear and Syndiotactic PVC vs. Linear Polyethylene

Here, we are comparing linear and syndiotactic poly(vinyl chloride) (PVC) with a number-average molecular weight of 500,000 g/mol and linear polyethylene with a number-average molecular weight of 225,000 g/mol. Since PVC and polyethylene are different polymers with different chemical structures, it is not possible to determine which one has a higher melting temperature based solely on their molecular weights.

04

(d) Syndiotactic vs. Atactic Polypropylene

We are comparing linear and syndiotactic polypropylene with a weight-average molecular weight of 500,000 g/mol to linear and atactic polypropylene with a weight-average molecular weight of 750,000 g/mol. Syndiotactic polymers have a higher degree of crystallinity than atactic polymers. Therefore, syndiotactic polypropylene has a higher melting temperature than atactic polypropylene, even though its molecular weight is lower.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Crystallinity in Polymers

Understanding the crystallinity of polymers is essential for predicting their melting temperatures. Crystallinity refers to the degree to which the molecular chains in a polymer are orderly packed in a well-defined, three-dimensional structure. Highly crystalline polymers have regions where the chains are aligned and tightly packed. This orderliness increases the thermal stability of the material, and as a result, a higher melting temperature.

Think of crystallinity like the arrangement of books on a shelf: when the books (or polymer chains) are neatly stacked, it's harder to remove one (or to melt the polymer). More crystalline polymers have stronger intermolecular forces as the chains interact closely. This means that more energy (in the form of heat) is required to break these interactions, leading to a higher melting temperature. However, if the polymer is amorphous with chains in a more random arrangement, it will have a lower melting temperature due to weaker intermolecular forces.

Polyethylene Molecular Structure

The molecular structure of polyethylene, one of the most commonly used polymers, varies based on its chain configuration. Polyethylene consists of long hydrocarbon chains, but the arrangement of these chains can differ. When we have a linear polyethylene, the chains are straight without any branching, allowing them to pack closely together and form crystalline regions. As a result, linear polyethylene exhibits higher crystallinity and, consequently, a higher melting temperature.

In contrast, branched polyethylene has side chains attached to the main chain, which can interfere with close packing and reduce crystallinity. This branching hinders the ability of the polymer chains to align, resulting in lower crystallinity and a lower melting temperature. The number-average molecular weight (\( \text{M}_\text{n} \) ) provides information about the size of the molecules but does not directly impact the melting temperature as much as the structure does.

Polypropylene Crystallinity

Similar to polyethylene, polypropylene also exhibits variations in structure that affect its crystallinity. Polypropylene can exist in different forms: atactic, isotactic, and syndiotactic. Atactic polypropylene is amorphous with its methyl groups randomly placed. In isotactic polypropylene, all methyl groups are on the same side of the carbon chain, resulting in a semicrystalline structure with higher melting points.

Meanwhile, syndiotactic polypropylene has methyl groups alternating sides, allowing for a more regular structure compared to the atactic form and, therefore, higher crystallinity. When comparing these different structures, the syndiotactic form will have a higher melting temperature because of the greater degree of order, which increases intermolecular forces. This higher crystallinity translates to better thermal stability. In the context of an exercise, when given the molecular weight and the tacticity (arrangement of side groups), you can often predict which type of polypropylene will have a higher melting temperature.