For each of the following pairs of polymers, do the following: (1) state whether or not it is possible to decide whether one polymer has a higher tensile strength than the other; (2) if this is possible, note which has the higher tensile strength and then cite the reason(s) for your choice; and (3) if it is not possible to decide, then state why. (a) Linear and isotactic poly(vinyl chloride) with a weight-average molecular weight of \(100,000 \mathrm{g} / \mathrm{mol} ;\) branched and atactic poly \((\) vinyl chloride) having a weight-average molecular weight of \(75,000 \mathrm{g} / \mathrm{mol}\) (b) Graft acrylonitrile-butadiene copolymer with \(10 \%\) of possible sites crosslinked; alternating acrylonitrile-butadiene copolymer with \(5 \%\) of possible sites crosslinked (c) Network polyester; lightly branched polytetrafluoroethylene

Poly(vinyl chloride) (PVC) is a widely used thermoplastic with a variety of applications, from pipes and cables to clothing and flooring. The mechanical properties of PVC, such as tensile strength, can vary significantly depending on its molecular structure.

Isotactic PVC, characterized by a repeated and orderly arrangement of pendant groups along the polymer chain, exhibits higher crystallinity as these regular structures can pack together more efficiently. This orderly structure contributes to higher tensile strength compared to atactic PVC, where the pendant groups are arranged randomly. Crystallinity in polymers, such as isotactic PVC, restricts the movement of polymer chains, resulting in a material that resists deformation under tensile stress.

Furthermore, the molecular weight of polymers correlates with their mechanical strength. A higher molecular weight, like the given 100,000 g/mol for linear isotactic PVC, tends to form longer chains, which provides more entanglements—this enhances the tensile strength. In contrast, branched and atactic PVC with a lower molecular weight of 75,000 g/mol will typically be weaker due to reduced crystallinity and fewer entanglements.

Copolymers are materials made from two or more different types of monomers. Crosslinking refers to the process where bonds form between polymer chains, creating a network that can significantly augment the mechanical properties of the material. Crosslink density, the number of crosslinks per unit volume, is a pivotal factor in determining the strength and rigidity of copolymers.

In the case of the acrylonitrile-butadiene copolymer, a higher crosslink density, as in the graft copolymer with 10% of possible sites crosslinked, results in a more interconnected and robust material. This three-dimensional network restricts the movement of polymer chains, which increases the material's resistance to deformation and enhances its tensile strength. On the other hand, the alternating copolymer with a lower crosslink density of 5% is less rigid and possesses lower tensile strength. The degree of crosslinking is directly proportional to the mechanical strength of the material—the more crosslinked it is, the stronger it tends to be.

Polymer molecular weight plays a significant role in determining a polymer’s mechanical properties. Molecular weight refers to the mass of a molecule of the polymer and is a measure of its chain length. Generally, higher molecular weight polymers possess longer chains, which lead to greater tensile strength, impact resistance, and toughness.

Long-chained polymers are able to entangle more effectively, creating a more complex network structure within the material. These entanglements act as physical crosslinks, providing resistance to external forces and impacts. Additionally, in many cases, higher molecular weights allow for better load distribution along the polymer chains when stress is applied, thus enhancing strength. This is why linear, higher molecular weight PVC is cited to have higher tensile strength than its lower molecular weight counterpart. However, it's essential to note that excessively high molecular weights can make processing more difficult and may lead to brittleness.

The structural composition of polymers—including the arrangement of atoms and the presence of branches or crosslinks—has a profound impact on their physical and mechanical properties. In polymers like polytetrafluoroethylene (PTFE) and network polyester, the structure dictates how the chains interact, their packing efficiency, and ultimately their tensile strength.

PTFE, known for its high melting point and non-stick properties, can exhibit different mechanical characteristics depending on the degree of branching. Likewise, network polyesters, which are heavily crosslinked polymers, can vary widely in their properties based on the specifics of their network structure. Tensile strength can be difficult to predict without detailed knowledge of the polymer’s architecture; this includes the degree of crosslinking, the length of the branches, and the nature of their connections. Thus, a direct comparison of tensile strength between two such structurally distinct polymers is not straightforward without additional information on their composition and morphology.