For each of the following pairs of polymers, do the following: (1) state whether 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) Syndiotactic polystyrene having a numberaverage molecular weight of \(600,000 \mathrm{~g} / \mathrm{mol}\); atactic polystyrene having a number-average molecular weight of \(500,000 \mathrm{~g} / \mathrm{mol}\) (b) Random acrylonitrile-butadiene copolymer with \(10 \%\) of possible sites crosslinked; block acrylonitrile-butadiene copolymer with \(5 \%\) of possible sites crosslinked (d) Network polyester; lightly branched polypropylene

Understanding the role of polymer molecular weight is essential when evaluating the tensile strength of polymers. The molecular weight, often measured in grams per mole (g/mol), refers to the mass of a mole of polymer chains. Generally, a higher molecular weight indicates longer polymer chains with more repeating units. This can lead to an increase in tensile strength as the longer chains have more entanglements, which act like physical knots, thereby providing resistance against applied forces.

Picture a nylon rope: the longer and more intertwined the fibers are, the harder it is to pull apart. Similarly, with polymers, longer chains will entangle more, making the material tougher and harder to break apart under tension. However, an important note is that the relationship is not indefinite; at extremely high molecular weights, the tensile strength might plateau or even decrease due to difficulties in chain movement and processing challenges.

In our example, the syndiotactic polystyrene with a molecular weight of 600,000 g/mol is expected to exhibit a higher tensile strength compared to the atactic polystyrene with a molecular weight of 500,000 g/mol, assuming all other factors are equal.

Polymer crosslinking is another critical factor impacting a polymer's tensile strength. Crosslinking involves creating chemical bonds between polymer chains, turning what can be visualized as a plate of spaghetti into a tightly knitted net. The degree of crosslinking—the number of crosslinks per mass of polymer—affects the mobility of the polymer chains and hence, the material strength.

A polymer with a higher degree of crosslinking typically displays a greater tensile strength because the crosslinks prevent the polymer chains from sliding past one another when a force is applied. The analogy here could be a chain mail armor, in which connected metal rings provide a strong barrier against external forces. In the textbook problem, the random acrylonitrile-butadiene copolymer with 10% of possible sites crosslinked is predicted to have higher tensile strength compared to the block copolymer with only 5% crosslinking for this very reason.

The polymer chain arrangement significantly affects the material's mechanical properties, including tensile strength. There are different types of chain arrangements, such as isotactic, syndiotactic, atactic, linear, branched, and crosslinked, among others.

Think of it in terms of building blocks; how you stack or organize them can drastically change the stability of the resulting structure. Isotactic polymers, where all repeating units have the same spatial arrangement, enable close packing of chains and result in high crystallinity and tensile strength. Conversely, atactic polymers have a random configuration of repeating units, preventing orderly packing, leading to lower tensile strength.

The comparison between linear and branched chain arrangements also illustrates this concept. Linear polymers, without side branches, can align and pack closely, while branches in the polymer backbone disrupt the alignment and reduce the material's tensile strength. Hence, in the exercise, the linear isotactic PVC with its ordered and tightly packable structure would be tougher and boast higher tensile strength than its branched atactic counterpart.

The overarching term polymer mechanical properties encompasses how a polymer behaves under stress, which includes not only tensile strength but also elasticity, ductility, and toughness. Tensile strength itself describes the maximum stress a polymer can withstand when being stretched before it breaks.

It's much like testing a rubber band; you pull it to assess how much force it can endure before snapping. Different polymers have diverse mechanical properties based on their molecular structure, and these properties define their suitability for various applications. For instance, the flexible yet strong nature of polyethylene makes it ideal for plastic bags, while the rigidity and high tensile strength of polycarbonate suit its use in bulletproof glass.

In applications where high tensile strength is essential, understanding the influence of factors like molecular weight, crosslinking, and chain arrangement on the mechanical properties is crucial. To say a polymer is 'strong' typically implies it has a high tensile strength, but the full picture includes an assessment of all mechanical properties in relation to the intended use of the polymer.