Polymer Architecture
Driving Questions
Natural rubber — latex — is gathered from certain trees and other plants. Ancient Mesoamericans processed and used rubber already by 1600 B.C.E (over 3600 years ago!) and the Aztec empire also used rubber (Tarkanian & Hosler, 2017). In the 19th century, rubber was used to make tires, but they would get sticky on a hot road, pick up debris, and eventually burst. Charles Goodyear (of Goodyear tires) was working to improve the tires in the 1830s. One day, he was trying to mix sulfur with rubber and accidentally dropped the mixture into a hot frying pan. To his surprise, the mixture got harder instead of melting, and kept getting harder as he increased the heat! Why might this have happened?
Here's another question: how can polyethylene make so many different things with vastly different properties? For example, as shown in Figure 9.5.1, it is used to make super lightweight packing foam and quite strong large water pipes.
The answers to both of these questions is that polymers with the same, or nearly the same, chemical make-up can have very different structures.

Figure 9.5.1 Polyethylene can be used to make materials with vastly different properties, such as light packing foams and strong piping material.
Polymer Architectures 1 - Linear vs Branched
It turns out the main difference between the two types of polyethylene in Figure 9.5.1, known as low-density polyethylene (LDPE) and high-density polyethylene (HDPE) is how much "branching" there is in the polymers. In HDPE, the polymer chains are linear with very few branches. The allows them to get close together and create many secondary bonds. In contrast, LDPE polymer chains are highly branched. This keeps the polymer chains further apart and reduces the number of secondary bonds. These two types of polymer architectures are shown in Figure 9.5.2.
Branching occurs as a normal part of processing, but the amount that it occurs depends on how the processing is conducted. Chemically, a branch in polyethylene is due to a $\ce{C-H}$ bond being replaced by a $\ce{C-C}$ bond from which a new chain can form as shown in Figure 9.5.3.

Figure 9.5.2 Linear vs branched polymers. Note, that in both cases, different polymer chains are only bonded through secondary bonding interactions.

Figure 9.5.3 Branched polyethylene forms when a $\ce{C-H}$ bond is replaced by a $\ce{C-C}$ bond.
Polymer Architectures 2 - Cross-linked and Networked
Returning to our question about rubber from above, it turns out that the sulfur can create links between the polymer chains of rubber (more formally known as polyisoprene). This is illustrated in Figure 9.5.4. Cross-linked polymers have covalent bonds linking different polymer chains. This is contrast to branched polymers shown in Figure 9.5.2 which have branches extending from these chains, but those branches don't have covalent bonds with other chains, only secondary bonds. The consequences of cross-linking the polyisoprene chains is that rubber becomes much stronger, keeps its shape better when stretched, and does not get sticky when hot.
When monomers can form 3 or more covalent bonds, they can form a fourth type of polymer structure: networked polymers. These may look like highly cross-linked polymers, but there is a meaningful distinction between them. Networked polymers are made from mers that pretty much always form 3+ covalent bonds with other mers. Cross linked polymers, in contrast, are made of mers that by default only form 2 covalent bonds with other mers and then go through a process to covalently link the polymer chains. Examples of networked polymers include epoxies, polyurethanes, and phenol-formaldhyde. Cross-linked and networked polymers are illustrated in Figure 9.5.5.

Figure 9.5.4 The "vulcanization" process combines sulfur with polyisoprene (rubber) to cross-link the polymer chains.

Figure 9.5.5 Cross-linked and networked polymers.
Polymer Architecture and Strength
The relationship between polymer structure and strength is shown in Figure 9.5.6. Branched polymers tend to be weakest, because chains are only held together by secondary bonds and the branches prevent extensive secondary bonding. Linear polymers are stronger than branched due to more secondary bonding. Both of these types of polymers are known as Thermoplastics, because they can be softened (and melted) repeatedly by raising the temperature. This also means they can be recycled easily.
Cross-linked polymers are the next strongest type of polymer due to covalent bonds between chains and networked polymers tend to the be strongest due to all the covalent bonds. These polymers are known as Thermosets, because once they are formed through heating, they are set and cannot be reshaped or remelted. This makes them difficult to recycle.

Figure 9.5.6 Branched polymer tend to be the weakest because they only have secondary bonds and not that many of them. Linear polymers are stronger due to more secondary bondings. Cross-linked are stronger still due to covalent bonds between chains. Network polymers tend to be the strongest due to all the covalent bonds.