Identifying Branched Polymers

Polymers are large molecules made up of repeating structural units called monomers. The way these monomer units link together determines the overall structure of the polymer chain. Polymers can have different structures:

• Linear Polymers: The monomer units are linked together to form straight, long chains. Examples include high-density polyethylene (HDPE) and nylon.
• Branched Polymers: The main polymer chain has smaller chains or branches extending from it. These branches prevent the polymer chains from packing closely together. Low-density polyethylene (LDPE) is a classic example.
• Cross-linked Polymers: Linear or branched chains are connected to each other at various points by covalent bonds, forming a network structure. Examples include vulcanized rubber and bakelite.

Let's look at the options provided:

• Low-density polymer (LDPE): This type of polyethylene is synthesized under high pressure and temperature, which leads to significant short and long chain branching along the main polymer backbone. This branching prevents the polymer chains from packing tightly, resulting in a lower density, more flexible, and less crystalline material. Therefore, low-density polyethylene is a branched polymer.
• Polyester: Polyesters are polymers characterized by ester linkages ($\text{-COO-}$) along the main chain. While some polyesters can be modified, typical polyesters like polyethylene terephthalate (PET) have predominantly linear structures, although some degree of chain entanglement exists.
• High-density polymer (HDPE): This type of polyethylene is produced under low pressure conditions, which results in very little branching. The polymer chains are mostly linear and can pack closely together, leading to high density, high crystallinity, and rigidity. Therefore, high-density polyethylene is a largely linear polymer.

Based on the structures, low-density polymer (specifically LDPE) is known for its significant branching compared to high-density polymer (HDPE) and typical linear polymers like polyester.

Therefore, a low-density polymer is a branched polymer.