High-pressure polyethylene differs from polyethylene, made with the aid of Ziegler catalysts, in having a lower density and lower \(\mathrm{T}_{\mathrm{m}} .\) It has been suggested that this is due to branches in the chains of the high-pressure material. Explain how such branches might arise in the polymerization process and how they would affect the density and \(\mathrm{T}_{\mathrm{m}}\).

High-pressure polyethylene, also known as low-density polyethylene (LDPE), is mainly produced through the process of free radical polymerization at high pressure and high temperature. The branching can occur when the free radical in the chain reacts with one of the hydrogen atoms of an existing chain instead of the ethylene monomer. This process creates a side chain, resulting in a branched structure.

The presence of branches in high-pressure polyethylene leads to a lower density compared to linear polyethylene (like high-density polyethylene, HDPE). This is because branches prevent the polymer chains from packing closely together. The branched chains occupy more space and create a less compact structure, leading to a decrease in density.

The melting temperature (Tm) is affected by the degree of crystallinity in a polymer. Branched polymers, such as high-pressure polyethylene, have less crystallinity compared to linear polymers due to the irregular structure caused by the side chains. The branches disrupt the regular alignment and reduce the ability of the chains to form an ordered, crystalline structure. As a result, the melting temperature of high-pressure polyethylene is lower than that of linear polyethylene. In conclusion, the branched structure formed during the polymerization process of high-pressure polyethylene results in a lower density and melting temperature compared to linear polyethylene made with Ziegler catalysts. The branches arise when free radicals in the chain react with hydrogen atoms of existing chains, leading to a less compact structure and lower crystallinity, which are responsible for the observed lower density and Tm.