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To understand the factors that make a polymer flexible, let's take a look at the molecular structure of polymers. Polymers consist of long chain-like molecules made up of repeating units called monomers. The backbone of the polymer chain significantly contributes to its properties, including flexibility. There are several factors that affect polymer flexibility: 1. Length of the polymer chain: Longer polymer chains generally exhibit more flexibility due to the increased freedom of motion they possess. A longer chain can rotate more freely around its bonds, allowing it to deform more easily when subjected to mechanical stress. 2. Type of chemical bonding: The flexibility of the backbone of a polymer is highly influenced by the type of chemical bonds between the monomers. Polymers with single bonds (e.g., polyethylene) in their backbone can exhibit high flexibility because single bonds can rotate freely. In contrast, polymers with double or triple bonds in their backbone (like polyacetylene) or strong intermolecular forces have more rigid structures and are less flexible. 3. Presence of side groups: If the monomers contain bulky or stiff side groups, the polymer may become less flexible due to spatial constraints that limit the rotation around the chemical bonds. 4. Degree of crystallinity: Amorphous polymers or those with a low degree of crystallinity have more randomness in their molecular structure. This disorder allows the chains to move and deform more easily, leading to increased flexibility. In contrast, highly crystalline polymers exhibit a more ordered structure and have less ability to deform, resulting in reduced flexibility.

Cross-linking refers to the process in which individual polymer chains are chemically connected to one another, forming a network structure. Cross-linking can occur naturally or be induced by chemical reactions, heat or radiation. The process significantly influences the properties of a polymer, including its flexibility. When a polymer is cross-linked, its flexibility is generally reduced. The cross-links act as physical constraints that hinder the free movement and rotation of the individual chains. Because the chains are interconnected, they are no longer able to move as independently from each other. This, in turn, restricts the polymer's ability to deform under stress and thus reduces flexibility. In summary, a cross-linked polymer is typically less flexible than its non-crosslinked counterpart due to the additional physical constraints introduced by the cross-links between the chains.