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Flexibility in polymers is determined by the free movement of their molecular chains. The three main features affecting the flexibility of a polymer are: 1. Chain length: Longer chains allow for more movement and hence increased flexibility. 2. Molecular structure: Linear and unbranched polymers are more flexible than branched and cross-linked polymers, as the latter structures restrict the movement of the chains. 3. Intermolecular forces: Weak intermolecular forces (such as van der Waals forces) between the polymer chains allow them to move more freely, resulting in a more flexible polymer. Polymers with stronger intermolecular forces (e.g. hydrogen bonding or dipole-dipole interactions) tend to be less flexible.

Cross-linking is the process of creating covalent bonds between polymer chains. This can be achieved through chemical reactions, irradiation, or heat treatment. The main purpose of cross-linking is to modify the properties of the polymer, such as increasing strength, rigidity, thermal stability, and resistance to chemicals.

Cross-linking affects the chemical properties of a polymer in the following ways: 1. Resistance to solvents: Cross-linked polymers have a higher resistance to solvents, as the covalent bonds between the polymer chains make it harder for solvents to penetrate the structure and dissolve the chains. 2. Durability: Cross-linked polymers are more durable and long-lasting than their non-crosslinked counterparts, as the covalent bonds between the chains reduce the rate of degradation resulting from chemical attacks or environmental factors.

Cross-linking affects the physical properties of a polymer in the following ways: 1. Rigidity and strength: Cross-linked polymers exhibit higher rigidity and strength due to the interchain covalent bonds, which restrict the movement of the polymer chains. 2. Elasticity: Cross-linked polymers usually have lower elasticity compared to non-crosslinked polymers, as the covalent bonds reduce the ability of the chains to move freely and retract to their original position after deformation. 3. Melting temperature: Cross-linked polymers have higher melting temperatures than non-crosslinked polymers. The additional covalent bonds increase the energy required to break the polymer's structure and cause it to melt. 4. Thermal stability: Cross-linking improves the thermal stability of a polymer, as the covalent bonds between the chains provide additional resistance to heat-induced degradation. In summary, the flexibility of a polymer depends on its chain length, molecular structure, and intermolecular forces. Cross-linking affects the chemical and physical properties of a polymer by increasing its durability, rigidity, strength, thermal stability, and resistance to solvents while reducing its elasticity and flexibility.