在有机聚甲染料中的线性和非线性两极分化的统一描述

Polymers that are made up of identical monomer units are called homopolymers. Only one repeating unit is involved in the construction of the homopolymer structure. For example, as depicted in Figure 1, polypropylene is a homopolymer constituted of propylene monomers. Here, the only repeating unit in the polymer chain is propylene.

Copolymers are the products obtained from the polymerization of multiple monomer species. So, in a polymer chain itself, there can be multiple repeating units that come from different monomers. The process of synthesizing a polymer from different monomer species is called copolymerization. When two monomers are involved, the polymer is known as a bipolymer. Polymers with three and four monomers are termed terpolymers and quaterpolymers, respectively. Figure 1 depicts the copolymerization of...

Polymers are classified as linear or branched on the basis of their chain architecture. The polymer chains in linear polymers have a long chain-like structure with minimal to no branching at all. Even if a polymer features large substituent groups on the monomer, which appear as branches to the skeleton, it is not considered a branched polymer. A branched polymer contains secondary polymer chains that arise from the main polymer chain. The branching occurs when the polymer growth shifts from...

Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...

Polymerization generates chiral centers along the entire backbone of a polymer chain. Accordingly, the stereochemistry of the substituent group has a significant effect on polymer properties. Polymers formed from monosubstituted alkene monomers feature chiral carbons at every alternate position in the polymer backbone. Relative to the predominant orientation of substituents at the adjacent chiral carbons, the polymer can exist in three different configurations: isotactic, syndiotactic, and...

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as: