What is the relationship between the degree of polymerization and the molecular weight?

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As the molecular weight of an N-acetylglucosamine (GlcNAc) unit within a chitin chain is ca. 203 g/mol (= 211 g/mol for GlcNAc minus 18 g/mol for a molecule of water released during formation of the glycosidic bond), the molecular weight of a chitin containing n GlcNAc residues is (n x 203 + 18) g/mol. As the molecular weight of a glucosamine (GlcN) unit within a chitosan chain is ca. 161 (= 179 - 18) g/mol, the molecular weight of a chitosan containing n GlcNAc residues and m GlcN residues, i.e. with the formula GlcNAcnGlcNm, is (n x 203 + m x 161 + 18) g/mol. Thus, the molecular weight of a chitosan is dependent on both its degree of polymerization and its degree of acetylation. There are no commonly accepted definitions for the terms "low MW", "medium MW" or "high MW" chitosans. It is important to note that like other polymers and biopolymers, chitins and chitosans are always mixtures of molecules differing in their chain lengths so that the molecular weight of a chitosan is always an average value. The molecular weight distribution of a chitin or chitosan sample is described as its polydispersity index. In contrast to polymers, samples of chitin oligomers or chitosan oligomers can have a defined molecular weight (though they are often also mixtures). The molecular weight of chitins/chitosans is most strongly determined by their degree of polymerization, but MW and DP are not the same. The molecular weight (and, hence, degree of polymerization) is one of the most important parameters influencing the material properties of chitosan polymers, and it also influences their biological activities.