Polymerisation is the chemical process by which small molecules called monomers combine to form high molecular mass substances known as polymers. Two major mechanisms of polymerisation are chain-growth polymerisation and step-growth polymerisation. The distinction between these mechanisms was clarified through the classical concepts developed by Carothers and later extended and mathematically described by Flory. Although both processes produce polymers, they differ significantly in the nature of the monomers, the sequence of reactions, molecular-weight development, stoichiometric requirements, and reaction kinetics. Carothers originally classified polymer-forming reactions largely on the basis of the functionality of the reacting molecules and the manner in which the polymer chains were constructed. His treatment was particularly important for step-growth polymerisation. According to Carothers, molecules containing two or more functional groups can react with one another to form progressively larger molecules. For example, a diacid can react with a diol to form a polyester. The reaction initially produces a dimer, which can react with another monomer or oligomer, and the process continues through successive reactions between functional groups. In step-growth polymerisation, any two molecular species having appropriate reactive functional groups may react with each other. Thus, monomer–monomer, monomer–oligomer, oligomer–oligomer, or oligomer–polymer reactions can occur at any stage. There is no special distinction between the beginning and the end of chain formation. The polymer molecular weight therefore increases gradually throughout the reaction. At low conversion, the reaction mixture contains mainly monomers and small oligomers. As conversion increases, larger oligomers are produced, and very high molecular weights are obtained only at very high conversion. A typical example is the formation of nylon-6,6 from hexamethylenediamine and adipic acid. Both reactants contain two functional groups, and amine and carboxylic acid groups react to form amide linkages. Similarly, polyethylene terephthalate is produced by the reaction of ethylene glycol with terephthalic acid. These reactions illustrate the fundamental Carothers concept that high polymers can be obtained through repeated reactions of functional groups. Carothers introduced the concept of functionality, represented by the number of reactive functional groups present in a molecule. A monofunctional molecule can generally terminate a growing structure, whereas bifunctional molecules can form linear polymers. Molecules with functionality greater than two can produce branched or cross-linked structures. Thus, functionality is an important factor in determining the architecture and physical properties of polymers formed by step-growth processes. Carothers also established a quantitative relationship between the extent of reaction and the degree of polymerisation. For an ideal system containing bifunctional monomers, the number-average degree of polymerisation is expressed as [ X_n=\frac{1}{1-p} ] where (X_n) is the number-average degree of polymerisation and (p) is the fraction of functional groups that have reacted. This equation shows the characteristic feature of step-growth polymerisation: a very high conversion is required to obtain a high molecular weight. For example, if (p=0.90), then (X_n=10), whereas at (p=0.99), (X_n=100). Therefore, the molecular weight rises sharply only as the