Branching Features of a Polymer

Two parameters characterizing the branching features of polymers, branching density (BD), and branching completeness (BC), are proposed. Both have values of zero (0) for linear polymers. Branching density has the values of 1/2, 2/3, and (f – 2)/(f – 1) for the fully and densest branched polymers formed from tri-, tetra-, and f-functional monomers typed AB _{f –1}. Branching completeness will reach the value of one (1) for a completely branched polymer, where all possible branching monomeric units have reacted at least tri-functionally and all units are either terminal or dendritic. Branching density is close to the mole fraction of terminal units, and BC is close to the mole fraction of dendritic and terminal units in the branching polymers. The major advantage of these parameters is their independence of the degree of polymerization (dp). Branching density depends on the functionalities (f) of monomer units; BC does not. The higher the fraction of the dendritic unit monomerically bonded to a higher number of other units (the higher the terminal units fraction), the denser branched the polymer and the higher the BD. The BC and BD can be used in a simple way for describing multicharacter branching systems and for comparing the branching characters among them without any theoretical limitations. Physical quantities (namely, the number of dendritic and terminal units and the degree of polymerization) used for BD and BC evaluation can be determined directly from practical analyses, where NMR is most useful. The BC and BD, however, do not concisely describe branching characteristics for a polymer with cyclization or crosslinking in its structure.