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Branched conformational properties of macromolecules in close relation to chemical synthesis. I. Unperturbed structures.

Similar to uniform linear chains, the unperturbed structure of branched polymers forms the basis for the development of a theory on the effect of excluded volume interactions. A clear overview over the skeleton of such complex structures is obtained with a simplifying modification of the general branching theory. The use of probability generating functions permits a direct incorporation of essential details from the chemical synthesis in this branching theory. The unperturbed structure parameters, the degree of polymerization DP(w), radius of gyration R(g), hydrodynamic radius R(h), and the angular dependence of scattered light P(q) are derived for three examples: (i) randomly branched f-functional polymers, (ii) branched copolymers from A3 with B2 monomers, and (iii) AB2 hyper-branched particles. The effect of excluded volume interaction is treated in Paper II [J. Chem. Phys. 143, 114907 (2015)].